Flow Characterization by PIV Measurements for Feedback Control
of Heat Transfer in Dual Impinging Jets
by
Kazuyuki YAMAMOTO, Tomoaki KATAYAMA and Koichi HISHIDA
Department of System Design Engineering
Faculty of Science and Technology, Keio University
Hiyoshi 3-14-1, Kohoku-ku, Yokohama, Japan
E-mail : kazu@mh.sd.keio.ac.jp
ABSTRACT
The control of scalar transport associated with flow structures is desired in many thermal engineering applications. Heat
transfer control by impinging jets is important due to its extensive use in practice. Previous studies of such systems were
performed to control time-averaged quantities via active or passive techniques. An experimental study has been
performed to investigate the effect of excitation on the local heat transfer distributions in time- and space-domain from a
plate to parallel planar impinging dual jets. The excitation used in the current investigation, called synthetic excitation,
was achieved by manipulating the local shear layers through fine slits at the nozzle exit with various amplitude patterns.
The excitation configuration included, all shear layers excitation mode, single-side jet excitation mode, as well as inner
and outer shear layer excitation mode. The results showed synthetic excitation was effective for controlling the local
heat transfer, that is, the profiles of local heat transfer coefficients could be controlled by excitation in time-averaged
and space-domain. Feedback control of the local heat transfer with performance function was conducted so that the
control was possible within a time scale in the order of the time constant of flow structure alternation.
40
30
Nu
Data Storage learning
PIV
Heat Transfer
20
unexcited
right jet excitation
all jets excitation
10
Neural
Network
0
-6
-4
-2
y/B
0
2
4
6
50mm/s
Performance
Function
y/B
Heated plate
Wall
Temperatures
Injection
&
Suction
x/B
Actuators
Excitation
Controller
Fig.1 Profiles of heat transfer coefficient and time-averaged vector map with right-side jet excitation(66seconds),
and applied control system.
1
1. INTRODUCTION
Feedback control applied to flow systems has been developed and yielded effective achievements as reported by
Kang(2002), Cohen(2003) and Kim(2003). It would bring higher efficiency of thermal fluid devices due to high
controllability of scalar transport, such as temperature or concentration, strongly dominated by the turbulent flow. As for
heat transfer in the impinging jets, control of the wall temperature in both space- and time-domain is required for
demand of more accurate processing of materials in industry. Many studies have been accomplished on heat transfer
from surface impinging jets as a means of enhancing transfer coefficients as reported in Martin(1977), Viskanta(1993),
Webb and Ma(1995). Therefore, time-averaged characteristics of heat transfer in space-domain has been well controlled
by existing control procedure such as constant excitation input (Lee, 2000) or altering the shape of the nozzle (Gau,
1997). And also for a more broad range of heat transfer control, an array of jets might have a large potential compared
with single jets, because an array of jets could be extended by a larger number of operation variables, which is directly
attributed to the extension of the controllable range of the flow.
We introduce dual impinging jets and the shear layer excitation as a means to control the heat transfer. The flow
configuration and the control system are schematically shown in Fig.1. A water jet issuing from dual rectangular nozzles
arranged in parallel impinges onto a heated surface. The objective of the current study is to develop a feedback control
system for control of the heat transfer distribution of dual planar impinging jets. To realize this system, detail
information, such as, heat transfer characteristics varied by the excitation mode and the relation between these and the
flow structures were obtained. Thus the current study hopes to clarify the characteristics of heat transfer and fluid flow,
and to combine these relations into a neural network for a controller by means of simultaneous measurements with PIV
for velocity measurement and thermocouples for temperature measurement on the impinging wall.
2. EXPERIMENTAL CONFIGURATION and PROCEDURE
2.1 Experimental Apparatus and Conditions
The flow system employed in the present investigation is shown schematically in Fig.2. A water jet issuing from two
identical rectangular nozzles (width: B=10mm, aspect ratio 10:1) arranged in parallel (nozzle spacing: s=36mm)
impinges on a horizontal, electrically heated surface. The heated surface was a rectangular plate and was made of a 5mm
thick expanded polystyrene plate covered with five 140mm×29mm×20µm stainless steel foil heaters. The heaters
produced a constant heat flux of 10kW/m2. All strips were glued onto the plate, and electrically connected in series to
supply the direct current. 11 copper-constantan thermocouples, 100 µm in diameter, were embedded on the backside of
the heater at 10 mm steps starting from y/B=0. In the coordinate system given in Fig.2, the origin is located at the center
of the two nozzles, and the x-axis extends in the streamwise direction while the y-axis is normal to the jet axis and
parallel to the plate. Instantaneous and mean velocity components in the x-y-plane are defined as u, U and v, V,
respectively.
Excitation was achieved using injection and suction through slits along the nozzle exits, which were connected to
syringes by silicon tubes. The syringes were actuated using stepping motors controlled by a PC using independent
frequencies of triangular waves and a phase lag φ of each excitation. Four excitation patterns were studied, such as, all
shear layers excitation mode, single-side jet excitation mode, as well as inner and outer shear layer excitation mode.
The nozzle-to-plate distance was set at H/B=4 where jets impinged with their potential cores and at H/B=8 where the
potential core ends in front of the plate. The jet Reynolds number is ReB=U0B/ν, where U0 is an axial mean velocity at
nozzle exit, B is the nozzle width and ν is kinetic viscosity. Though the experiments were conducted for both Re=500
and 1000, the results presented here are limited to Re=500. The Strouhal numbers, defined as St=fexB/U0 with fex the
excitation frequency (fex=1, 3, 5Hz are corresponding to St=0.22, 0.67, 1.0 for Re=500). The excitation intensity Aex was
defined as the maximum velocity of injection from the slits, which is 40mm/s at maximum.
The local Nusselt number Nu to determine the local heat transfer coefficients was expressed as: Nu=hB/λ=qwB/λ(Tw-T0),
where the heated surface provides a uniform wall heat flux qw, and Tw and T0 were wall temperature and ambient fluids
temperature, respectively.
2
PC
Digital
Imaging
Board
Ether net
PC
Data
Storage
Server
Trigger Pulse
Generator
Clock Pulse
Generator
A/D
Converter
Stepping Motor
Controller
Stepping Motor Driver
Amplifier
････
Thermo-couples
SM SM SM SM
Heat Impingement Surface
Nd-YAG
Double Pulse
Laser
H/B =4
x,U
Syringe
s/B=3.6
y,V
CCD Camera
励起スリット
SM:Stepping Motor
拡大図
Fig.2 The flow configuration and the measurement system.
2.2 Velocity Measurements
Particle image velocimetry (PIV) was employed to obtain the velocity vectors in a planar section of the flow. The flow
field was illuminated by a 1mm thick laser sheet (Nd:YAG laser, New Wave Research, 30mJ) while the scattered light
of tracer particles(mean diameter: 10µm) were recorded via a CCD camera (Kodak ES1.0, 8bit, 1008×1018pixels). The
spatial resolution of images was 0.067 mm/pixel. A hierarchical interrogation method was applied for the correlation
calculation and the sub-pixel displacement was estimated by means of Gaussian peak of fitting. The sampling rate of the
velocity vectors was set at 15Hz and images were double exposed with a pulse interval 5ms. The statistical analysis was
based on 1000 samples of the velocity distributions (which is corresponding to the averaging time of 66seconds).
As illustrated in Fig.2, recording of the CCD camera frame, firing of the double pulse laser, acquisition of wall
temperature from thermo-couples by A/D converter and actuation of the stepping motor for the jet excitation are all
synchronized by a PC with a clock pulse generator board.
3
(a) streamwise mean velocity
unexcited
St=0.22
St=0.67
St=1.0
U/U0
1.0
0.5
0.0
(b) streamwise turbulent intensity
u'/U0
0.6
0.4
0.2
0.0
0
1
2
3
4
y/B
Fig.3 Inlet flow conditions with and without excitation at x/B=0.5;
(a) mean streamwise velocity; (b) streamwise turbulent intensity.
2.3 Inlet Flow Conditions
It was well known that the initial conditions such as velocity profiles and turbulent intensities of jets influence the heat
transfer characteristics. Figure 3 shows the inlet flow conditions of the right jet with and without excitation at x/B=0.5.
The mean velocity profiles have negative values outsides the nozzle and turbulent intensities reach nearly 40~50% in the
shear layers, because the vortices generated by the excitation cause enhancement of both the entrainment and the mixing
in the shear layers.
3. CHARACTERISTICS of HEAT TRANSFER and FLUIDS FLOW
Figure 4 presents the heat transfer distributions for various excitation patterns and figure 5 shows time-averaged velocity
vector maps. As to unexcited case, the heat transfer distribution reveals a “saddle shape”, i.e. high heat transfer rates at
two stagnation points (y/B≈±3) of the dual jets and low values in the area between the dual jets (|y/B|<1). This could be
confirmed by Fig.5(a) showing the time-averaged velocity vector map.
The other distributions of the heat transfer coefficient and the vector maps are for the cases with excitation. The mean
flow structure was considerably influenced by the excitation compared to a single jet configuration. The range of
variation of the heat transfer distribution due to excitation was larger for the case with H/B=4 than for the case with
H/B=8.
When all of the shear layers of the two jets were excited, heat transfer coefficients became higher on the whole, while
the distribution remained “saddle shaped”. In Fig.5(b), both double jets move straight towards the impinging plate,
according to the mixing enhancement in the area surrounded by the two jets (|y/B|<1), the so called “recirculation zone”.
Especially, here the entrainment into the jets is increasing.
4
Unexcited
All shear layer excitation
Outer shear layer excitation
Inner shear layer excitation
Left jet excitation
Right jet excitation
(a)
(b)
(c)
(d)
(e)
(f)
40
Nu
30
20
10
0
-4
-2
y/B 0
2
4
Fig.4 Heat transfer coefficient distributions
for various excitation patterns.
50mm/s
50mm/s
4
4
2
2
0 -4
-2
0
2
0 -4
y/B 4
(a) Unexcited
-2
0
2
(b) All shear layer excitation
50mm/s
50mm/s
4
4
2
2
0 -4
-2
0
2
0 -4
y/B 4
(c) Outer shear layer excitation
-2
0
2
50mm/s
50mm/s
4
2
2
-2
0
2
y/B 4
(d) Inner shear layer excitation
4
0 -4
y/B 4
0 -4
y/B 4
(e) Left jet excitation
-2
0
2
(f) Right jet excitation
Fig.5 Time-averaged velocity vector maps for various excitation patterns(66seconds).
(Arrows indicate the location of the excitation)
5
y/B 4
With outer shear layer excitation, the two jets approach each other close to the nozzle exit so that the heat transfer
becomes higher between the two jets. When inner shear layer excitation was conducted, the heat transfer rates ascended,
because the flow rate in the recirculation zone increased while the jets move away from each other. One-side jet
excitation corresponding to Fig.5(e) and (f) results in an asymmetric heat transfer distribution. The heat transfer on the
side of the excited jet, i.e.y<0 in the left jet excitation case, was locally enhanced. These one-sided excitations can
spatially manipulate the heat transfer rate thus they are useful control inputs to construct the control system.
4. CONTROL ALGORITHM and STRATEGY
4.1 Algorithm for Heat Transfer Control
In order to control the heat transfer distribution precisely, a model correlating the jet excitation and the heat transfer rate
would be required. However, an exact model cannot be obtained since the fluid motion has a strong non-linearity as
described by the Navier-Stokes Equations. Feedback control, which adjusts the excitation by sensing the instantaneous
conditions, such as the wall temperature or the velocity field in real time, is one of the possible solutions.
An expression between the jet excitation and the heat transfer rates is likely to be required as exact as possible in order
to design precise control systems so that we introduced a neural network, which can express a non-linear behaviors.
Figure 6 indicates the schematic block diagram of the conducted feedback control system. A performance function
defined as mean square error of the measured Nu numbers from the target values given by Eq.(1) was introduced to
evaluate the achievement of the control process.
P =
N = 11
∑
( Nu
i
− Nu
TARGET
i
(1)
)2 / N
i =1
The controller determines the excitation amplitude in terms of the value of the performance function to be as small as
possible. Thereby, a database to predict the relation between the excitation and the heat transfer rate is required before
Wall
Target Wall
Temperature
Excitation
Flow Field
Heat Transfer
Controller
N.S. Eq.
Energy Eq.
Look Up
Temperatur
Heat Transfer
Data Base
Table
Fig.6 The schematic block diagram of
the feedback control system.
Heat transfer coefficients
PIV data
Neural
Network
Excitation
Flow
Field
Heat
Transfer
Excitation
amplitudes
Fig.7 Recurrent neural network for the forword model of
the flow system including transitional states.
6
Heat
transfer
coefficients
the control execution. Different methods of constructing the database were considered, namely, (i)Look-up table,
(ii)Neural network trained for the relation between the excitation amplitude and the heat transfer rate, (iii)Neural
network trained for taking into account the velocity field information acquired by PIV. The look-up table was
considered as discrete value table while the neural network could create continuous values by approximate interpolation.
With a database constructed by the neural network, i.e. (ii) and (iii), the steepest descent method was also applied to
determine the excitation amplitude for the minimum of the performance function.
In this context, the neural network can learn steady state (static) relations. In order to achieve time-dependant (dynamic)
relations of the heat transfer distribution and the flow field, a recurrent neural network is better choice, as described in
Fig.7. Information of the heat transfer distribution and the flow field in the past state would be used as input of the
neural network so that the neural network would bring out the excitation amplitude coupled with the past state. The
number of necessary past samples depends on the order of the assumed system for the fluid flow motion as well as deadand delay-time. So as to investigate the time constant of the flow structure alternation as well as the heat transfer
variation, simultaneous measurements of both were performed in the next section.
50mm/s
4
2
0 -4
-2
0
2
(a) t = 29.6 s
y/B 4
50mm/s
4
2
0 -4
-2
0
2
(b) t = 30.5 s
y/B 4
50mm/s
4
2
0 -4
-2
0
2
y/B 4
(c) t = 31.1 s
Fig.8 Transitional variation of the flow field
corresponding to excitation switching
(left jet excitation to right jet excitation).
7
Excitation Timing
Wall Temperature
36
y/B=-1
y/B=1
35
34
33
32
31
30
28
30
32
34
time [s]
36
38
40
Fig.9 The time-series temperature
distribution on excitation switching.
0
[-]
-5
t=28.9s
5
v [mm/s]
0.0
0.1
0.2
0.3
0.4
5
v [m/s]
P.D.F [-]
10
10
t=31.5s
0
-5
-10
29
30
time [s]
31
32
-10
0.0
0.1
0.2
0.3
0.40.0 0.1 0.2
0.3
0.4
(b) P.D.F. before and after
excitation switching
Fig.10 Transition of P.D.F. of v velocity along the wall.
(The sampling area: x/B=0-2, y/B=2-4)
(a) Contour of P.D.F. in time-series
4.2 Time-Dependant Flow Characteristics
Figure 8 shows the temporal variation of the flow field resulting from an excitation alternation shifting from the left jet
excitation to the right jet excitation. The alternation of the excitation was started at t = 30s as indicated in Fig.9, which
also denotes the wall temperature at y/B=-1 and 1 in time-series. When the left jet was excited, more fluid was provided
to the left hand side of the impinging plate, hence it becomes cooler at y/B=-1 than at y/B=1. In the recirculation zone,
the flow along the wall moved rightward disturbing the impingement of the right jet. As alternation of the excitation
started, the above feature faded and the opposite feature appeared in Fig.8(b), (c).
Figure 10 depicts the time-variation of the P.D.F. of the v velocity component in the area which is close to y/B=1 of the
wall. Figure 10(b) are sections of the contour graph (a) before and after the excitation switching. It reveals that the trend
of the v component direction is changed from positive to negative, i.e. right to left. For the positive v component the
flow moves from the left jet along the heated wall. Thus the fluid is less effective to cool the wall at y/B=1.
The wall temperatures were changed taking 3 seconds while it took 0.5 seconds as for velocity field variation depicted
in Fig.10. The difference of the time constant of flow field and wall temperature is because there is a time delay to
refresh the velocity boundary layer and the thermal boundary layer. The thermal boundary layer thickness in this dual jet
configuration depends on the velocity boundary layer and the arrived fluid temperature especially in the recirculation
zone. At the stagnation point, such as |y/B|=3, the thermal boundary layer refreshes when the velocity boundary layer
refreshes, however, in the recirculation zone, such as |y/B|<2, the thermal boundary layer refreshment is delayed from
the velocity boundary layer refreshment. This indicates that the time constant of the wall temperature is different for the
relative location to the stagnation point.
8
No control
Controlled
Nu number
40
t=10s
40
30
30
20
20
40
t=20s
40
30
30
20
20
40
t=30s
40
30
30
20
20
-4
-2
0
y/B
2
4
-4
-2
0
y/B
2
4
Fig.11 Time-series distribution of Nu
number with/without feedback control.
4.3 Control Result of Local Heat Transfer
Figure 11 shows time-series of the Nu number distributions for the control case. The no control case with all shear layer
excitation is also shown for comparison. The target Nu number distribution was given uniformly as Nu=26.5. The
relations between the heat transfer distribution and the different excitation, i.e. all shear layer excitation, right and left jet
excitation and no excitation were prepared in the look-up table. The Nu numbers are calculated based on time-averaged
wall temperature over 10 seconds before the denoted time(Fig.11). Compared to the case without control, the mean
square error from the target Nu distribution was decreased from 6.3 to 2.0. It was confirmed that the control system
which consists of a performance function and a look-up table was operative for controlling the Nu number distribution
for the case of dual impinging jets.
While controlling, the mean square error is smaller than that of the uncontrolled case over the whole period, however it
was strongly oscillating. This is because the designated excitation amplitude is specified in the look-up table to be
discrete, i.e. no excitation or maximum excitation. The neural network could substitute for the look-up table in order to
suppress such oscillation.
5. CONCLUSION
An experimental study has been performed to investigate the effect of excitation on the local heat transfer distributions
in time- and space-domain from a plate to parallel planar impinging dual jets. The excitation method was based on the
manipulation of the local shear layers through fine slits at the nozzle exit with various amplitude patterns. The excitation
configuration included, all shear layers excitation mode, single-side jet excitation mode, as well as inner and outer shear
layer excitation mode. A practical control system was applied in accordance with a performance function and a neural
network, which was substituted by a look-up table. The feedback control system could manipulate the heat transfer
distribution compared to the all shear layer excitation mode. The results revealed that control was possible within a time
scale in the order of the time constant of the flow structure alternation.
9
ACKNOWLEDGEMENT
This work is supported in part by Grant in Aid for the 21st century center of excellence for “System Design: Paradigm
Shift from Intelligence to Life” from Ministry of education, Culture, Sport, and Technology in Japan.
REFERENCES
Kang, S. and Choi, H. (2002). “Suboptimal feedback control of turbulent flow over a backward-facing step”, Journal of
Fluid Mechanics, 463, pp.201-227.
Cohen, K., Siegel, S., McLaughlin, T and Myatt, J. (2003). “Fuzzy Logic Control of a Circular Cylinder Vortex
Shedding Model”, AIAA2003-1290.
Gau.C, Sheu, W.Y. and Shen, C.H. (1997). “Impingement Cooling Flow and Heat Transfer under Acoustic Excitations”,
Journal of Heat Transfer, Transaction of the ASME, 119, pp.810-817.
Kang, S. and Choi, H. (2002). “Suboptimal feedback control of turbulent flow over a backward-facing step”, Journal of
Fluid Mechanics, 463, pp.201-227.
Kim, J., Park, J. and Choi, H. (2003). “Active Control of Free and Impinging Jets for Modification of Mixing”, Third
International Symposium on Turbulence and Shear Flow Phenomena, Sendai, Japan, pp525-530.
Lee, J. and Lee, S.J. (2000). “The effect of nozzle aspect ratio on stagnation region heat transfer characteristics of
elliptic impinging jet”, International Journal of Heat and Mass Transfer, 43, pp.555-575.
Martin, H. (1977). “Heat and Mass Transfer Between Impinging Gas Jets and Solid Surfaces”, Advanced Heat
Transfer,13, pp.1-60.
Viskanta, R. (1993). “Heat Transfer to Impinging Isothermal Gas and Flame Jets”, Experimental Thermal & Fluid
Science, 6, pp.111-134.
Webb, B.W. and Ma, C. -F. (1995). “Single-Phase Liquid Jet Impinging Heat Transfer”, Advanced Heat Transfer, 26,
pp.105-217.
10