EXAMINATION OF THE LOCAL AND FLUCTUATING HEAT
TRANSFER DUE TO SWIRLING JETS IMPINGING UPON A HEATED
HORIZONTAL SURFACE
Karl J. BROWN*, Tim PERSOONS*, Darina B. MURRAY*
* Department of Mechanical and Manufacturing Engineering, Trinity College, Dublin, Ireland.
1.
ABSTRACT
In the area of heat dissipation, impinging jets have been researched over many years and are a well
defined method of attaining high heat transfer coefficients. Many different techniques have been looked at
over past years in an attempt to discover a way to enhance this heat transfer further. This study investigates
the effect of introducing a swirling motion into the fluid flow before exiting a jet nozzle. The final objective
is to discover an optimal swirl geometry which will increase the heat transfer within a system compared to
what would be achieved from a non-swirling jet with the same external nozzle geometry. The impinging jets’
performance is determined through experimental testing using thermal imaging techniques and hot film
sensors with high response times. Results from comparing the heat transfer distributions of the non-swirling
jet to four swirling jet geometries have shown both enhanced and diminished performance. The changes in
the Nusselt number distributions are found to be highly dependant on the swirl generator geometries. The
fluctuating heat transfer results provided by a hot film sensor have illustrated the regions where the swirl
generators influence the heat transfer.
2.
INTRODUCTION
Impinging jets are not a new idea when it comes to surface cooling. They are used commonly for
electronic thermal management, for instance keeping chips and circuitry from getting too hot, and can also
be found in manufacturing processes, such as in the cooling of machined parts or of the tools themselves.
Much research and study has gone into the understanding and manipulation of the dissipation of heat which
occurs as a jet of fluid, usually at room temperature, comes in contact with a surface of higher temperature.
Changing the velocity of the fluid and the height of the jet nozzle above the impingement surface are two of
the most common approaches to changing the level of cooling. Other techniques include changing the fluid
used, adjusting the nozzle geometry, creating an array of jets or altering the flow structure of the fluid.
In a review by Jambunathan [1], the differences between nozzle geometries, such as long pipes,
contoured nozzles and orifice plates, are addressed for singular circular jets. This assessment also discusses
the attributes of an impinging jet before and after impingement and explores the significance of the potential
core of the fluid flow. These characteristics are common for all impinging jets; however they can change as
the flow is altered in some way, i.e. such as the potential core reducing in length due to the inclusion of swirl
generators.
The use of swirling impinging jets and their comparison to normal impinging jets has been studied in
the past and has been examined under different approaches using different nozzle geometries and different
swirl generation techniques. A swirling flow can be developed using a number of different techniques with
the following three being the most popular: a fixed insert with angular vanes placed within the section
containing the flow, an axial flow joined by a tangential flow, a rotating device conveying a swirling motion
to the flow. Bakirci and Bilen [2], for example, explored the idea of inserting swirl generators into a long
straight pipe. The generators were axially rotated so that the air jet impinged upon the surface at a desired
angle. Due to the large blockage along the centre of the pipe from the insert, the separated swirling flows
remained separate after exiting the nozzle, causing a significantly decreased heat transfer coefficient at the
stagnation point. Similar experiments were conducted by Hee Lee et al. [3] using swirl generating inserts in a
long straight pipe setup. However, like that of [2], the insert caused a blockage effect in the centre of the
pipe, such that separate impinging jets emerged from the nozzle exit and the heat transfer at the stagnation
point was lower than that of a standard impinging jet. The straight pipe and swirl insert approach was used
also by Huang and El-Genk [4] but in this instance a length equivalent to one diameter of the jet nozzle was
allocated after the insert which allowed the flow to develop and merge before the swirling flow left the
nozzle. The use of a space between the end of the swirl insert and the nozzle exit was also applied by
Alekseenko et al. [5] and the resulting flow was observed through two-dimensional particle image
velocimetry. While axial swirl generators are the most common, work has also gone into the understanding
of swirl generators with a radial geometry. Sheen et al. [6] investigated this idea and developed a correlation
to calculate the swirl number of a swirling flow generated radially.
Most research done in this area has found that the swirling flow explored has led to an overall reduction
in heat transfer compared to that of a normal impinging jet but these results include large drops in heat
transfer at the stagnation point due to blockages in the flow and to separation of flow streams. It has been
noticed at the same time that there are regions of high heat dissipation away from the stagnation point which
merit further investigation.
From this review of past studies, the present analysis sets out to explore the effect that changes in swirl
generator design have on the flow and their impact on the heat dissipated from a heated surface compared to
that dissipated by a normal impinging jet. Through analysing the heat transfer fluctuations caused by the jets
being tested, together with flow visualisation techniques, a greater understanding about the influence of
swirling impinging jets can be made.
3.
EXPERIMENTAL APPARATUS
This research explores the heat transfer behaviour of a swirling impinging air jet compared to that of a
normal impinging jet with the same external nozzle geometry. To develop a swirling flow component,
separate swirl generators were designed and manufactured using a rapid prototyper. These generators were
placed inside the nozzle enclosure and secured.
Position of
Swirl Insert
Figure 1. Jet Elevation and photograph showing Base Nozzle Geometry
and Position of Swirl Insert
Four swirl generators were created.
Figure 2. (From left to right) Swirl Generating Inserts A, B, C and D.
Inserts A and C are the same in size and shape aside from A having a ‘swirl core’ in the centre. The
‘swirl core’ is an addition to the swirl design which is placed in the neck of the nozzle. Its design is a ‘+’
cross-section twisted about its centre to have a 45° angle with the horizontal. Insert C in contrast, has a
converging element which guides the flow downwards through the nozzle in place of the ‘swirl core’. Inserts
B and D are scaled down versions of C and A respectively to test the effect of the generators fluid entry
height on the swirl development. In order to evaluate the level of enhancement due to the swirl induced
change in the flow, two separate testing rigs were designed, one for the measurement of local, time averaged
heat transfer using infrared thermography and one for time resolved measurements using hot film sensors.
Aluminium Frame
Jet Assembly
Impingement Surface
Thermal Imaging Camera
Figure 3. Experimental Rig for Time Averaged Heat Transfer Measurements
Perspex Mount
Perspex Slider
Stainless Steel Foil
Figure 4a. Impingement Surface
Figure 4b. Foil as seen by thermal imaging
camera during cooling process
For the time averaged data, the local heat transfer coefficients are calculated using the method of
infrared thermography. A thin stainless steel foil, with one side coated in a layer of matt black paint, is
ohmically heated. This approach creates a uniform wall flux boundary condition. The foil is mounted
horizontally, with the painted side facing downwards, with each end clamped between a pair of copper bars.
The bars are connected to a power supply and a spring mechanism which keeps the foil taut at all times
during testing. The impinging jet is positioned above the foil so that the flow, at room temperature, impacts
in the centre of the foil. A thermal imaging camera [FLIR SystemsTM ThermovisionTM A40] is placed
underneath the foil, facing the matt black coating, axisymmetric to the jet. The influence of the jet as it
impinges on the heated surface is determined using specific heat transfer corrections outlined in Section 4 to
take into account effects of lateral conduction, natural convection from the underside of the foil and
radiation. The thermal imaging camera records a set of images of the foil while the jet is active with the
power to the foil off, these are taken as adiabatic temperature images, and then with a specific amount of
power passing through the foil, these are taken as heated temperature images. The images display the
temperature around the foil, covering an area of 110mm x 150mm. The sets of temperature maps are
averaged for each of the testing parameters, i.e. height of jet over impingement surface, Reynolds number
and swirl scenario. The resulting maps are used in the calculations via Matlab to evaluate the heat transfer of
the system to compare with all the other scenarios tested by way of the Nusselt number.
The second experimental rig is used to determine the fluctuating heat flux and Nusselt number due to
the impinging jets, caused by mixing within the flow. The rig uses a hot film sensor flush mounted on a
copper plate which is heated uniformly by a heating mat placed underneath. This setup creates a nominally
uniform wall temperature boundary condition. The sensor works off a wheatstone bridge setup through a
constant temperature anemometer, CTA. The hot film sensor has a voltage passing through it which relates
to a certain temperature. As the jet cools the sensor, the voltage needed to increase the temperature back to it
original state is related to the heat flux at that point. A normal impinging jet has been tested using this
method in the past and these results validate the testing performed for this study. The swirling flow,
however, has not previously been tested in this way, so this system will show the effect the change in the
flow structure has on the fluctuations in heat transfer and should help to explain the heat flux results found
using the thermal imaging procedure.
Figure 5. Experimental Setup for Fluctuating Heat Transfer Measurements [7]
4.
THEORY
As discussed previously, the aim of this study is to evaluate the effect a swirling impinging jet has on
the convective heat transfer from a heated surface when compared to a normal impinging jet of the same
external geometry. To examine the change in heat transfer, the Nusselt number was calculated for each
scenario and the following equations were used in determining Nu. Using the images recorded by the thermal
imaging camera, the temperature of the foil is determined over a specific area. Two images are used,
representing the adiabatic and surface temperature, Tadiabatic and Tsurface respectively, to calculate the film
temperature, Tfilm, which is in turn used to determine the air properties to be used in the relevant equations.
The following equation, based on Newton’s law of cooling,
q"
conv,
upper
 h.(Tsurface  Tadiabatic)
(1)
is then used to estimate the value of the local heat transfer coefficient, h. Having calculated the heat transfer
coefficient, the Nusselt number, Nu, is determined from:
Nu D 
h.D
k
(2)
Each test is performed at a specified Reynolds number which is estimated using
Re D 
UD

(3)
where ρ is the density of air, μ is the viscosity of air, U is the mean jet velocity at the nozzle exit, D is the
nozzle diameter and A is the nozzle area. To measure heat losses from the surface to the surroundings the
effects from natural convection and radiation, as well as lateral conduction, are taken into account.
The following equation describes the energy balance of the system.
q"
conv,
 q"
upper
gen
q"
conv,
q"
lower
rad ,
q"
upper
rad ,
lower
 q"
lc
(4)
Natural convection heat loss from the underside of the foil is estimated from
q"
conv,
lower
m
C .Gr . Pr  .k .(T
T
)
surface
adiabatic

L
(5)
where Gr is the Grashof number, Pr is the Prandtl number, C and m are constants depending on the Rayleigh
number and boundary conditions of the system outlined by Holman [8] and L is the corresponding length
parameter, in this case calculated using the area of the foil, A, and the perimeter, P, such that:
L
A
P
(6)
The radiative heat loss from both the uncoated stainless steel upper side and the lower matt black paint
coated side can be estimated using the following expression with different values of ε for each side of the
foil:
4
4
q"
  . .(T
T
)
rad
surface
adiabatic
(7)
and the lateral conduction term, as discussed by Geers et al. [9], can be quantified as:
  2T
( x, y )  2T
( x, y ) 

surface
surface
q"  k .t .


lc
x 2
y 2




(8)
where t is the thickness of the foil, k is the thermal conductivity and T is the temperature.
These corrections allow the true heat flux due to the forced convection of the jet to be determined,
which then is used to determine the corresponding Nusselt number.
To understand the convective heat transfer mechanisms responsible for the changes in the Nusselt
number when the different swirl generators are placed within the jet, an analysis into the variation of the
surface heat transfer fluctuations was performed. This was carried out using a hot film sensor and a constant
temperature anemometer. To calculate the heat flux using this device, the voltage produced by it was first
calibrated against a known correlation which was outlined by Liu and Sullivan [10]:
Nu
o


Pr 0.4 Re 0.5  0.585
D
(9)
where Nuo is the Nusselt number at the stagnation point of the impinging jet. The equation can be converted
using the theory in equations 1 and 2 to express the heat flux at the stagnation point. This heat flux is then
combined with the rms value given by the sensor along with other factors, as outlined by Liu and Sullivan
[10] and O’Donovan and Murray [7], to finalise the fluctuating heat flux and, following from that, the
fluctuating Nusselt number.
The 95 percent confidence uncertainty of the instrumentation used for testing was estimated for the
worst case scenario. The values were calculated using known techniques outlined by Moffat [11] and are
shown in the following table.
Measurement
Re
q”
h
Nu
Nu’
Units
W/m2
W/m2K
-
Uncertainty %
3.3
0.86
4.1
4.45
30.05 [12]
5.
RESULTS & DISCUSSION
Experimental local and fluctuating heat transfer tests were performed for Reynolds numbers ranging
from 8000 to 20000 along with nozzle to surface heights ranging from 2.5mm to 50mm, or 0.5D to 10D.
Each jet scenario, i.e. the non-swirling jet and the four swirling jet setups, was tested with each of these
parameters. Due to the quantity of data produced, not all of the results are presented here, with a Reynolds
number of 14000 being the focus of investigation here.
5.1.
Heat Transfer Results
H/D=0.5
H/D=2
H/D=8
80
70
60
Nu
50
40
30
20
10
0
0
2
4
6
8
10
r/D
Figure 6. Non-Swirling Jet for Re = 14000 at all H/D
H/D=0.5
H/D=2
H/D=8
80
70
60
60
50
50
Nu
Nu
70
40
40
30
30
20
20
10
10
0
0
2
4
6
8
r/D
Figure 7. Nusselt Number Distribution for Swirling
Jet with Insert A for Re = 14000 at all H/D
10
H/D=0.5
H/D=2
H/D=8
80
0
0
2
4
6
8
10
r/D
Figure 8. Nusselt Number Distribution for Swirling
Jet with Insert B for Re = 14000 at all H/D
H/D=0.5
H/D=2
H/D=8
80
70
60
60
50
50
Nu
Nu
70
40
40
30
30
20
20
10
10
0
0
2
4
6
8
H/D=0.5
H/D=2
H/D=8
80
0
0
10
2
4
r/D
Figure 9. Nusselt Number Distribution for Swirling
with Insert D for Re = 14000 at all H/D
8
10
Figure 10. Nusselt Number Distribution for Swirling Jet
Jet with Insert C for Re = 14000 at all H/D
Numean vs H/D for each Jet Scenario for a Reynolds number of 14000
35
No Insert
Insert A
Insert B
30
Insert C
Insert D
25
No Insert
Insert A
Insert B
Insert C
Insert D
80
70
60
50
Nu
Numean
6
r/D
20
40
30
15
20
10
10
5
0
2
4
6
8
10
H/D
Figure 11. Mean Nusselt Number for all Jet Scenarios at
Re = 14000 averaged over a radial distance equivalent to
0
0
2
4
6
8
10
r/D
Figure 12. Nusselt Number Comparison for
each jet scenario at Re=14000 10D and H/D=2
The results presented in figures 6 to 10 represent the heat transfer due to the specified impinging jet,
radially averaged about the stagnation point of the jet, r/D=0. Figure 6 shows the resulting heat transfer from
the non-swirling impinging jet. The graph shows that the heat transfer peaks approximately 0.5D from the
stagnation point for low nozzle to surface heights and at the stagnation point for higher spacing. The
maximum stagnation point heat transfer occurs for a height of 6D while the maximum mean heat transfer,
illustrated by figure 11, is at a height of 4D. The experimental testing discovered the reason behind this; at a
height of 4D, the heat transfer distribution revealed a slight secondary peak at r/D=2 which increases the
mean heat transfer at this height, whereas at a height of 6D no secondary peak was noticed.
The first swirling jet tested, Insert A, produced substantially different results. In figure 7, the jet seems
to have its maximum heat transfer at the low nozzle to surface spacing and as this spacing is increased the
local heat transfer decreases at a steady rate; this was seen at all Reynolds numbers examined. This result is
understandable in the context of the swirl induced flow field. Thus, with the non-swirling jet, the direction of
the fluid is specifically downwards along the jet’s axis. A swirling jet encompasses a radial effect on the
fluid which causes it to move downwards along the jet axis while rotating about the axis radially outwards.
This results in a reduction in the heat transfer at high heights since the fluid has spread radially. Each of the
swirling jets tested show signs of this effect. As seen in figures 8, 9 and 10, for the swirl generating inserts B,
C and D respectively, the high nozzle to surface spacing produces the lowest heat transfer as it did with swirl
insert A. There is a change in the distribution for low heights within a 10mm radius of the stagnation point.
The maximum heat transfer occurs at approximately r/D=0.5, similar to that of insert A and the non-swirling
jet, but it is preceded by a large decrease at the stagnation point. This distribution was noticed at all the
Reynolds numbers tested. This result is demonstrated in figure 12, which plots the local Nusselt number for a
Reynolds number of 14000 and a nozzle to surface height equivalent to 2D for each of the jet scenarios. The
change in the heat transfer as the graph moves radially outwards from the stagnation point explains the
higher mean Nusselt number for H/D=2 seen in figure 11.
Figure 11 illustrates the resulting mean Nusselt number of each of the scenarios at a Reynolds number
of 14000 as the height increases. The mean Nusselt number was averaged over a circular area with a radius
equivalent to 10D with the stagnation point as the centre. This graph shows that the swirling jets have the
best impact on the heat transfer at low heights and this was seen at each of the Reynolds numbers
investigated.
5.2.
Fluctuating Heat Transfer Results
Examples of the fluctuating heat transfer, from the stagnation point radially outwards, are presented in
figures 13 to 15. These graphs represent the fluctuations in heat transfer on the surface of the plate due to the
impinging jet along with the mixing and turbulence which occurs in the flow. The three sets of graphs shown
illustrate the difference in the fluctuating behaviour as each jet impinges upon it. Three nozzle to surface
heights are shown, 0.5D, 2D and 8D, for a Reynolds number of 14000 for each jet scenario.
Fluctuating Nusselt Number Distribution for H/D=0.5
10
No Insert
Insert A
Insert B
Insert C
Insert D
8
Nu`
6
4
2
0
0
1
2
3
4
5
r/D
6
7
8
9
10
Figure 13. Fluctuating Nusselt Number for all Jet Scenarios at H/D = 0.5 and Re = 14000
Fluctuating Nusselt Number Distribution for H/D=2
10
No Insert
Insert A
Insert B
Insert C
Insert D
8
Nu`
6
4
2
0
0
1
2
3
4
5
r/D
6
7
8
9
Figure 14. Fluctuating Nusselt Number for all Jet Scenarios at H/D = 2 and Re = 14000
10
Fluctuating Nusselt Number Distribution for H/D=8
10
No Insert
Insert A
Insert B
Insert C
Insert D
8
Nu`
6
4
2
0
0
1
2
3
4
5
r/D
6
7
8
9
10
Figure 15. Fluctuating Nusselt Number for all Jet Scenarios at H/D = 8 and Re = 14000
Figure 13 shows the fluctuating heat transfer for each of the five jet flow situations examined with the
nozzle positioned 2.5mm above the heated surface and a Reynolds number set for 14000. At low nozzle to
surface heights and all Reynolds numbers, the non-swirling jet has an area of near-zero fluctuations around
the stagnation point. This area corresponds with the potential core of the jet, a region of uniform velocity
within the flow unaffected by the surrounding fluid. The potential core begins with a diameter equal to the
nozzle diameter but as it moves from the nozzle this diameter reduces to zero due to shearing and mixing
with the surrounding fluid. This evolution in potential core width can be inferred from figures 13 to 15. Thus
the region of near-zero fluctuations is reduced at a height of 2D and is gone at a height of 8D, demonstrating
that the flow is no longer part of the potential core but instead mixing is occurring. The same cannot be said
for the swirling jets, however. While at the high nozzle to surface heights the fluctuations are similar, figure
15, at closer proximities high fluctuations can be seen within the stagnation zone, signifying that no potential
core exists in the flow and that the swirling flow causes high mixing even at low heights. These high levels
of fluctuation mirror the heat transfer results; for example the high fluctuations 0.5D from the stagnation
point reflects the high heat transfer peaks at the same point, as seen in figures 6 to 10. When comparing the
local Nusselt number distribution in figure 12 with the fluctuating Nusselt number distribution in figure 14;
the high levels of fluctuations seen from 0.5<r/D<1 correspond with the high Nusselt number peaks in the
same region for the swirling impinging jets.
5.3.
Flow Visualisation
Flow visualisation was performed for the five different nozzle configurations explored, for each of the
nozzle to surface heights and Reynolds numbers discussed. Presented below is a sample of such images.
These images represent the flow from the jet for a Reynolds number of 14000 and heights equivalent to 2D
and 8D and a radial distance from the stagnation point equivalent to 7D, as seen in figures 16 and 21.
Figure 16. Flow Visualisation for Non-Swirling Jet
at H/D = 8 and Re = 14000
Figure 17. Flow Visualisation for Swirling Jet
with Insert A at H/D = 8 and Re = 14000
Figure 18. Flow Visualisation for Swirling Jet
with Insert B at H/D = 8 and Re = 14000
Figure 19. Flow Visualisation for Swirling Jet
with Insert C at H/D = 8 and Re = 14000
Figure 20. Flow Visualisation for Swirling Jet
with Insert D at H/D = 8 and Re = 14000
The flow visualisation technique illustrates the influence the swirl generating inserts have on the jet
structure. In figure 16, the non-swirling jet scenario demonstrates the classic flow structure of an impinging
jet including the initial uniform formation, giving way to axisymmetric vortex development due to shearing
with the surrounding fluid and the eventual high mixing zone as it impacts upon the surface. When the swirl
generators are placed in the flow a dramatic change is noticed. For inserts A and D, the inserts with a swirl
core, the uniform structure seen for the non-swirling jet is no longer present. The jet’s diameter also widens
appreciably sooner than that of the non-swirling jet, which was expected since the swirling flow has a radial
aspect which the non-swirling jet does not. Insert B and C have a different flow structure. It seems, from the
images taken, that the particles used to track the flow are concentrated around the outside of the jet flow.
This is not due to a blockage in the flow as the inserts do not have a central section which could cause such
an effect, see figure 2. From what is visualised it seems that the swirling effect causes the particles to move
outwards but more analysis must be performed to check this.
(a)
(b)
(c)
(d)
(e)
Figure 21 (a-e). Flow Visualisation for (a) Non Swirling Jet, (b) Swirling Jet with Insert A,
(c) Insert B, (d) Insert C and (e) Insert D at H/D=2 and Re = 14000
Figure 21 illustrates the flow development from each of the jet scenarios at a height of 2D and a
Reynolds number of 14000. These images support the trends noticed in the local and fluctuating Nusselt
number distributions, figure 12 and 14 respectively. The high peaks show on each of these graphs can be
related to these flow visualisations. The areas of high mixing and turbulence in the region of r/D=1 explain
these peaks. As for the low Nusselt numbers at the stagnation point; this can be explained by the area of
recirculation of warm fluid, specifically noticeable in figure 21(c).
6.
CONCLUSIONS
Time-averaged and fluctuating heat transfer measurements have been conducted for a range of
Reynolds numbers and heights to study the effect of generating a swirling motion in a steady impinging jet.
The results indicate that the swirling impinging jets have a level of enhancement of heat transfer over a
non-swirling impinging jet for low nozzle to surface heights. The enhancement predominantly occurs near
the stagnation point where the swirling jets cause a higher level of mixing and heat transfer fluctuations.
Using flow visualisation, preliminary recordings of each of the flows allow this recirculation to be observed.
Mean Nusselt numbers for each of the scenarios tested reveal that for low heights the swirling jets have
an enhancement factor over the non-swirling scenario. but as the jet is moved further from the heated
surface, the swirling jets begin to have the same influence as a non-swirling jet. If higher nozzle to surface
heights were to be studied, the non-swirling jet would have a higher level of heat transfer.
7.
ACKNOWLEDGMENTS
This research was supported by the Irish Research Council for Science, Engineering and Technology
“Embark Initiative”.
8.
NOMENCLATURE
A:
D:
Gr :
h:
Impingement surface area
Diameter of the jet nozzle
Grashof Number
Heat Transfer Coefficient
[m2]
[m]
[W/m2K]
k:
Nu :
Nu’:
P:
Pr :
q:
q”:
r:
Re :
t:
T:
U:
x, y :
Thermal conductivity
Nusselt Number
Fluctuating Nusselt Number
Perimeter of Foil
Prandtl Number
The power applied to the foil
Heat flux
Radial distance
Reynolds Number
Thickness of foil
Temperature
Velocity
Cartesian coordinates across foil
[W/mK]
[m]
[W]
[W/m2]
[m]
[m]
[K]
[m/s]
[m]
Greek symbols
ε:
σ:
μ:
ρ:
Material Emissivity
Stefan-Boltzmann constant
Viscosity
Density
[W/m2K4]
[kg/ms]
[kg/m3]
[13]
9.
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
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