COOLING DEVICES FOR DENSELY PACKED,
HIGH CONCENTRATION PV ARRAYS
by
ANJA RØYNE
A thesis submitted to
the University of Sydney
for the degree of
MASTER OF SCIENCE
March 2005
ABSTRACT
Photovoltaic (PV) cells under concentrated illumination experience a high heat load
which must be dissipated efficiently in order to maintain a low cell temperature. Tower
and dish solar concentrators typically use arrays of densely packed cells where all of the
heat must be removed in the direction normal to the surface. This thesis identifies jet
impingement cooling as a promising technology for this type of configuration. A
prototype ‘side drainage’ device is made and laboratory testing facilities are constructed
in order to measure the heat transfer and flow characteristics of this device. The local
heat transfer distribution under single and multiple jets is studied in detail. Correlations
for average heat transfer coefficient and pressure drop are established and combined to
form a model for required pumping power at a given average heat transfer coefficient.
This model is used to make general predictions for the optimal cooling device
configuration and to propose an optimising design procedure. Combining this model
with a model for PV output as a function of temperature gives the optimal system
operating range. The effect of a nonuniform heat transfer coefficient distribution on
single and interconnected PV cells is investigated and found to be minor.
i
ACKNOWLEDGEMENTS
I would like to extend my warmest thanks to my supervisors, Christopher Dey and David
Mills. Chris has given me invaluable effort and time and in sharing his wealth of
experience in everything from home renewal to sailing has managed to make somewhat
of an experimental physicist of me. David has been a great inspiration in showing me
what is possible in the world of solar energy.
The solar energy group consists of a bunch of always friendly and extremely
knowledgeable people. Thanks to Anne Gerd, Damien, Steven, Scott, Matt, Yongbai and
Ned for doing your best to answering even the stupidest questions.
There are also a number of other individuals within the School of Physics who carry
years of invaluable experience and knowledge. I would particularly like to thank Terry
Pfeiffer for teaching me how to draw legible construction drawings and for
manufacturing what I needed of experimental equipment; John Piggott for sharing his
wealth of experience in designing experiments; Phil Denniss for helping me with all
things electrical and Michael Proschek for teaching me to use Labview and for his
patience in sorting out seemingly unexplainable problems. Brian Haynes in Chemical
Engineering also took the time to put me on the right track when I was trying to
understand the world of heat transfer and cooling.
Outside the University, I would like to extend my warmest gratitude to my family away
from home: Rolf, Cathy, Anita and Heidi Jacobsen, thank you for providing endless
support, a place to feel at home, wonderful family dinners and of course Rolf ’s very
thorough proofreading. Thanks to my sister Frida Røyne for providing inspiration from
all corners of the world, to my mother Marit Larssen for keeping me up to date and thus
making me feel like I’m not so far away from home, and of course to my father Odd
Røyne for raising me to be a scientist.
Finally to Asbjørn Gjerding-Smith, my partner and the love of my life, without whom I
would certainly never have done this. Thank you for being my greatest inspiration, for
convincing me to work even when I have a thousand excuses made up, your thorough
proofreading and for your amazing ability to cheer me up no matter how frustrated I am.
ii
DECLARATION
This thesis contains no material that has been accepted for the award of any other degree
or diploma in any university. To the best of the author’s knowledge and belief, no
material previously written or published by another person has been included in this
thesis, except where due reference is made in the text.
Anja Røyne
March 2005
iii
PAPERS PUBLISHED
JOURNAL ARTICLES
Royne, A., Dey, C.J. and Mills, D.R. (2005) Cooling of photovoltaic cells under
concentrated illumination: a critical review. Solar Energy Materials and Solar Cells 86 (4),
451-483.
Royne, A. and Dey, C. (Submitted December 2004) Experimental study of nozzle
geometry effects in submerged jet arrays. International Journal of Heat and Mass Transfer
CONFERENCE PAPERS
Royne, A., Dey, C. and Mills, D. (2004) Cooling of photovoltaic cells under concentrated
illumination: a review. EuroSun 2004, Freiburg, Germany.
Royne, A. and Dey, C. (2004) Experimental study of a jet impingement device for
cooling of photovoltaic cells under high concentration. ANZSES Solar 2004 - Life, the
Universe and Renewables, Perth, Australia.
iv
LIST OF SYMBOLS
a
A
b
C
Cc
Cd
Cv
c
d
De
g
h
H
I
k
kB
l
L
m
m&
mb
n
N
Nu
p
P
q
q&
Q
r
rs
Pr
R
R2
Re
s
S
t
T
v
V
W
X
z
cell efficiency parameter
area
cell efficiency parameter
heat transfer correlation
coefficient
contraction coefficient
discharge coefficient
velocity coefficient
specific heat capacity
nozzle diameter
equivalent heat source diameter
acceleration of gravity
heat transfer coefficient
enthalpy
current
thermal conductivity
Boltzmann constant
orifice plate thickness
length
Reynolds number dependence
mass flow rate
mass of bus bars
Prandtl number dependence
number of nozzles
Nusselt number
pressure
power
electronic charge
heat flux per unit area
volume flow rate
radial distance
series resistance
Prandtl number
thermal resistance
correlation coefficient
Reynolds number
nozzle pitch
solar irradiation
thickness
temperature
mean fluid velocity
voltage
pumping power
optical concentration
nozzle-to-plate spacing
Subscripts
0
stagnation point
a
ambient
ad
adhesive
avg
average
b
bus bar
c
cell
cool cooling system
conv convection
c-sub cell junction to substrate
el
electrical
f
fluid
fo
foil
g
glass
g-c
cover glass to cell junction
heat heater
in
inlet
max maximum
oc
open-circuit
opt
optimal
out
outlet
rad
radiation
rise
temperature rise through
substrate
s
surface
sc
short-circuit
sol
solder
sub
substrate
t
total
w
water
Greek letters
ε
emissivity
η
PV efficiency
κ
thermal diffusivity
ν
kinematic viscosity
ρ
density
σ
uncertainty
σB
Stephan-Boltzmann constant
v
TABLE OF CONTENTS
1
2
3
Introduction
1
1.1 Background
1
1.2 Thesis aims
2
1.3 Outline of thesis
3
Cooling of photovoltaic cells under concentrated illumination
5
2.1 Introduction
2.1.1 Cooling requirements for concentrator cells
2.1.2 Concentrator geometries
2.1.3 Heat transfer coefficients and thermal resistances
5
5
6
8
2.2 One-dimensional thermal model of cell and encapsulation layers
8
2.3 Examples of cooling of concentrating PV in literature
2.3.1 Single cell geometry
2.3.2 Linear geometries
2.3.3 Densely packed cells
14
14
16
19
2.4 Other cooling options
2.4.1 Passive systems
2.4.2 Forced air cooling
2.4.3 Liquid single-phase forced convection cooling
2.4.4 Two-phase forced convection cooling
21
21
22
23
26
2.5 Comparison of cooling options
27
2.6 Conclusion
34
Heat transfer under single-phase, submerged and axisymmetric jets
35
3.1 Single jets
3.1.1 Hydrodynamic flow structure of single impinging jets
3.1.2 Radial variation in local heat transfer and the influence of nozzle-toplate spacing
3.1.3 Effect of nozzle configuration
3.1.4 Correlations for the stagnation point and average Nusselt number
37
39
40
3.2 Arrays of jets
3.2.1 Flow structure and heat transfer characteristics of jet arrays
3.2.2 Effect of nozzle-to-plate spacing
3.2.3 Effect of nozzle pitch
3.2.4 Correlations for average Nusselt number
45
45
45
47
48
3.3 Other parameters influencing heat transfer
51
vi
36
36
3.3.1 Surface modifications
3.3.2 Effect of mesh screen or perforated plate between nozzle exit and
impingement plate
4
5
6
51
51
3.4 Experimental methods
51
3.5 Conclusions
52
3.6 Design of a jet impingement cooling device for concentrating PV
54
Experimental design and procedure
56
4.1 Experimental setup
4.1.1 Design of jet testing unit
4.1.2 Measuring temperatures using thermographic liquid crystals
4.1.3 Instrumentation and data acquisition
4.1.4 Jet devices tested
56
57
58
60
61
4.2 System characterisation
62
4.3 Uncertainty analysis
65
4.4 Improvements of the experimental setup for later experiments
67
Results and discussion
69
5.1 Single jets
69
5.2 Arrays of jets
73
5.3 Predictive correlations
78
5.4 Nozzle geometry effects
81
5.5 Pressure drop through an orifice
83
5.6 Total pumping power
85
5.7 Central drainage device
87
5.8 Conclusions
90
Optimised design of cooling devices
6.1 Correlation for pumping power
6.1.1 Pressure drop
6.1.2 Two correlations for heat transfer coefficient
6.1.3 Comparison with experimental data
6.1.4 Model predictions
6.1.5 Experimental validation
6.2 Net PV output – cooling system optimisation
vii
91
91
91
91
94
95
98
101
7
8
6.3 Guidelines for device optimisation
102
6.4 Conclusion
104
Effects of nonuniform temperature
105
7.1 Influence on PV output
7.1.1 Single cells
7.1.2 Interconnected cells
106
106
106
7.2 Using the metal substrate as a heat diffuser
110
7.3 Conclusion
113
Conclusions and recommendations for further work
115
8.1 Conclusions
115
8.2 Recommendations for further work
8.2.1 Fundamental work on jet impingement cooling
8.2.2 Photovoltaics
8.2.3 Prototype design
116
116
117
117
References
118
viii
1
Chapter
INTRODUCTION
1.1 BACKGROUND
The Sun is the world’s primary source of energy. In fact, all of the energy being used on
the Earth today, except for nuclear, geothermal and tidal energy, originates from the Sun.
The Earth annually intercepts as much as 1.05 x 1012 GWh [1] from the Sun, a staggering
amount when comparing with the 1.6 x 107 GWh [2] of installed electrical production
capacity in the world: The energy received from the Sun in only 8 minutes equals the
total installed yearly energy production. However, most of the energy that is used today
is in the form of fossil fuels, which also originated from the Sun but has been stored in
the Earth for millions of years. If the current trends of global energy use and demand
continue, the supply of fossil fuels are predicted to be exhausted within 100-500 years
from now [3].
Burning fossil fuels releases stored carbon into the environment. This disturbs the global
carbon cycle and leads to an increase in atmospheric CO2 levels. There is now
overwhelming evidence that the observed global warming is at least partially caused by
human carbon emissions [4]. Global climate models are predicting significant
temperature changes in the near future (Figure 1.1, [4]) which could have detrimental
effects to ecosystems and humankind.
Figure 1.1: Predicted temperature change under several emissions
scenarios according to the IPCC report (Figure courtesy of [4])
1
1 INTRODUCTION
Because of the increase in world energy demand and the threat of global warming, there
is a pressing need for the development of reliable, cost-effective sources of renewable
energy. With renewable sources of energy, there is no risk of depletion such as we have
with fossil fuels. They also do not introduce new carbon to the carbon cycle and do
therefore not generally contribute to global warming. Renewable energy sources include
indirect solar energy such as hydro, wind and biomass energy, and direct solar energy
conversion through thermal receivers or photovoltaics.
Photovoltaic (PV) cells are semiconductor devices that can convert sunlight into
electricity. Photons below a threshold wavelength have enough energy to break an
electron-hole bond in the semiconductor crystal, which in turn can drive a current in a
circuit. The solar radiation consists of photons at a range of wavelengths and
corresponding energies. Photons with wavelengths above the threshold are converted
into heat in the PV cells. This waste heat must be dissipated efficiently in order to avoid
excessively high cell temperatures, which have an adverse effect on the electrical
performance of the cells.
The cells are the most expensive part of a photovoltaic system. A simple way of reducing
system costs is therefore to replace some of the photovoltaic area with less expensive
optics such as mirrors or lenses. The optical devices focus the sunlight onto a small area
of cells. Because fewer cells are needed, one can afford to use higher efficiency cells.
Under high concentration there is also a considerably higher heat load that needs to be
dissipated. Concentrating systems for solar energy production have been developing
since the 1970s. An excellent overview of the history and current status of photovoltaic
concentrators is given in [5]. Figure 1.2 shows a selection of currently installed
photovoltaic concentrators: The Solar System dishes [6], the linear trough EUCLIDES
concentrator [7] and the faceted dish concentrator at the University of Ferrara [8]. These
systems are all described in more detail in Chapter 2.
1.2 THESIS AIMS
When photovoltaic cells are used under concentrated illumination, they experience a high
heat load because the photons not converted to electricity are dissipated in the cells as
heat. Thus, a crucial requirement for a successful photovoltaic concentrator is a cooling
system which can efficiently remove the dissipated heat while keeping the cells at the
desired temperature. The aims of this thesis are to:
•
investigate the effect of temperature on PV cells and assess what level of cooling
is required for a given concentrator design;
•
review possible cooling options and recommend on the most suitable one(s);
•
design and conduct measurements of the cooling performance of candidate
devices;
•
develop a thermal model to simulate the cooling performance for a range of
device configurations; and
•
recommend a cooling device design or design procedure that can be used as a
tool for future PV receiver design.
2
1 INTRODUCTION
a)
b)
c)
Figure 1.2: A collection of photovoltaic concentrators: a)
The Solar Systems dish concentrators (artist’s
impression) [6]; b) the linear trough EUCLIDES system
[7]; c) dish concentrator at the University of Ferrara [8].
1.3 OUTLINE OF THESIS
In Chapter 2, an extensive literature review is presented which looks into not only past
and present methods for cooling of photovoltaic cells, but also cooling technologies
from other areas of research which may be applicable to photovoltaics. This chapter
shows that efficient cooling is of prime importance in concentrating photovoltaic
systems, in particular for those using arrays of densely packed cells under high
concentration. A number of possible cooling mechanisms are suggested, the most
promising being microchannels and impinging jets. Microchannels have been widely
researched and are also currently being implemented with concentrating photovoltaics in
Italy [8]. Impinging jets, on the other hand, have not yet been trialled in this area. Jet
3
1 INTRODUCTION
impingement is an attractive solution because a high heat transfer coefficient can be
achieved using simple manufacturing methods and possibly with lower pumping power
requirements than other options. It was therefore decided to proceed with investigating
the suitability of jet impingement cooling devices for densely packed, high concentration
PV.
Chapter 3 presents a review of previous studies of jet impingement, limited to
axisymmetric, submerged and single-phase jets for reasons explained in Chapter 3. The
heat transfer characteristics of impinging jets have been extensively researched and are
well known. However, the performance of a given jet device is difficult to predict
because of the numerous parameters influencing the heat transfer, such as nozzle
geometry, nozzle pitch, nozzle-to-plate distance Reynolds number, impingement surface
conditions etc. Some general results are identified which can help predict suitable design
properties. Based on the findings from the literature, four types of possible device for
the particular requirements of PV cooling are presented.
One of the possible devices, labelled the ‘side drainage device’ was identified as the most
promising and a prototype was made. The experimental facilities used to investigate the
flow and heat transfer characteristics of variations of this device are described in Chapter
4. The results from the experiments are presented in Chapter 5. The local heat transfer
distribution under single and multiple jets is studied in detail. Correlations are found for
the stagnation point and average heat transfer coefficients and compared with
correlations from the literature. Correlations are also developed for the pressure drop
through the nozzles and different nozzle configurations are compared. For comparison, a
few measurements were made for another one of the suggested geometries but the
results presented in Chapter 5 suggest that this performs poorly.
For cooling of photovoltaics, it is preferential to minimise the pumping power
requirements in order to maximise the total electrical output of the system. In Chapter 6,
the findings from the literature and from the experiments are combined to develop an
analytical model that predicts the pumping power required for a given device
configuration. The model is then used to make some general predictions on the
optimised design of a cooling device and an optimisation process is outlined. It is also
used to show that there exists a broad optimal operating range for a photovoltaic cell
using the cooling device.
Lastly, Chapter 7 discusses the issue of nonuniformity in heat transfer coefficient and
temperature. One of the initial assumptions was that a uniform temperature across the
cells was important for the total array efficiency. However, calculations given in Chapter 7
show that the difference in temperature across single or interconnected cells only have a
weak effect on efficiency compared to that of the average temperature. For this reason,
the thickness of the substrate between the cells and the cooling system should be kept as
small as possible.
Conclusions and recommendations for further work are given in Chapter 8.
4
2
Chapter
COOLING OF
PHOTOVOLTAIC CELLS
UNDER CONCENTRATED
ILLUMINATION
This chapter has been published in its entirety in Solar Energy Materials and Solar Cells [9].
The text and figures are identical to that published except for cosmetic changes.
2.1 INTRODUCTION
2.1.1 Cooling requirements for concentrator cells
Concentrating sunlight onto photovoltaic cells, thus replacing expensive photovoltaic
area with less expensive concentrating mirrors or lenses, is seen as one method to lower
the cost of solar electricity. Because of the smaller area, more costly, but higher efficiency
PV cells may be used. However, only a small portion of the incoming sunlight onto the
cell is converted into electrical energy (a typical efficiency value for concentrator cells is
25% [10]). The remainder of the incoming energy will be converted into thermal energy
in the cell and cause the junction temperature to rise unless the heat is efficiently
dissipated to the environment.
Major design considerations for cooling of photovoltaic cells are listed below:
Cell temperature. The photovoltaic cell efficiency decreases with increasing temperature
[11-13]. Cells will also exhibit long-term degradation if the temperature exceeds a certain
limit [14, 15]. The cell manufacturer will generally specify a given temperature
degradation coefficient and a maximum operating temperature for the cell.
Uniformity of temperature*. The cell efficiency is known to decrease due to nonuniform temperatures across the cell [16, 17]. In a photovoltaic module, a number of
cells are electrically connected in series, and several of these series connections can be
connected in parallel. Series connections increase the output voltage and decrease the
current at a given power output, thereby reducing the ohmic losses. However, when cells
are connected in series, the cell that gives the smallest output will limit the current. This
is known as the current matching problem. Because the cell efficiency decreases with
Temperature nonuniformities were initially assumed to be important to the cell output but a later
investigation (see chapter 7) showed that this is not necessarily the case.
*
5
2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION
increasing temperature, the cell at the highest temperature will limit the efficiency of the
whole string. This problem can be avoided through the use of bypass diodes [18] (which
bypass cells when they reach a certain temperature - in this arrangement you loose the
output from this cell, but the output from other cells is not limited) or by keeping a
uniform temperature across each series connection.
Reliability and simplicity. To keep operational costs to a minimum, a simple and low
maintenance solution should be sought. This also includes the avoidance of toxic
materials due to health and environmental issues. Reliability is another important aspect
because a failure of the cooling system could lead to the destruction of the PV cells. The
cooling system should be designed to deal with "worst case scenarios" such as power
outages, tracking anomalies and electrical faults within modules [15, 19].
Useability of thermal energy. Use of the extracted thermal energy from cooling can
lead to a significant increase in the total conversion efficiency of the receiver [20]. For
this reason, subject to the constraints above, it is desirable to have a cooling system that
delivers water at as high a temperature as possible. Further, to avoid heat loss through a
secondary heat exchanger, an open-loop cooling circuit is an advantage.
Pumping power. Since the power required of any active component of the cooling
circuit is a parasitic loss [20], it should be kept to a minimum.
Material efficiency. Materials use should be kept down for the sake of cost, weight and
embodied energy considerations.
2.1.2 Concentrator geometries
It is sensible to distinguish between concentrators according to their method for
concentrating (mirrors or lenses), concentration level or geometry. In this review,
concentrators will be grouped according to geometry, because the requirements for cell
cooling differ considerably between the various types of concentrator geometries. The
issue of shading, however, is different for lens and mirror concentrators. If lenses are
used, the cells are normally placed underneath the light source, and so shading by the
cooling system does not occur. For mirror systems, the cells are generally illuminated
from below, which makes shading an important issue to consider when designing the
cooling system. Concentrators can be roughly grouped as in the following sub-sections.
2.1.2.1 Single cells
In small point-focus concentrators, the sunlight is usually focused onto each cell
individually. This means that each cell has an area roughly equal to that of the
concentrator available for heat sinking, as shown in Figure 2.1. A cell under 50 suns
concentration should have an area 50 times its area available for spreading of heat. This
geometry means passive cooling can be used at quite high concentration levels (see
Section 2.3.1). Single cell systems commonly use various types of lenses for
concentration. Another variant is where larger concentrators transmit the concentrated
light through optical fibres onto single cells.
6
2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION
Figure 2.1: Single-cell concentrator. The dashed line
shows the area available for heat sinking.
2.1.2.2 Linear geometry
Line focus systems typically use parabolic troughs or linear Fresnel lenses to focus the
light onto a row of cells. In this configuration, the cells have less area available for heat
sinking because two of the cell sides are in close contact with the neighbouring cells, as
shown in Figure 2.2. The areas available for heat sinking extend from two of the sides
and the back of the cell.
Figure 2.2: Linear concentrator. The dashed lines show the area
available for heat sinking.
2.1.2.3 Densely packed modules
In larger point-focus systems, such as dishes or heliostat fields, the receiver generally
consists of a multitude of cells, densely packed. The receiver is usually placed slightly
away from the focal plane to increase the uniformity of illumination. Secondary
concentrators (kaleidoscopes) may be used to further improve flux homogeneity [21].
Densely packed modules present greater problems for cooling than the two previous
shown, because, except for the edge cells, each of the cells only has its rear side available
7
2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION
for heat sinking, as seen in Figure 2.3. This implies that, in principle, the entire heat load
must be dissipated in a direction normal to the module surface. This generally implies
that passive cooling cannot be used in these configurations at their typical concentration
levels.
Figure 2.3: Densely packed cells. The area available for
cooling is only the rear side of the cell.
2.1.3 Heat transfer coefficients and thermal resistances
The commonly used quantities for comparing the heat transfer characteristics of cooling
systems are heat transfer coefficients h or thermal resistances R. These can be defined in
several different ways depending on the application. When dealing with passive cooling
systems, h is generally defined as
h=
q&
,
Ts − Ta
(2.1)
where q& is the heat input per unit area, Ts is the mean surface temperature, and Ta is the
ambient temperature. R, when used per unit area, is just the inverse of h. In the case of
single-phase forced convection cooling, one will generally use a local heat transfer
coefficient
h=
q&
,
Ts − Tf
(2.2)
where Ts and Tf are the mean surface and fluid temperatures at any given point. For
natural convection, boiling and radiation, q& is not proportional to ∆T. R and h therefore
vary with temperature [22]. In the case of radiation, a simplification is often used to
linearize the calculation (given in Section 2.2.1.1). The literature sometimes quotes values
for h or R with natural convection or two-phase forced convection, and these are
included in this article. However, these should be read with caution and not be assumed
to be valid for a large range of temperatures.
2.2 ONE-DIMENSIONAL THERMAL MODEL OF CELL AND
ENCAPSULATION LAYERS
To examine the best cooling system for a given concentrator requires the development of
a thermal model that will predict the heating and electrical output of cells. In this review,
a one-dimensional model is used because this is consistent with a closely packed set of
8
2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION
cells where heat flow is primarily directed in the normal direction. Models for other
layouts can be easily extended from this model, or they can be found in literature (e.g.
[11]). Models for single-cell point focus are described in [17, 23, 24] and for linear
geometry in [25-27]. The idealised cell and its mounting are shown schematically in
Figure 2.4, where S is the incoming solar radiation, and tg, tad, tc, tsol and tsub denote the
thicknesses of the various layers.
IS
tg
tad
tc
tsol
tsub
cover glass
adhesive
cell
solder
substrate
Figure 2.4: Cell and mounting layers with thicknesses t.
Figure 2.5: Equivalent thermal
circuit of cell, mounting and
cooling system.
This configuration can be represented by the equivalent thermal circuit shown in Figure
2.5, where R denotes a thermal resistance. Note that because this model is onedimensional, all relevant values are per unit area; the units of R are [K m2 W-1] while the
units of q& are [W m-2]. Tg, Ts and Ta are the temperatures of the top surface of the cover
glass, the bottom surface of the substrate and the ambient, respectively. Rg-c, Rc-sub and
Rcool denote the thermal resistances from cover glass to the cell junction, from cell
junction to substrate bottom, and from substrate, through cooling system, to the
ambient. Tc denotes the temperature of the cell junction, which is assumed to be in the
middle of the cell. This temperature determines the efficiency of the cell. The simple
model assumes that all incoming radiation, S, is transmitted through the encapsulants and
absorbed in the cell junction, where a percentage determined by the cell temperature is
converted to electricity, and the remainder is converted to heat. It is also assumed that
some heat is lost through radiation and convection from the cover glass surface, and that
the remainder of the heat is removed by the cooling system on the substrate surface.
9
2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION
2.2.1.1 Heat loss through radiation and natural convection
The radiative heat flux (per unit area) is related to the cover glass surface temperature as
follows [28]:
(
)
q& rad = 4εσ B Tg 4 − Ta4 ,
(2.3)
where Tg is the glass surface temperature, Ta is the ambient temperature, ε is the surface
emissivity and σB is the Stephan-Boltzmann constant. However, for simplification, it is
common to linearise this equation in the following manner [11]:
(
)
q& rad = 4εσBTa 3 Tg − Ta .
(2.4)
For an ambient temperature of 25 °C, this approximation gives an error in q& rad of less
than 50% for cell temperatures up to 170 °C.
By determining a thermal resistance Rconv for convective heat transfer from a surface,
depending on surface and ambient parameters, the heat flux through convection from
the surface is simply given by
q& conv =
Tg − Ta
Rconv
.
(2.5)
Values for Rconv are discussed later.
2.2.1.2 Electrical power output
The cell efficiency varies with both temperature and concentration. There are various
models for temperature and concentration dependency found in literature [11, 12, 27, 29,
30]. As shown in Figure 2.6, most of the models predict quite similar slopes in the lower
temperature range. The different values predicted arise from the fact that different cells
have different peak efficiencies. Therefore, a simple approach is used in this article by
assuming a linear decrease in efficiency with temperature, and no dependency on
concentration, as in [29]. This gives the following model:
η = a(1 − bTc ) ,
(2.6)
where a and b are parameters from [29], and η is the cell efficiency at a given cell
temperature Tc. The electrical output per unit area is given by
Pel = ηS .
10
(2.7)
2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION
aa Florschuetz
[29]
Florschuetz [20]
bb Sala
Sala [11]
[2]
cc O’Leary
andClements
Clements
[27]
O'Leary and
[18]
dd Mbewe
et al.
al.11sun
sun[3][12]
Mbewe et
Mbewe et
[3][12]
ee Mbewe
et al.
al.100
100suns
suns
Edenburn [21]
ff Edenburn
[30]
0.3
30
Cell efficiency (%)
0.25
25
0.2
20
f
c
0.15
15
e
b
0.1
10
d
0.055
40
60
80
100
120
140
160
a
180
200
Cell temperature (°C)
Figure 2.6: Comparison of different models for cell efficiencies at various
temperatures.
2.2.1.3 Energy balance
If S denotes the incoming solar irradiation, and
q&cool =
Ts − Ta
Rcool
(2.8)
is the thermal energy removed by the cooling system, the following relation must be
satisfied to achieve thermal equilibrium:
S − q& rad − q& conv − Pel − q& cool = 0
(2.9)
Solving Equations 2.4 through 2.9 gives the value for Tc at any given illumination value. It
should be noted that q& cool is very large compared to q& rad and q& conv in most cases of
concentration, and so the significance of the model and parameters chosen for these
aspects of the actual cells becomes less important.
Figure 2.7 shows the electrical power output that would result from various illumination
levels using this model and the values given in Table 2.1. The different curves correspond
to different values of Rcool. There is clearly a definitive maximum power output for all
curves. However, these curves must be seen together with Figure 2.8, which shows the
cell temperature rise with increasing concentration. It shows that the maximum power
points correspond with very high cell temperatures. The actual power output will be
limited by the bounds on the cell operating temperature. This implies temperature is
always the limiting factor for concentrator cells. A low thermal resistance in the cooling
system is crucial, and becomes even more important with increasing concentration level.
11
2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION
Table 2.1: Parameters used in thermal model
Layer
Material
Thickness
Thermal
conductivity
t [m]
k [ W m-1 K-1 ]
Cover glass
Ceria-doped glass [14]
3 x 10-3
1.4 [28]
Adhesive
Optical grade RTV
(room temperature
vulcanization) silicone
[14]
1 x 10-4
145 [11]
Top half of
cell
Silicon [14]
6 x 10-5 [14]
145 [11]
Bottom half
of cell
Silicon [14]
6 x 10-5 [14]
145 [11]
Solder
Sn:Pb:As: [11]
1 x 10-4 [11]
50 [11]
Substrate
Aluminum nitride [14]
2 x 10-3 [11]
120 [14]
Total thermal resistance
R=∑
ti
[ K m2 W-1 ]
ki
Rg-c = 2.14 x 10-3
Rc-s = 1.91 x 10-5
Other parameters
Symbol
Description
Value
Symbol
Description
Value
Ta
Ambient
temperature
25 °C
Rconv
Convective thermal
resistance
0.2 K m2 W-1
[11]
ε
Hemispherical
surface emissivity
0.855 [9]
a
Cell efficiency
parameter
0.5546 [29]
σB
StephanBoltzmann
constant
5.67 x 10-8 W m-2 K-4
[28]
b
Cell efficiency
parameter
1.84 x 10-4 K-1
[29]
S
Insolation
1 x 103 W m-2
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2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION
106
R=10-6
R=10-5
Power output (W/m2)
105
R=10-3
104
R=10-2
3
10
R=10-1
102
101
103
104
105
106
107
2
Illumination level (W/m
)
Figure 2.7: Electrical power output per area versus illumination level for various
Rcool [K m2 W-1 ].
300
250
R = 10-1
-2
Cell temperature (°C)
R = 10
-3
R = 10
200
-4
R = 10
-5
R = 10
150
100
50
0
103
104
105
106
107
2
Illumination level (W/m
)
Figure 2.8: Cell temperature versus illumination level for various Rcool
[K m2 W-1 ].
13
2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION
2.3 EXAMPLES OF COOLING OF CONCENTRATING PV IN
LITERATURE
In the textbook Cells and optics for photovoltaic concentration, edited by Luque, there is an
informative chapter by Sala on the cooling of solar cells [11]. It does not focus on
concentrating PV in particular. The text presents models for calculating heat transfer
through cells and the temperature effect on solar cell parameters. It also contains separate
discussions on passive cooling through radiation, natural convection and conduction, and
on forced liquid cooling. The text has been widely used as a reference for other research
dealing with photovoltaic cooling systems.
Florschuetz [29] presents another general, theoretical approach to the cooling of solar
cells under concentration. He uses the relations between illumination, cell temperature
and cell efficiency to find an equation for the illumination level that gives the maximum
power output for a given cooling system. This would be the equivalent of the equation
for a line passing through the peaks in Figure 2.7. However, as explained earlier, the
maximum power points coincide with very high cell temperatures. The possibility of cell
degradation has not been taken into account in this model. Florschuetz also explores the
importance of contact resistance between the cell and the cooling system (represented by
Rc-s in Section 2.2.1). He shows that the relative importance of the contact resistance
increases substantially as the illumination levels rise. This is because the temperature
difference across a boundary is given by ∆T = q&R and thus it increases with increasing
heat flux q& and increasing thermal contact resistance R. In high-concentration systems
where q& is large, a small contact resistance is needed to achieve the same temperature
difference.
2.3.1 Single cell geometry
As described in the following section, passive cooling is found to work well for single-cell
geometries for flux levels as high as 1000 suns. This is because of the large area available
for heat sinking, as introduced in Section 2.1.2.1.
2.3.1.1 Passive cooling
Edenburn [30] performs a cost-efficiency analysis of a point-focus Fresnel lens array
under passive cooling. The cooling device is made up of linear fins on all available heat
sink surfaces (see Figure 2.9). The concentration values under consideration were 50, 92
and 170 suns. The analysis consists of using given values for the cost of aperture (lens
and cell) area and for cooling device area and cost optimising the cooling geometry. Cell
degradation at high temperatures is not considered. This implies that arrays that employ
the passive cooling devices developed under this model must have a mechanism for
defocusing under extreme thermal conditions (very low wind speed, high insolation and
high ambient temperatures). In the search for cost-effectiveness, Edenburn also suggests
housing the cell assembly in a painted aluminium box, and to use the bottom of this as a
finless heat sink. He states that during calm air conditions, radiation is the most
important component of heat loss. A finned surface will radiate less than a finless one
because of the temperature drop from the base of the fins to the tips. Thus, with the
finless box design, the cells could be kept below 150 °C even on extreme days at a
concentration level of about 90 suns, and a defocusing mechanism might not be
necessary. This is still a very high temperature for photovoltaic cells.
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2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION
Figure 2.9: Passive heat sink for a single cell
as suggested by Edenburn [30].
Edenburn concludes that for point focus arrays, the cost of passive cooling increases
with lens area, while it remains almost unchanged with concentration. The reason is that
as the aperture area is increased, a thicker and more expensive heat exchanger is required.
When concentration goes up, the heat sink optimal design does not change by much, but
a low contact thermal resistance between the substrate and the heat sink becomes
increasingly important to keep the cell temperature down.
Miñano [23] presents a thermal model for the passive cooling of a single cell under high
concentrations. Like Edenburn, he concludes that passive cooling is increasingly efficient
for cells as their size is reduced. Comparing the given cell efficiencies of the GaAs cells
used in this case, it seems likely that a concentration of 1000 suns would be possible as
long as the temperatures are kept low. Miñano advises that cells be kept below 5 mm
diameter. Heat sinks for these cells would be similar to those used for power
semiconductor devices.
Araki et al. [24] presents further results that show the effectiveness of passive cooling of
single cells. In this study, an array of Fresnel lenses focus the light onto single cells
mounted with a thin sheet of thermally conductive epoxy onto a heat-spreading
aluminum plate. The concentration level is about 500 suns. Outdoor experiments show a
temperature rise of cells over ambient of only 18 °C, without conventional heat sinks. It
is shown that good thermal contact between the cell and the heat spreading plate is
crucial to keep the cell temperature low. Techniques to enhance this could be to use a
thinner epoxy layer, or to increase the heat conductance coefficient of the epoxy.
Graven et al. [31] have patented a single cell lens array which employs a heat sink with
longitudinal fins. The thermal contact between the cells and the heat sink is provided by a
set of rod springs that force the surfaces together. A thin polyester film between the cells
and the heat sink ensures thermal conductance and electrical insulation.
2.3.1.2 Active cooling
Edenburn [30] also considered using active cooling on his point focus arrays described
above. He placed cells in rows, and had one rectangular coolant channel run along the
back of each row. To enable a cost comparison between the different cooling regimes, he
did not take into consideration the possible advantage of using the extracted heat for
thermal energy supply purposes. However, he states that if this were done, active cooling
would almost certainly be the most cost-efficient solution. Without this extra advantage,
however, the parasitic power losses involved in pumping and in dissipating the waste heat
make active cooling more expensive than passive cooling for single cells. The only
exemption would be for very large lenses (more than 300 mm in diameter). At this size,
the costs of active and passive cooling become almost the same.
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2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION
2.3.2 Linear geometries
2.3.2.1 Passive cooling
Florschuetz [29] uses his model to assess both active and passive cooling options for a
linear geometry. For the passive solution, the cells are mounted along either a planar or a
finned metal strip. The illumination levels at the maximum power input are compared for
the different cooling systems. Pin fins are found to perform better than plane ones, but
because pin fins are more costly to manufacture, they may still not be the best option.
The model suggests that the plane strip would be sufficient for very low concentration
levels (less than 5 suns) and the finned strip only for slightly higher levels (10 suns). With
2.2 m s-1 wind speed, the plane strip should work up to about 10 suns and the finned one
up to 14 suns. Note that this analysis does not take cell efficiency degradation into
account.
The EUCLIDES is a trough-type photovoltaic concentrator located in Spain [32]. In this
system, thermal energy is passively transferred to the ambient through a lightweight
aluminium-finned heat sink. The fins have been optimised for the relatively low
concentration (about 30 suns) used on the EUCLIDES. The optimisation gave fin
dimensions to be 1 mm thick, 140 mm long and spaced about 10 mm apart. This could
not be manufactured by ordinary means, but was accomplished by stacking fin- and
separator-plates, and tightening them with screws. This method is quite costly. The heat
sink is projected to contribute to 15.7% of the total cost of a EUCLIDES-type plant,
while the photovoltaic modules and the mirrors contribute 11.9% and 10.8%,
respectively. Cells have been measured to run at about 58 °C.
Edenburn [30] considers the cooling of a linear trough design. In his system, the cells are
mounted in two lines in a V-type geometry (Figure 2.10). The passive heat exchanger
consists of a finned mast that avoids shading the concentrator. The concentration levels
under consideration are 20, 30 and 40 suns. Edenburn finds that because of higher cell
temperatures, resulting from the longer path length for the heat to the fins of the heat
sink, passive cooling of a linear design is much more expensive than for a single cell
design. Passive cooling seems not to be cost-efficient for this setup. To increase the
performance, he suggests filling the cavity of the "mast" with an evaporative fluid that
would work as a thermosyphon to transport heat away from the cells at a very low
temperature differential.
16
2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION
Figure 2.10: Passive cooling of a linear
design as suggested by Edenburn [30].
The heat pipe approach is further explored by Feldman et al. [33] on a concentration ratio
of about 24 suns. The "mast" is made out of extruded surface aluminium, and the
evaporative working fluid is benzene. This gives a maximum evaporator surface
temperature of about 140 °C. The cell temperature would be even higher than this given
the thermal resistance between the cell and the evaporator surface. The model shows that
the heat transfer in this system is highly dependent on the condenser surface area. The
prototype has an evaporator area of 0.61 m2 and a condenser area of 2.14 m2. Outdoor
testing also shows that the operating temperature is a strong function of wind speed, and
less of ambient temperature, wind direction and mast tilt angle. Under the worst case
scenario, which is an ambient temperature of 40 °C and 19.2 kW m-2 illumination, a
minimum wind speed of 1 m s-1 is required to keep the evaporator temperature below
140 °C. The surface area would have to be increased by a factor of 2.1 to achieve the
same in no-wind conditions. Thermal resistance from base surface to the ambient is
0.114 K m2 W-1 in the 1 m s-1 case.
Akbarzadeh and Wadowski [34] report on a linear, trough-like system which also uses
heat pipes for cooling (Figure 2.11). In this case, the reflector is not a parabola, but an
"ideal reflector" which is said to give a uniform illumination across the cells. Each cell is
mounted vertically on the end of a thermosyphon, which is made of a flattened copper
pipe with a finned condenser area. The system is designed for 20 suns concentration, and
the cell temperature is reported not to rise above 46 °C on a sunny day, as opposed to 84
°C in the same conditions but without fluid in the cooling system.
17
2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION
Figure 2.11: Schematic of heat pipe based
cooling system as suggested by Akbarzadeh
and Wadowski [34].
2.3.2.2 Active cooling
Florschuetz [29] considers cooling his strip of cells actively by either forced air through
multiple passages or water flow through a single passage. He notes that with forced air
cooling, there is a substantial temperature rise along the cells due to the low heat capacity
of air. The required pumping power is also quite large compared to the effective cooling.
For these reasons, forced air cooling does not seem to be a viable alternative. Water
cooling, on the other hand, permits operation at much higher concentration levels.
Edenburn [30] suggests a cooling system for his linear design that consists of a channel
of quadratic cross-section, tilted 45°, with the V-shaped PV receiver placed on two of
the channel sides. Active cooling was found to be more cost-efficient than passive
cooling in linear designs.
O'Leary and Clements [27] give a theoretical analysis of the thermal and electrical
performance for an actively cooled system. The cooling methods considered consist of
various geometries of coolant flow through extruded channels, the coolant liquid being a
water-ethylene glycol mixture. An optimal geometry is suggested based on maximum net
collector output versus coolant flow. The required pumping power rises proportionally
with increased coolant mass flow rate, which is characteristic for laminar flow in
channels. Although it would seem favourable to operate at the highest possible mass flow
rate in order to obtain the lowest cell temperatures and highest cell performances, there is
actually shown to be a definite optimum operation region, because the rate of increase in
R drops as the mass flow increases.
A system of linear Fresnel lenses, cooled by water flow through a galvanised steel pipe, is
described by Chenlo and Cid [25]. The system has a concentration level of about 24 suns.
The cells are soft soldered to a copper-aluminum-copper sandwich, which is in turn
soldered to the rectangular pipe. This mounting gives a satisfyingly low cell to steel tube
thermal resistance (R = 8 x 10-5 K m2 W-1). The soft soldering allows for some difference
in the thermal expansions between the cells and the steel tube to be accommodated. The
convective thermal resistance of the coolant tube is found to be R = 8.7 x 10-4 K m2 W-1
18
2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION
for Reynolds number Re = 5000. This paper also presents good electrical and thermal
models for uniform and non-uniform cell illuminations.
Russell [35] has patented a heat pipe cooling system (Figure 2.12). His design uses linear
Fresnel lenses, each focusing the light onto a string of cells mounted along the length of
a heat pipe of circular cross-section. Several pipes are mounted next to each other to
form a panel. The heat pipe has an internal wick that pulls the liquid up to the heated
surface. Thermal energy is extracted from the heat pipe by an internal coolant circuit,
where inlet and outlet is on the same pipe end, ensuring a uniform temperature along the
pipe. The coolant water is fed and extracted by common distribution pipes. An
alternative system where the coolant enters at one end of the pipe and leaves at the other
is also considered, but found to be less preferable because this would cause a temperature
gradient along the pipe length.
Figure 2.12: Heat pipe based cooling system as suggested by Russell [35].
The CHAPS system at the Australian National University [36] is a linear trough system
where the line of cells is cooled by liquid flow through an internally finned aluminum
pipe. The coolant liquid is water with anti-freeze and anti-corrosive additives and the
optical concentration is 37x. Under typical operating conditions (fluid temperature 65 °C,
ambient 25 °C, direct radiation 1 kW m-2), the thermal efficiency is 57% and the electrical
efficiency is 11% for the prototype collector. The cells, which are manufactured at the
ANU, are run at a fairly high temperature (about 65 °C). Nothing is reported about the
temperature gradient along the line of cells, which would result from the single coolant
pipe, and whether this has a significant result on cell performance. This may be because
the preliminary results are from a shorter prototype collector where the temperature
difference is insignificant.
2.3.3 Densely packed cells
No reports of passive cooling of densely packed cells under concentration have been
found.
19
2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION
2.3.3.1 Active cooling
Verlinden et al. [37] describes a monolithic silicon concentrator module with a fully
integrated water cooled cold plate. The module consists of 10 cells and is supposed to
act as a "tile" in a larger array. With an optimised coolant flow rate of 0.0127 kg s-1 on an
area of 3600 mm2, the total thermal resistance from cell to water (including all layers in
between) is measured to be 2.3 x 10-4 K m2 W-1. The design is further described by
Tilford et al. [38], with module pictures and some further specifications. However, details
are not given on the way in which the water flows through the cold plate.
John Lasich [39] recently patented a water cooling circuit for densely packed solar cells
under high concentration. The circuit is said to be able to extract up to 500 kW m-2 from
the photovoltaic cells, and to keep the cell temperature at around 40 °C for normal
operating conditions. This concept is based on water flow through small, parallel
channels in thermal contact with the cells. The cooling circuit also forms part of the
supporting structure of the photovoltaic receiver. It is built up in a modular manner for
ease of maintenance, and provides good solutions for the problem of different thermal
expansion coefficients of the various materials involved.
Solar Systems Pty. Ltd. has reported some significant results from their parabolic dish
photovoltaic systems located in White Cliffs, Australia [20, 40]. They work with a
concentration of about 340 suns, and use the above mentioned patent [39] for cooling
the cells. With a water flow rate of 0.56 kg s-1 over an area of 57600 mm2 and an
electrical pumping power of 86 W, they maintain an average cell temperature of 38.52 °C
and achieve a cell efficiency of 24.0% using the HEDA312 Point-Contact solar cells
from SunPower [40]. If all of the thermal energy extracted were being used, the overall
useful energy efficiency in this system would be more than 70%. This demonstrates
clearly the benefits of active cooling if one can find uses for the waste heat.
Vincenzi et al. [8, 41] at the University of Ferrara have suggested using micromachined
silicon heat sinks for their concentrator system. The photovoltaic receiver at Ferrara is
300 mm x 300 mm and operates under a concentration level of 120 suns. By using a
silicon wafer with microchannels circulating water directly underneath the cells, the
cooling function is integrated in the cell manufacturing process. Microchannel heat sinks
will be presented in more detail in Section 2.4.3.1. The reported thermal resistance is 4 x
10-5 K m2 W-1, which is comparable to other microchannel systems (see later in Table
2.2), although perhaps slightly higher.
A system is patented by William Horne [15] in which a paraboloidal dish focuses the
light onto cells mounted in quite an innovative way (see Figure 2.13). Instead of being
mounted on a horizontal surface, they are situated vertically on a set of rings, designed to
cover all of the solar receiving area without shading. Water is transported up to the
receiver by a central pipe and then flows behind the cells, cooling them, before running
back down through a glass "shell" between the concentrator and the cells. In this way, the
water not only cools the cells, it also acts as a filter by absorbing a significant amount of
UV radiation that would otherwise have reached the cells. Normally, cells need to be
protected from UV radiation by a cover glass or lenses. In Horne's case, the water also
absorbs some of the low energy radiation, resulting in higher cell efficiency and a lower
amount of power converted to heat in the cells. The patent incorporates a phase-change
material in thermal contact with the cells, which works to prevent cell damage at "worstcase scenario" high temperatures.
20
2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION
Figure 2.13: Cooling of dense module as suggested by Horne [15].
An idea somewhat similar to that of Horne is patented by Koehler [42]. His idea is to
submerge the cells in the circulating coolant liquid, whereby heat is transferred from two
cell surfaces instead of just one. In this way the coolant acts like a filter by absorbing
much of the incoming low-energy radiation before it reaches the cells. By choosing the
right coolant and regulating the pressure, one can achieve local boiling on the PV cells,
which give a uniform temperature across the surface and a much higher heat transfer
coefficient.
2.4 OTHER COOLING OPTIONS
Cooling problems are not exclusive to photovoltaics. Recently, extensive research has
been performed on the issue of cooling of electronic devices. The rapid progress
towards denser and more powerful semiconductor components require the removal of a
large amount of heat from a confined space [43-48]. Other areas where much research is
being conducted on the subject of cooling include the nuclear energy and gas turbine
industries. Both of these have a large cooling load and strict temperature limitations due
to material properties. These applications generally deal with larger areas and different
geometries from the electronics industry. Research from these three fields should provide
a broad base for finding better options for cooling of photovoltaics.
The following section presents some studies that might be relevant for PV cooling,
especially for the more demanding cases like densely packed cells under high
concentration.
2.4.1 Passive systems
There is a wide variety of passive cooling options available. The simplest ones involve
solids of high thermal conductivity, like aluminium or copper, and an array of fins or
other extruded surface to suit the application. More complex systems involve phase
changes and various methods for natural circulation.
It should be noted that passive cooling is just a means of transporting heat from where it
is generated (in the PV cells) to where it can be dissipated (the ambient). Complex
passive systems reduce the temperature difference between the cells and the ambient, or
they can allow a greater distance between the cells and the dissipation area. However, if
the area available for heat spreading is small and shading is an issue, no complex
21
2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION
solutions will help avoid the use of active cooling. Heat dissipation is still limited by the
contact point between the terminal heat sink and the ambient, where the convective heat
transfer coefficient, and less the radiative heat transfer (except at very high temperatures)
are the limiting factors.
Kraus and Bar-Cohen [49] give an extensive and very useful introduction to the design of
heat sinks. Their book contains an overview of typical convective thermal resistances for
different configurations, as a useful guide when choosing the cooling system. It also
presents a step-by-step procedure for heat sink design and optimization procedures both
for single fins and fin arrays. Optimum dimensions for fins of common heat sink
materials are given, as well as the heat transfer properties for optimised arrays.
One way of passively enhancing heat conduction is the use of heat pipes. The theory on
and use of these devices is thoroughly described by Dunn and Reay [50]. It seems that
the use of heat pipes is probably not feasible for high concentrations because heat pipe
performance is limited by the working fluid saturation temperature and the point at
which all liquid evaporates (burnout). For water, a heat flux of 250-1000 kW m-2 can be
accommodated but only at temperatures above 140 °C. Launay et al. [51] study the effect
of micro-heat pipe arrays etched into the silicon wafer. They show an improvement of
conductivity through the silicon, depending on the geometry of the heat pipes and the
fluid charge. In the search for better cooling options for computer components, heat
pipes provide an alternative for transporting the heat away from the component and to a
place better suited for a fan or other heat sink (remote heat exchangers). Pastukhov et al.
[52] and Kim et al. [47] show promising results for these systems. Xuan et al. [53] describe
the flat plate heat pipe (FPHP), which is a flat copper shell filled with a working fluid. A
layer of sintered copper powder is applied to the heated surface of the FPHP in order to
enhance heat transfer. The FPHP is studied under various orientations. When installed
horizontally, the extra working fluid forms a liquid layer on the heated surface and
reduces heat transfer. The best result is achieved when the FPHP is installed in the
vertical direction, when the working fluid is distributed across the heated surface by the
capillary action of the sintered layer, ensuring there is not too much fluid at the surface at
any time. It is shown that the FPHP is a good alternative to a solid heat sink due to its
low thermal resistance, isothermality and lightweight features.
Chen and Lin [54] study the capillary pumped loop used as a heat transfer device. Their
system is capable of dissipating a heat load of 25 kW m-2 from an area of 42 mm x 38
mm while keeping the heated surface below 100 °C. The device works better if the
vertical distance between the evaporator and the condenser is increased above 10 mm.
The effect of orientation is not included in the study.
2.4.2 Forced air cooling
The thermal properties of air make it far less efficient as a coolant medium than water
[49]. This implies that more parasitic power (to power fans) will be needed to achieve the
same cooling performance. Air cooling also reduces the possibility of thermal energy
use. Hence, air is a less favourable option in many cases. However, in some situations
where water is limited, forced air may still be the preferred option. The heat transfer of
forced air cooling can be enhanced in much the same ways as with water. Detailed
information on the design of forced air heat sinks can be found in [49]. Other studies on
forced air cooling are not included in this review.
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2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION
2.4.3 Liquid single-phase forced convection cooling
2.4.3.1 Microchannel heat sinks
The microchannel heat sink is a concept well suited for many electronic applications
because of its ability to remove a large amount of heat from a small area. Tuckerman and
Pease [55] were the pioneers who first suggested the microchannel heat sink, based on
the fact that the convective heat transfer coefficient scales inversely with the channel
width. The best reported thermal resistance from the experiments was 9.0 x 10-6 K m2 W1
for a heated area and heat sink of 10 mm x 10 mm, flow rate of 8.6 mL s-1 and a
pressure drop of 213.7 kPa. This paper significantly raised the experimental limit on heat
removal per area, and may have allowed for further miniaturisation of electronic
components.
Later studies have showed two major drawbacks to the microchannel heat sink. These are
a large temperature gradient in the streamwise direction, and a significant pressure drop
that leads to high pumping power requirements. Much work have been published on the
modeling and optimisation of various aspects of the microchannel heat sink [46].
Ryu et al. [44] presents a numerical optimization that minimises the thermal resistance
subject to a specified pumping power. For a heat sink of 10 mm x 10 mm, the lowest
reported thermal resistance is 9 x 10-6 K m2 W-1. The associated pressure drop is 103.42
kPa and the optimal dimensions are 56 µm channel width, 44 µm wall width, and 320 µm
channel depth. More on the pressure drop and heat transfer in a heat sink of rectangular
microchannels is given by Qu and Mudawar [56]. The modelling and experiments deal
with laminar flow only. Channel dimensions were 231 µm width and 713 µm depth. The
study concludes that conventional Navier-Stokes and energy conservation equations can
accurately predict the pressure drop and heat transfer characteristics for microchannels
of this dimension.
An experimental study of heat transfer in rectangular microchannels by Harms et al. [57]
concludes that heat transfer performance can be increased by decreasing the channel
width and increasing the channel depth. Developing laminar flow is found to perform
better than turbulent flow due to the larger pressure drop associated with turbulent flow.
The lowest reported thermal resistance is 1.26 x 10-4 K m2 W-1 for a flow rate of 118
mL s-1 over an area of 3930 mm2 and a 169 kPa pressure drop.
Owhaib and Palm [58] present an experimental study which verifies the best correlations
to use for modelling heat transfer in circular microchannels. Tubes of three different
diameters were studied. The results show that in the laminar flow regime, the heat
transfer coefficient is largely independent of channel diameter, while in the turbulent
regime (Re > 6000), smaller channels are clearly better. The best reported thermal
resistances are 10-4 K m2 W-1 for 0.8 mm tubes in the turbulent flow regime, and 4 x 10-4
for laminar flow. No data on pressure drops or flow rates are given.
The effect on tip clearance on the thermal performance of microchannels has also been
studied. Tip clearance denotes the spacing between the channel walls and the top surface.
It has generally been assumed that tip clearance would lower the efficiency of the heat
sink because of the phenomenon of flow bypass: as the tip clearance is raised, for a
given pumping power, the flow rate will decrease between the channels while increasing
through the tip clearance. As a result, less heat is transferred near the base of the
channels. However, Min et al. [59] found that in microchannel heat sink, the added heat
23
2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION
transfer through the fin tips lead to an increased heat sink performance as long as the
ratio of tip clearance to channel width is kept below 0.6. Similar results are found by
Moores and Joshi [60] for a shrouded pin fin heat sink.
The search of a microchannel design that deals with the problem of non-uniform
temperatures and pressure drops has been carried out by a number of researchers, and
several innovative solutions have been found.
Alternating flow directions is one way of reducing the streamwise temperature gradient
in the microchannel heat sink. This was first proposed by Missagia and Walpole [61].
Their design consists of a silicon wafer with microchannels machined into them,
attached to a manifold plate that directs the water to flow in alternating directions
through the channels. The results indicate a thermal resistance of 1.1 x 10-5 K m2 W-1, for
a laminar flow of 28 mL s-1. The associated pressure drop for a 100 mm long heat sink
would be 452 kPa.
Vafai and Zhu [43] suggest using two layers of counter-flow microchannels. Numerical
results show that the streamwise temperature gradient is significantly lowered compared
to a one-layer structure. This in turn allows for a smaller pressure drop to fulfil the same
cooling requirements. No specific data for thermal resistances or pressure drops are
given.
Chong et al. [46] optimised the counter flow principle for single and double layer
channels as the two described above. The simulation models both designs for laminar
and turbulent flows. The results show that laminar flow is to be preferred over turbulent
for both cases. The single layer counter flow heat sink gives an overall thermal resistance
of 4.8 x 10-6 K W-1 with a pressure drop of 122.4 kPa. For the double layer design the
values are 6.6 x 10-6 K W-1 and 54.6 kPa, both under laminar flow conditions. The paper
does not arrive at any conclusions as to whether single or double layer counter flow is the
preferable alternative.
A two-layered microchannel heat sink with counter flow, called the manifold
microchannel heat sink, is also designed to lower the temperature gradient and pressure
drop. This design has been successfully modelled and optimised by Ryu et al. [48] (Figure
2.14). In the manifold microchannel heat sink, the coolant flows through alternating inlet
and outlet manifolds in a direction normal to the heat sink. This way the fluid spends a
relatively short time in contact with the base, thus resulting in a more uniform
temperature distribution. With laminar flow, it is shown that the thermal resistance is
lowered by more than 50% compared to the traditional microchannel heat sink, while
drastically reducing the temperature variations on the base. A number of numerical
calculations are performed to find the optimal channel depth, channel width, fin
thickness and inlet/outlet width ratios. All optimisations are constrained by a given
pumping power. Optimal dimensions are found to be divider width ≥ 500 µm and inlet
width + outlet width ≥ 1000 µm, with an associated thermal resistance of 3.1 x 10-6 K m2
W-1.
24
2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION
Figure 2.14: Manifold microchannels as suggested by Ryu [48].
Inspired by the superior mass flow capacity of the mammalian circulatory and
respiratory system, Chen and Cheng [62] use this idea to design a fractal net of
microchannels. On a purely theoretical basis, they conclude that fractal-like
microchannels can increase the heat transfer while reducing the pressure drop when
compared with parallel microchannels. This is based on the assumptions of laminar, fully
developed flow, and negligible pressure drop due to bifurcation.
2.4.3.2 Impinging jets
Very low thermal resistances (generally 10-5 - 10-6 K m2 W-1) [63] can be achieved through
the use of impinging liquid jets. When high velocity liquid is forced through a narrow
hole (axisymmetric jet) or slot (planar jet), into the surrounding air, a free surface forms.
The impinging jets are capable of extracting a large amount of heat because of the very
thin thermal boundary layer that is formed in the stagnation zone directly under the
impingement and extends radially outwards from the jet. However, the heat transfer
coefficient decreases rapidly with distance from the jet. To cool larger surfaces, it is
therefore desirable to use an array of jets. A problem arises when water from one jet
meets the water from the neighbouring jet. Disturbances arise which are very hard to
model but have been shown to decrease the overall heat transfer drastically [64, 65]. If
measures are taken to deal with this "spent flow" (through drainage openings), impinging
jets have been predicted to be a superior alternative to microchannel cooling [65] for
target dimensions larger than the order of 0.07 m x 0.07 m.
Webb and Ma [64] give an extensive overview of the literature available on liquid
impinging jets. The review distinguishes between free and submerged jets, and
axisymmetric and planar jets, and deals with single phase jets only. The article points out
a number of areas where further studies are needed. These include the effect of curved
surfaces and spent flow, and the local heat transfer coefficient at points other than the
stagnation zone directly underneath the jet.
25
2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION
Womac et al. [66] present an experimental study of the heat transfer coefficient in free
and submerged 2x2 and 3x3 arrays of liquid jets without treatment of spent flow. The
effect of nozzle-to-plate spacing is studied, and found to be insignificant for free jets, but
to have an effect on submerged jets. Correlations for the heat transfer in both types of
jets are presented.
2.4.4 Two-phase forced convection cooling
By allowing the coolant fluid to boil, the latent heat capacity of the fluid is used to allow
for a significantly larger heat flux and an almost isothermal surface. However, two-phase
flows are more complicated to model and to predict. Any comprehensive heat transfer
textbooks such as [28] will give an introduction to forced convection boiling.
When the bulk liquid is below saturation temperature, but the heat flux is high enough
that liquid at the surface can reach saturation temperature, subcooled boiling occurs.
Under subcooling, bubbles will collapse as they are released from the wall and travel into
the surrounding liquid. Subcooled forced convection boiling in small channels is among
the most efficient heat transfer methods available [67, 68]. This is often used in
applications with extremely large heat fluxes such as fusion reactors first walls and plasma
limiters. The most important parameter in this case is the critical heat flux (CHF). If the
heat flux is raised above the CHF, a very large increase in temperature will occur and
most likely result in overheated and damaged equipment. Thus, to achieve maximum
cooling, one wants to run the system close to the CHF, but never above. Higher heat
transfer coefficients, and thus lower wall temperatures, can be found at lower heat fluxes.
Predicting the CHF is difficult because it depends on a number of parameters. High
velocities, large subcoolings, small diameter channels and short heated lengths are known
to increase the CHF.
Two-phase flows may be a good option for the cooling of photovoltaic cells when the
heat fluxes are high. The saturation temperature of water can be brought to 50 °C at a
pressure of 0.13 bar [28]. To avoid pressurised systems, other working fluids may be used
such as Vertrel XF used in [45].
A number of studies are devoted to the detailed analysis of bubble formation, onset of
different boiling regimes, and CHF for subcooled boiling. These include [67, 69, 70].
Bartel et al. [71] present a very good literature review on subcooled boiling. The review
points out that there is a lack of available data on local measurements in the subcooled
boiling region.
There are a number of studies dealing with two-phase flow in microchannels. Ghiaasiaan
and Abdel-Khalik [68] give an extensive literature review of the subject. Microchannels
with hydraulic diameters of the order 0.1 to 1 mm and long length-to-hydraulic diameter
ratios are considered. The review includes a thorough description of flow regimes in
horizontal and vertical channels, correlations for pressure drops, forced flow subcooled
boiling and CHF. Detailed studies of bubble formation and flow boiling in
microchannels are found in [72-74].
Hetsroni et al. [45] describes a microchannel heat sink that keeps the electronic device of
a temperature of 50-60 °C, a temperature highly suited for photovoltaic purposes. The
working fluid is Vertrel XF, which has the desired saturation temperature and is dielectric,
so that it can be brought into contact with the active electronics. The study was
performed at relatively low heat fluxes (< 60 kW m-2). Results show a much more
26
2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION
uniform temperature across the surface compared to water cooling at comparable flow
rates (5 °C as opposed to 20 °C). However, some nonuniformities in heat transfer
occurred because of two circumstances specific to parallel microchannels: the two phases
may split unevenly on entering the channels, leading to different heat transfers for
different channels; secondly, the wall superheat for the onset of nucleate boiling is very
low, something which leads to pressure fluctuations and uneven heat transfer.
Temperature and pressure fluctuations were also found to be characteristic of boiling in
minichannels by Hapke et al. [75]. The lowest thermal resistance reported by Hetsroni et
al. [45] was 9.5 x 10-5 K m2 W-1 at a mass flux of 290 kg m-2 s-1.
Inoue et al. [76] study the use of boiling in confined jets to cool a very high heat flux
(nearly 30 MW m-2) in a fusion reactor (Figure 2.15). This system proposes an innovative
way of dealing with the spent flow, and at the same time preventing splash of water from
the violent boiling that may occur at the surface under these conditions. The jets
proposed are planar jets, but the experiments only look at the two-dimensional version.
Therefore, the potential problem of outgoing water heating the incoming water and thus
lowering the cooling capacity is not considered. The CHF is studied as a function of jet
flow velocity, subcooling and curvature of heated surface. The results show that the CHF
in confined flow is almost double that of a free flow jet. Surface curvature does not seem
to give any significant effect.
Figure 2.15: Confined planar jet as suggested by
Inoue et al. [76]. Water is fed through the inner
tube, forms a planar jet through the slit in the
bottom, and then returns through the outer tube.
2.5 COMPARISON OF COOLING OPTIONS
It is problematic to compare such a wide range of cooling options. Depending on the
application, one may want to compare parameters such as pumping power, weight,
materials use, ease of manufacturing and maintenance, maximum heat removal,
temperature uniformity, shading etc. All of these criteria can obviously not be
incorporated into one review. In addition, literature generally does not give information
on all of these aspects.
Table 2.2 gives a summary of the various cooling options described in this review. In
order to enable a comparison of pumping powers, which is an important parameter
when it comes to power generating systems, the pumping power has been calculated as
27
2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION
P = m& × ∆p in cases where only mass flow rate and pressure drops are given. It should be
noted that pressure drops may or may not incorporate manifolds or other external
factors. Articles also may use slightly different definitions for thermal resistances. Extra
care should be taken when comparing different systems such as jets versus passive
cooling or two-phase versus single-phase flows. Thermal resistances, flow rates and
pumping powers are all given per unit area for easier comparison.
All precautions taken, Figures 2.16 – 2.19 still provide a comparison between options.
The letters in the graphs mark where they are taken from in Table 2.2. There is a wide
variety between the different studies, even within the same categories. This shows that
experimental work is still very important for determining the best cooling methods.
What seems to do best in all comparisons is the category "improved microchannels"
which includes various forms of alternating flows. This method provides the clearly
lowest thermal resistance along with low power requirements. In all microchannel studies,
laminar flow seems to outperform turbulent. Etching microchannels into the silicon
substrate as a part of the manufacturing process of photovoltaic modules may prove a
very good option for photovoltaic cell cooling (eg. [8]).
Impinging jets seem to be a promising alternative, provided measures are taken to deal
with spent flow. No studies have yet come up with a solution to this problem when
dealing with single-phase liquid flows.
passive cooling, no wind
forced air
water, plane surface
water, channels
water, microchannels
water, improved microchannels
water, impinging jets
microchannels, two-phase flow
101
a
Thermal resistance (K m2/W)
100
10-1
d
e
-2
10
-3
10
-4
10
-5
10
10-6
f
l
i
o
j
b
k
s
B
h
u
c
r
g
m
t
n
v
x
y
p
w
q
z
A
10-7
Figure 2.16: Comparison of different cooling options. The letters refer to the
references listed in Table 2.2. Note that the position on the x-axis is of no
significance.
28
2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION
-3
Thermal resistance (K m 2/W)
10
water, microchannels
water, improved microchannels
microchannels, two-phase flow
-4
10
10-5
10-6
100
101
102
103
104
105
106
2
Pumping power (W/m )
Figure 2.17: Comparison of different cooling options and the pumping power they
require.
10
forced air
water, channels
water, microchannels
water, improved microchannels
water, impinging jets
microchannels, two-phase flow
-2
2
Thermal resistance (K m /W)
f
10
l
-3
g
m
10
r
-4
h
10
x
z
10
n
-5
v
B
p
y w
q
u
-6
10
-2
10
-1
10
0
10
1
10
2
10
3
2
Flow rate (kg/m s)
Figure 2.18: Comparison of different thermal resistance cooling options and flow
rates. The letters refer to the references listed in Table 2.2.
29
2
Thermal resistance (K m /W)
2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION
10
-3
10
-4
10
-5
water, microchannels
water, improved microchannels
microchannels, two-phase flow
r
B
v
w
10
u
q
p
x
y
-6
10
0
10
1
10
2
10
3
10
4
Pressure drop (kPa)
Figure 2.19: Thermal resistance versus pressure drop for different cooling options.
The letters refer to the references listed in Table 2.2.
30
31
-
-
* Use caution with thermal resistances for natural convection or two-phase flow (see Section 2.1.3)
Water flow through rectangular steel pipe
Chenlo and Cid
[25]
-
-
Finned strip, calm air
-
6.10 x 10-1
Luque et al. [32]
-
2.58 x 10-3
Impinging jet, nozzle-plate distance = 0.16 cm
Finned heat pipe, calm air
-
1.52 x 10-1
Water cooling
-
-
-
-
-
-
-
1.52 x
Forced air through multiple passages
10-1
-
-
-
-
-
-
-
-
-
kPa
Pressure drop
-
-
-
Finned strip, calm air
No extruded surface, calm air
Feldman et al. [33]
Florshuetz [29]
-
-
Water cooling, plane surface: laminar mode
turbulent mode
-
Air cooling, plane surface,
W m-2
m2
Sala [11]
Pump power
Heated area
Configuration
Work
Table 2.2: Values cited in references
10-1
-
-
-
7.75 x 100
3.03 x 100
3.95 x
-
-
-
-
f
2.6 x
8.7 x 10-4
2.2 x 10-3
k
j
i
h
5.1 x 10-5
9.8 x 10-3 *
g
4.3 x 10-4
10-3
e
d
c
b
a
1.1 x 10-2 *
3.3 x 10-2 *
2.7 x 10-4
2.6 x
10-3
2.0 x 100 *
K m2 W-1
kg m-2 s-1
-
Thermal
resistance
Mass flow
rate
2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION
32
.
+ Calculated from given data as P = m∆p
3.00 x 104 +
2.48 x 102
-
1.21 x 102
-
3.74 x 101
4.0 x 10-4
1.3 x 10-4
4.7 x 10-3 *
4.0 x 10-5
2.3 x 10-4
1.3 x 10-3
1.1 x 10-5
2.30 x 10-4
-
1.69 x 102
-
1.82 x 101
3.51 x 100
3.48 x 10-1
K m2 W-1
kg m-2 s-1
Microchannels, single layer counter flow
* Use caution with thermal resistances for natural convection or two-phase flow (see Section 2.1.3)
Missaggia and
Walpole [61]
-
Circular microchannels, laminar flow
Owhaib and Palm
[58]
6.32 x 103 +
-
-
-
-
Thermal
resistance
Mass flow
rate
1.0 x 10-4
3.93 x 10-3
Microchannels
Harms et al. [57]
-
8.82 x 102
-
-
kPa
Pressure drop
turbulent flow
1.68 x 10-2
3.40 x 10-5
Microchannels
Vincenzi et al. [8]
Parallel fin heat sink, calm air
3.60 x 10-3
Water cooled cold plate
Verlinden [37]
Kraus and BarCohen [49]
1.15 x 10-1
Water flow through internally extruded channel
W m-2
m2
Coventry [36]
Pump power
Heated area
Configuration
Work
Table 2.2: Values cited in references (continued)
u
t
s
r
o
n
m
l
2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION
Microchannels, single layer counter flow, laminar
Chong et al. [46]
33
1.00 x 10-4
Impinging jets
Two-phase microchannels
Rohsenow et al. [63]
Hetsroni et al. [45]
+ Calculated from given data as P = m∆p
1.00 x 10-4
Manifold microchannels
8.70 x 102
-
1.50 x 104
1.48 x 102 +
turbulent
Ryu et al. [44]
5.25 x 101 +
5.04 x
101 +
7.70 x 100 +
W m-2
m2
1.00 x 10-4
Pump power
Heated area
Microchannels, double layer counter flow, laminar
turbulent
Configuration
Work
Table 2.2: Values cited in references (continued)
4.50 x
3.00 x 100
-
-
5.64 x 102
5.64 x 102
2.90 x 102
-
1.40 x 10-1
2.62 x 10-1
9.31 x 10-2
10-1
1.12 x
102
w
4.8 x
9.5 x 10-5
1.0 x 10-6
3.1 x 10-6
5.8 x 10-6
6.6 x 10-6
B
A
z
y
x
v
10-6
6.9 x 10-6
K m2 W-1
kg m-2 s-1
6.53 x 10-2
Thermal
resistance
Mass flow
rate
1.18 x 102
kPa
Pressure drop
2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION
2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION
2.6 CONCLUSION
With single-cell geometries, research shows that passive cooling is feasible for
concentration values of at least 1000 suns, provided the cells and lenses are kept small.
Linear concentrators can also be cooled passively, but the heat sinks tend to get very
intricate and therefore expensive for concentration values as low as 20 suns. A heat pipe
based solution is one way to increase the passive cooling performance. Different ways of
active cooling by water or other coolants have also been found to work well and should
be considered for concentration levels over 20 suns.
For densely packed cells, it seems that active cooling is the only feasible solution. At high
concentrations, the high heat flux makes a low contact resistance from cell to cooling
system extremely important. There are also numerous challenges for the cooling system
itself in order to achieve a low thermal resistance for a low pumping power requirement
with a simple, reliable and inexpensive system. New solutions such as microchannels or
impinging jets may prove to be good solutions, especially if incorporated in the cell
manufacturing process.
Owing to the complexity of obtaining accurate modelling results, careful experimental
work is still important for determining the best method of cooling for a given
application. However, the comparisons in this review provide a good background to
assessing the different options.
Because the use of microchannels as a cooling technique for concentrating PV is already
being trialled in Italy, it was decided to proceed with investigating the possibility of jet
impingement cooling. A closer literature study of this particular technique was therefore
needed. The results of this study are presented in the following chapter.
34
3
a
Chapter
HEAT TRANSFER UNDER
SINGLE-PHASE,
SUBMERGED AND
AXISYMMETRIC JETS
This chapter contains a literature survey on jet impingement cooling. It is limited to jets
that can be characterised as axisymmetric and submerged. The term axisymmetric refers
to jets issuing from round holes, as opposed to planar jets issuing from slots. Arrays of
axisymmetric jets have been found to yield a higher total heat transfer per unit flow rate
than planar jets [77]. The term ‘submerged’ refers to jets issuing into a pool of the same
fluid, while free-surface jets impinge into a less dense medium such as water into air.
Several studies [66, 78, 79] have established that submerged liquid jets yield a higher
overall heat transfer than free-surface liquid jets. One of the most important parameters
for jet flow behaviour is the ratio of nozzle-to-plate spacing z, to nozzle diameter, d.
Only relatively small ratios (z/d < 6, sometimes referred to as confined) are considered
here because the heat transfer deteriorates significantly beyond this spacing. This
behaviour is further explained in Section 3.1.2.
In arrays consisting of many jets, the jets close to the drainage point are affected by the
spent liquid from jets further away. This spent liquid is referred to as crossflow. Because
crossflow generally has an adverse effect on heat transfer, this study is limited to single
jets and relatively small arrays where the effect of crossflow is minor or negligible.
When dealing with convective heat transfer, the Nusselt number, Reynolds number and
Prandtl number are dimensionless groups that are frequently used. The Nusselt and
Reynolds numbers are based on a characteristic length, which in the case of jets is taken
to be the nozzle diameter unless otherwise explained. The Nusselt number is a
dimensionless form of the heat transfer coefficient, given as
Nu =
hd
,
k
(3.1)
where h is the heat transfer coefficient and k is the fluid thermal conductivity. By
definition, the Nusselt number is the ratio of convective heat transfer to the conductive
heat transfer that would have occurred in the fluid under stagnant conditions.
The Reynolds number is based on the fluid mean velocity, and is proportional to the
inertial force divided by the viscous force. At low Reynolds numbers, the viscous effects
dominate and the flow is laminar. Inertia effects become more important at higher
35
3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS
Reynolds numbers, followed by a transition to turbulent flow. The Reynolds number is
defined as
Re =
vd
ν
,
(3.2)
where v is the mean fluid velocity and ν is the kinematic viscosity of the fluid.
In jet impingement heat transfer, the thermal and boundary layers are important
concepts. In essence, the thermal boundary layer is the region of fluid close to the heated
surface which “feels” the temperature of the wall. The velocity boundary layer is the
region of fluid that “feels” the no-slip condition along the wall. The fluid outside the
boundary layers is completely unaffected by the heated surface. The Prandtl number Pr
denotes the ratio of the thickness of the velocity boundary layer to the thermal boundary
layer. This value is constant for a given fluid at a given temperature. Water at room
temperature has Pr ~ 7, while air at room temperature has Pr ~ 0.7. The Prandtl number
is defined as the ratio of kinematic viscosity to thermal diffusivity (a material constant
which describes the rate at which heat is conducted through the medium) κ :
Pr =
ν
.
κ
(3.3)
3.1 SINGLE JETS
3.1.1 Hydrodynamic flow structure of single impinging jets
Figure 3.1 depicts the characteristic flow regions of a single impinging jet. As the jet
issues from the nozzle, the outer layer of the jet, called the mixing region, interacts with
the surrounding liquid. The centre of the jet, often referred to as the potential core,
remains undisturbed for a region of about 3 - 8 nozzle diameters beneath the jet exit.
The exact length of the potential core depends on the jet Reynolds number and nozzle
configuration [78, 80]. Interaction with the surrounding liquid causes the jet velocity to
fall off proportionally with the vertical distance below the tip of the potential core. As
the jet approaches the impingement plate, it is deflected and slowed down. The
deflection region is found to extend 1.2 – 2 nozzle diameters from the impingement plate
surface [81]. Due to jet deceleration and the resulting increase in pressure, hydrodynamic
and thermal boundary layers are formed in the impingement zone directly beneath the
jet, which may only be a few micrometers thick [64]. The thin thermal boundary layer is
what causes the high heat transfer capabilities of impinging jets. The region of flow
parallel to the impingement surface is often referred to as the wall jet. In this region, the
jet velocity rises rapidly to a maximum before it falls off radially away from the
impingement zone. For some configurations, there is a transition from laminar to
turbulent flow close to the stagnation point. The thermal and velocity boundary layers
grow thicker with radial distance from the jet axis until they encompass the full thickness
of the jet flow.
36
3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS
d
l
1
2
z
3
4
5
Figure 3.1: Flow regions of an impinging jet (from
Jambunathan et al. [81]). 1: Potential core; 2: mixing
region; 3: deflection region; 4: wall jet; 5: stagnation
point. The nozzle diameter, orifice plate thickness and
nozzle-to-plate distance are denoted by d, l, and z,
respectively.
3.1.2 Radial variation in local heat transfer and the influence of nozzleto-plate spacing
The local heat transfer under an impinging jet is strongly dependent on r/d, which is the
ratio of radial distance away from the stagnation point to the nozzle diameter. Figure 3.2
shows the typical radial variation of Nusselt number under a single jet for nozzle-to-plate
spacing to diameter ratios of 2 ≤ z/d ≤ 24 [81]. The distributions for all spacings are
characterised by high heat transfer close to the stagnation point (r/d = 0), followed by a
rapid decrease in heat transfer in the wall jet region. For z/d ≤ 6, the distributions tend to
converge, apart from local variations which are explained below. This is because these
spacings are within the length of the potential core, where the jet velocity remains
unchanged from the nozzle exit. Although the heat transfer remains relatively unchanged
for spacings within the potential core, some studies have found that the overall
magnitude increases slightly with z/d due to increased turbulence [78]. For higher nozzleto-plate spacings, the overall heat transfer is drastically reduced because of interaction
with the surrounding liquid. For r/d > 7, the Nusselt number distributions for all z/d
start to converge. This is because flow deflection and interaction with the surrounding
liquid has completely reshaped the initial flow structure.
At low z/d, two peaks appear in the Nusselt number distribution. The inner peak at r/d ~
0.5 occurs partly because of acceleration of the fluid out of the stagnation region, which
decreases the thickness of the thermal boundary layer, and also because of the influence
of shear layer generated turbulence. The inner secondary peak has been found to
become less pronounced as the Reynolds number is decreased and the nozzle-to-plate
distance is increased[82]. The outer peak at r/d ~ 2 is caused by the transition from
laminar to turbulent flow. The location of this peak has been found to move away from
the stagnation point as Re or z/d is increased. For z/d beyond the length of the potential
core (z/d ~ 6), the maximum Nusselt number is found at the stagnation point and there
are no secondary maximums.
37
3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS
z/d
r/d
Figure 3.2: Radial variation of heat transfer coefficient under a jet impinging on a flat plate
for various nozzle-to-plate spacing to diameter ratios (reproduced from [81]).
The studies of Womac et al. [78] and Garimella and Rice [79] suggest that the optimal
nozzle-to-plate spacing for single jets is found at z/d ~ 3-4. Womac et al. [78] studied
nozzle-to-plate separations of 1 ≤ z/d ≤ 14.5 for a variety of nozzle diameters and
Reynolds numbers, and found that the average heat transfer coefficient was relatively
insensitive to separation distance at low Reynolds numbers (Re ≤ 4000). For higher Re,
the average heat transfer remained undisturbed or increased slightly with increasing z/d
for 1 ≤ z/d ≤ 4 and dropped off as the separation distance was further increased. This
was used to determine that the length of the potential core was approximately four
nozzle diameters. Garimella and Rice [79] studied the local heat transfer under
submerged jets with square-edged orifices over a range of nozzle-to-plate spacings (1 ≤
z/d ≤ 14). The working fluid was FC-77 which is a dielectric liquid with Pr ~ 25. The
stagnation point heat transfer coefficient was found to be almost constant up to z/d = 4,
but to decrease from z/d = 5, which corresponded with the length of the potential core
for this configuration. For z/d < 5, secondary peaks appeared at r/d ~ 2. The magnitudes
of these peaks were found to increase with increasing Reynolds number. The local and
average Nusselt number was highest for all nozzles at z/d ~ 3. The stagnation point heat
transfer coefficient is generally highest at the very end of the potential core. This was
shown by, among others, Webb and Ma [64] who found that the stagnation point heat
transfer reached a maximum at z/d ~ 5. However, lower z/d tends to shift the Nusselt
number peak outwards from the stagnation point, so that the region of high heat transfer
occupies a relatively larger area. The highest average heat transfer is thus generally found
slightly below the end of the potential core.
The shape of the radial heat transfer distribution is a complex function of r/d, z/d, Re
and nozzle configuration, something which makes it a challenge to find accurate
correlations. Hoogendoorn [83] gave a correlation based on turbulence intensity values at
38
3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS
radial positions in a free jet. This requires extensive measurements before the correlation
can be used and is thus not very practical for design purposes. Jambunathan [81]
presented a correlation for the local Nusselt number under single jets of the form
Nu = k Re a ,
(3.4)
where a = f (r / d , z / d ) and k = f ( r / d , z / d , nozzle configuration ).
While a is given explicitly, k remains to be found graphically from [81], which makes this
a poor correlation for making predictions. In this form only qualitative assumptions can
be made for the detailed heat transfer under impinging jets.
3.1.3 Effect of nozzle configuration
The heat transfer coefficient is highly sensitive to the level of turbulence in the flow,
which in turn is determined by the nozzle configuration. Orifice nozzles have generally
been found to introduce a higher level of turbulence and thereby a higher heat transfer
coefficient than pipe-like nozzles [84]. Figure 3.3 shows an overview of commonly used
orifice nozzle configurations.
d
d
a)
b)
d
c)
Figure 3.3 : Overview of orifice nozzle configurations: a) square-edged, b) sharp-edged,
c) countersunk. The liquid flows though the nozzle from above.
Garimella and Nenaydykh [80] found the developing length of the nozzle (l/d) to be a
major influence on the heat transfer under liquid jets. The range under consideration was
0.25 ≤ l/d ≤ 12. It was found that short developing lengths (l/d < 1) yielded the highest
stagnation point heat transfer coefficients. At l/d = 4, there was a minimum in the heat
transfer coefficient, with a slight increase for l/d above this value. These trends were
explained by the separation bubble which is formed at the inlet of a nozzle. Previous
studies had shown that the reattachment length for this bubble is between 0.8 and 1.9
nozzle diameters. For short developing lengths, the separation bubble would not reattach
within the nozzle, thus resulting in a reduced effective cross-section of the nozzle. The
higher velocities created by this contraction were thought to cause the high heat transfer
for l/d < 1. For l/d > 1, the flow reattaches within the nozzle. The increase in heat
transfer above l/d = 4 was attributed to the flow velocity profile changing from uniform
to fully developed. The fully developed flow has a higher velocity in the centre and lower
velocity along the edges. This would result in a higher heat transfer coefficient at the
stagnation point.
The heat transfer characteristics of sharp-edged, square-edged and an intermediate case
of nozzles were compared by Lee and Lee [84] for air jets for 5000 < Re < 30 000. The
sharp-edged orifice was found to yield the highest local and average Nusselt number
because of its more vigorous turbulence behaviour. It also shows a stronger Reynolds
number dependence than the straight and intermediate nozzles. The sensitivity to nozzle
configuration was found to be stronger at low z/d, which ranged from 2 to 10 in this
study. This finding was supported by Garimella and Nenaydykh [80], who explained this
phenomenon by the fact that interaction with ambient fluid downstream from the jet exit
tends to smooth out differences in the original flow structure.
39
3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS
When designing an optimum jet impingement device, it is generally relevant to optimise
the system for a given pump power instead of a given flow rate. The pump power is
proportional to the product of flow rate and pressure drop across the device. Most
studies of the effect of nozzle configuration do not take the pressure drop into account,
which make them incomplete as a tool for designers. Brignoni and Garimella [85]
performed a study comparing the heat transfer and pressure drop characteristics for
orifice nozzles countersunk at two different angles compared with a regular square-edged
orifice nozzle. Previous studies have found that countersunk orifices yield lower heat
transfer coefficients when compared with square or sharp-edged orifices. However,
Brignoni and Garimella showed that countersinking the nozzle significantly reduced the
pressure drop while only slightly lowering the heat transfer coefficient. A countersunk
angle of about 30° (angle to normal) seems to yield the best result. At higher angles, the
nozzle again starts to resemble a sharp corner which increases the pressure drop through
it. The difference in heat transfer between different nozzles was found to become more
significant with increasing Reynolds number.
Lee et al. [86] stated that the nozzle diameter, with all dimensionless parameters held
constant, had an influence on the Nusselt number in the impingement zone out to r/d ~
0.5. In this region, the local Nusselt number was found to increase by about 10% from
the smallest to the largest nozzle. Long pipe nozzles were used to ensure fully developed
flow at the nozzle exit. The length of the potential core (in units of nozzle diameter) was
shown to increase with increasing nozzle diameter. This indicates that for the same z/d,
large nozzles create a higher mean velocity. The turbulence level was also higher for the
larger nozzles. The higher velocity and turbulence intensity would account for the
increased heat transfer under the larger nozzles. Only relatively large nozzles of d = 13.6
to 34.0 mm and one Reynolds number of Re = 23 000 were used in this study [86].
Garimella and Rice [79] also found the stagnation point Nusselt number to be dependent
on the nozzle diameter but could find no systematic relationship.
3.1.4 Correlations for the stagnation point and average Nusselt number
Table 3.1 presents a summary of correlations for the stagnation point (Nu0) and average
Nusselt number (Nuavg) under single jets. Following from theoretical hydrodynamic
studies of the jet flow structure, the correlations for stagnation point Nusselt numbers
are generally of the form
Nu 0 = C Re m Pr n .
(3.5)
The Reynolds number dependence, m, is normally determined experimentally and found
to lie in the range 0.4 ≤ m ≤ 0.7, and is strongly dependent upon nozzle configuration.
Because most studies looks only at one liquid at one temperature, the Prandtl number
dependence n is most commonly assumed. Most correlations use n ~ 0.4. Li and
Garimella [87] performed a study using different Prandtl number liquids to obtain the Prdependence as a part of the curve-fitting process. The resulting correlation for confined
and submerged jets for a range of fluids is given in Table 3.1. Other correlations, valid
only for specific fluids but with a smaller error, are given in Li and Garimella [87].
Garimella and Nenaydykh [80] proposed a correlation with correction factors for z/d and
l/d. The data for the smallest nozzle (d = 0.79 mm) was not included in the correlation
because it showed a somewhat different behaviour from the other nozzles. Very small
nozzles have often yielded unexpected results (an example is Womac et al. [78]),
40
3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS
something which suggests there is a size dependency which becomes more significant for
small nozzle diameters. The same correlation was used by Garimella and Rice [79].
Lee and Lee [84] proposed specific correlations for different nozzle configurations, but
because they contained no Prandtl number dependence they are not easily compared
with or applied to other cases, and are therefore not included in Table 3.1.
The correlations for average Nusselt number under single jets are generally based on area
averaged heat transfer coefficients over either round or square heated areas with the jet
centred on the heater. Round heaters are characterised by their radius in units of r/d
while square heaters have side lengths Lheat. The common usage of heaters to study the
heat transfer characteristics of impinging jets is described in Section 3.4.
The correlation of Womac et al. [78] assumes a square heater with sides of length Lheat.
The first part of the equation describes the impingement region while the second
describes the wall jet region. Reynolds number dependences of m = 0.5 and 0.8 are
assigned to each part respectively to represent laminar and turbulent flow. Garimella and
Rice [79] presented a correlation for the average Nusselt number over a heater with
constant dimensions of 10 mm x 25 mm. The square-edged nozzles had diameters in the
range 0.79 mm ≤ d ≤ 6.35 mm. The average heat transfer for a given area will be highly
dependent on nozzle diameter, but is not included in the correlation. This correlation is
thus relevant only for a limited number of cases. Another correlation is given by Li and
Garimella [87] which is corrected for the ratio of equivalent heat source diameter, De, to
nozzle diameter. The correlation is calculated for a heated area, Aheat, of any geometry
and is thus more useful for a variety of cases within the range of validity for this
correlation. The correlation of Tawfek [88] is valid for a circular heater area of radius r
out for 2 ≤ r/d ≤ 30, but only for large z/d (z/d > 6). By including a correction factor
which is a function of both z/d and r/d, Huang and El-Genk [89] obtained a correlation
which was valid for a circular heater area for r/d < 10. The derivative of this function
provides the basis of a correlation for maximum average Nusselt number, which can be
used to find the optimum z/d for a given r/d. The optimal z/d is given as
z / d opt = −b / 2c ,
(3.6)
where b and c are defined in Table 3.1. This correlation can be useful for single nozzles
but as will be shown in Section 3.2, other factors come into play with arrays of nozzles
which influence the choice of z/d.
41
Table 3.1: Correlations for stagnation point and average Nusselt numbers under single jets
Range of validity
Liquid
Nozzle
configuration
Correlation
Garimella and
Nenaydykh
[80]
Re
4000 – 23 000
FC-77
z/d
0.25 – 12
square-edged
orifice
Nu 0 = 0.492 Re 0.585 Pr 0.4 (z / d )
l/d
1–5
d
1.59 - 6.35 mm
Re
4000 - 23 000
FC-77
square-edged
orifice
⎛z⎞
Nu avg = 0.160 Re 0.695 Pr 0.4 ⎜ ⎟
⎝d ⎠
fully developed
flow
Nu avg = Re 0.76 Pr 0.42 a + b(z / d ) + c( z / d ) ,
Garimella and
Rice [79]
42
Huang and ElGenk [89]
Average
(maximum)
deviation (%)
0.024
−0.11
(l / d )−0.09
⎛l⎞
⎜ ⎟
⎝d ⎠
10 (N/A)
14 (N/A)
−0.11
.
z/d
1-5
l/d
0.25 – 12
d
1.59- 6.35 mm
Re
6000 - 60 000
z/d
1 – 12
l/d
25.8
2
3
4
a = 10 −4 506 + 13.3(r / d ) − 19.6(r / d ) + 2.41(r / d ) − 9.04(r / d ) ,
r/d
0 – 10
b = 10 − 4
d
6.2 mm
c = −3.85 × 10 −4 [1.147 + (r / d )]
air
[
2
]
12 (15)
[
[32 − 24.3(r / d ) + 6.53(r / d ) − 0694(r / d ) + 2.57 × 10
2
−0.0904
3
−2
]
(r / d ) ]
4
3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS
Reference
Table 3.1: Correlations for stagnation point and average Nusselt numbers under single jets (continued)
Range of validity
Li and
Garimella [87]
Re
4000 - 23 000
Liquid
Nozzle
configuration
comparison
of results
for a range
of liquids
square edged
nozzles
Correlation
Average
(maximum)
deviation (%)
Nu 0 = 1.427 Re
Pr
0.444
⎛l⎞
⎜ ⎟
⎝d ⎠
−0.058
z/d
1 -5
l/d
0.25 - 12
d
1.59 - 25.2 mm
Pr
0.7 - 25.2
⎛l⎞
Nu avg = 1.179 Re 0.504 Pr 0.441 ⎜ ⎟
⎝d ⎠
De
11.28 - 22.56
mm
+ 1.211 Re
0.637
Pr
1/ 2
43
⎛ 4 Ah2 ⎞
⎟⎟
De = ⎜⎜
⎝ π ⎠
Martin [97]
0.496
Re
2000 - 400 000
z/d
2 – 12
r/d
2.5 –7.5
air
various nozzle
configurations
Nu avg =
0.441
⎛ De ⎞
⎜ ⎟
⎝ d ⎠
⎛ De ⎞
⎜ ⎟
⎝ d ⎠
−0.071
9.08 (27.12)
−0.272
⎛ De ⎞
⎜ ⎟
⎝ d ⎠
.
−0.283
Ar
−1.062
1 − Ar ⎞⎟⎠
⎛⎜
⎝
8.57 (27.79)
2
⎛ 1.9d ⎞
⎟⎟ .
, Ar = ⎜⎜
⎝ De ⎠
1 − 1.1(d / r )
⎛d ⎞
0.42
⎜ ⎟ F Pr ,
1 + 0.1[( z / d ) − 6](d / r ) ⎝ r ⎠
⎛ Re 0.55 ⎞
⎟
F (Re ) = 2 Re ⎜⎜1 +
200 ⎟⎠
⎝
,
N/A
0.5
0.5
Tawfek [88]
Re
3400 – 41000
z/d
6 – 58
r/d
2 – 30
d
3 – 7mm
air
tapered nozzles
Nu avg = 0.453 Pr 1 / 3 Re 0.691 (z / d )
−0.22
(r / d )−0.38
10 (N/A)
3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS
Reference
Table 3.1: Correlations for stagnation point and average Nusselt numbers under single jets (continued)
Range of validity
Liquid
Nozzle
configuration
Womac et al.
[78]
Re
2000 – 32 000
z/d
1–4
water and
FC-77
contoured
nozzle
l/d
10.9
d
1.65mm
Pr
7, 25
Correlation
Nu Lheat ,avg
Pr 0.4
L∗ =
(0.5
Average
(maximum)
deviation (%)
= 0.785 Re 0d.5
L
Lheat
(1 − Ar ) ,
Ar + 0.0257 Re 0L*.8 heat
L∗
d
)
2 Lheat − 1.9d + (0.5Lheat − 1.9d )
,
2
If Ar > 1 or Lheat < 0, Ar should be set equal to 1.
Ar = π
(1.9d )2
L2heat
7.2 (16)
44
3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS
Reference
3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS
3.2 ARRAYS OF JETS
3.2.1 Flow structure and heat transfer characteristics of jet arrays
For cooling of large surfaces, it is most often beneficial to use an array of multiple
nozzles. Submerged jets in an array interact with each other in two fundamental ways.
The first is interference between the mixing regions of the two jets before impingement
as shown in Figure 3.4. This phenomenon is most pronounced at close jet-to-jet spacings
s/d and at high z/d due to mixing region expansion beneath from the jet exit. The effect
of this interference is probably a weakened jet and a subsequent lowering of the overall
heat transfer [90]. On the other hand, Womac et al. [66] thought the jet interference to
lead to a higher heat transfer because of the increase in turbulence level. The second
effect occurs when two wall jets meet face-to-face. If the jets are otherwise equal, this
interaction occurs along the centreline between two adjacent jets. At low flow rates and
large s/d, it will result in increased turbulence and higher heat transfer in the region of
interaction. At high jet velocities, however, the interaction can become strong enough to
cause a jet fountain to form. This can cause heated fluid to re-enter the core of the jets
as seen in Figure 3.5, and result in a lower overall heat transfer under the array.
Several studies have shown that the stagnation point Nusselt number is not sensitive to
array configuration in well-drained arrays where crossflow is negligible. Huber and
Viskanta [82] showed that spent air exits located between the jets in a 3x3 jet array had
negligible effect on the heat transfer except for very low nozzle-to-plate spacings (z/d =
0.25). This suggests that the spent flow tends to drain well between the jets without
creating adverse effects in arrays of this size. Huber and Viskanta [91] also showed that
there is little difference between the heat transfer under central and perimeter jets in 3x3
arrays, except for a slight asymmetry in the perimeter jets caused by the higher flow
restriction towards the centre of the array.
3.2.2 Effect of nozzle-to-plate spacing
Aldabbagh and Sezai [92, 93] modelled an array of square, laminar jets at low Reynolds
numbers (100-400), and found the Nusselt number to be significantly higher at very small
z/d (0.25-0.5) than at z/d = 2. This was attributed to the fact that no upwash fountain
has room to form at these low spacings, and thus the jet fills up the whole space.
Garimella and Schroeder [94] observed the same trend in an experimental study of
confined multiple air jets. For 0.5 ≤ z/d ≤ 4, a reduction in nozzle-to-plate spacing leads
to an increase in the average heat transfer coefficient, with the effect being stronger at
higher Reynolds numbers (5000 ≤ Re ≤ 20 000). The authors explain this effect by the
turbulence intensity of the jet being increased by stronger interaction with the spent flow
from neighbouring jets, at the same time as there is less effect of heated liquid reentering the jets at small z/d. However, the heat transfer distribution was found to be less
uniform at low nozzle-to-plate spacings.
45
3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS
Interference
z
Figure 3.4: Jet interference before impingement (reproduced from San and Lai [90]).
Fluid from the mixing regions of the two jets interacts and can cause a weakening of
the jet, thereby resulting in a decrease in heat transfer.
Fountain
Deflection
z
Figure 3.5: Interference along centreline of jets (reproduced from San and Lai [90]). The
depicted jet fountain can form for high Reynolds numbers and close jet-to-jet spacings,
and cause heated fluid to re-enter the core of the jets.
When studying spacings of 2x2 and 3x3 arrays of liquid jets, Womac et al. [66] found a
reduced heat transfer for sparse arrays at small z/d and, similarly, for dense arrays at large
z/d. The authors gave no explanation for these phenomena. A reason for the
discrepancies could be the complex interaction between Re, z/d and s/d. At low Re, the
upwash fountain becomes less significant, and the heat transfer can be increased at high
z/d by increased turbulence levels. Lower s/d also needs a lower z/d to avoid interaction
before impingement.
46
3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS
3.2.3 Effect of nozzle pitch
As the jets are placed closer together, the total mass flow rate over a given area will
increase for a given Reynolds number. For those studies where the average heat transfer
is calculated for a given area, this will in most cases lead to an increased average heat
transfer. If the average is calculated for a unit cell around one jet, the average should also
increase for a decreasing nozzle pitch because relatively more of the unit area is covered
by the high heat transfer impingement zone. However as jets are moved closer together,
negative interference effects such as the jet fountain and shear layer interference will
become more significant.
Womac et al. [66] studied 2x2 and 3x3 in-line arrays of liquid jets and compared the total
heat transfer over the heater surfaces. For the 2x2 array, two pitches (s/d = 6.22 and 9.96)
were tested. The overall heat transfer was found to be higher for the smaller pitch. The
authors attributed this to less area being covered by the weak wall jet, as well as mutual
interactions before impingement, which were thought to induce turbulence and to
enhance heat transfer. In the case of the large pitch, the nozzles were placed almost in
the corners of the square heater, whilst for the smaller pitch they were centred on each
quadrant of the heater.
Yan and Saniei [95] used a pair of impinging air jets to study the detailed heat transfer
between the two jets. The nozzle pitch under consideration ranged from 1.75 to 7.0. The
pipe-type nozzle provided fully developed flow, and only one Reynolds number was used
(Re = 23 000). It was shown that as the jet pitch decreases, the region of influence of
one jet on the flow field and the heat transfer of the other increases until it encompasses
the entire jet. The heat transfer under one jet deteriorates on the side facing the other jet,
probably due to the reversed pressure field where the two jets meet. An area of enhanced
heat transfer was observed along the centreline between the jets. For low nozzle pitches
(s/d < 3.5), the magnitude of this heat transfer coefficient maximum exceeded that at the
stagnation point. Note that these observations can not directly be translated to arrays of
nozzles because each jet was meeting another jet only on one side, which made the flow
conditions asymmetric, compared with arrays where the jets meet other jets on all sides.
San and Lai [90] searched for optimal values for the jet-to-jet spacing in staggered arrays
with five air jets. The Reynolds numbers under consideration were 10 000 – 30 000. The
analysis is based on the central jet stagnation point heat transfer coefficient only, which
means that only the deteriorating effects of jet interference before and after
impingement are taken into account. Maxima were found for two different nozzle
pitches. When s/d is increased, the stagnation point heat transfer coefficient is increased
because of less interference before impingement, but also decreased because the
temperature of the jet fountain is raised as the wall jet area is increased. The first
maximum is found where the former effect loses dominance to the latter. At larger s/d,
the heat transfer starts to increase as the jet fountain is diminished, and at the second
maximum the stagnation point Nusselt number is equal to that of a single jet. Note that
the jet fountain effect is highly significant at these high Reynolds numbers. The second
relative maximum disappeared at low Re (~10 000) because of the weak jet fountain.
Optimum nozzle pitches were found for each combination of Re and z/d. For Re =
10 000 and z/d = 4 and 5, the optimum pitch was found at s/d = 6.0.
Brevet et al. [96] studied the heat transfer under a row of impinging jets with nozzle pitch
varying from 2 to 10. The heat transfer over a given area was compared on the basis of
47
3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS
total mass flow rate. It was found that to optimise the total heat transfer rate, one should
increase s/d, which in turn decreases the number of nozzles and increases the Reynolds
number. A nozzle pitch of s/d = 4 - 5 was identified as an optimal value. Reducing the
nozzle pitch below this would not be efficient because the small increase in heat transfer
is not justified by the larger increase in mass flow. This result is supported by Huber and
Viskanta [82]. They found the heat transfer under a jet in an array to be significantly
lower (14 – 21%) than that under an equivalent single jet. This was attributed to adjacent
jet interaction prior to impingement. As expected, the influence of adjacent jets was
found to decrease as the nozzle pitch was increased or the nozzle-to-plate spacing was
decreased. Jet interference was also observed to dampen the secondary peaks in Nusselt
number and thus create a more uniform distribution. Optimizing on a mass flow basis, it
was found that increasing the nozzle pitch and thereby increasing the Reynolds number
would increase the average heat transfer of the total array. The Reynolds numbers were
in the range 3500 – 20 400.
When comparing only two nozzle pitches of s/d = 3 and 4, Garimella and Schroeder [94]
found the heat transfer coefficients for s/d = 3 to lie above those of s/d = 4 for r/d ≤ 2,
but to drop below them for r/d > 2. As a result, the average heat transfer of the two
configurations was found to be the same (within 5%). There was also a slight increase in
heat transfer compared with single jets in the area where the two jets meet. When
comparing the effectiveness of a single jet with an array of four jets, the array clearly
provided the higher heat transfer coefficient. Compared on a mass flow basis, however,
the single jet yielded the higher heat transfer. This was on the other hand accompanied
by a very large pressure drop and, in a comparison based on total pressure drop, the array
again performed better. No comparison was made for total pumping power in their
study.
3.2.4 Correlations for average Nusselt number
The correlations for average Nusselt numbers presented below are all given along with
their range of validity in Table 3.2. The correlation given by Womac et al. [66] is made for
arrays of liquid jets on a square heater of length Lheat. As in Womac et al. [78], it contains
one part for the impingement region and another for the wall jet region. Nusselt
numbers for the four jet array of small nozzles (d = 0.513 mm) were only about half that
of the rest and were not included in the correlation.
Garimella and Schroeder [94] presented a correlation for a square heat source with a
fixed area of 20 mm x 20 mm. Nozzle-to-plate spacing is included as a correction factor,
but the effect of nozzle pitch was recognised as being not researched well enough to be
taken into account in the correlation. Huber and Viskanta [82] include a correction factor
for s/d in their study, which is based on the average heat transfer for a square unit cell
under the central jet in the array. The correlation given by Martin [97] has been verified in
several studies, including Garimella and Schroeder [94] and Huber and Viskanta [82].
This correlation is based on a unit cell in an array and includes correction factors for z/d
and s/d.
48
Table 3.2: Correlations for average Nusselt numbers in jet arrays
Range of validity
Fluid
Nozzle
configuration
Correlation
Garimella and
Schroeder [94]
Re
5000 – 20 000
air
s/d
3-4
square-edged
orifices
Nu avg = 0.127 Re 0.693 Pr 0.4 ( z / d )
z/d
0.5 – 4
l/d
1
d
1.59 – 3.18 mm
Re
3400 – 20 500
air
s/d
4–8
square-edged
orifices
Nu avg = 0.285 Re0.710 Pr 0.33 ( z / d )
z/d
0.25 – 6.0
l/d
1.5
d
6.35 mm
Re
2000-100 000
s/d
4.43-14
z/d
2-12
Huber and
Viskanta [82]
Martin [97]
Average (maximum)
deviation (%)
9 (28.2)
−0.105
−0.123
(s / d )−0.725
10 (20)
no crossflow
(open spent air
exits)
air
N/A
N/A
Nu avg = 0.5 KG Pr 0.42 Re 2 / 3 ,
⎡ ⎛ z / d f ⎞6 ⎤
⎟ ⎥
K = ⎢1 + ⎜⎜
⎢ ⎝ 0.6 ⎟⎠ ⎥
⎣
⎦
f =
π ⎛d ⎞
2
⎜ ⎟ .
4⎝s⎠
−0.05
, G=2
f
1 − 2 .2 f
,
1 + 0 .2 z / d − 6 ) f
(
)
3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS
49
Reference
Table 3.2: Correlations for average Nusselt numbers in jet arrays (continued)
Reference
Range of validity
Fluid
Nozzle
configuration
Womac et al.
[66]
Re
water and
FC-77
pipe-like nozzles
500 – 20 000
2–4
s/d
5 – 10
l/d
4.69 – 9.32
d
0.513 - 1.02mm
Average (maximum)
deviation (%)
Nu avg, Lheat
Ar =
50
L* =
9.93 (30)
⎛ Lheat ⎞
0.8 ⎛ Lheat ⎞
⎟
⎜
A + 0.363 Re L* ⎜ * ⎟(1 − Ar ) ,
= 0.509 Re
⎜ d ⎟ r
⎝ L ⎠
⎠
⎝
0.5
d
Nπd 2
(Ar = 1 if it exceeds unity)
4 L2heat
[(
)
]
2 s / 2 − 1.9d + [(s / 2) − 1.9d ]
2
3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS
z/d
Correlation
3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS
3.3 OTHER PARAMETERS INFLUENCING HEAT TRANSFER
3.3.1 Surface modifications
Modification of the impingement surface by adding small extended surfaces generally
leads to an increased heat transfer in single-phase convective cooling systems because of
the increased total surface area and the increased turbulence level of the flow. However,
because of the specific characteristics of jet impingement flow, surface modifications can
in some instances have an adverse effect on the heat transfer [64].
Priedeman et al. [98] studied the effect of surface enhancements on the heat transfer
under single, free-surface liquid jets of both water and FC-77. Roughening of the surface
was found to enhance the heat transfer by disrupting the momentum boundary layer, but
this effect was most pronounced for the liquids with higher Prandtl number. In the case
of water, the total heat transfer increased by as much as a factor of 3. The ability of the
surface modification to increase heat transfer was observed to decrease with increasing
Reynolds number, the range of which was 6000 < Re < 40 000. In comparison, Webb
and Ma [64] found that surface effects became more pronounced with increasing
Reynolds number, due to thinning of the boundary layer leading to a larger fractional
penetration of the roughness elements. Although surface modifications and surface
roughening generally have a positive effect on the heat transfer from liquid jets, this
effect was shown to be most significant for liquids with high Prandtl number, such as
FC-77. For water (Pr ~ 7), surface modifications could sometimes lead to a decrease in
heat transfer. Chakorun et al. [99] found surface roughness to increase the local and
average Nusselt numbers by up to 28%, increasing with increasing Reynolds number
(6500 ≤ Re ≤ 1900).
3.3.2 Effect of mesh screen or perforated plate between nozzle exit and
impingement plate
Techniques for enhancing the turbulence level of the jet by disturbing the flow can be
used as a way to increase the heat transfer under the jet. One such method is the
installation of a perforated plate between the nozzle and the impingement plate. Lee et al.
[100] found this to significantly increase the average Nusselt number, but also to increase
nonuniformity under the single jet. The best results were obtained for small perforation
holes. The vertical position of the perforated plate with respect to the nozzle and
impingement plate was found not to have a large effect. A pipelike nozzle of large
diameter (d = 34 mm) was used to provide fully developed flow and high spatial
resolution in the measurement. Zhou and Lee [101] investigated the effect of a mesh
screen inserted upstream of the jet nozzle exit. A small increase in heat transfer (less
than 4%) at z/d = 4 was observed. Smaller enhancements were observed for smaller z/d,
while for larger z/d the mesh screen had an adverse effect on the heat transfer.
3.4 EXPERIMENTAL METHODS
In order to obtain correct information both on local and average heat transfer
coefficients in experimental investigations of impinging jets, a high spatial resolution is
necessary because of the highly nonuniform heat transfer distribution. When not enough
measurement points are obtained, the calculated average heat transfer could have serious
errors. The spatial resolution can be increased by either decreasing the distance between
measurement points, or by increasing the size of the jet. However, because very high
51
3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS
heat transfer coefficients are achieved, especially in liquid jet measurements, the size of
the heated area is often limited by the available power supply.
Depending on the heater configuration, thermocouples can be attached to the back of a
heated foil or in holes in a heater block. Some studies have used a single thermocouple
located on the back of a stainless steel foil heater, which was in turn moved in small
increments relative to the jet. The spatial resolution is in these cases limited by the size of
the thermocouples and their spacing.
Several studies have used thermographic liquid crystals (TLC) as a way of obtaining a
very high spatial resolution. The TLC is generally applied as a coating on a black
background. The colour of the TLC coating typically passes from black to red and
through the whole colour spectrum back to black at prescribed temperatures. The colour
changes are fully reversible. A CCD camera is used to record the colour distribution and
digital image analysing tools are used to translate these values into temperatures and then
into heat transfer coefficients or Nusselt numbers. Some researchers calibrate the TLC
hue versus temperature, which allows them to take only one picture at one power setting,
provided the TLC gives a colour response across the entire surface. Others use optical
filters to obtain pictures of isothermal contours, which are obtained at several power
settings. The TLC is normally applied to the back of a thin film or foil metal heater such
as stainless steel or gold. Transient measurements have also been made using TLC, but
only for air jets with relatively low heat transfer levels so that the time constants obtained
are long enough to make reliable measurements.
Infrared thermography is another method of obtaining a high spatial resolution which
has been used by some researchers, but since the equipment is expensive compared to
TLC, it is less commonly used. Table 3.3 shows an overview of the experimental
methods used in the studies mentioned in this chapter.
3.5 CONCLUSIONS ON JET IMPINGEMENT
The local heat transfer and flow structure characteristics of single impinging jets have
been studied extensively and are well known. The exact shape of the local heat transfer
distribution has, however, not been successfully correlated because it is such a complex
function of Reynolds number, nozzle diameter, nozzle-to-plate spacing and nozzle
configuration. The nozzle configuration has a significant influence on the heat transfer
because it determines the level of turbulence in the flow. More accurate correlations exist
for the stagnation point and average heat transfer coefficients of single jets.
In jet arrays, adjacent jets can interfere destructively prior to impingement and either
constructively or destructively where the two wall jets meet, depending on Reynolds
number, nozzle pitch and nozzle-to-plate spacing. A number of different correlations
predict the average heat transfer coefficient under of arrays of jets with different ranges
of validity.
Surface modifications have been found to increase the average heat transfer coefficient
by as much as a factor of three for water jets, and more for liquids with higher Prandtl
number. However, some methods of surface modifications can lead to a decrease in heat
transfer. Other methods of disturbing the flow such as inserting mesh screens or a
perforated plate have shown the same trend of mostly increasing, but sometimes
decreasing, the average heat transfer coefficient.
52
3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS
Measuring the local heat transfer coefficient for impinging jets is a challenge because of
the high spatial nonuniformity achieved. When using thermocouples, the spatial
resolution is limited by their size and spacing. Infrared thermography can be used with
good results but involves costly equipment. Most recent studies have used a coating of
thermographic liquid crystals applied to a heater foil and recorded the temperature
distribution using a CCD camera. This method can yield high spatial and temperature
resolutions.
Table 3.3: Overview of experimental methods used in literature.
Reference
Experimental method
Brevet et al. [96]
Infrared thermography on plate of epoxy resin with copper circuit
heaters
Brigoni and Garimella [85]
Single thermocouple on back of moving stainless steel heater
Chakroun et al. [99]
37 thermocouples on back of heated plate
Garimella and Nenaydykh [80]
Single thermocouple on back of moving stainless steel heater
Garimella and Rice [79]
Single thermocouple on back of moving stainless steel heater
Garimella and Schroeder [94]
Single thermocouple on back of moving stainless steel heater
Huang and El-Genk [89]
29 thermocouples on back of stainless steel foil
Huber and Viskanta [82]
Isothermal contours from TLC with stainless steel foil
Huber and Viskanta [91]
Isothermal contours from TLC with stainless steel foil
Lee and Lee [84]
Isothermal contours from TLC with gold film
Lee et al. [100]
Isothermal contours from TLC with gold film
Lee et al. [86]
Isothermal contours from TLC with gold film
Li and Garimella [87]
Single thermocouple on back of moving stainless steel heater
Priedeman et al. [98]
32 thermocouples in heater block
San and Lan [90]
26 thermocouples on back of stainless steel foil
Womac et al. [66]
7 thermocouples in heater block
Yan and Sanei [95]
Transient TLC with hue calibration
Zhou and Lee [101]
37 thermocouples on back of gold film
Womac et al. [78]
7 thermocouples in heater block
53
3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS
3.6 DESIGN OF A JET IMPINGEMENT COOLING DEVICE FOR
CONCENTRATING PV
As shown in Chapter 2, it is of utmost importance in high concentration photovoltaic
systems to ensure a high average heat rate transfer across the entire surface. A jet
impingement cooling device for PV should therefore incorporate drainage of the cooling
fluid in a direction perpendicular to the impingement surface.
One may consider a range of designs that incorporate back drainage. Two possibilities
are shown in Figure 3.6. In setup a), water enters into a plenum chamber ending in an
orifice plate, through which the jets impinge onto the heated surface. The water then
returns through an outlet cavity which encompasses the plenum chamber. An advantage
of this configuration is that the flow patterns under the jet array are thought not to be
affected by the drainage flow. A disadvantage might be that the heat can be transferred
from the higher temperature water in the return chamber to the plenum chamber fluid.
However, because the water spends just a short time in contact with the heated surface,
the temperature difference is most likely too small to cause any significant heating. The
same effect would be more or less equally relevant for any back drainage configuration.
Another issue with the side drainage is that the area along the edges might experience a
lower heat transfer coefficient due to eddy formation along the steep corners of the
outlet cavity or because the jets are not placed close enough to the edges. The second
option, shown in Figure 3.6 b), is a central drainage configuration in which it is possible
to place the jets very close to the edges and thus diminish any eddy formation. However,
it is possible that the relatively small return flow pipe would disturb the pressure
distribution and thereby the flow pattern of the jet array.
b)
a)
Figure 3.6: Example of jet configurations with drainage direction normal to the impingement
surface: a) side drainage and b) central drainage.
If the number of nozzles required for the cooling module is found to be large enough
that effects of crossflow become significant, it may become necessary to have distributed
drainage exits throughout the cooling device. Two examples of possible distributed
drainage configurations are presented in Figure 3.7. The first configuration was used with
air jets by Huber and Viskanta [82]. It consists of a thick orifice plate through which long
nozzles are drilled in a square configuration. Between the rows of nozzles, outlet pipes
are drilled through the length of the plate, perpendicular to the nozzles. The spent liquid
flows into the outlet pipes through drainage holes along the bottom of the pipes. Shown
in Figure 3.7 a) is a cross-section of the orifice plate. The next configuration, Figure 3.7
54
3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS
b), is a simplified variation of the first. The water enters through parallel inlet pipes and
impinges through holes along the bottom of the pipes. The water is drained through
gaps between the pipes into an outlet chamber.
b)
a)
Figure 3.7: Two examples of distributed drainage configurations: a) drainage through
channels in impingement plate; b) drainage between plenum pipes.
The side drainage configuration shown in Figure 3.6 a) was chosen for the first jet
impingement prototype in the present study. A detailed description of the orifice plates
chosen and the experimental setup is given in Chapter 4. Because so much is known
about the effect of z/d (Section 3.1.2 and 3.2.2) and s/d (Section 3.2.3) for both single
jets and arrays, it was decided to look more closely at the effects of nozzle configuration
as well as general characteristics of the side drainage device such as the heat transfer
along the edges. Particular attention is given to how the pressure drop and pumping
power is related to average heat transfer, as this is a topic which is highly relevant in
power producing systems but one that is not well covered in literature. The results of the
measurements are presented in Chapter 5.
55
4
Chapter
EXPERIMENTAL DESIGN
AND PROCEDURE
In order to study the heat transfer characteristics of the side drainage jet device described
in Section 3.6, a testing unit was designed and constructed. The major challenges in the
design process were finding a heat source which would supply a large but uniform heat
flux, and measuring local temperatures accurately with high spatial and temperature
resolutions. Following on from prior research on experimental methods for jet
impingement studies (see Section 3.4) it was decided to use a thin stainless steel foil as a
heated surface with thermographic liquid crystals to measure local temperatures. The
experimental design and procedures are described in this chapter. Results are presented in
the following chapter.
4.1 EXPERIMENTAL SETUP
Water outlet
Clamping rod
Return
flow
chamber
Water inlet
Plenum
chamber
O-ring seal
Orifice plate showing
three nozzles
Stainless steel
heater foil
Silicone seal
Aluminium
L-support
Aluminium
bus-bar
Bakelite support
base
Camera view
Figure 4.1: Schematic diagram of jet testing unit.
56
4 EXPERIMENTAL DESIGN AND PROCEDURE
4.1.1 Design of jet testing unit
A schematic overview of the jet testing unit is given in Figure 4.1. Photographs of the
setup in the laboratory are shown in Figure 4.2. The interchangeable jet part consists of a
90 mm x 90 mm stainless steel top plate with 8 mm tube fittings for water inlet and
outlet. The water flows through the inlet into a plenum chamber manufactured from a 21
mm long x 20 mm wide square stainless steel tube, with a wall thickness of 1.2 mm and
rounded corners. This tube was welded onto the top plate. A stainless steel orifice plate
was welded onto the bottom of the plenum chamber. The water is forced through the
orifice and impinges onto the heated surface. It then returns through a 25 x 29 mm2
return flow chamber, the outer walls of which consist of a 21 mm thick Perspex plate.
The corners of the outlet chamber were rounded for ease of manufacturing.
Figure 4.2: The jet testing device as it appears in
the laboratory. The camera is normally attached to
the metal device seen attached to the wooden
support. In the picture on the left one can see how
the power supply is connected through thick
cables to the bus bars. The picture above shows a
head-on view without the power leads connected.
The heater consists of a 31 mm x 25 mm, 0.05 mm thick stainless steel foil supplied by
AllFoils Pty Ltd. The area of the heater is limited to this size because of the large
currents required to achieve the desired heat fluxes. The foil is clamped and stretched
tightly between two aluminium bus-bars. The power was supplied from a Variac variable
AC power source, with the voltage further stepped down in a second transformer. Heat
losses from the bottom of the foil can be assumed to be negligible because the expected
heat transfer coefficient from foil to water is orders of magnitudes higher than that of
natural convection and radiation under the foil. The foil was stretched by adjusting
screws through the bus bars and two aluminium L-supports that were attached to the
bakelite base. To make a water tight seal the foil was clamped between Perspex support
pieces and the Perspex outlet chamber piece over a width of about 1 mm on either side
so that the resulting heater area is 25 mm x 29 mm. The power dissipated in the outer 1
mm of the foil was assumed to lead to Perspex heating only, and not to have a significant
effect on the temperature measurements of the adjacent foil due to lateral conduction.
This assumption was confirmed through Finite Element Modelling using the software
package Strand7 [102]. Silicone sealant is used to make a water tight seal between the
Perspex, the bus bars and the heated foil. Threaded rods through the top plate, the
57
4 E XPERIMENTAL DESIGN AND PROCEDURE
Perspex plate and the bakelite base are used to clamp the jet testing unit to the support
frame shown in Figure 4.2.
4.1.2 Measuring temperatures using thermographic liquid crystals
The stainless steel foil temperature distribution was recorded using Thermographic
Liquid Crystals (TLC) and a digital camera with a CCD chip. The camera was placed
below the jet testing unit and looked at the foil through a circular hole in the bakelite
base. A sheet of R35C1WA TLC supplied by Liquid Crystal Resources Pty Ltd was
attached to the back of the heated foil. The sheet was manufactured with the following
layers: adhesive, black backing ink, TLC and a polyester sheet. The TLC nominally turns
from black to red at 35 °C and then through the rest of the spectrum to blue at 36 °C.
The colour change was in practice found to take place at lower temperatures, with red
showing up at about 32 °C. The colour change was calibrated by impinging the unheated
foil with water of a known temperature and recording the colour distribution of the foil.
The change in colour with 0.3 °C increments is shown in Figure 4.3. Because of the high
heat transfer coefficient associated with impingement, the foil can be assumed to have
the same temperature as the impinging water. The foil was illuminated by two LED lights
from the sides through the Perspex support pieces. A characteristic of the LED lights is
that they produce only small amounts of heat, which meant the influence of heat
radiation from the lamps can be assumed negligible.
33.0°C
34.2°C
33.3°C
34.5°C
33.9°C
34.8°C
Figure 4.3: Development of colours for increasing temperatures with the TLC premade foil from Liquid Crystal Resources. The reasons for and consequences of the
nonuniform colours are discussed in Section 4.3.
For each series of measurements, a single calibration picture was taken at 33.8 °C. At this
temperature, the TLC across nearly the entire surface of the heated foil had a response
within the most sensitive colour range, as Figure 4.3 shows. This temperature therefore
58
4 E XPERIMENTAL DESIGN AND PROCEDURE
gave the most accurate temperature calibration. The nonuniform TLC response and its
consequences are discussed in Section 4.3. After taking the calibration picture, the
camera and lighting were left undisturbed for the duration of the measurements. This
ensured that the lighting and placement of the camera would remain identical for the
calibration and the measurement pictures. When taking the actual measurements, the
water temperature was turned down to 32.4 °C and pictures were taken at increasing
electrical power levels. Some typical thermal images at increasing power levels together
with the calibration picture are shown in Figure 4.4.
q& = 20.5 kW/m 2
q& = 30.4 kW/m 2
q& = 42.8 kW/m 2
q& = 80.4 kW/m 2
Calibration picture at 33.8°C
Figure 4.4: Typical thermal images recorded at increasing power levels. A calibration picture is
shown on the left.
The data from the thermal images were compared with the calibration picture using a
procedure developed in Matlab software. A colour image of m x n pixels can be treated in
Matlab as an m x n x 3 matrix, where each pixel is assigned a value of red, green and blue
(RGB). Each picture was compared pixel by pixel with the calibration picture. If a pixel
(i,j) had the same RGB value as the (i,j) pixel in the calibration picture, the (i,j) cell in an
m x n matrix was assigned the calibration temperature. The other cells were assigned a
value of zero. The temperature was translated into a heat transfer coefficient using
h=
q&
,
Tfo − Tw
(4.1)
where h is the local heat transfer coefficient, Tfo and Tw are the temperatures of the foil
and the water, respectively, and q& is the power per area dissipated in the foil. Finally, the
heat transfer matrixes from all of the pictures were combined to produce an overall map
of the heat transfer distribution for the given flow rate. “Holes” in the matrix due to the
finite power intervals at which the pictures were taken were smoothed out using a linear
59
4 EXPERIMENTAL DESIGN AND PROCEDURE
interpolating algorithm. This resulting matrix was used to find the maximum and average
heat transfer coefficients. The stagnation point heat transfer coefficient was found as an
average of the 5% highest values in the matrix in order to minimize the effect of errors.
4.1.3 Instrumentation and data acquisition
The water was circulated and kept at a constant temperature using a Julabo F20
circulating chiller. A manual ball valve at the water outlet was used to control the flow
rate. The temperature of the inlet and outlet water was measured by two PT100 platinum
resistance thermometers in copper temperature pockets. The response time of the
temperature sensors in the pockets is in the order of one minute because of the thermal
mass of the copper, so care was taken to use measurements recorded only after the
readings had stabilized. The chiller was found to keep the water at a given temperature
with a precision of ± 0.03 °C.
The flow rate was recorded by a Dataflow Compact Inline Flow Transmitter. The
transmitter consists of a sensor body with a twin-vaned turbine rotor, which rotates at a
speed proportional to flow rate. As the rotor spins, the blades interrupt the continuous
infra red signal from opposing photo-transistors mounted on opposite external sides of
the clear sensor body. This is converted into a pulse signal which can be read by a
standard counter. The pressure was recorded by a micro differential pressure transducer
placed between the inlet and outlet pipes of the jet testing unit as shown in Figure 4.5.
The pressure transducer is based on a piezoresistive bridge construction, and gives a
millivolt output proportional to pressure difference.
Figure 4.5: Placement of the
pressure transducer.
The voltages, temperatures and pressure difference were read by several Fluke FL4428A
digital multimeters and recorded by Labview software to a laptop computer through an
IEE-488 GPIB interface and a GPIB-USB converter. A Datalogger DT505 was used to
count the pulses of the flow meter and this was transmitted to the computer through a
serial interface and serial-USB converter. Thermocouples were used with the Datalogger
and computer to monitor the ambient air temperature as well as the temperatures of the
bus bars and Perspex of the jet testing unit. Figure 4.6 shows an overview of the data
acquisition setup.
60
4 EXPERIMENTAL DESIGN AND PROCEDURE
Differential
pressure
transducer
Temperature
pockets
Shunt resistor
Jet testing unit
V
Transformer
Variac
V
Valve
Flow meter
Camera
Circulating
chiller
Support frame
Computer
Figure 4.6: Schematic of experimental setup and data acquisition system.
4.1.4 Jet devices tested
For the first set of experiments (results discussed in Sections 5.1-5.6), nine different
orifice plates were tested, shown in Table 4.1. The first two had nine nozzles of small
diameter, d = 0.7 mm, the next four had four nozzles with d = 1.4 mm and the last three
had a single nozzle of varying diameter. All of the arrays had the same nozzle pitch to
diameter ratio s/d = 7.14. The two dimensional placement of the nozzles is shown in
Figure 4.7. The nozzle-to-plate spacing to diameter ratio was set to z/d = 3.57 for the
four-nozzle arrays because several studies have shown that the maximum average heat
transfer coefficient for submerged jets occurs at a nozzle-to-plate spacing z/d ≈ 3-4 [78,
79]. However, because the distance between the orifice plate and the impingement plate
was kept constant at 5 mm, the dimensionless spacing z/d was twice as large for the ninenozzle arrays as for the other four. The single nozzle arrays had z/d = 3.33, 2.5 and 2 for
increasing nozzle diameter. The thickness of the orifice plates was 1 mm for all plates
except for the one called ‘long/straight’ which was 2 mm thick. The contouring of the
sharp-edged and countersunk nozzles was made using a conventional 30° countersinking
tool.
a)
b)
a)
Figure 4.7: Two-dimensional placement of a)
nine/dense nozzles, b) nine/sparse and c) fournozzle arrays.
61
4 EXPERIMENTAL DESIGN AND PROCEDURE
Table 4.1: Overview of orifice plates used in the experiments.
Number
of
nozzles
N
Nozzle
diameter
nine/dense
9
nine/sparse
Nozzle-toplate
spacing z/d
Nozzle
pitch
0.7
7.14
7.14
9
0.7
7.14
10.0
short/straight
4
1.4
3.57
7.14
long/straight
4
1.4
3.57
7.14
sharp-edged
4
1.4
3.57
7.14
countersunk
4
1.4
3.57
7.14
single S1
1
1.5
3.33
-
single S2
1
2.0
2.50
-
single S3
1
2.5
2.00
-
Device
d (mm)
Nozzle configuration
s/d
4.2 SYSTEM CHARACTERISATION
To become more familiar with the thermal characteristics of the experimental setup, a
number of tests over a range of flow rates, water temperatures and power settings were
performed using the short/straight jet array. The inlet and outlet water temperatures,
pressure drop across the device, bus bar temperature and power level were recorded. The
pressure drop through the system as a function of flow rate was found to follow a
parabolic curve as shown in Figure 4.8. No effects of temperature and the corresponding
change in viscosity could be detected. This gives an indication that the level of
uncertainty for the flow rate measurements is relatively large. This is further discussed in
Section 4.3.
For each water temperature and flow rate, the rate of change of enthalpy H& of the
water was calculated from
H& = cm& (Tout − Tin ) ,
(4.2)
where c and m& are the specific heat capacity and mass flow rate of the water. A
temperature-dependent heat capacity calculated at the water input temperature was used.
The rate of enthalpy change for a range of temperatures and flow rates without power
supplied to the foil is shown in Figure 4.9. Around room temperature, which was just
below 20 °C, the rate of change in enthalpy was found to increase linearly with flow rate.
This suggests a linear relationship between flow rate and heating by friction through the
62
4 EXPERIMENTAL DESIGN AND PROCEDURE
jet device. When the water is at a different temperature from the ambient, there is some
exchange of heat between the water running through the pipes and the surrounding air.
For water temperatures below room temperature, the graphs are seen to curve
downwards. At low flow rates, heating by friction is low while the heat gain from the
ambient, which decreases at higher flow rates, dominates. This results in the rate of
change in enthalpy decreasing for increasing flow rates up to the point where heating by
friction becomes dominant, whereby H& starts to increase. Above room temperature,
especially at low flow rates, heat is lost to the ambient. This causes the graph to curve
upwards.
40
35
Twater
30
10°C
15°C
20°C
25°C
30°C
35°C
40°C
45°C
50°C
∆p [ kPa ]
25
20
15
10
5
0
0
5
10
15
20
25
30
35
Q [ mL s-1 ]
Figure 4.8: Pressure drop versus flow rate for a range of water
temperatures. The second degree polynomial regression lines that fit the
data for the various temperatures are also shown.
10
8
6
Twater
.
H[W]
4
2
0
-2 0
5
10
15
20
-4
-6
25
30
35
10°C
15°C
20°C
25°C
30°C
35°C
40°C
45°C
50°C
-8
-10
Q [ mL s-1 ]
Figure 4.9: Rate of change of enthalpy of water versus flow rate at various water
temperatures together with the linear or polynomial regression lines.
63
4 E XPERIMENTAL DESIGN AND PROCEDURE
Figure 4.10 shows the relationship between the rate of change in enthalpy for water and
the power input to the foil. In all cases the valve was fully open, so that the flow rate was
at maximum. The difference in H& between the different temperatures agrees well with
the expected heat exchange with the ambient through the pipes. The y-intercept of the
linear fit, corresponding to zero power input, agrees well with the expected power loss or
gain at this temperature and maximum flow rate according to Figure 4.9. The slope of
the fit is about 0.91 for all temperatures. This suggests that an extra 9% of the heat is
lost, not through exchange with the ambient through the pipes but somewhere else in the
system. The voltage across the foil was measured where the cables were connected to the
bus bars, so that any voltage drops through the bus bars would be included.
70
60
Twater
50
10°C
15°C
20°C
25°C
30°C
35°C
40°C
45°C
50°C
.
H[W ]
40
30
20
10
0
0
10
20
30
40
50
60
-10
P[W]
Figure 4.10: Rate of change of enthalpy of water versus input power at a range of
water temperatures and the corresponding linear fits.
The temperature rise in the bus bars was recorded in order to investigate if bus bar
heating could account for the missing 9%. The bus bars are made of solid aluminium,
and their thermal mass can be calculated accurately by finding their volume and
multiplying by the known heat capacity of aluminium. The thermal mass of the bus bars
was found to be cmb = 60 J K-1. Figure 4.11 shows the relationship between the rate of
temperature change in the bus bars and the total input power. The scatter arises from the
uncertainty associated with the thermocouple, which was attached with tape to the
outside of the bus bar. No correlation was found between bus bar temperature rise and
water temperature.
Because the rate of temperature rise in the bus bars is given by
q& b = cm bT& ,
(4.3)
q&
T& = b ,
cm b
(4.4)
which can be rewritten as
the relationship between bus bar temperature rise and total power input can be written as
64
4 E XPERIMENTAL DESIGN AND PROCEDURE
q& / cmb
T& = b
q& t ,
q& t
(4.5)
where q& t is the total power input and q& b is the power dissipated in the bus bars. The
gradient of temperature rise versus power input is found to be
dT& q& b / cm b
=
= 7.48 × 10 −4 KJ −1 .
dq& t
q& i
(4.6)
Thus, the relationship between total power input and power dissipation is found as
q& b dT&
=
cmb = 0.045
q& t dq& t
(4.7)
for each bus bar, which amounts to 0.09 = 9% for the two bus bars. This is in good
agreement with the extra heat loss that occurs when the foil is electrically heated.
The temperature of the bus bars was found to remain at about 19 °C even when the
outlet temperature of the water was at 10.3 °C Because the temperature is still rising in
the bus bars when the water temperature is lower than the bus bar temperature, it must
be assumed that the temperature input to the bus bars comes from electrical heating of
the bus bars directly and not from the foil via contact with the water. It is not clear why
the power dissipation in the bus bars is so high, but it could arise from resistive heating
in the aluminium, the stainless steel screws conducting current, or contact resistance
between the aluminium and the stainless steel foil.
0.05
0.04
Twater
0.03
T [ K s-1 ]
0.02
.
0.01
0
0
10
20
30
-0.01
40
50
60
10°C
15°C
20°C
25°C
30°C
35°C
40°C
45°C
50°C
-0.02
P[W]
Figure 4.11: Rate of temperature change of bus bars plotted versus input power for
different water temperatures. The slope of the linear fit is 7.48 x 10-4 K J-1 .
4.3 UNCERTAINTY ANALYSIS
The standard deviations of the flow meter, pressure transducer, PT100s and voltage
measurements were all calculated from a range of measurements and found to be stable
for measurements made on different days and under different conditions. However,
because of a problem with the pressure transducer in the earlier series of measurements,
65
4 E XPERIMENTAL DESIGN AND PROCEDURE
only the pressure data for later measurements are included in the subsequent chapters.
The measured foil area was estimated to have an uncertainty of ± 0.5 mm in each
direction which for an area of 25 mm x 31 mm results in a total uncertainty of 3.4%.
Fraction of pixels recognized
The dominant uncertainties contributing to the uncertainty in havg are those of the foil
area and the foil temperature. Because the same heater was used for all measurements,
the area uncertainty yields a systematic error and would not influence trends or increase
the scatter in havg. The error in foil temperature, however, is not systematic. The TLC
sheet did not yield a uniform colour when it was unheated and impinged with water of a
known temperature, as seen in Figure 4.3. The reason for this is a variation in the sheet
adhesive as it was supplied from the manufacturer. This was partly corrected by
comparing each pixel individually against the calibration picture, as explained in Section
4.1.2. As Figure 4.12 shows, the TLC colour sensitivity is very high and results in a
maximum error of ± 0.2 °C. However, the camera shutter had to be released manually,
which made the camera move slightly. This meant the pixels were sometimes compared
with calibration picture pixels with a slight displacement. In addition, the camera’s
automatic focus would sometimes focus at the bus-bars or the support instead of the
TLC, so that the foil was sometimes out of focus. An analysis of the repeatability of the
measurements showed that the total uncertainty in heat transfer coefficient was less than
8%. The uncertainty in the temperature distribution was inferred from this value to be
about 7.2%.
Twater [ °C ]
Figure 4.12: TLC colour sensitivity over a range of temperatures. Images of a range of
water temperatures at 0.1 °C increments are compared with a calibration picture taken
at 33.8 °C.
With the uncertainty σ given in terms of a percentage of the mean value, the combined
uncertainty in a variable y = f( x 1 , … , xi ) is calculated from
66
4 E XPERIMENTAL DESIGN AND PROCEDURE
σ total =
∑σ
2
i
.
(4.8)
i
The uncertainties in power and temperature difference, and subsequently heat transfer
coefficient, are calculated in this manner. The resulting list of uncertainties is given in
Table 4.2.
There were also some uncertainties associated with the heat transfer near the edges of
the array. There is poor thermal resolution in the edge region due to experimental
difficulties such as stray silicone sealant along the edges of the foil and poor adhesion of
the TLC to the foil. These contribute little to the value of havg, but complicate the
interpretation of local heat transfer maps. Figure 4.13 shows a typical map of heat
transfer coefficients along with typical errors and their sources. Array edge effects are
discussed in more detail in Chapter 5.
Table 4.2: Uncertainties of the
measurements along with the associated
combined uncertainties.
Measurement
Uncertainty (%)
Foil area
3.4
Foil temperature
7.2
Flow rate
4.2
Pressure
0.6
Water temperature
0.1
Foil voltage
0.1
Shunt voltage
0.1
Power
3.4
Temperature difference
7.2
Heat transfer coefficient
8.0
4.4 IMPROVEMENTS OF THE EXPERIMENTAL SETUP FOR
LATER EXPERIMENTS
For some later measurements (the ones described in Section 5.7 and 6.1.5), the camera
and TLC setup was slightly improved. A method was found by which the camera could
be remotely controlled. This allowed the same placement and focus of the camera
throughout the measurements. Also, to diminish the nonuniformity of the TLC film, a
new TLC spray coating was used, which eliminated the need of adhesive. A black
backing paint and the liquid TLC was applied using an airbrush. This gave a much more
uniform result, as shown in Figure 4.14. The temperature window response for the TLC
was chosen to be closer to room temperature, in order to reduce the effect of heat loss
to the surroundings. The water was kept at 25.3 °C during these measurements. Due to
67
4 E XPERIMENTAL DESIGN AND PROCEDURE
these improvements, the accuracy of the later measurements is thought to be slightly
higher than in the first measurements. However, not enough data were collected to
perform an accurate uncertainty analysis.
stray silicone
sealant
variations in TLV
adhesive combined
with camera
movement
dust particles
on camera lens
or TLC surface
Figure 4.13: Sources of errors in local heat transfer distribution maps.
Figure 4.14: Airbrush applied
TLC coating at 26.5°C.
68
5
Chapter
RESULTS AND DISCUSSION
This chapter presents the results of the measurements of the side drainage device as well
as some measurements of the central drainage device, using the experimental setup
described in Chapter 4.
5.1 SINGLE JETS
As introduced in Table 4.1, three different single jet orifice plates (labelled S1, S2 and S3)
were tested. There were two motivations for studying single jets. Firstly, the shape of the
distribution of local heat transfer under a single jet needed to be investigated and
compared with findings from the literature, both to verify the experimental method and
to gain more insight into the characteristics of jet impingement cooling. Secondly, it was
necessary to investigate how the edges and corners of the return flow cavity of the side
drainage device would affect the overall heat transfer of the device.
Figure 5.1 shows a typical heat transfer distribution under a single jet. While being quite
symmetrical around the centre, the perimeter region appears ‘flattened’. A better
representation of the local heat transfer distribution is given by the cross-section through
the impingement area (shown in Figure 5.2). The impingement zone (r/d < 1) is seen to
be characterised by a region of high heat transfer in the centre followed by a sharp drop
at about r/d ~ 0.4. For r/d > 1, the local heat transfer drops off monotonically. As
shown in Figure 5.3, the shape of the heat transfer curve can be estimated reasonably
well by a linear function, which reaches the value of half maximum at r/d ~ 3.5:
⎛ 1
⎞
h = hmax ⎜1 − r / d ⎟ .
⎝ 7
⎠
(5.1)
This simplification helps to facilitate the estimation of temperature variations across the
heated surface, a subject which will be discussed in more detail in Chapter 7.
69
5 RESULTS AND DISCUSSION
Distance along bus-bar [ mm ]
h [ W m-2 K-1 x 104 ]
Distance between bus-bars [mm]
-2
-1
Wm
m -2 K
hh /[ W
K-1 ]
Figure 5.1: Local heat transfer distribution for the S2 single
nozzle at Re = 11 600.
80000
80 000
70000
70 000
60000
60 000
50000
50 000
40000
40 000
30000
30 000
20000
20 000
10000
10 000
00
Re = 11 600
Re = 5 610
-7 -6 -5 -4 -3 -2 -1
0
1
2
3
4
5
6
7
r /d
Figure 5.2: Two cross-sections through the stagnation point of local heat
transfer coefficients for the single S2 nozzle.
70
5 RESULTS AND DISCUSSION
Re = 11 600
-1
h [ W m-2 K
]
h / W m -2 K-1
80000
80
000
70000
70 000
Re = 5 610
Linear (Re = 11 600)
60000
60
000
50000
50 000
Linear (Re = 5 610)
40000
40
000
30000
30 000
20000
20
000
10000
10
000
00
0
1
2
3
4
5
6
r/ d
Figure 5.3: Shapes of the local heat transfer distribution for the
single S2 nozzle estimated by linear functions.
The experimental curves in Figure 5.2 can be compared with the theoretical distributions
in Figure 3.2. The theoretical distributions show an inner secondary peak at r/d ~ 0.5,
something which is not visible in the experimental results. This is as expected because the
experimental data are obtained at relatively low Reynolds numbers, and the inner
secondary peak is expected to become less pronounced and to disappear as Re decreases.
Figure 3.2 also predicts a change in slope or a secondary peak at r/d ~ 2 caused by the
transition from laminar to turbulent flow. A slight change in slope at this position can be
recognised in both of the experimental curves given. The magnitude of this change is
also small because of the low Reynolds number.
Another interesting aspect of Figure 5.2 is the dramatic drop in heat transfer near the
edge which is visible only on the left hand side of the graph. An equivalent drop is likely
to be present on the right hand side as well, but it is not visible because of the problems
with the liquid crystals and stray silicone sealant described previously. According to
Figure 2.2 and other studies, no such drop in heat transfer is expected for jets impinging
on a smooth surface. Finite element modelling using the software Strand7 showed that
the effects of lateral conduction from the edges of the foil would be insignificant 0.5
mm away from the edges, whereas the drop found in the experiments extended up to 2-3
mm. This indicates that the drop in heat transfer coefficient is most likely caused by eddy
formation along the steep edges of the outlet cavity.
71
5 RESULTS AND DISCUSSION
As a numerical verification, the experimental local heat transfer distribution is compared
with the model from Tawfek [88] given in Table 3.1. This model predicts the average heat
transfer coefficient in a circular area around the impingement zone for a given r/d. The
average heat transfer coefficient is calculated from the measured distribution of heat
transfer coefficients by numerical integration of the following:
havg
2
= 2
r
r
∫ r ×h × dr.
(5.2)
0
The values and trends are found to be in reasonable agreement with the results for the
single S2 nozzle at two different Reynolds numbers as shown in Figure 5.4. Perfect
agreement is not expected because the Tawfek correlation is only valid for z/d ≥ 6,
which corresponds to jet impingement beyond the potential core. The measured values
are for z/d = 2.5. A higher Reynolds number dependence is also expected for the higher
nozzle-to-plate spacing because of turbulence created in the interaction with the
surrounding liquid. This is evident from Figure 5.4 in that the correlation graph changes
more with differing Reynolds number than the measured values. The shape of the
correlation graph corresponds well with the measured values for mid range values of r/d,
but overestimates the values for the areas close to the edges because of the heat transfer
deterioration along the edges of the cavity.
Re = 11 600
have [ W m-2 K-1 ]
0
100 000
0
90 000
Re = 7 120
Tawfek, Re = 11 600
0
80 000
0
70 000
Tawfek, Re = 7 120
0
60 000
0
50 000
0
40 000
0
30 000
0
20 000
0
10 000
0
1
2
3
4
5
r/d
r/d
Figure 5.4: Comparison of area averaged heat transfer for the single S2
nozzle with the correlation from Tawfek [88].
72
6
5 RESULTS AND DISCUSSION
5.2 ARRAYS OF JETS
The distribution of local heat transfer for each individual jet in an array was found to be
similar to that of a single jet. The heat transfer coefficient drops off monotonically with
radial distance away from the stagnation point, and reaches a value of half that of the
stagnation point at about r/d ~ 3.5. However, as expected, interactions between the jets
lead to some heat transfer characteristics that are different from those of single jets.
Figure 5.5 presents a typical heat transfer coefficient distribution for an array of four
nozzles, while Figure 5.6 shows a cross-section of the local heat transfer coefficient
through two stagnation points for a range of Reynolds numbers. One of the
characteristics of jets in an array is a slight asymmetry in the outer jets, which is seen in
Figure 5.5. The heat transfer distribution is found to drop off more steeply towards the
middle of the array than towards the outside. The same phenomenon was found by
Huber and Viskanta [91]. The reason for this is that the jet experiences less restriction in
the outward direction, and is thus decelerated more slowly.
Location of the
outlet pipe
-2
Distance between bus-bars [ mm ]
Figure 5.5: Heat transfer distribution for the countersunk
orifices at Re =5 380.
73
-1
4
h [ W m K x 10 ]
Distance along bus-bar [ mm ]
Jet
interference
region
5 RESULTS AND DISCUSSION
Cross-section
along the
dotted line
90000
90
000
h (W/m
[ W m2-2K)
K-1 ]
h
Jet
interference
effects
Centreline
between
nozzles
Re = 6 250
Re = 4 410
80000
80
000
Re = 2 740
70000
70
000
Re = 982
60000
60
000
50000
50
000
40000
40
000
30000
30
000
20000
20
000
10000
10
000
0
-6
-4
-2
0
2
4
6
8
10
12
14
r/d
r/d
Figure 5.6: Cross-section through impingement zones under the
long/straight array, plotted against r/d measured from the centre of
the upper jet, for various Reynolds numbers. Jet interaction can be
seen from r/d = 2.4 or 1.2 diameters away from centreline between
the nozzles.
No systematic difference in local heat transfer distribution could be found between
individual nozzles of different placements within the array. The shift in placement of the
central jet in the nine/dense array (Figure 5.7) is caused by a small inaccuracy in the
drilling of the holes. There was no similar asymmetry in the nine/sparse array (Figure
5.8). Because the drainage exit was situated in the corner of the return fluid chamber
(indicated in Figure 5.5), it was expected that crossflow could deteriorate the heat
transfer of the jet situated closest to the exit. This was not observed, something which
suggests a symmetric flow pattern in the lower region of the return chamber. The central
jet of the nine nozzle array had a similar or only slightly higher stagnation point heat
transfer coefficient compared with the surrounding jets, something which further
indicates that there are negligible crossflow effects.
74
5 RESULTS AND DISCUSSION
h [ W m-2 K-1 x 104 ]
Distance along bus-bar [ mm ]
25
20
15
10
5
5
0
10
15
20
25
Distance between bus-bars [ mm ]
Figure 5.7: Local heat transfer distribution for the nine/dense
nozzle array at Re = 4480.
h [ W m-2 K-1 x 104 ]
Distance along bus-bar [ mm ]
25
20
15
10
5
0
5
10
15
20
25
Distance between bus-bars [ mm ]
Figure 5.8: Local heat transfer distribution for the nine/sparse
nozzle array at Re = 4 480. The poor resolution and apparent
difference in the perimeter jets are due to a problem with the
camera focus on the day of testing.
75
5 RESULTS AND DISCUSSION
In Figure 5.5 a region of enhanced heat transfer in the area along the centreline between
the nozzles is indicated. This region was observed for all Reynolds numbers in both the
nine and four nozzle arrays. However, because of the lower resolution achieved for the
smaller jets, the pattern is not seen as clearly in Figure 5.7 and Figure 5.8. The pattern is
caused by increased turbulence where the neighbouring wall jets meet head-on (see
Section 3.2.1). The heat transfer coefficient profiles in Figure 5.6 show that this
interaction region extends about 0.6-1.2 nozzle diameters away from the centreline
between the jets. This value was found to be relatively constant for all of the four-nozzle
arrays, while it extended about 1.5 nozzle diameters for the nine-nozzle arrays. Where the
interaction region starts, the heat transfer distribution stops decreasing and instead
increases slightly towards the centreline. Studies in the literature also predict a possible
deterioration because of jet interference before impingement (Section 3.2.1). No
indication of this was found, which is as expected because s/d is relatively large and Re is
low.
None of the previous studies referred to in Chapter 3 had documented any temporal
instability of the flow patterns of the jet arrays. Nevertheless, in the current
measurements, oscillations were clearly observed for all of the four-nozzle arrays. In the
nine-nozzle arrays some flow instability was observed around the perimeter of the array,
but not to the same extent as with four nozzles. This might be related to the poorer
spatial resolution of the measurements with the smaller nozzles. The oscillations
observed in the four-nozzle arrays were characterised by the interaction region between
the jets not being constant along the centreline, but shifting slightly toward the stagnation
point of one jet and then the other in an irregular manner. The positions of maximum
heat transfer at the stagnation points of the jets remained constant. The oscillations were
not regular enough to enable an accurate analysis of amplitude and frequency to be
performed with the current experimental setup. The amplitude of the movement was
found to be about 1.5 mm. The frequency of the oscillations could not be established.
No significant difference in oscillation pattern could be found between the different
nozzle configurations. One possible reason for the oscillations could be the remaining
structure of the jet which is formed at the inlet of the plenum chamber, as shown in
Figure 5.9. Other studies of jet impingement have often had diffusing structures such as
honeycombs or meshes located in the upper region of the plenum chamber to ensure a
very low fluid velocity at the nozzle inlet. However, because the current study is not so
much concerned with the basic mechanisms of jet impingement as to provide
understanding of the performance of real impingement devices, no such mechanisms
were included since they were thought to add an unnecessary pressure drop. The orifice
plate is located a distance of 4.9 inlet diameters beneath the water inlet. At this distance,
the inlet jet is likely to have much of its original structure left. The oscillations probably
arise due to temporal structures in the turbulence of the jet propagating through the
orifice plate.
Another phenomenon which had not been expected prior to the measurements was the
problem of blocking of holes in the smaller orifices. The 0.7 mm diameter nozzles had a
tendency to become blocked, resulting in a highly deteriorated local heat transfer,
something which is shown in Figure 5.10. The cause of the blocking could not be found,
but was thought to be small particles suspended in the water. Although clean water was
used, there was no filter in the circuit and thus there were always some particles present.
This is an important factor in the design of practical jet devices. The presence or absence
of a filter is a determining factor for the minimum safe nozzle diameter. In real systems
it should be kept significantly larger than the 0.7 mm nozzles used here.
76
5 RESULTS AND DISCUSSION
water inlet
ambient
fluid
potential
core
turbulent
interaction
zone
nozzles
Figure 5.9: Flow regions in the plenum chamber.
b)
a)
Figure 5.10: Heat transfer distributions for nine/dense array with the top-right hole
a) partially and b) fully blocked. The colour scales are not the same for the two
images.
77
5 RESULTS AND DISCUSSION
5.3 PREDICTIVE CORRELATIONS
As explained in Section 3.1.4, it is common to correlate the stagnation point and average
heat transfer coefficients for impinging jets using the basic form
Nu 0 , Nu avg = C Re m Pr n .
(5.3)
This form was chosen to correlate the experimental results. Because the Prandtl number
dependence was not investigated, the dependence n = 0.444 from the study of Li and
Garimella [87] was used. The coefficients C and m for the stagnation point Nusselt
number for the orifices studied are given in Table 5.1 along with the correlation
coefficient R2, which gives a measure of how the correlation fits the data. R2 = 1 for a
perfect fit. Table 5.2 gives C and m for Nuave. In the case of the single nozzles, not
enough measurements were made to justify making correlations.
Table 5.1: Correlations for stagnation
point Nusselt numbers for experimental
data.
Table 5.2: Correlations for average
Nusselt numbers for experimental data.
Orifice
C
m
R2
Orifice
C
m
R2
nine/dense
0.441
0.513
0.983
nine/dense
0.095
0.678
0.983
nine/sparse
0.666
0.456
0.988
nine/sparse
0.222
0.519
0.979
short/straight
1.598
0.429
0.952
short/straight
0.472
0.491
0.963
long/straight
1.539
0.437
0.976
long/straight
0.450
0.497
0.978
sharp-edged
1.370
0.461
0.930
sharp-edged
0.464
0.512
0.958
countersunk
1.065
0.476
0.986
countersunk
0.222
0.580
0.994
The results were also compared with correlations from the literature. Figure 5.11 shows
the experimental stagnation point Nusselt numbers plotted with the correlations from
Garimella and Nenaydykh [80] and Li and Garimella [87] given in Table 3.1. The slope of
the Garimella and Nenaydykh [80] correlation agrees well with the experimental data on
a log-log plot, which indicates that the Reynolds number dependence is correct. The
correlation is accurate to within 2% for the four-nozzle arrays but overestimates the
results for the nine-nozzle arrays and the single nozzles by about 7%. Because the nozzle
diameter in the nine-nozzle arrays falls outside the range of validity for the correlation, a
discrepancy for these arrays is expected. The developing length of the single nozzles is
also outside the range of validity. The experimental results therefore confirm the
accuracy of the Garimella and Nenaydykh [80] correlation within its range of validity.
The correlation from Li and Garimella [87] fits very well to the nine-nozzle results but
underpredicts the results for the other arrays. This is somewhat surprising because the
nine-nozzle arrays have a smaller diameter and a higher value of z/d than what this
correlation is valid for. The other nozzles all fall within the range of validity but are
under predicted by about 3%. This correlation is built on a range of measurements for
different liquids and is made to encompass them all with a relatively large average error
of 9%. The four-nozzle results therefore fall within the range of uncertainty of the
correlation. The almost perfect fit for the nine nozzle arrays is most likely coincidental.
78
5 RESULTS AND DISCUSSION
_________Nu0________
0.4
0.024
(l/d)-0.09
0.492Pr (z/d)
1000
a)
100
nine/dense
nine/sparse
short/straight
long/straight
10
sharp-edged
1000
Re
10000
countersunk
single-S1
1000
single-S2
__________Nu0___________
0.444
(l/d)-0.058(De/d)-0.272
1.427Pr
b)
single-S3
correlation
100
10
1000
Re
10000
Figure 5.11: Comparison of experimental results for the stagnation point Nusselt
number with correlations from a) Garimella and Nenaydykh [80] and b) Li and
Garimella [87].
In Figure 5.12, the average Nusselt numbers for the four and nine nozzle arrays are
compared with the correlations from Huber and Viskanta [82], Martin [97] and Garimella
and Schroeder [94] given in Table 3.2. All of the correlations agree reasonably well with
the experimental data. The Huber and Viskanta [82] correlation has the poorest fit to the
experimental results, underestimating the values by around 6% for the nine and 16% for
the four nozzle arrays. This can be explained by the correlation being valid for only one
developing length (l/d = 1.5) and one nozzle diameter (d = 6.35 mm). The latter is
substantially larger than the nozzles used in the current experiments, and the nozzle
diameter is known to have some influence on the Nusselt number as discussed in
Section 3.1.
79
5 RESULTS AND DISCUSSION
__________Nuave_______
0.33
-0.123
(s/d)-0.725
0.285Pr (z/d)
1000
a)
nine/dense
nine/sparse
short/straight
long/straight
100
sharp-edged
1000
Re
1000
countersunk
10000
correlation
___Nuave__
0.42
0.5KGPr
b)
100
1000
Re
10000
1000
______Nuave_____
0.4
-0.105
0.127Pr (z/d)
c)
100
1000
10000
Re
Figure 5.12: Comparison of average Nusselt versus Reynolds number for
nine and four nozzle jet arrays with the correlations from a) Huber and
Viskanta [82], b) Martin [97]and c) Garimella and Schroeder [94].
The Martin [97] correlation agrees with the experimental data within about 3% and has
thus the best fit of the average heat transfer correlations. However, it tends to
overestimate the values for the nine-nozzle arrays and underestimate those of the fournozzle arrays. The overestimation of the nine-nozzle arrays is probably due to the fact
that the correlation is based on a square area with side lengths s around the central jet,
while in the present study the area around the array is also included, with a larger area of
low heat transfer taken into account. The fact that the orifice plates of the four-nozzle
arrays all had short developing length probably contributes to the underestimation of
these values, as the Martin correlation is made on the basis of several experimental
studies with a range of nozzle configurations but has no correction for developing
length. The correlation by Garimella and Schroeder [94] overestimates the values for
nine-nozzle arrays and underestimates them for four-nozzle arrays just like the Martin
80
5 RESULTS AND DISCUSSION
correlation, but with a higher error of about 5.5%. The overprediction for the ninenozzle arrays is expected, both because of the geometry of the heated area, as explained
above, and because of the z/d for these arrays being outside the range of validity. The
correlation is only claimed to be valid to within 9%, which makes the agreement with the
current results satisfactory.
5.4 NOZZLE GEOMETRY EFFECTS
Figure 5.13 shows how the stagnation point Nusselt number (Nu0) varies with Reynolds
number for the different nozzle configurations. Examining Nu versus Re is equivalent to
comparing the heat transfer under different jets at the same jet velocity. When comparing
the nine-nozzle arrays to those with four nozzles, the former are found to yield a
significantly lower Nu0 than the latter. This could be related to nozzle size, as previous
studies have found larger nozzles to yield slightly higher Nusselt numbers [86] because of
increased turbulence levels. However, in the current measurements this effect is
overshadowed by the higher nozzle-to-plate spacing. For the smaller nozzles, this was
well above the length of the potential core (z/d = 7.14), while the larger nozzles can
conservatively be assumed to impinge within the potential core (z/d = 3.57). This would
explain the lower stagnation point heat transfer under the nine-nozzle arrays. Out of the
four-nozzle arrays, the sharp-edged nozzle was found to yield the highest heat transfer
coefficient. This is the result expected from previous findings in the literature, which
attribute this effect to the higher turbulence levels introduced by the sharp edge of the
entrance to the orifice. Differences in the heat transfer behaviour of the other
configurations can not be distinguished within the range of uncertainty.
nine/dense
nine/sparse
short/straight
180
long/straight
160
sharp-edged
140
countersunk
Nu 0
120
100
80
60
40
20
0
0
2000
4000
6000
8000
Re
Figure 5.13: Stagnation point Nusselt number versus Reynolds
number for different nozzle configurations. Error bars are shown
for the countersunk nozzles only to show the typical uncertainties.
81
5 RESULTS AND DISCUSSION
In the design of jet impingement cooling systems, it can be more useful to compare the
value of the stagnation point heat transfer coefficient h0 for a given flow rate per nozzle
QN-1. This is depicted in Figure 5.14, which shows that for a given flow rate, the smaller
nozzles yield a higher heat transfer coefficient, despite their larger nozzle-to-plate
spacing. This illustrates how the stagnation point heat transfer coefficient is much more
dependent on jet velocity than parameters like z/d. For a given flow rate, if one wants to
achieve the highest possible heat transfer coefficient over a small area, the smaller
nozzles would yield the better result because of their high velocity. However, the local
heat transfer coefficient distribution drops off monotonically away from the stagnation
point and reaches a value of half maximum at about r/d ~ 3, which means there is a
smaller area of high heat transfer under the small nozzle jets.
80000
70000
h0 [ W m-2 K-1 ]
60000
50000
nine/dense
40000
nine/sparse
short/straight
30000
long/straight
20000
sharp-edged
10000
countersunk
0
0
2
4
6
- -1
QN
8
10
-1
[ mL s ]
Figure 5.14: Stagnation point heat transfer coefficients versus flow rate per
nozzle for different nozzle configurations.
havg [ W m-2 K-1 ]
nine/dense
40000
nine/sparse
35000
short/straight
long/straight
30000
sharp-edged
25000
countersunk
20000
15000
10000
5000
0
0
10
20
30
40
-1
Q [ mL s ]
Figure 5.15: Average heat transfer coefficient versus total flow rate for different
nozzles.
82
5 RESULTS AND DISCUSSION
Figure 5.15 shows how the average heat transfer coefficients across the entire heated
surface for the different nozzle configurations vary with total flow rate through the array.
In this figure, the nine-hole arrays are found to yield results comparable with the fournozzle arrays. The shift from high performance in terms of h0 (Figure 5.14) to average
performance in terms of havg arises mainly because of the the increase in number of
nozzles and thereby flow rate serves to eliminate the advantage of the smaller nozzles for
a given nozzle flow rate. While the smaller nozzles yield a higher stagnation point heat
transfer coefficient, the local heat transfer distribution drops off more quickly in the
radial direction. To achieve the same uniformity of heat transfer, it is necessary to use the
same nozzle pitch ratio s/d and therefore more nozzles for a given area. It can also be
seen that the nine/dense array yield a higher heat transfer coefficient than the
nine/sparse array, because there is a large perimeter area in the nine/dense array that is
only cooled by the significantly weakened wall jet. The nine/sparse array performs
similarly to the sharp-edged nozzles while the nine/dense array has an average heat
transfer coefficient within the range of the remaining four-nozzle arrays.
5.5 PRESSURE DROP THROUGH AN ORIFICE
When designing a jet impingement device, it is not only the flow rate which is important,
but also the pressure drop through the device. The preferred cooling system will in many
cases be the one that delivers the highest rate of cooling at a given pumping power. The
total pumping power is proportional to the product of flow rate and pressure drop.
The pressure drop through the various models can be easily predicted from theory.
Bernoulli’s equation gives the relationship between fluid velocity, gravitational head and
pressure for an incompressible fluid in steady flow as [103]
gz1 +
p1
ρ
+
v12
p
v2
= gz 2 + 2 + 2 ,
2
ρ 2
(5.4)
where subscripts 1 and 2 refer to conditions immediately before and after the orifice,
respectively. This can be used to find the pressure difference across the orifice. Assuming
the height difference is negligible across the orifice, the z-term can be left out. This is
justifiable because, for the minimum flow rate of these measurements, g∆z/∆v 2 ≈ 3 x
10- 3. In this experiment, v1 is also sufficiently small compared with v2 to be ignored. The
resulting expression for ∆p becomes
∆p =
ρ
2
v22 .
(5.5)
Other pressure drops through the jet device include the contraction from supply pipe to
inlet pipe, expansion from inlet pipe to jet chamber, expansion after orifice plate,
deflection at impingement plate and in outlet chamber, contraction to outlet pipe and
expansion from outlet pipe to drainage pipe. These are all at least two orders of
magnitude smaller than the pressure drop through the orifice and can thus be ignored. It
is also assumed that all of the kinetic energy in the jet is dissipated and lost by frictional
effects after the jet hits the wall and mixes, so that the pressure after the nozzle does not
increase back to the original free stream value.
The velocity after the orifice must be found using the area of the vena contracta instead of
the nozzle area. The vena contracta refers to the phenomenon of a jet continuing to
83
5 RESULTS AND DISCUSSION
contract for some distance after exiting the nozzle. Thus, the resulting cross-sectional jet
area is smaller than the nozzle area. The vena contracta arises because of a transverse
pressure gradient between the edge and centre of the nozzle. The pressure at the centre
is higher than the ambient pressure at the edge, which causes the jet to continue to
accelerate after leaving the nozzle until ambient pressure is achieved throughout the
cross-section [104]. The area of the vena contracta is determined by the nozzle geometry,
which is characterised by the contraction coefficient Cc, given as
Ac d c2
Cc =
=
.
An d n2
(5.6)
The value of Cc is ≈ 0.6 for a perfectly sharp lip, and rises to Cc ≈ 1 for a bell-mouthed
opening. From theoretical limitations, the absolute limits for the contraction coefficient
are 0.5 ≤ Cc ≤ 1 [103].
Taking into account the losses through the orifice, the theoretical velocity is reduced by a
factor Cv called the velocity coefficient, defined as the ratio of actual to theoretical velocity at
the orifice exit. Typical values for Cv lie between 0.95 and 0.99 [103]. Because Cv and Cc
are difficult to measure independently, they are often combined to a discharge coefficient Cd
= CvCc.
The resulting expression for pressure drop through the device is
∆p =
Q2
1 2 1
8
ρv2 = ρ 2 2 = ρQ 2 2 2 2 4 .
2
2 Cd A2
N π Cd d
(5.7)
The discharge coefficient is known to vary slowly with Reynolds number, and can be
assumed constant for the range of Re in this study. A least-square fitting to the
experimental data gave the discharge coefficients given in Table 5.3. The pressure drop
distributions with the correlations are shown in Figure 5.16. The coefficients of
determination for all correlations were R2 ≥ 0.969. As the expected values for Cd lie in
the range 0.6 x 0.95 – 1.0 x 0.99 = 0.57 – 0.99, the experimental values are quite low. In
fact, the value obtained for the sharp-edged nozzle lies outside the expected range,
although it is not below the theoretical limit of 0.5 x 0.95 = 0.475. However, it is known
that very small diameter orifices behave differently from larger orifices (see Section
3.1.4). Most data for contraction coefficients exist for measuring orifices that are 50 mm
in diameter or larger [105]. A value of Cd = 0.52 for the sharp-edged orifice is therefore
not unreasonable.
Comparing the different four-nozzle arrays, Cd is found to be highest for the countersunk
and lowest for the sharp-edged nozzle. The straight nozzles are both intermediate cases.
The difference in discharge coefficient for the straight, contoured and sharp-edged
nozzles can be explained by the degree of sharpness at the flow inlet. In addition, the
measured Cd is lower for the short/straight nozzle than for the long/straight nozzle. This
difference is not easily explained in terms of sharp or gradual variations. Garimella and
Nenaydykh [80] found a significant change in heat transfer coefficient for l/d <1 and l/d
> 1. They explained this by the observation that at a small developing length, a
separation bubble is formed at the inlet. This acts as a contraction, and results in the
effective nozzle area being only 60% of the actual cross-section. At higher l/d, the
separated flow at the nozzle entrance reattaches within the nozzle, and the reduction of
the effective nozzle area is eliminated. This change in effective nozzle area would also
84
5 RESULTS AND DISCUSSION
explain the smaller pressure drop through the longer nozzles. In this study, l/d = 0.7 for
the short/straight and 1.4 for the long/straight nozzle.
Table 5.3: Coefficients of
discharge for different nozzle
configurations.
Nozzle configuration
Cd
short/straight
0.582
long/straight
0.613
sharp-edged
0.520
countersunk
0.653
45
40
35
short/straight
∆p [pkPa ]
30
Cd = 0.582
25
long/straight
20
Cd = 0.613
15
sharp-edged
Cd = 0.520
10
countersunk
5
Cd = 0.653
0
0
10
20
30
40
50
Q [ mL s-1 ]
Figure 5.16: Pressure drop correlations for different nozzle configurations.
5.6 TOTAL PUMPING POWER
As discussed above, the optimal nozzle configuration for a given system will be
determined by two factors: the required pressure drop and the flow rate required to
achieve a given average heat transfer coefficient. To improve the performance of an
orifice plate with simple straight nozzles, one could choose to countersink the holes to
reduce the pressure drop, thereby achieving a higher heat transfer coefficient at the same
pumping power. Alternatively, one could make the holes sharp-edged to achieve a higher
heat transfer at a comparable flow rate. It is not immediately obvious which
configuration would prove optimal.
Figure 5.17 shows how the flow rate and pressure drop varies with average heat transfer
coefficient for the various four-nozzle arrays. It shows that, to achieve a given heat
85
5 RESULTS AND DISCUSSION
Q [ mL s-1 ]
transfer coefficient, the short/straight nozzles involve the highest pressure drop. The
long/straight nozzles perform a little better, while the results for the countersunk and
sharp-edged nozzles are virtually indistinguishable. This relates to the fact that while the
sharp-edged nozzles yield a higher pressure drop at a given Reynolds number, they also
are better in terms of higher heat transfer coefficient at lower Reynolds numbers. At the
same time, the sharp-edged orifices require a lower flow rate for a given heat transfer
coefficient than the other orifices. This leads to the conclusion that for a given pumping
power, the nozzle configurations yield increasing average heat transfer coefficients in the
order: short/straight, long/straight, countersunk and finally sharp-edged.
40
short/straight
35
long/straight
30
sharp-edged
25
countersunk
20
15
10
5
0
0
10000
0
10000
20000
30000
40000
40
∆p [ kPa ]
35
30
25
20
15
10
5
0
20000
-2
30000
40000
-1
h[Wm K ]
Figure 5.17: Flow rate and pressure versus average heat transfer
coefficient for different nozzle configurations.
A good indication of the pumping power required for the various orifice plates is
illustrated by the maximum average heat transfer coefficients shown for each
configuration (Figure 5.15). The values for the highest achieved havg and Q are also given
in Table 5.4 for easier comparison. The maximum flow rate for each device is achieved
when the valve is fully open, so that the flow circuit outside the jet device itself is
identical. These values therefore correspond to the same pumping power. Comparing the
short and long straight nozzles, the decrease in pressure drop and the corresponding
increase in flow rate for the longer nozzles result in a higher maximum heat transfer
coefficient for the longer nozzle, which would imply that l/d > 1 is the preferable
configuration for straight nozzles. The countersunk and sharp-edged nozzles yield
maximum heat transfer coefficients which can not be distinguished within the range of
uncertainty. However, as the sharp-edged nozzle yields this result at a considerably lower
flow rate, this could be the preferable option in many systems.
86
5 RESULTS AND DISCUSSION
Table 5.4: Maximum flow rates and average heat
transfer coefficients for different nozzle
configurations.
Device
Maximum Q
Maximum havg
(mL s-1)
(104 W m-2 K-1)
nine-nozzle
23.2 ± 1.2
2.9 ± 0.2
short/straight
29.9 ± 1.5
3.1 ± 0.3
long/straight
31.7 ± 1.6
3.4 ± 0.3
sharp-edged
27.7 ± 1.4
3.5 ± 0.3
countersunk
33.3 ± 1.7
3.5 ± 0.3
5.7 CENTRAL DRAINAGE DEVICE
Because of the lowered heat transfer in the perimeter region of the arrays discussed in
Section 5.1, a central drainage device (see Section 3.6 and Figure 3.6b) was constructed in
order to try to improve the perimeter heat transfer by placing the jets closer to the edges.
In this device the nozzles had diameters of 2.5 mm, to allow for a higher flow rate, in a 1
mm thick orifice plate. A total of 12 nozzles were distributed on the array as shown in
Figure 5.18. The minimum nozzle pitch was s/d = 2.24 and the nozzle-to-plate distance
was z/d = 4.
location of
water inlet
water outlet
Figure 5.18: Central drainage orifice plate.
This device was found to function poorly for several reasons. Firstly, the nozzle pitch
chosen was, as expected for reasons described in the previous section, small enough to
cause a significant level of interaction between the jets prior to impingement. In addition,
the inlet jet located in one corner of the array gave a very asymmetric flow field under
the array. The central jets were found to perform even more poorly than the perimeter
ones. This is most likely caused by crossflow and the high velocity of drainage water at
the small outlet pipe.
During the first measurements with this device, there were so many disturbances in the
flow that none of the individual jet stagnation points could be recognised in the
temperature distributions. Typically there would be a cool area close to the water inlet
and a highly oscillating temperature field decreasing towards the far corner. Sometimes
87
5 RESULTS AND DISCUSSION
cooler areas would appear and disappear at other positions on the heated foil. It was
recognised that this highly asymmetric temperature distribution was due to the inlet jet,
which in this configuration is located towards one corner of the array. To diminish the
effect of this jet, several layers of wire mesh were inserted in the upper region of the
plenum chamber. This caused the flow to become more uniform, and the stagnation
points of the perimeter jets could be recognised. However, the flow was still highly
unstable. Some pictures of the TLC taken at successive power settings are shown in
Figure 5.19. This shows how the placements of the different temperature regions vary
with time. It is also very difficult to see any cooling effect of the central nozzles. Due to
the highly oscillating flow, the images could not successfully be used to produce a heat
transfer distribution map. An approximate distribution is shown in Figure 5.20. The very
low heat transfer shown in the perimeter region is probably due to poor lighting, as seen
in Figure 5.19, but a closer inspection of the thermal images indicated that a low heat
transfer region is present along the edges despite this design having the jets placed closer
to the edges. Thus it seems that central drainage might not be useful for diminishing the
eddy formation along the edges.
1
4
2
3
5
6
Figure 5.19: Recorded temperature distributions under the central drainage array with diffusing
mesh inserted, shown at increasing power levels. The locations of the cooler areas vary
significantly with time due to the highly unstable flow.
As mentioned above, it was difficult to see any cooling effects of the four central
nozzles. It was thought that this might relate to the jets being strongly affected by the
pressure field around the outlet, in effect getting “sucked” into the exit before impinging
onto the heated surface. To try to diminish this effect the outlet pipe was extended down
from the orifice plate as shown in Figure 5.21 so that the exit was located 2 mm above
the impingement plate. This was not found to yield any significant change in the
88
5 RESULTS AND DISCUSSION
temperature distribution. It is therefore likely that the low heat transfer under the central
jet is caused by a combination of crossflow from the perimeter jets and, more
importantly, vortex formation around the outlet.
havg [ W m-2 K-1 x 104]
Figure 5.20: Approximate heat transfer coefficient distribution
under the central drainage jet array. Because of the unstable flow
conditions, it was not possible to record an accurate distribution.
The apparently low heat transfer along the edges is due to lighting
problems.
a)
b)
Figure 5.21: Central drainage cooling device a) without and b) with
extended outlet pipe.
89
5 RESULTS AND DISCUSSION
5.8 CONCLUSIONS
The shape of the local heat transfer distribution was found to be relatively similar for
single jets and jets in arrays. It can be approximated by a linear function reaching a value
of half maximum at r/d = 3.5. A significant drop in heat transfer coefficient was
identified for the perimeter region up to 3 mm away from the edges of the impingement
area, which is attributed to eddy formation along the sharp corners of the return flow
cavity. The local heat transfer beneath the jet arrays was characterised by asymmetry away
from the centre of the array, due to the difference in flow restriction, and by interference
creating a region of increased heat transfer coefficient along the centreline between jets.
Temporal oscillations were identified in the interaction regions of the four-nozzle arrays.
The stagnation point and average heat transfer coefficient were correlated using a
standard form, with good agreement. The experimental data were also shown to agree
well with several correlations from the literature. The pressure drop through the nozzles
could be correlated using the coefficient of discharge for each nozzle. When comparing
the total pumping power required for a certain average heat transfer coefficient, the
countersunk and the sharp-edged nozzles were found to outperform the straight nozzles.
The central drainage device was also tested but did not eliminate the problem of low
heat transfer along the edges. On the contrary, the average heat transfer achieved with
this device was low compared with the side drainage device. This was due both to
nonuniform flow patterns created because the inlet jet was placed off-centre, and to
vortex formation around the narrow outlet pipe.
The results obtained for the impinging jet device are highly promising when comparing
to previously reported results for microchannel devices. The highest average heat transfer
coefficient obtained in the experiments (h = 3.5 x 104 W m-2 K-1 which is equivalent to R
= 2.9 x 10-5 K m2 W-1) is higher than most of the results reported for regular
microchannels and only slightly poorer than the typical values obtained with ‘improved’
microchannels (see Figure 2.16). At the same, the pressure drop through the device is
about an order of magnitude lower than what is typical for microchannel devices (Figure
2.19). Considering that there is much room for improvement of the proposed jet device
design, there is a strong possibility that impinging jets may prove superior to
microchannels in terms of heat transfer and pumping power. Possibilities for optimising
the jet device design are explored in Chapter 6.
90
6
Chapter
OPTIMISED DESIGN OF
COOLING DEVICES
The aim of studying the characteristics of jet impingement devices is to gather enough
knowledge to be able to design an optimised cooling device. This thesis seeks to find a
device for cooling PV at a low pumping power requirement which ensures the highest
possible net electrical output from the PV array. In this chapter, correlations for average
heat transfer coefficient and pressure drop are used to build a model which predicts the
pumping power requirements for a jet impingement device at a given havg. This model can
be used to optimise the size and number of nozzles for a give size of cooling unit.
Subsequently, it can be used to find the flow rate settings which will yield the highest PV
output at a given illumination value.
6.1 CORRELATION FOR PUMPING POWER
6.1.1 Pressure drop
The pumping power W required for any forced convection device is given as the product
of flow rate and pressure drop
W = ∆pQ .
(6.1)
As shown in Section 5.5, the pressure drop through an orifice device is correlated by
∆p = ρ Q 2
8
.
N π Cd2 d 4
2
2
(6.2)
Equation 6.2 can be substituted directly into Equation 6.1.
In the subsequent sections it will be assumed that Cd is independent of nozzle diameter.
This is consistent with the theory from textbooks such as [103], however some studies
suggest that small diameter nozzles show a slightly different behaviour (see Section 5.5).
6.1.2 Two correlations for heat transfer coefficient
The next objective is to eliminate the flow rate Q from the equation. This can be done by
including the correlation for average heat transfer coefficient havg in terms of Q, solving
for Q, and substituting this into Equation 6.1. Several correlations exist that can be used
for the heat transfer part of the model. It was decided to use two different models with
different s/d dependence. The first is the Martin [97] correlation presented in Section 3.2.
The second model, which will be referred to as the Huber model, has a better fit to the
experimental results from the current study. It incorporates the constant C and Reynolds
91
6 OPTIMISED DESIGN OF COOLING DEVICES
number dependence m from the experimental data (Section 5.3) with the Prandtl-number
dependence from Li and Garimella [87] and the s/d dependence from Huber and
Viskanta [82]. As seen in Figure 6.1, the two chosen models are qualitatively different
with respect to their s/d dependence. The Martin model has a negative second derivative,
while the Huber model has the opposite shape. This will be shown to result in quite
different behaviours for the pumping power correlations made using these models.
80
70
60
Nu
Nu
50
40
30
M artin
20
Huber
10
0
4
5
6
s/d
s /d
7
8
Figure 6.1: Predicted Nusselt number as a function of s/d
using the correlations from Martin [97] and Huber and
Viskanta [82] for an arbitrary jet configuration.
6.1.2.1 The Martin model
The Martin [97] model is described in Section 3.2.4, but is repeated below:
Nu avg = 0.5 KG Re 2 / 3 Pr 0.42 ,
(6.3)
where
⎧ ⎛ (z / d ) f ⎞ 6 ⎫
⎪
⎟ ⎪⎬
K = ⎨1 + ⎜
⎜
⎟
⎪⎩ ⎝ 0.6 ⎠ ⎪⎭
G=2 f
−0.05
,
1 − 2.2 f
1 + 0.2(z / d − 6) f
(6.4)
(6.5)
an
f =
π ⎛d ⎞
2
⎜ ⎟ .
4⎝s⎠
(6.6)
The correlation is rewritten in terms of h and Q instead of Nu and Re:
havg =
k
k
Nu = 0.5KG Re 2 / 3 Pr 0.42 ,
d
d
and
92
(6.7)
6 OPTIMISED DESIGN OF COOLING DEVICES
Re =
vd
ν
=
4Q
,
Nπdν
(6.8)
so that
havg
k
⎛ 4Q ⎞
= 0.5KG ⎜
⎟
d
⎝ Nπdν ⎠
2/3
Pr 0.42 .
(6.9)
Solving for flow rate, Q, yields
⎞
Nπν 5 / 2 ⎛ havg
Q=
d ⎜⎜
Pr − 0.42 ⎟⎟
4
⎝ 0.5KGk
⎠
3/ 2
.
(6.10)
Substituting 6.2 and 6.10 into 6.1 gives us a correlation for pumping power W:
W = ∆pQ
= ρQ 2
=ρ
8
Q
N π Cd2 d 4
2
2
8
Q3
N π Cd2 d 4
2
2
8
=ρ 2 2 2 4
N π Cd d
3/ 2
⎡ Nπν 5 / 2 ⎛ havg
⎤
− 0.42 ⎞
⎟⎟ ⎥
Pr
d ⎜⎜
⎢
⎢⎣ 4
⎠ ⎥⎦
⎝ 0.5 KGk
3
⎞
8
⎛ Nπν ⎞ 15 / 2 ⎛ havg
Pr − 0.42 ⎟⎟
=ρ 2 2 2 4⎜
⎟ d ⎜⎜
N π Cd d ⎝ 4 ⎠
⎠
⎝ 0.5 KGk
⎞
Nπν 3d 7 / 2 ⎛ havg
⎜⎜
Pr − 0.42 ⎟⎟
=ρ
2
8Cd
⎠
⎝ 0.5 KGk
3
(6.11)
9/2
9/ 2
.
6.1.2.2 The Huber model
The second model, which incorporates the experimental correlations from Chapter 5
with the Huber s/d dependence, is given by
Nu = C Re m Pr 0.444 (s / d )
−0.725
,
(6.12)
where C and m are correlation coefficients given in Section 5.2. In terms of havg and Q
this becomes
m
havg =
k ⎛ 4 ⎞ m 0.444
− 0.725
C⎜
.
⎟ Q Pr (s / d )
d ⎝ Nπdν ⎠
(6.13)
Solving for Q yields
1/ m
⎛h d ⎞
Q = ⎜⎜ avg ⎟⎟
⎝ Ck ⎠
⎛ Nπdν ⎞ − 0.444 / m
(s / d )0.725 / m .
⎜
⎟ Pr
⎝ 4 ⎠
The resulting pumping power correlation becomes
93
(6.14)
6 OPTIMISED DESIGN OF COOLING DEVICES
8
W =ρ 2 2 2 4
N π Cd d
⎡⎛ havg d ⎞1 / m ⎛ Nπdν
⎟⎟ ⎜
⎢⎜⎜
⎢⎣⎝ Ck ⎠ ⎝ 4
3
⎤
⎞ − 0.444 / m
0.725 / m
(
)
Pr
s
/
d
⎥.
⎟
⎠
⎥⎦
(6.15)
For simplicity, in the following sections only square arrays of jets are considered so that
the number of jets is restricted to N = n2 where n is an integer, and the heated surface is
supposed to be square with sides Lheat. The jet pitch, s, is then given as a function of N
and Lheat by
s=
Lheat
.
N
(6.16)
6.1.3 Comparison with experimental data
1.40
1.20
a)
W [W]
1.00
0.80
0.60
0.40
0.20
0.00
10000
15000
20000
25000
-2
30000
35000
30000
35000
-1
havg [ W m K ]
1.40
1.20
nine/dense
short/straight
long/straight
sharp-edged
countersunk
nine/dense, model
40000
short/straight, model
long/straight, model
sharp-edged, model
countersunk, model
b)
W [W]
1.00
0.80
0.60
0.40
0.20
0.00
10000
15000
20000
25000
40000
havg [ W m-2 K-1 ]
Figure 6.2: Experimental results for pumping power from the different configurations
plotted together with predictions from a) the Martin model and b) the Huber model. The
Huber model shows a better fit to the experiments, which is expected because it is built on
these data. The Martin model overpredicts the pumping power required for the four-nozzle
arrays and underpredicts that for the nine-nozzle arrays.
94
6 OPTIMISED DESIGN OF COOLING DEVICES
Figure 6.2 shows the pumping power W = ∆pQ from the experiments together with the
predictions from the Martin and Huber models. As expected, the Martin model does not
quite fit the experimental values. This is because the Martin model underestimates the
heat transfer coefficient for the four-nozzle arrays and overestimates it for the ninenozzle arrays, as described in Section 5.3. The Huber model on the other hand fits the
data closely because it is built on these results. The slopes of the two correlations are
quite different, and this becomes apparent if they are compared for a similar device over
a range of heat transfer coefficients, as shown in Figure 6.3. Outside the range of the
experimental data, the two lines cross over and the Huber model starts to predict higher
W levels than the Martin model.
2
10
1
10
0
10
10-1
-2
W [W]
10
Martin
-3
Huber
10
10-4
10-5
-6
10
-7
10
0
10000
20000
30000
40000
50000
60000
70000
-2 -1
havg [ W m K ]
Figure 6.3: Variation of pumping power for a range of average heat transfer coefficients
using the Martin and Huber models.
These observations show how important it is to have accurate values for the
characteristics of the orifice types under consideration in order to make reliable
predictions. Ideally, the discharge coefficient Cd as well as the Reynolds number
dependence for the possible configurations should be determined experimentally.
However there is available information regarding this in literature for standard type
orifices which may be used.
6.1.4 Model predictions
The major difference between the predictions from the Martin model and the Huber
model is shown in Figure 6.4. While the former predicts a definite optimal nozzle
diameter, dopt, for a set of conditions, the latter recommends always using the smallest
possible nozzles. This discrepancy arises from the difference in s/d dependency for the
Martin and Huber correlations shown in Figure 6.1. It is the K and G correction factors
of the Martin correlations that lead to an optimum pitch value (s/d)opt, which since s/d is
a function of Lheat, N and d, gets translated into an optimum nozzle diameter. K and G
are functions for s/d and z/d only, and will therefore predict an (s/d)opt for each value of
z/d. Figure 6.5 shows how the product KG varies with s/d within the z/d range of
validity. In all cases, (s/d)opt < 6, and for the lower values of z/d there is no optimum to
be found. However, the values of dopt and the corresponding (s/d)opt predicted from the
95
6 OPTIMISED DESIGN OF COOLING DEVICES
pumping power correlation did not coincide with the optimal s/d shown in Figure 6.5.
This indicates that the optimum nozzle diameters predicted are determined by an
interaction between the pressure drop and heat transfer correlations.
10
b)
10
1
1
W]
WW[/ W
W /[ W
W
W]
a)
0.1
0.01
0.1
0.01
0.001
0.001
0.0001
0
0.5
1
1.5
2
2.5
0
0.5
mm ]
dd/[mm
KG
KG
havg = 10 000
havg = 20 000
havg = 30 000
havg = 40 000
1
1.5
2
dd[ /mm
mm ]
Figure 6.4: Pumping power from varying
nozzle diameter at different h levels (N =
4) using a) the Martin model and b) the
Huber model.
0.28
0.26
0.24
0.22
0.2
0.18
0.16
z/d = 2
z/d = 3
z/d = 4
z/d = 5
z/d = 6
z/d = 7
0.14
0.12
0.1
z/d = 8
z/d = 9
4
6
8
10
s /d
12
14
z/d = 10
z/d = 11
z/d = 12
Figure 6.5: Variation of KG as a function of s/d for a range of z/d
according to the Martin correlation.
The existence of a dopt seems intuitively correct. When the nozzle diameter is decreased,
the increase in jet velocity leads to a higher heat transfer coefficient. This, however,
comes at the cost of a highly increased pressure drop. Moreover, the heat transfer
distribution drops off more rapidly away from the impingement point. At some specific
diameter, the negative effects would be expected to become dominant and to lead to an
increased pumping power for a given havg, as the Martin model predicts.
Both models predict a lower pumping power for a higher number of nozzles,
independent of other variables. This result is contrary to the conclusions from several
studies that optimise against flow rate. Brevet et al. [96] found that a decrease in the
number of nozzles, and the subsequent increase in Reynolds number, would result in a
higher havg. However, the pressure drop, which was not taken into account in this
optimisation, increases drastically when the total orifice cross-section is decreased.
Garimella and Schroeder [94] also found the heat transfer to be highest for a single jet
96
2.5
6 OPTIMISED DESIGN OF COOLING DEVICES
when optimised for flow rate, but noted that the pressure drop, and thus the pumping
power, would be lower for a high number of nozzles.
As we have seen, increasing the number of nozzles and thereby reducing s/d is beneficial
to the average heat transfer coefficient. However, when the jets are too closely spaced,
the negative effects of jet interaction before impingement (see Section 3.2.1) become
increasingly significant. Beyond a certain s/d, the benefit gained by adding nozzles is lost
to increased jet interference. Garimella and Schroeder [94] found the average heat
transfer to level off for s/d < 4. The Huber and Martin models are also only valid down
to s/d = 4 and s/d = 4.43, respectively. A spacing of s/d = 4 seems therefore to be a
reasonable lower limit for design purposes.
The predicted pressure drop variation with nozzle diameter is shown in Figure 6.6 for a
range of N. The Huber model predicts the smaller nozzles to be superior under all
conditions, and shows no difference in trend for the different numbers of nozzles. The
Martin model, on the other hand, predicts an optimum nozzle diameter which shifts
towards smaller nozzles for increasing N. The latter makes sense because with fewer
nozzles, a larger area has to be covered by each jet. Increasing the nozzle diameter makes
the local heat transfer distribution fall off more slowly away from the stagnation point in
terms of absolute distance, so that a larger area is covered by the central high heat
transfer region.
N
N=1
N=4
N
a)
100
10
b)
N=9
N
10
W [W]
W/W
W /[W
W]
N=16
N
1
1
0.1
0.01
0.1
0
2
mm]
dd [/mm
4
6
0
2
mm ]
dd [/ mm
4
6
Figure 6.6: Varying nozzle diameter for different numbers of nozzles (Lheat = 80 mm, havg =
10 000 W m-2 K -1) using a) the Martin model and b) the Huber model.
The optimal nozzle diameter, dopt, is found to be independent of havg, Cd and Pr. However
it depends on N and Lheat as shown in Figure 6.7. This figure also includes the required
pumping power per area for havg = 104 W m-2 K-1 to illustrate the large variation in
pumping power for an increasing number of nozzles. Note that W/A also increases with
the heater size. This reflects back on the benefit of a high number of nozzles per area.
As N is kept constant but the area is increased, W/A increases as well.
The optimal nozzle diameter is also dependent on the nozzle-to-plate spacing z/d as
shown in Figure 6.8. It can be seen that dopt decreases linearly with increasing z/d. The
slope of the graph is dependent on N but independent of Lheat. In the Martin model, the
nozzle-to-plate separation, z/d, has an effect in that it shifts the size of dopt (Figure 6.5).
It also predicts a higher havg at low z/d. In the majority of the measurements made for
97
6 OPTIMISED DESIGN OF COOLING DEVICES
this thesis the parameter z/d was kept constant at z/d = 3.57 because several studies had
observed the maximum havg to occur at 3 < z/d < 4 (Section 3.1.2). These studies
generally found very little change in havg with changing z/d within the length of the
potential core. However, other studies including Martin [97] have found low z/d to be
favourable, especially at low s/d.
10000
-2
W /AW[ /W
Wm ]
mm ]
ddopt
opt /[mm
12
10
8
6
4
2
0
1000
100
10
1
0.1
0
50
100
0
50
N=1
LLheat
/ mm
heat [ mm ]
N=4
Figure 6.7: Optimal nozzle diameter as a function of heater size,
with the corresponding power requirement per area for havg =
104 W m-2 K-1 using the Martin model. The results for dopt are
independent of havg.
N=9
N = 16
100
LLheat
heat [/ mm ]
7
6
opt
doptd [ mm
]
/ mm
5
4
Lheat = 100 mm
Lheat = 80 mm
Lheat = 60 mm
Lheat = 40 mm
Lheat = 20 mm
3
2
1
0
2
3
4
5
z /d
Figure 6.8: dopt as a function of z/d for a range of Lheat.
The value of s/d at dopt was calculated for all of the examples mentioned. It was found to
vary with z/d only, and not to drop below the critical value of s/d = 4.
6.1.5 Experimental validation
Both the Martin and the Huber models predict that for a given pumping power, a higher
havg will be achieved with a greater number of nozzles, provided s/d > 4. It was decided
to run some simple measurements to test if the predicted trends could be verified
experimentally.
An already existing orifice plate (the short/straight) was modified to perform
measurements with one, four and nine nozzles. To get nine nozzles in this plate,
additional holes were drilled between the corner nozzles. The single jet measurements
were made last by blocking the outer nozzles using epoxy glue. Because the model
presented in this chapter assumes the nozzles are placed evenly across the surface, with a
98
6 OPTIMISED DESIGN OF COOLING DEVICES
distance of s between each jet and s/2 between the edge and the nearest jet, the average
heat transfer coefficient was calculated for an area of sides Lheat = 20 mm for the four
and one nozzle arrays, and Lheat = 15 mm for the nine-nozzle array, as shown in
Figure 6.9.
Figure 6.9: Areas from which the average heat transfer coefficients
are calculated for the single, four and nine-nozzle arrays.
First, a few measurements were performed with the original four nozzles to confirm that
the results obtained with the new TLC coating and the water running at a different
temperature were consistent with those from the previous experiments. The
measurements showed excellent agreement with previous results. Figure 6.10 shows the
predicted curves for the various numbers of nozzles. The N = 4 results shown in pink
are calculated from the previously measured heat transfer coefficient distributions, and
the corresponding curve is calculated for this water temperature. The predictions shown
are thus all for different water temperatures and different Lheat and can therefore not be
directly compared against each other.
Due to experimental limitations, only a very limited range of flow rates could be
obtained for the single nozzle. However, the values of havg and W obtained fall nicely
onto the predicted curve as seen in Figure 6.10. This serves as a good verification of the
model. It also gives an indication that for the s/d used in the four nozzle arrays, jet
interaction does not play a significant role. If it did, then the correlation constants C and
m found for the four nozzle array would not have predicted the correct heat transfer
coefficient for the single nozzle.
99
6 OPTIMISED DESIGN OF COOLING DEVICES
1.2
1.0
W [W]
0.8
N=1
0.6
N=4
N=9
0.4
N = 1 results
N = 4 results
0.2
N = 9 results
0.0
0
10000
10
000
20000
20
000
30000
30
000
40000
40
000
50000
50
000
60000
60
000
-2 -1
h[Wm K ]
Figure 6.10: Predicted and measured pumping power versus average heat
transfer coefficient for single, four and nine-nozzle arrays.
Figure 6.10 shows that the average heat transfer coefficients under the nine-nozzle arrays
were much lower than predicted. The reason for this is illustrated in Figure 6.11, which
shows a highly nonuniform local heat transfer distribution under the nine-nozzle array.
The heat transfer coefficient was found to be highest under the central jet, and to
become lower for jets further away from the centre. The worst performance was found
for the corner jets. The bottom middle jet indicated in Figure 6.11 a) yielded a low heat
transfer coefficient due to imperfections in the nozzle. In order to eliminate the effect of
this, only the top half of the distribution was used in the calculation of havg. It is likely
that this pattern of nonuniform heat transfer between the different placement nozzles is
caused by some form of jet interaction. Because s/d is only 3.57 for the nine-nozzle
array, some amount of destructive interference prior to impingement is expected. The jet
fountain effect may also play a role although it should not be significant at such low
Reynolds numbers. In addition, it seems from the pattern in Figure 6.11 that the flow
from the central jet drains diagonally between the middle jets and interferes with the
corner jets, resulting in a further deterioration in the corners. These findings serve to
further emphasize the importance of keeping s/d > 4.
100
6 OPTIMISED DESIGN OF COOLING DEVICES
areas used for
calculating havg
a)
b)
low heat transfer coefficient
due to nozzle imperfections
Figure 6.11: Comparison of local heat transfer distribution for a) nine nozzles and b)
four nozzles at similar Reynolds numbers. The colour scales for the two plots are the
same.
6.2 NET PV OUTPUT – COOLING SYSTEM OPTIMISATION
In Section 2.2 a one-dimensional thermal model for PV cells was presented which could
be used to predict the electrical output from the cell as well as the cell temperature as a
function of illumination level and cooling system thermal resistance. As explained in
Section 2.1.3, the heat transfer coefficient h is just the inverse of the thermal resistance,
R. This model can therefore be used together with the correlation for pumping power as
a function of havg presented in this chapter to find the optimal cooling performance for a
given illumination level.
Figure 6.12 shows typical plots of the net PV output for different conditions. The blue
line shows the PV output as a function of havg, while the green line shows the change in
cell temperature. These two graphs are from the model presented in Section 2.2. As
expected, a low average heat transfer coefficient results in a high cell temperature and a
subsequent low cell output. The pink line shows the net electrical output, which is the
cell output minus the power required for the cooling system as given by the Martin or
Huber model. The pumping power is slightly underestimated because only the
mechanical, not electrical, power requirement is calculated. The graphs in Figure 6.12 are
based on an area of 50 mm x 50 mm, and the parameters N = 4, d = 1.4 mm, Cd = 6.1, C
= 1.96 and m = 0.491. The cell properties are given in Table 2.1.
101
6 OPTIMISED DESIGN OF COOLING DEVICES
125
120
50
115
50
110
40
110
40
105
30
105
30
100
20
100
20
95
10
95
10
90
0
90
20000
40000
PP[ /W
]
W
60
0
60000
20000
140
c)
120
80
60
PP [/ W
W]
100
40
20
0
0
20000
40000
60000
350
330
310
290
270
250
230
210
190
170
150
PPtotal
total
Tcell
T
cell
60000
140
d)
120
100
80
60
40
20
0
0
-2 -1
havg [ W m K ]
PPcell
cell
40000
-2 -1
havg [ W m K ]
T [ °C ]
P /W
350
330
310
290
270
250
230
210
190
170
150
60
0
0
-2 -1
havg [ W m K ]
P [W]
70
b)
115
T [ °C ]
P [W]
120
70
o
C ]
TT /[ °C
a)
TT [/ o°C
C ]
125
20000
40000
60000
-2 -1
havg [ W m K ]
Figure 6.12: Cell and total power output and cell temperature plotted for
cooling system average heat transfer coefficient for various models and
concentration levels: a) 200 suns, Martin model; b) 200 suns, Huber
model; c) 500 suns, Martin model; d) 500 suns, Huber model.
From Figure 6.12 it can be seen that there is a definite optimal, although broad, havg at
which the net electrical output reaches a maximum. The predictions from both the
Martin and the Huber models are shown for concentration levels of for 200 and 500
suns. In this range there is not much difference between the two models. The Huber
model predicts a lower W for a given havg below havg = 42 x 103 W m-2 K-1 and a higher W
above this level because the two models cross over as shown in Figure 6.3. For a
concentration level of 200 suns, the Martin model gives the optimal havg to be 27 x 103 W
m-2 K-1 while the Huber model predicts it to be havg = 28 x 103 W m-2 K-1. For 500 suns
the same models predict the optimal havg to be found at 38 and 37 x 103 W m-2 K-1,
respectively.
6.3 GUIDELINES FOR DEVICE OPTIMISATION
The correlations developed in this and in previous chapters can be employed to find an
optimal device design. The design process is outlined in the following steps, which are
described more closely below:
1) Determine the size of the cooling unit, Lheat,
2) Determine the number of nozzles, N,
102
6 OPTIMISED DESIGN OF COOLING DEVICES
3) Find a suitable nozzle-to-plate to diameter ratio, z/d,
4) Find the optimal nozzle diameter, d,
5) Determine the nozzle configuration and possible surface modifications,
and
6) Find the optimal operating conditions.
The size of the cooling unit is an external parameter which is set by the size of the
surface that needs to be cooled. For large arrays of closely packed, small PV cells, it can
be preferable to build up the array of individual modules, each complete with one
cooling unit. A practical size for a module could be about 100 mm x 100 mm.
The number of nozzles, N, should be made as high as possible while still being low
enough to avoid negative crossflow effects. 3x3 arrays have been shown not to
experience negative crossflow effects. The performance of 4x4 arrays may be slightly
reduced, but considering the large increase in heat transfer that can be achieved by
increasing the number of nozzles, the 4x4 arrays can probably be used with benefit.
However in the configuration with back drainage around all four sides, on which most of
the attention has been focused in the previous chapters, 4x4 should probably be used as
the maximum number of nozzles for a unit cell. If another drainage configuration is
found where exits for spent liquid are distributed throughout the array (Section 3.5), it
would be preferable to use the highest possible number of nozzles, only limited by
s/d > 4.
The nozzle-to-plate distance was kept at z/d = 3.57 in the experiments performed here,
but there is likely to be a benefit from reducing this distance. This will make the unit less
bulky and in some studies [94, 97] it has also been predicted to increase the array
performance. The Martin model is only valid down to z/d = 2, which it predicts to be the
most favourable separation. Depending on manufacturing constraints, z/d = 2 can be
used as the optimal separation distance, with the possibility of being increased up to z/d
= 4 without a significant penalty.
In the next part of the design procedure, the nozzle diameter dopt is found as a function
of Lheat, N and z/d. If s/d is found to be below 4 for this configuration, the nozzle
diameter or number of nozzles should be reduced. Reducing d would have a smaller
impact on W, however a lower limit to d can be set from practical reasons. In addition to
manufacturing constraints, perhaps the most important restriction on nozzle diameter
has to do with the clogging of the nozzles due to small particles in the coolant water. In
the experiments, the 0.7 mm nozzles had a tendency to be easily blocked. If no filter is
used in the coolant circuit, the nozzle diameter should probably be at least 1.5 mm.
The choice of the parameters described above is independent of nozzle configuration.
When dopt is determined, the next step is to decide on the type of nozzle. Countersinking
the orifices from above or below is found to reduce W significantly (Section 5.6), but the
improvement has to be weighed up against the cost of an extra manufacturing step.
Another factor to consider is surface modification. As explained in Section 3.3.1, this can
lead to as much as a threefold improvement in havg if done successfully. However, the
type of modifications must be chosen with care, as some have been found to lead to a
decrease in heat transfer. If a method of surface modification is known to increase the
heat transfer to a level high enough to justify the extra manufacturing work, this should
be included in the device design.
103
6 OPTIMISED DESIGN OF COOLING DEVICES
When the final design is known, some simple experiments are needed for the subsequent
optimisation. One approach could be to connect the cooling unit and the PV cells and
run the assembly at a range of flow rates while monitoring the module short-circuit
current, water temperature and pressure drop across the unit. If the properties of the PV
cells are well-known, the average junction temperature can be inferred from the module
short-circuit current, and this in turn can be used to find havg. Other methods include
thermographic liquid crystals or some other way of measuring the heated surface
temperature. A series of measurements will give the heat transfer correlation constants C
and m which are used in the Huber model (Section 5.3) and the discharge coefficient Cd.
Orifices are commonly used as flow rate measurement devices and an extensive
collection of data for Cd values for larger, standard orifice nozzles have been developed
in literature which could be applicable in the design process.
The final stage of the optimisation procedure is to find the optimal value of havg at which
to run the cooling system, as described in Section 6.2. The electrical and thermal
properties of the PV cells to be used in the system need to be known and incorporated
in the model for PV output presented in Section 2.2. To predict the required pumping
power for the cooling system, it is better to use the Huber model, using the constants C
and m found in the above described measurements, because it is built on experimental
data and thus gives more accurate predictions within the experimental range. By
performing this final optimisation, one can find the optimal operating conditions for the
system at any illumination level, and predict the typical electrical output for the chosen
conditions.
6.4 CONCLUSION
The correlations for pressure drop and average Nusselt number presented in Chapters 3
and 5 can be combined to predict the pumping power required for a given average heat
transfer coefficient and jet array configuration. When using the Martin [97] correlation
for Nusselt number, the model predicts an optimum nozzle diameter for any given
number of nozzles. The Huber [82] correlation, on the other hand, predicts increasing
heat transfer with decreasing nozzle diameter without an optimum point. Both models
predict a higher number of nozzles to yield a significantly higher heat transfer coefficient
at a given pumping power.
The pumping power model can in turn be used together with the correlation for PV
output as a function of temperature which was presented in Section 2.2 to find the
optimal operating conditions for a given illumination level. A broad optimum operating
range exists.
The recommended design procedure for jet impingement photovoltaic cooling devices
was presented in Section 6.3.
The predicted optimal nozzle diameters were not verified experimentally because of time
constraints. Some studies (Section 5.5) suggest that the discharge coefficient Cd might be
dependent on nozzle diameter, while the model predictions rely on the assumption that
Cd is constant. It is not thought that the possible diameter dependence would have a large
influence on the model predictions, but this should still be investigated experimentally in
later studies.
104
7
Chapter
EFFECTS OF NONUNIFORM
TEMPERATURE
All categories of cooling systems inherently produce some degree of nonuniformity in
temperature across a uniform heat flux surface. A uniform heat flux would, naturally,
only be found in ideal cases, but this assumption is necessary to isolate the effects of a
nonuniform heat transfer coefficient from the effects of other nonuniformities. With
water running through channels, nonuniformities arise due to gaps between the channels
and along the length of the channel because of heating of the coolant. As seen in
Chapter 5, impinging jets produce a highly nonuniform local heat transfer distribution.
This is something which should be taken into account when designing an optimised jet
array.
Nonuniformities across an array of photovoltaic cells may have both electrical and
mechanical implications. The latter refers to stresses in the material resulting from
different thermal expansions across the surface, which may result in adhesion problems
or cracking. Despite being an important problem, the mechanical aspects of PV arrays
are beyond the scope of this thesis and it will therefore not be further addressed. The
question of how nonuniform temperatures influence the output from single and
interconnected PV cells is investigated in Section 7.1. Section 7.2 describes how the
temperature nonuniformities can be reduced by introducing a sheet of metal of
appropriate thickness between the cells and the impinging jets, and discusses the tradeoff between reduced nonuniformity and increased average temperature which is caused
by this extra layer.
An issue which is often confused with nonuniform temperature is the occurrence of ‘hot
spots’ resulting from nonuniform illumination of a PV array. When one cell in a series
connection is shaded, its short circuit current is severely degraded and the cell is easily
driven into reverse bias, dissipating energy instead of producing it. This results in a
considerable loss of power, and may lead to irreversible damage because of overheating
of the cell. As shown in Section 7.1, however, the degradation resulting from
temperature alone is much less severe and does not necessarily lead to the cell being
driven into reverse bias.
105
7 EFFECTS OF NONUNIFORM TEMPERATURE
7.1 INFLUENCE ON PV OUTPUT
7.1.1 Single cells
Even in cases where the incident solar flux is perfectly uniform, temperature
nonuniformities are always present in concentrator cells, as a result of imperfections
(voids) in the cell-to-substrate bond [16] or as a result of the cell and heat sink geometry
[17]. Despite this, only two studies could be found that investigate the effect of
temperature nonuniformities under uniform illumination. Sanderson et al. [16] addressed
the problem of hot areas caused by voids in the bond. A theoretical model was made in
which the unit cell was divided into element areas, each operating at a unique
temperature. The model was verified experimentally by impinging the back of the cell
mounting plate with water of two different temperatures, separated by a divider. The
electrical characteristics of the cells were then found for a number of illumination values
ranging from 1 to 100 suns. The experimental results showed good agreement with the
model, except at high concentrations, when voids and nonuniform illumination caused by
the Fresnel lens became more pronounced. For a step function in temperature with ∆T =
50 K, the predicted cell efficiency was found to decrease from 13.1% to 12.2% at 100
suns and from 12.6% to 11.6% at 10 suns. More specifically, the nonuniform
temperature was found to result in a decreased open-circuit voltage.
Mathur et al. [17] used a slightly different approach, subdividing a circular cells into
concentric rings with a temperature gradient from the centre to the edge of the cell,
which is realistic for a circular cell bonded onto a large, flat heat sink. It was found that
with increasing thermal nonuniformities, the short-circuit current would show an
increase, whereas the open-circuit voltage and conversion efficiency would both decrease.
However, both of the above studies indicate that the effects of temperature
nonuniformities across one cell are relatively small.
7.1.2 Interconnected cells
To obtain an understanding of how a temperature difference between cells connected in
a module affect the electrical output, it is sufficient to study the behaviour of two cells at
different temperatures connected in series and parallel. The connections are shown in
Figure 7.1, where T1 ≥ T2. The electrical characteristics of the cells are found using a
semi-empirical model for concentrator silicon solar cells presented by Mbewe et al. [12].
The open-circuit voltage and short-circuit current for a cell of area Ac (cm2) at a given
temperature Tc (K) and concentration level X (suns) are given by
Voc = 1.25 −
0.63 − 0.06 log X
Tc
300
(7.1)
and
[
]
I sc = 0.034 Ac X 1 + 3 × 10−4 (Tc − 300) .
(7.2)
When Voc and Isc are known, the current I can be calculated at any voltage level V < Voc
iteratively from the transcendent function
⎡
⎛ V − Irs − Voc ⎞⎤
⎟⎟⎥
I = I sc ⎢1 − exp⎜⎜
kT
q
/
c
⎝
⎠⎦
⎣
106
(7.3)
7 EFFECTS OF NONUNIFORM TEMPERATURE
where rs denotes the series resistance, which is assumed to be a cell property
independence of temperature. Equation (6.3) can be rearranged to yield an expression
for V:
V=
k BTc ⎛ I sc − I ⎞
⎟⎟ + Voc − Irs .
ln⎜⎜
q
⎝ I sc ⎠
(7.4)
The values rs = 0.02 Ω cm-2, Ac = 1 cm and X = 100 suns are all chosen for the
subsequent calculations.
Figure 7.1: Two cells at temperatures T1 and T2
connected in a) series and b) parallel.
When the two cells are connected in series, the current I through the two must be equal.
If the two cells are of different temperature, Isc will increase and Voc decrease in the
hotter cell, while the opposite takes place in the colder cell. The following procedure is
used to find the maximum power point for the series connection:
1) Voc and Isc are calculated for each cell.
2) A suitable range of voltages V1 for the hotter cell is established, all below Voc1.
3) For each V1, the current I is found by iteration.
4) V2 is found as a function of I.
5) The maximum power point is found where P = I (V1 + V2) has its maximum
value. This value of P is used to find the cell efficiency η = Pel / S, where Pel is
the electrical output and S is the incident solar flux.
By keeping the average cell temperature constant and changing the temperature
difference between the two cells, one can study how the module efficiency changes as a
function of temperature difference. The results are shown in Figure 7.2 together with the
corresponding values of Voc1, Voc2, V1 and V2. In essence, the results show virtually no
effect from temperature difference on the total conversion efficiency. Figure 7.3 shows
the total and short-circuit currents for the two cells. As seen from Equations 7.1 and 7.2,
Voc and Isc are both linear functions of cell temperature, something which is also evident
from Figure 7.2 and Figure 7.3. As the short-circuit current of the colder cell degrades
relatively slowly, it does not go below the original maximum power point current even for
107
7 EFFECTS OF NONUNIFORM TEMPERATURE
very high temperature differences. On the other hand, there is an equal but opposite
change in Voc for the two cells, which results in a nearly equal but opposite change in V
at a constant current. As the gain in power for one cell equals the loss in power from the
other cell, the total conversion efficiency stays constant. Only at very high temperature
differences, where the cells are at unrealistic operating temperatures, does the shortcircuit current of the cold cell degrade below I.
0.85
0.8
efficiency
η
0.75
0.184
18.4
0.182
18.2
0.7
0.18
18.0
0.178
17.8
0.6
0.65
V1
V1
V V[ V
/ V]
%]
η η[ /%
0.19
19.0
0.188
18.8
0.186
18.6
0.55
0.176
17.6
0.174
17.4
V2
V2
Voc1
Voc1
Voc2
Voc2
0.5
0.45
0.172
17.2
0.17
17.0
0.4
0
20
40
60
80
100
∆T /[ KK ]
∆T
Figure 7.2: Efficiency and voltages in two silicon cells connected in series with a
constant average temperature of Tavg = 320 K.
I
IIsc1
sc1
3.7
3.6
IIsc2
sc2
I [A]
I/A
3.5
3.4
3.3
3.2
3.1
3
0
20
40
60
80
∆T[ /KK]
∆T
Figure 7.3: Current and short-circuit currents for two cells at different
temperatures connected in series, Tavg = 320 K.
108
100
7 EFFECTS OF NONUNIFORM TEMPERATURE
A similar approach is used for two cells connected in parallel. The voltage across the two
cells must be equal, while the currents are allowed to differ. The following procedure is
used:
1) Voc and Isc are calculated for each cell.
2) A suitable range of currents for Cell 1 is established, all below Isc1.
3) The value of V is calculated for each value of I1.
4) I2 is found by iteration.
5) The maximum power point is found and used to calculate the cell efficiency.
Contrary to the results from series connected cells, the total efficiency does decrease with
temperature difference for two cells connected in parallel. This is seen in Figure 7.4,
which shows that the efficiency is a relative 12% lower when ∆T = 100 K than when the
cell temperatures are equal. As the voltage across the parallel connection must be equal
for the two cells, the currents I1 and I2 must be adjusted up and down to keep the
conversion efficiency constant. However, I2 quite quickly approaches Isc2, forcing the
voltage down. The voltage degradation is shown in Figure 7.5, and is the reason for the
reduction in efficiency over a parallel connection. However, as the change is very small
and a temperature differential of 100K is highly unlikely, it seems that a temperature
differential across a parallel connection should not be a major cause for concern in
concentrating PV modules.
3.6
0.185
18.5
3.5
0.18
18.0
3.4
efficiency
η
I1I1
3.3
3.2
0.17
17.0
3.1
0.165
16.5
3
0.16
16.0
I I[ A
/ A]
/ %]
η η[ %
0.175
17.5
I2I2
Isc1
Isc1
Isc2
Isc2
2.9
0.155
15.5
2.8
0
20
40
60
80
100
∆T
∆T /[ K ]
Figure 7.4: Efficiency, currents and short-circuit currents in two cells
connected in parallel with a constant average temperature of Tavg = 320 K.
109
7 EFFECTS OF NONUNIFORM TEMPERATURE
0.85
0.80
0.75
V /V
V [V]
0.70
V
V
0.65
0.60
V
Voc1
oc1
0.55
V
oc2
Voc2
0.50
0.45
0.40
0
20
40
60
80
100
∆T∆T[ /KK]
Figure 7.5: Voltage and open-circuit voltages in two cells connected
in parallel with a constant average temperature of Tavg = 320 K.
7.2 USING THE METAL SUBSTRATE AS A HEAT DIFFUSER
A simple solution for reducing thermal nonuniformities across the cells is to use a metal
substrate between the cells and the cooling system as a thermal diffuser. A thick substrate
allows for more lateral conduction to take place and hence a lower temperature
difference across the cells. However, the increased uniformity comes at the cost of an
additional temperature rise through the substrate, ∆Trise, which is linearly proportional to
the substrate thickness and is given by
∆Trise =
q&t
.
k
(7.5)
Here, q& is the heat flux, t is the substrate thickness and k is the thermal conductivity of
the substrate. The temperature through a copper substrate (k = 400 W m-1 K-1) of
thickness t for q& = 2.5 x 104 W m-2 is shown in Figure 7.6.
7
∆Trise [ K ]
6
5
4
3
2
1
0
0
2
4
6
8
10
t [ mm ]
Figure 7.6: Increase in temperature, ∆Trise, through a
copper substrate of thickness t for q& = 2.5 x 104 W m-2.
110
7 EFFECTS OF NONUNIFORM TEMPERATURE
A two-dimensional finite element model was used to investigate how the level of
nonuniformity is affected by the substrate thickness. The model is shown in Figure 7.7
together with a typical temperature result obtained using the software package Strand7
[102]. Strictly speaking, an array of axisymmetric jets impinging on a surface should be
represented by a three-dimensional model. However, it is conceptually easier to work
with the problem in two dimensions, and the results should be comparable. The twodimensional model represents two infinitely long planar jets separated by a distance s.
The local heat transfer coefficient is estimated by a linear function (see Section 5.1 for
justification). Only the region from the stagnation point of one jet to the centreline
between the two jets is modelled, because of symmetry. No region of increased heat
transfer between the jets due to interference has been included. There is also a constant
heat flux along the bottom and a constant ambient (coolant) temperature.
h1
h2
t
T1
.
q
s/2
Figure 7.7: Two-dimensional thermal model of a copper substrate with havg = 7.5 x 104 W m-2 K-1,
q& = 2.5 x 104 W m-2, h 1/h 2 = 4, s = 10 mm, t = 2 mm and ambient temperature Ta = 300 K.
The model was solved for a substrate of copper with a range of nozzle pitches (10 mm ≤
s ≤ 40 mm) and substrate thicknesses (2 mm ≤ t ≤ 10 mm). For the same average heat
transfer coefficient, four different slopes were used for the linear heat transfer coefficient
distribution so that h1/h2 = 2.5, 3.0, 2.5 and 4.0. These values were chosen because they
represent reasonable nozzle pitches and nozzle diameters. The corresponding nozzle
diameters and s/d values for the range of s and h1/h2 used were calculated using the linear
correlation for local heat transfer distribution given as Equation 5.1. The resulting values
are given in Table 7.1. For each configuration, the temperature difference across the
bottom surface, ∆Ts = T2 – T2 where T1 and T2 are shown in Figure 7.7, was calculated.
The results for q& = 2.5 x 104 W m-2 and havg = 2.5, 5.0 and 7.5 x 104 W m-2 K-1 are given in
Figures 7.8 through to 7.10. On solving the model for a range of heat fluxes it was found
that ∆Ts varies linearly with q& . A simple dependency of h1, h2, t or s on ∆Ts could not be
found.
111
T2
7 EFFECTS OF NONUNIFORM TEMPERATURE
Table 7.1: s/d and d corresponding to the h 1/h 2 and s used in Figures 6.8 - 6.10.
h1/h2
2.5
2.5
2.5
2.5
3.0
3.0
3.0
3.0
3.5
3.5
3.5
3.5
4.0
4.0
4.0
4.0
s (mm)
10
20
30
40
10
20
30
40
10
20
30
40
10
20
30
40
s/d
4.4
4.4
4.4
4.4
5.3
5.3
5.3
5.3
6.1
6.1
6.1
6.1
7.0
7.0
7.0
7.0
d (mm)
2.3
4.6
6.9
9.1
1.9
3.8
5.7
7.6
1.6
3.3
4.9
6.5
1.4
2.9
4.3
5.7
The graphs show that even with the thinnest substrate (t = 2 mm), only relatively small
temperature differences arise from the nonuniform heat transfer coefficient distribution.
The highest value of nonuniformity found was ∆Ts = 5.8 K at h1/h2 =4.0, s = 40 mm
and t = 2 mm. The differential can be reduced to 3.6 K by doubling the substrate
thickness to 4 mm, but at the expense of an additional temperature rise of 1.1 K (Figure
7.6). Because the PV efficiency is much more dependent on average temperature than on
the temperature difference (see Section 2.2 and previously in this chapter), a thick
substrate would not be beneficial to the electrical output. The substrate thickness needed
for mechanical strength is likely to be a sufficient thermal diffuser. If a specific limit to
thermal nonuniformity is set, Figures 7.8 through 7.10 can be used to find the required
substrate thickness. However it should be kept in mind that thermal nonuniformities due
to voids in the cell-to-substrate bond, as discussed in [16], are likely to be more
prominent than those created by the cooling system.
5.0
h1/h2 = 2.5
4.0
∆Ts [ K ]
∆Ts [ K ]
4.0
3.0
2.0
3.0
2.0
1.0
1.0
0.0
0.0
2
6.0
4
6
t [ mm ]
8
2
10
7.0
h1/h2 = 3.5
5.0
4.0
3.0
2.0
1.0
4
6
t [ mm ]
8
10
h1/h2 = 4.0
6.0
5.0
∆Ts [ K ]
∆Ts [ K ]
h1/h2 = 3.0
5.0
4.0
3.0
2.0
1.0
0.0
0.0
2
4
∆Ts, s = 10 mm
∆Ts, s = 20 mm
∆Ts, s = 30 mm
∆Ts, s = 40 mm
6
t [ mm ]
8
10
2
4
6
t [ mm ]
8
Figure 7.8: The temperature difference across the surface (∆Ts)
for a copper substrate layer with different h 1/h 2, t and s for havg
= 2.5 x 104 W m-2 K-1 and q& = 2.5 x 104 W m-2.
112
10
7 EFFECTS OF NONUNIFORM TEMPERATURE
7.3 CONCLUSION
Temperature nonuniformities were thought to be an important issue in PV arrays
because of how the temperature affects the electrical output of a PV cell. However, the
investigation in this chapter has shown that the electrical performance of both single and
interconnected cells is weakly affected by temperature differentials. Only at very large
differences (in the order of 50 K) is there a marked reduction in efficiency. Furthermore,
finite element modelling showed that trying to reduce the temperature difference by
increasing the thickness of the substrate between the cells and the cooling system would
lead to a decrease in overall cell performance due to the increased average cell
temperature. Some substrate is still needed for mechanical strength, but it should be kept
as thin as possible.
These findings indicate that thermal nonuniformities are of only minor importance in
designing a cooling system for PV arrays, and that the system which yields the highest
average heat transfer coefficient should be chosen regardless of uniformity. However, the
results obtained for interconnected cells still need to be verified experimentally.
3.0
3.5
h1/h2 = 2.5
2.0
∆Ts [ K ]
∆Ts [ K ]
2.5
1.5
1.0
0.5
2.5
2.0
1.5
1.0
0.5
0.0
0.0
2
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
4
6
t [ mm ]
8
10
2
4
6
t [ mm ]
8
10
8
10
5.0
h1/h2 = 3.5
h1/h2 = 4.0
4.0
∆Ts [ K ]
∆Ts [ K ]
h1/h2 = 3.0
3.0
3.0
2.0
1.0
0.0
2
4
∆Ts, s = 10 mm
∆Ts, s = 20 mm
∆Ts, s = 30 mm
∆Ts, s = 40 mm
6
t [ mm ]
8
10
2
4
6
t [ mm ]
Figure 7.9: The temperature difference across the surface (∆Ts)
for a copper substrate layer with different h 1/h 2, t and s for havg
= 5.0 x 104 W m-2 K-1 and q& = 2.5 x 104 W m-2.
113
7 EFFECTS OF NONUNIFORM TEMPERATURE
2.5
2.5
h1/h2 = 2.5
2.0
∆Ts [ K ]
∆Ts [ K ]
2.0
1.5
1.0
0.5
1.5
1.0
0.5
0.0
0.0
2
4
6
t [ mm ]
8
10
2
3.0
h1/h2 = 3.5
2.5
2.0
∆Ts [ K ]
∆Ts [ K ]
h1/h2 = 3.0
1.5
1.0
0.5
0.0
2
4
∆Ts, s = 10 mm
∆Ts, s = 20 mm
∆Ts, s = 30 mm
∆Ts, s = 40 mm
6
t [ mm ]
8
10
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
4
6
t [ mm ]
8
h1/h2 = 4.0
2
4
6
t [ mm ]
8
Figure 7.10: The temperature difference across the surface
(∆Ts) for a copper substrate layer with different h 1/h 2, t and s
for havg = 7.5 x 104 W m-2 K-1 and q& = 2.5 x 104 W m-2.
114
10
10
8
Chapter
CONCLUSIONS AND
RECOMMENDATIONS FOR
FURTHER WORK
8.1 CONCLUSIONS
In the opening chapters of this thesis it was established that cooling is an integral aspect
of designing a concentrating photovoltaic system. Arrays of densely packed cells such as
those found in dish or tower receivers, which normally utilize quite high concentrations,
are particularly reliant on an efficient cooling system, because of the very high heat
fluxes that need to be removed while maintaining a low cell temperature. Microchannels
and impinging jets were identified as promising cooling technologies, and it was decided
to proceed with investigating the possibility of jet impingement cooling.
Based on findings from the literature, a jet device was designed where the liquid was
drained in a direction normal to the heated surface around the edges of the central array,
called the ‘side drainage device’. An experimental facility was designed based on the most
promising techniques reported in the literature. The local heat transfer under both jets
and arrays of four and nine jets with side drainage was studied, and the results for local
heat transfer distribution, average heat transfer coefficient and stagnation point heat
transfer coefficient were found to agree with literature. It was shown that eddy formation
created a narrow zone of lowered heat transfer coefficient along the edges of the
impingement plate for both single and multiple jets. The jet arrays also displayed
particular characteristics such as a slight asymmetry in the jets away from the centre, a
region of increased heat transfer due to turbulence along the centreline between the jets,
and temporal flow oscillations. Nozzles of different geometry were found to behave
slightly differently in terms of average heat transfer coefficient and pressure drop
through the nozzles. The latter could be explained by assigning a specific discharge
coefficient to each nozzle. A correlation for the pressure drop through the nozzles in
terms of discharge coefficient was presented. The nozzles which were countersunk from
above or below were found to yield a higher heat transfer coefficient at a given pumping
power than the straight nozzles. A device where the spent liquid was drained through a
central drainage pipe was also tested, but found to perform poorly largely due to vortex
formation around the outlet. The results obtained for the side drainage device were
highly promising when compared with the typical performance of microchannel cooling
devices.
Based on correlations from the literature and experimental results, a model was made
which predicts the pumping power required for an average heat transfer coefficient for
different device configurations. The model predicts a higher number of nozzles per unit
area to perform better than a lower number of nozzles. This was verified experimentally.
115
8 CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER WORK
It also predicts an optimal nozzle diameter for a given area and number of nozzles.
Combined with a model for cell performance at different temperatures, it was found that
there exists a broad optimal operating region for any system of photovoltaic cells and
cooling device at a given illumination level. A cooling system design procedure was
presented.
The nonuniform heat transfer coefficient distribution, which is an inherent property of
jet impingement devices, was shown to have only a weak effect on the electrical output
of the photovoltaic system compared with the effect of average temperature. Therefore,
the cooling system should be optimised to yield a high heat transfer coefficient rather
than a high level of uniformity. It is also beneficial to place the cooling system as close to
the cells as possible without sacrificing the mechanical strength of the structure.
8.2 RECOMMENDATIONS FOR FURTHER WORK
During the course of this work, a number of areas have been identified which could be
addressed in future work.
8.2.1 Fundamental work on jet impingement cooling
Although much is known about jet impingement cooling, here are still some fundamental
areas which are not well understood. One of these is the issue of surface modifications.
There are numerous ways of modifying the impingement surface, but the research
should limit itself to investigating practically realisable methods. Systematic research
should be carried out in order to identify how surface modifications affect the flow
patterns and heat transfer under arrays of jets and to identify what sort of modifications
can provide the large gain in heat transfer which has been shown in some studies.
Nozzle geometry effects have also been extensively researched, but not in terms of
cooling performance at a given pumping power requirement. In this thesis it was shown
that countersinking the nozzles from above or below gave similar benefits in terms of
pumping power, although the flow conditions for these two nozzles are fundamentally
different. Experiments could be designed with a higher precision in the flow rate and
pressure measurements than those performed for this thesis, where the performance of
nozzles countersunk at different angles could be compared to obtain a better
understanding of the mechanisms involved in the heat transfer coefficients and pumping
power of these nozzles. This could provide the basis for a better conclusion on the
preferred type of nozzle to use.
An issue which has not been given much attention in literature, but which could be
relevant for cooling devices that are used continuously for years, is the problem of
abrasion. The jets impinge onto the heated surface with a considerable pressure. If the
impingement surface consists of a relatively soft material, such as copper which is a
natural choice because of its high thermal conductivity, there may be significant wearing
of the surface from the impact of the jets during long periods of operation. A simple
laboratory experiment could be constructed to investigate the significance of this effect
for different materials, jet velocities and time scales.
116
8 CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER WORK
8.2.2 Photovoltaics
Chapter 7 described the effects of nonuniform temperature on cells that are connected
in series or parallel. Numerical modelling showed that there is very little effect on the
overall efficiency of the two cells. This result should be verified experimentally by
interconnecting two cells at different temperatures but at the same illumination,
preferably at a range of temperature differences and concentrations.
While the immediate effects of temperature effects on photovoltaic cells are well known,
degradation of cells due to prolonged periods of high temperatures have been observed
but the mechanisms involved are not fully understood. This is another problem which
should be studied experimentally, at a range of temperatures and concentrations, to
establish more scientifically based limits for operating temperature.
8.2.3 Prototype design
In this thesis, the cooling ability of a small jet impingement device has been
demonstrated on a laboratory scale. The next important step is to demonstrate the
feasibility of a larger scale device prototype. A device much larger than the one presented
in this thesis can not be tested in the laboratory with presently available equipment due
to the high power fluxes required. However, concentrated sunlight represents an
excellent source of heat. A device of about 100 mm x 100 mm size should be
manufactured and tested under solar conditions. At first, it should use a black absorber
of known emissivity as the heated surface. Later, if the first step proves successful, it can
be incorporated with an array of photovoltaic cells.
Modelling performed in this thesis has shown having a large number of jets is desirable
for cooling a large surface. Thus, when designing a device of the dimensions mentioned
above, crossflow can become a significant problem. This could be solved by designing a
device in which the spent liquid is drained through exits distributed throughout the jet
array. Perhaps the most promising option for this is the configuration consisting of
parallel pipes shown in Figure 3.7b. A prototype of this design should be tested and
compared with the side drainage configuration presented in this thesis.
117
REFERENCES
REFERENCES
1.
Zahedi, A. (1997) Energy: Concerns and possibilities. Academia Press, Melbourne.
2.
IEA Energy Statistics (cited March 2005) [Available online from
http://www.iea.org/]
3.
World Energy Council: Survey of Energy Resources 2001 (cited March 2005)
[Available online from http://www.worldenergy.org]
4.
Intergovernmental Panel on Climate Change (IPCC): Climate Change 2001 (cited
March 2005) [Available online from http://www.ipcc.ch]
5.
Swanson, R.M. (2000) The Promise of Concentrators. Progress in Photovoltaics:
Research and Applications 8, 93-111.
6.
Website of Solar Systems Pty Ltd. (cited March 2005) [Available online from
http://www.solarsystems.com.au/]
7.
Website of EN.ERGO - Club per la riconversione del sistema energetico e per la
promozione delle fonti di energia rinnovabili (cited March 2005) [Available online
from http://www.energoclub.it/a%20solarebis.htm]
8.
Vincenzi, D., Stefancich, M., Bizzi, F., Antonini, A., Ronzoni, A., Butturi, M.A.,
Malagu, C. and Martinelli, G. (2003) Micromachined silicon heat exchanger for
water cooling of concentrator solar cells. ISES, Gothenburg
9.
Royne, A., Dey, C.J. and Mills, D.R. (2005) Cooling of photovoltaic cells under
concentrated illumination: a critical review. Solar Energy Materials and Solar Cells 86
(4), 451-483.
10.
Sinton, R.A., Kwark, Y., Gruenbaum, P. and Swanson, R.M. (1985) Silicon point
contact concentrator solar cells. 18th IEEE Photovoltaic Specialists Conference, pp. 6165.
11.
Sala, G. (1989) Chp. 8: Cooling of solar cells, in Cells and optics for photovoltaic
concentration, ed. Luque, A. Adam Hilger, Bristol, pp. 239-267.
12.
Mbewe, D.J., Card, H.C. and Card, D.C. (1985) A model of silicon solar cells for
concentrator photovoltaic and photovoltaic thermal system design. Solar Energy
35 (3), 247-258.
13.
Dalal, V.L. and Moore, A.R. (1977) Design considerations for high-intensity solar
cells. Journal of Applied Physics 48 (3), 1244-1251.
14.
SunPower (2002) Application notes for HED312 Silicon Concentrator Solar Cell.
15.
Horne, W.E. (1993) Solar energy system. Patent no. US5269851.
118
REFERENCES
16.
Sanderson, R.W., O'Donnell, D.T. and Backus, C.E. (1980) The effects of
nonuniform illumination and temperature profiles on silicon solar cells under
concentrated sunlight. 14th IEEE Photovoltaic Specialists Conference, San Diego, pp.
431-436.
17.
Mathur, R.K., Mehrotra, D.R., Mittal, S. and Dhariwal, S.R. (1984) Thermal nonuniformities in concentrator solar cells. Solar Cells 11, 175-188.
18.
Edenburn, M.W. and Burns, J.R. (1981) Shading analysis of a photovoltaic cell
string illuminated by a parabolic through concentrator. 15th IEEE Photovoltaic
Specialists Conference, Orlando, pp. 63-68.
19.
(2002) e-mail discussions on solar concentrators [Available online from
http://www.cichlid.com/mailman/listinfo/solar-concentrator]
20.
Faiman, D. (2002) Large-area concentrators. 2nd Workshop on "The path to ultra-high
efficiency photovoltaics", JRC Ispra
21.
Kreske, K. (2002) Optical design of a solar flux homogenizer for concentrating
photovoltaics. Applied Optics 41 (10), 2053-2058.
22.
Rose, J.W. (2004) Heat-transfer coefficients, Wilson plots and accuracy of thermal
measurements. Experimental Thermal and Fluid Science 28 (2-3), 77-86.
23.
Miñano, J.C., González, J.C. and Zanesco, I. (1994) Flat high concentration
devices. 24th IEEE Photovoltaic Specialists Conference, Hawaii, pp. 1123-1126.
24.
Araki, K., Uozumi, H. and Yamaguchi, M. (2002) A simple passive cooling
structure and its heat analysis for 500 x concentrator PV module. 29th IEEE
Photovoltaic Specialists Conference, New Orleans, pp. 1568-1571.
25.
Chenlo, F. and Cid, M. (1987) A linear concentrator photovoltaic module:
Analysis of non-uniform illumination and temperature effects on efficiency. Solar
Cells 20, 27-39.
26.
Luque, A., Sala, G. and Arboiro, J.C. (1998) Electric and thermal model for nonuniformly illuminated concentration cells. Solar Energy Materials and Solar Cells 51,
269-290.
27.
O'Leary, M.J. and Clements, L.D. (1980) Thermal-electric performance analysis
for actively cooled, concentrating photovoltaic systems. Solar Energy 25, 401-406.
28.
Incropera, F.P. and DeWitt, D.P. (1996) Fundamentals of heat and mass transfer. 4th
ed., John Wiley & Sons.
29.
Florschuetz, L.W. (1975) On heat rejection from terrestrial solar cell arrays with
sunlight concentration. 11th IEEE Photovoltaic Specialists Conference, New York, pp.
318-326.
119
REFERENCES
30.
Edenburn, M.W. (1980) Active and passive cooling for concentrating
photovoltaic arrays. 14th IEEE Photovoltaic Specialists Conference, San Diego, pp.
776-776.
31.
Graven, R.M., Gorski, A.J., Schertz, W.W. and Graae, J.E.A. (1978) Modular
assembly of a photovoltaic solar energy receiver. Patent no. US4118249.
32.
Luque, A., Sala, G., Arboiro, J.C., Bruton, T., Cunningham, D. and Mason, N.
(1997) Some results of the EUCLIDES photovoltaic concentrator prototype.
Progress in Photovoltaics: Research and Applications 5 (3), 195-212.
33.
Feldman, K.T., Kenney, D.D. and Edenburn, M.W. (1981) A passive heat pipe
cooled photovoltaic receiver. 15th IEEE Photovoltaic Specialists Conference, Orlando,
pp. 165-172.
34.
Akbarzadeh, A. and Wadowski, T. (1996) Heat pipe-based cooling systems for
photovoltaic cells under concentrated solar radiation. Applied Thermal Engineering
16 (1), 81-87.
35.
Russell, R.F. (1982) Uniform temperature heat pipe and method of using the
same. Patent no. US4320246.
36.
Coventry, J.S. (2003) Performance of the CHAPS collectors. Destination Renewables
- ANZSES 2003, Melbourne, pp. 144-153.
37.
Verlinden, P., Sinton, R.A., Swanson, R.M. and Crane, R.A. (1991) Single-wafer
integrated 140 W silicon concentrator module. 22nd IEEE Photovoltaic Specialists
Conference, Las Vegas, pp. 739-743.
38.
Tilford, C.L., Sinton, R.A., Swanson, R.M., Crane, R.A. and Verlinden, P. (1993)
Development of a 10 kW reflective dish PV system. 23rd IEEE Photovoltaic
Specialists Conference, Louisville, pp. 1222-1227.
39.
Lasich, J.B. (2002) Cooling circuit for receiver of solar radiation. Patent no.
WO02080286.
40.
Verlinden, P.J., Terao, A., Smith, D.D., McIntosh, K., Swanson, R.M., Ganakas, G.
and Lasich, J.B. (2001) Will We Have a 20%-Efficient (PTC) Photovoltaic
System? 17th European Photovoltaic Solar Energy Conference, Munich
41.
Vincenzi, D., Bizzi, F., Stefancich, M., Malagu, C., Morini, G.L., Antonini, A. and
Martinelli, G. (2002) Micromachined silicon heat exchanger for water cooling of
concentrator solar cells. PV in Europe Conference and Exhibition - From PV technology
to Energy Solutions, Rome
42.
Koehler, H.C. (2000) Cooling photovoltaic (PV) cells during concentrated solar
radiation in specified arrangement in coolant with as low electric conductivity as
possible. Patent no. DE19904717.
120
REFERENCES
43.
Vafai, K. and Zhu, L. (1999) Analysis of two-layered micro-channel heat sink
concept in electronic cooling. International Journal of Heat and Mass Transfer 42 (12),
2287-2297.
44.
Ryu, J.H., Choi, D.H. and Kim, S.J. (2002) Numerical optimization of the thermal
performance of a microchannel heat sink. International Journal of Heat and Mass
Transfer 45 (13), 2823-2827.
45.
Hetsroni, G., Mosyak, A., Segal, Z. and Ziskind, G. (2002) A uniform
temperature heat sink for cooling of electronic devices. International Journal of
Heat and Mass Transfer 45 (16), 3275-3286.
46.
Chong, S.H., Ooi, K.T. and Wong, T.N. (2002) Optimisation of single and double
layer counter flow microchannel heat sinks. Applied Thermal Engineering 22 (14),
1569-1585.
47.
Kim, K.-S., Won, M.-H., Kim, J.-W. and Back, B.-J. (2003) Heat pipe cooling
technology for desktop PC CPU. Applied Thermal Engineering 23 (9), 1137-1144.
48.
Ryu, J.H., Choi, D.H. and Kim, S.J. (2003) Three-dimensional numerical
optimization of a manifold microchannel heat sink. International Journal of Heat
and Mass Transfer 46 (9), 1553-1562.
49.
Kraus, A.D. and Bar-Cohen, A. (1995) Design and analysis of heat sinks. 1st ed., John
Wiley & Sons.
50.
Dunn, P.D. and Reay, D.A. (1994) Heat pipes. 4th ed., Pergamon.
51.
Launay, S., Sartre, V. and Lallemand, M. (2004) Experimental study on silicon
micro-heat pipe arrays. Applied Thermal Engineering 24 (2-3), 233-243.
52.
Pastukhov, V.G., Maidanik, Y.F., Vershinin, C.V. and Korukov, M.A. (2003)
Miniature loop heat pipes for electronics cooling. Applied Thermal Engineering 23
(9), 1125-1135.
53.
Xuan, Y., Hong, Y. and Li, Q. (2004) Investigation on transient behaviors of flat
plate heat pipes. Experimental Thermal and Fluid Science 28 (2-3), 249-255.
54.
Chen, P.-C. and Lin, W.-K. (2001) The application of capillary pumped loop for
cooling of electronic components. Applied Thermal Engineering 21 (17), 1739-1754.
55.
Tuckerman, D.B. and Pease, F.W. (1981) High-performance heat sinking for
VLSI. IEEE Electron Device Letters 2 (5), 126-129.
56.
Qu, W. and Mudawar, I. (2002) Experimental and numerical study of pressure
drop and heat transfer in a single-phase micro-channel heat sink. International
Journal of Heat and Mass Transfer 45 (12), 2549-2565.
57.
Harms, T.M., Kazmierczak, M.J. and Gerner, F.M. (1999) Developing convective
heat transfer in deep rectangular microchannels. International Journal of Heat and
Fluid Flow 20 (2), 149-157.
121
REFERENCES
58.
Owhaib, W. and Palm, B. (2004) Experimental investigation of single-phase
convective heat transfer in circular microchannels. Experimental Thermal and Fluid
Science 28 (2-3), 105-110.
59.
Min, J.Y., Jang, S.P. and Kim, S.J. (2004) Effect of tip clearance on the cooling
performance of a microchannel heat sink. International Journal of Heat and Mass
Transfer 47 (5), 1099-1103.
60.
Moores, K.A. and Joshi, Y. (2003) Effect of tip clearance on the thermal and
hydrodynamic performance of a shrouded pin fin array. Journal of Heat Transfer
125, 999-1006.
61.
Missaggia, L.J. and Walpole, J.N. (1991) A microchannel heat sink with alternating
directions of water flow in adjacent channels. Integrated Optoelectronics for
Communication and Processing 1582, 106-111.
62.
Chen, Y. and Cheng, P. (2002) Heat transfer and pressure drop in fractal tree-like
microchannel nets. International Journal of Heat and Mass Transfer 45 (13), 26432648.
63.
Rohsenow, W.M., Harnett, J.P. and Cho, Y.I. eds (1998) Handbook of heat transfer.
3rd ed., McGraw-Hill.
64.
Webb, B.W. and Ma, C.-F. (1995) Single-phase liquid jet impingement heat
transfer. Advances in Heat Transfer 26, 105-217.
65.
Lee, D.-Y. and Vafai, K. (1999) Comparative analysis of jet impingement and
microchannel cooling for high heat flux applications. International Journal of Heat
and Mass Transfer 42 (9), 1555-1568.
66.
Womac, D.J., Incropera, F.P. and Ramadhyani, S. (1994) Correlating equations for
impingement cooling of small heat sources with multiple circular liquid jets.
Journal of Heat Transfer 116, 482-486.
67.
Vandervort, C.L., Bergles, A.E. and Jensen, M.K. (1992) Heat transfer
mechanisms in very high heat flux subcooled boiling. ASME HTD-Vol.217,
Fundamentals of subcooled flow boiling, 1-9.
68.
Ghiaasiaan, S.M. and Abdel-Khalik, S.I. (2001) Two-phase flow in microchannels.
Advances in heat transfer 34, 145-254.
69.
Hejzlar, P. and Todreas, N.E. (1996) Consideration of critical heat flux margin
prediction by subcooled or low quality critical heat flux correlations. Nuclear
Engineering and Design 163 (1-2), 215-223.
70.
Prodanovic, V., Fraser, D. and Salcudean, M. (2002) On the transition from
partial to fully developed subcooled flow boiling. International Journal of Heat and
Mass Transfer 45 (24), 4727-4738.
122
REFERENCES
71.
Bartel, M.D., Ishii, M., Masukawa, T., Mi, Y. and Situ, R. (2001) Interfacial area
measurements in subcooled flow boiling. Nuclear Engineering and Design 210 (1-3),
135-155.
72.
Qu, W. and Mudawar, I. (2002) Prediction and measurement of incipient boiling
heat flux in micro-channel heat sinks. International Journal of Heat and Mass Transfer
45 (19), 3933-3945.
73.
Hapke, I., Boye, H. and Schmidt, J. (2002) Flow boiling of water and η-heptane
in microchannels. Microscale Thermophysical Engineering 6, 99-115.
74.
Ghiaasiaan, S.M. and Chedester, R.C. (2002) Boiling incipience in microchannels.
International Journal of Heat and Mass Transfer 45 (23), 4599-4606.
75.
Hapke, I., Boye, H. and Schmidt, J. (2000) Onset of nucleate boiling in
microchannels. International Journal of Thermophysical Science 39, 505-513.
76.
Inoue, A., Ui, A., Yamazaki, Y. and Lee, S. (2000) Studies on cooling by twodimensional confined jet flow of high heat heat flux surface in fusion reactor.
Nuclear Engineering and Design 200 (1-2), 317-329.
77.
Goldstein, R.J. and Seol, W.S. (1991) Heat transfer to a row of impinging circular
air jets including the effect of entrainment. International Journal of Heat and Mass
Transfer 34 (8), 2133-2147.
78.
Womac, D.J., Ramadhyani, S. and Incropera, F.P. (1993) Correlating equations for
impingement cooling of small heat sources with single circular liquid jets. Journal
of Heat Transfer 115, 106-115.
79.
Garimella, S.V. and Rice, R.A. (1995) Confined and submerged liquid jet
impingement heat transfer. Journal of Heat Transfer 117, 871-877.
80.
Garimella, S.V. and Nenaydykh, B. (1996) Nozzle-geometry effects in liquid jet
impingement heat transfer. International Journal of Heat and Mass Transfer 39 (14),
2915-2923.
81.
Jambunathan, K., Lai, E., Moss, M.A. and Button, B.L. (1992) A review of heat
transfer data for single circular jet impingement. International Journal of Heat and
Fluid Flow 13 (2), 106-115.
82.
Huber, A.M. and Viskanta, R. (1994) Effect of jet-to-jet spacing on convective
heat transfer on confined, impinging arrays of axisymmetric jets. International
Journal of Heat and Mass Transfer 37 (18), 2859-2869.
83.
Hoogendoorn, C.J. (1977) The effect of turbulence on heat transfer at a
stagnation point. International Journal of Heat and Mass Transfer 20, 1333-1338.
84.
Lee, J. and Lee, S.-J. (2000) The effect of nozzle configuration on stagnation
region heat transfer enhancement of axisymmetric jet impingement. International
Journal of Heat and Mass Transfer 43 (18), 3497-3509.
123
REFERENCES
85.
Brignoni, L.A. and Garimella, S.V. (2000) Effects of nozzle-inlet chamfering on
pressure drop and heat transfer in confined air jet impingement. International
Journal of Heat and Mass Transfer 43 (7), 1133-1139.
86.
Lee, D.H., Song, J. and Jo, M.C. (2004) The effect of nozzle diameter on
impinging jet heat transfer and fluid flow. Journal of Heat Transfer 126, 554-557.
87.
Li, C.-Y. and Garimella, S.V. (2001) Prandtl-number effects and generalized
correlations for confined and submerged jet impingement. International Journal of
Heat and Mass Transfer 44 (18), 3471-3480.
88.
Tawfek, A.A. (1996) Heat transfer and pressure distributions of an impinging jet
on a flat surface. Heat and Mass Transfer 32, 49-54.
89.
Huang, L. and El-Genk, M.S. (1994) Heat transfer of an impinging jet on a flat
surface. International Journal of Heat and Mass Transfer 37 (13), 1915-1923.
90.
San, J.-Y. and Lai, M.-D. (2001) Optimum jet-to-jet spacing of heat transfer for
staggered arrays of impinging air jets. International Journal of Heat and Mass Transfer
44 (21), 3997-4007.
91.
Huber, A.M. and Viskanta, R. (1994) Comparison of convective heat transfer to
perimeter and center jets in a confined, impinging array of axisymmetric jets.
International Journal of Heat and Mass Transfer 37 (18), 3025-3030.
92.
Aldabbagh, L.B.Y. and Sezai, I. (2002) Numerical simulation of three-dimensional
laminar multiple impinging square jets. International Journal of Heat and Fluid Flow
23 (4), 509-518.
93.
Sezai, I. and Aldabbagh, L.B.Y. (2004) Three-dimensional numerical investigation
of flow and heat transfer characteristics of inline jet arrays. Numerical Heat
Transfer, Part A 45, 271-288.
94.
Garimella, S.V. and Schroeder, V.P. (2001) Local heat transfer distributions in
confined multiple air jet impingement. Journal of Electric Packaging 123, 165-172.
95.
Yan, X. and Sanei, N. (1996) Measurements of local heat transfer coefficients
from a flat plate to a pair of circular air impinging jets. Experimental Heat Transfer
9, 29-47.
96.
Brevet, P., Dejeu, C., Dorignac, E., Jolly, M. and Vullierme, J.J. (2002) Heat
transfer to a row of impinging jets in consideration of optimization. International
Journal of Heat and Mass Transfer 45 (20), 4191-4200.
97.
Martin, H. (1977) Heat and mass transfer between impinging gas jets and solid
surfaces. Advances in Heat Transfer 13, 1-60.
98.
Priedeman, D., Callahan, V. and Webb, B.W. (1994) Enhancement of liquid jet
impingement heat transfer with surface modifications. Journal of Heat Transfer 116,
486-489.
124
REFERENCES
99.
Chakroun, W.M., Abdel-Rahman, A.A. and Al-Fahed, S.F. (1998) Heat transfer
augmentation for air jet impinged on a rough surface. Applied Thermal Engineering
18 (12), 1225-1241.
100.
Lee, D.H., Lee, Y.M., Kim, Y.T., Won, S.Y. and Chung, Y.S. (2002) Heat transfer
enhancement by the perforated plate installed between an impinging jet and the
target plate. International Journal of Heat and Mass Transfer 45 (1), 213-217.
101.
Zhou, D.W. and Lee, S.-J. (2004) Heat transfer enhancement of impinging jets
using mesh screens. International Journal of Heat and Mass Transfer 47, 2097-2108.
102.
Strand7 Pty Ltd. website [Available online from http://www.strand7.com/]
103.
Walshaw, A.C. and Jobson, D.A. (1972) Mechanics of fluids. 2nd ed., Longman
Group Ltd., London.
104.
Faber, T.E. (1995) Fluid dynamics for physicists. Cambridge University Press,
Cambridge.
105.
Reader-Harris, M.J., Sattary, J.A. and Spearman, E.P. (1995) The orifice plate
discharge coefficient equation - further work. Flow measurement and instrumentation 6
(2), 101-114.
125