1

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.

Fig.1 Profiles of heat transfer coefficient and time-averaged vector map with right-side jet excitation(66seconds),

and applied control system.

y/B-6 -4 -2 0 2 4 6

Nu

0

10

20

30

40

unexcitedright jet excitationall jets excitation

y/B

x/B

50mm/sy/B

-6 -4 -2 0 2 4 6

Nu

0

10

20

30

40

unexcitedright jet excitationall jets excitation

y/B

x/B

50mm/s

Heated plate

Actuators Excitation

Controller

Performance

Function

Wall Temperatures

Neural

NetworkData Storage PIV Heat Transfer

learning

Injection&

Suction

2

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.

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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.

Fig.2 The flow configuration and the measurement system.

DigitalImagingBoard

PC

x,Ux,Ux,Uy,Vy,Vy,V

Syringe

s/B=3.6

励起スリット拡大図

Syringe

s/B=3.6

Syringe

H/ =4B

s/B=3.6

Stepping Motor Driver

CCD Camera

SM SM SM SM

Amplifier

A/DConverter

Stepping MotorController

Trigger PulseGenerator

Clock PulseGenerator

PCDataStorageServer

Ether net

SM:Stepping Motor

Heat Impingement Surface

････

Nd-YAGDouble PulseLaser

Thermo-couples

4

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.

Fig.3 Inlet flow conditions with and without excitation at x/B=0.5;

(a) mean streamwise velocity; (b) streamwise turbulent intensity.

U/U

0

0.0

0.5

1.0

unexcitedSt=0.22 St=0.67 St=1.0

(a) streamwise mean velocity

y/B0 1 2 3 4

u'/U

0

0.0

0.2

0.4

0.6(b) streamwise turbulent intensity

5

y/B-4 -2 0 2 4

Nu

0

10

20

30

40

UnexcitedAll shear layer excitationOuter shear layer excitationInner shear layer excitationLeft jet excitationRight jet excitation

Fig.4 Heat transfer coefficient distributions

for various excitation patterns.

(a) (b) (c) (d) (e) (f)

Fig.5 Time-averaged velocity vector maps for various excitation patterns(66seconds).

(Arrows indicate the location of the excitation)

(e) Left jet excitation

0-2-4 20

2

4

y/B

50mm/s

4

(f) Right jet excitation

0-2-4 20

2

4

y/B

50mm/s

4

0-2-4 20

2

4

y/B

50mm/s

4

(a) Unexcited 0-2-4 20

2

4

y/B

50mm/s

4

(b) All shear layer excitation

0-2-4 20

2

4

y/B

50mm/s

4

(c) Outer shear layer excitation

0-2-4 20

2

4

y/B

50mm/s

4

(d) Inner shear layer excitation

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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.

∑=

=

−=11

1

2 /)(N

i

TARGETii NNuNuP (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

Fig.6 The schematic block diagram of the feedback control system.

Heat Transfer

Energy Eq.

Excitation

Controller

Wall

Temperatur

Target Wall

Temperature

Heat Transfer Data Base

Look Up Table

Flow Field

N.S. Eq.

Excitation amplitudes

Neural Network

Flow Field

Heat Transfer

Excitation

PIV data

Heat transfer coefficients

Heat transfer coefficients

Fig.7 Recurrent neural network for the forword model of the flow system including transitional states.

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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 dead- and 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.

Fig.8 Transitional variation of the flow field

corresponding to excitation switching

(left jet excitation to right jet excitation).

(a) t = 29.6 s

(b) t = 30.5 s

0-2-4 20

2

4

y/B

50mm/s

4

0-2-4 20

2

4

y/B

50mm/s

4

(c) t = 31.1 s 0-2-4 20

2

4

y/B

50mm/s

4

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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.

time [s]29 30 31 32

v [m

/s]

-10

-5

0

5

100.0 0.1 0.2 0.3 0.4

Fig.10 Transition of P.D.F. of v velocity along the wall. (The sampling area: x/B=0-2, y/B=2-4)

time [s]28 30 32 34 36 38 40

Wal

l Tem

pera

ture

30

31

32

33

34

35

36y/B=-1y/B=1

Fig.9 The time-series temperature distribution on excitation switching.

[-]

(a) Contour of P.D.F. in time-series

P.D.F [-]

0.0 0.1 0.2 0.3 0.4

v [m

m/s

]

-10

-5

0

5

10

0.0 0.1 0.2 0.3 0.4

t=28.9s t=31.5s

(b) P.D.F. before and after excitation switching

Excitation Timing

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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.

20

30

40

Nu

num

ber

20

30

40

y/B-4 -2 0 2 4

20

30

40

20

30

40

20

30

40

y/B-4 -2 0 2 4

20

30

40

Fig.11 Time-series distribution of Nu number with/without feedback control.

t=10s

t=20s

t=30s

No control Controlled

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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.