effect of orifice shape in synthetic jet based impingement cooling

Experimental Thermal and Fluid Science 34 (2010) 246–256

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Experimental Thermal and Fluid Science

journal homepage: www.elsevier .com/locate /et fs

Effect of orifice shape in synthetic jet based impingement cooling

Mangesh Chaudhari, Bhalchandra Puranik, Amit Agrawal *

Mechanical Engineering Department, Indian Institute of Technology Bombay, Mumbai 400 076, India

a r t i c l e i n f o

Article history:Received 30 April 2009Received in revised form 30 October 2009Accepted 2 November 2009

Keywords:Synthetic jetImpinging flowCavity orifice shapeImpingement heat transferElectronics cooling

0894-1777/$ - see front matter � 2009 Elsevier Inc. Adoi:10.1016/j.expthermflusci.2009.11.001

* Corresponding author. Tel.: +91 22 2576 7516; faE-mail address: [email protected] (A. Agraw

a b s t r a c t

The effect of shape of the orifice of a synthetic jet assembly on impingement cooling of a heated surface isexperimentally investigated in this study. The shapes considered are square, circular, and rectangular, ofdifferent aspect ratios (in the range of 1–20) and hydraulic diameters (3.8–8 mm). The average heattransfer coefficient as a function of the distance between the orifice and the heated surface is obtained.The Reynolds number (Re) is in the range of 950–4000 based on average velocity, while the normalizedaxial distance varies between 1 and 25. The heat transfer enhancement with a square orifice is found tobe larger than that with rectangular and circular shapes at larger axial distances z=d > 5, for the same setof boundary conditions. It is also found that rectangular orifice with aspect ratio between 3 and 5 givesbest performance at smaller axial distances. An attempt is made to explain this behavior on phenomeno-logical grounds. The effect of orifice shape on cooling with a synthetic jet is reported for the first time, andthe present results are expected to have significant practical implications.

� 2009 Elsevier Inc. All rights reserved.

1. Introduction

In the new generation electronic devices, due to high end pro-cessing and increase in frequency of operation the heat dissipationis expected to be high. For reliable operation of integrated circuitseffective thermal management system is essential. Generally heatsinks with different fin geometries and fan arrays are used for heatremoval, with air as a working fluid. Air has advantages of cost,availability and reliability for heat removal in electronic coolingsystems. However, fans require relatively large power to drivethe flow because of narrow passages provided by the heat sinks.Use of synthetic jet is a relatively new approach for electronicscooling. A synthetic jet is a zero-net-mass flux device commonlyformed by suction and ejection of fluid from a small cavity [1].Due to pulsating nature of the flow, the entrainment of ambientfluid into the jet is high as compared to that in a continuous jet,which helps in effective cooling [2].

In the past numerous studies are reported for a continuous tur-bulent jet impinging on a flat smooth surface. The experimentalstudy of heat and flow characteristics of an impinging steady jetis reported by several researchers [3–9]. The effect of shape of noz-zle on local heat transfer enhancement for different jet to platespacings and Reynolds numbers is reported in Gulati et al. [9]. Itis observed for rectangular jets that there is a distinct differencebetween the distribution of Nusselt numbers along the majorand minor axes. At larger axial distances, the shape of the nozzle

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(of same hydraulic diameter) has a negligible effect on the heattransfer characteristics.

Relatively few studies on impinging synthetic jets have howeverbeen undertaken. Garg et al. [10] designed a meso scale syntheticjet to provide a maximum velocity of 90 m/s issuing from a0.85 mm hydraulic diameter rectangular orifice. Microscopic infra-red thermal imaging technique was used for temperature mea-surements on the foil heater. The forced convective thermalresistance with the synthetic jet was found to be 82% less thanthe natural convective thermal resistance. Malingham and Glezer[11] discussed the design and thermal performance of syntheticair-jet based heat sink for high power dissipation electronics.Approximately 40% more heat dissipation occurred with the syn-thetic jet based heat sinks as compared to that with a steady flowfrom a ducted fan blowing air through the heat sink. The averageheat transfer coefficient in the channel flow between the finswas 2.5 times that of steady flow in the duct at the same Reynoldsnumber. Pavlova and Amitay [12] experimentally investigated theefficiency and mechanism of cooling a constant heat flux surface byimpinging synthetic jet; also, comparison with continuous jet waspresented. In their measurements, high frequency (1200 Hz) jetswere found to be more effective at smaller axial distances andthe low frequency (420 Hz) jets were found to be more effectiveat larger axial distances. At the same Reynolds number, the syn-thetic jet is found to be three times more effective in cooling thana continuous jet. Gillespie et al. [13] studied the effect of rectangu-lar synthetic jet on local convective heat transfer from a flat plate.Particle image velocimetry was used for velocity measurementsand thermocouples for temperature measurements. Substantial

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Nomenclature

English symbolsA area of heated copper block ðm2Þd hydraulic diameter (4A/P) (m)AR aspect ratio (l/w)f excitation frequency (Hz)h heat transfer coefficient ðW=m2 KÞH cavity depth (m)I current (A)k thermal conductivity (W/mK)l length of orifice (m)L length of orifice plate (m)Nu Nusselt number (hd/k)P perimeter (m)Pr Prandtl numberQ loss total heat loss (W)qconv net heat flux convected to the impinging jet ðW=m2Þqjoule imposed ohmic heat flux ðW=m2Þqloss total heat loss ðW=m2Þr radial distance (m)R half length of heated copper block (m)Re Reynolds number ðUod=mÞt thickness of orifice plate (m)

Ts surface temperature (�C)Tinf ambient temperature (�C)Uo average velocity during blowing part of the cycle (m/s)uðtÞ instantaneous velocity (m/s)V voltage (V)v velocity (m/s)w width of orifice (m)y co-ordinate normal to copper block (m)z axial distance (m)zmax axial distance corresponding to maximum Nusselt num-

ber (m)

Greek symbolsm kinematic viscosity of jet fluid (m2/s)s time period (s)

Subscriptsavg averagemax maximumrms root mean square

M. Chaudhari et al. / Experimental Thermal and Fluid Science 34 (2010) 246–256 247

enhancement in heat transfer is observed due to the strong mixingcharacteristics of synthetic jet. Zhang and Tan [14] experimentallystudied the flow and heat transfer characteristics of synthetic jetusing piezoelectric actuator with rectangular shape of orifice. Theflow measurements were done with the hot-wire anemometryand PIV techniques while an infrared camera was used for temper-ature measurements. It was noticed that the synthetic jet spreadrapidly along the minor axis direction of the orifice, while alongthe major axis the synthetic jet initially contracted and then spreadslowly. The cooling region was observed to be wider with a syn-thetic jet than with a continuous steady jet, as deduced from thelocal temperature distribution. Arik [15] studied the heat transferand acoustic aspects of small-scale synthetic jets. The changes inthe heat transfer rates were discussed with different parameterssuch as jet location, driving voltage, driving frequency, and heatpower. Heat transfer enhancement over specific heater sizes wasalso presented for the same jet. Arik [16] further studied the localand global heat transfer coefficients with high-frequency imping-ing synthetic jet on a flat surfaces. The experiments are conductedat a resonance frequency of 4500 Hz, with different voltage inputs.Heat transfer enhancements was found to be between 4 and 10times that of natural convection. In our earlier work [2], the heattransfer coefficient for an impinging circular synthetic jet wasmeasured, for a wide range of input parameters. It was found thatthe impinging jet can yield a heat transfer coefficient 10 times lar-ger than that for natural convection. Also it was noticed that theNusselt number varies as Reynolds number to the power of 1.25,under certain condition. Apart from the above impingement stud-ies, Chaudhari et al. [17] studied the heat transfer characteristics ofimpinging synthetic jet placed in a duct, for a certain electroniccooling (server/router) application. The heat transfer experimentsconducted include both direct impingement and cross-flow cre-ated using fan and another synthetic jet.

In the present work, the effect of shape of the orifice on heattransfer from an impinging synthetic jet has been studied. Theshape of the orifice can affect the value of the heat transfer coeffi-cient and the optimal distance (distance corresponding to hmax) be-tween the orifice and the heated surface; therefore, the results ofthis study can have significant practical implications. From the

literature survey it is noticed that such a study is perhaps beingundertaken for the first time.

The average heat transfer characteristics for different shapes oforifice, aspect ratio of orifice, hydraulic diameter of orifice, Rey-nolds number, and jet to plate spacing have been investigated inthis study. Some velocity measurements over the heated surfaceusing hot-wire anemometry have also been performed. The quali-tative trend for the heat transfer coefficient as a function of axialdistance is found to be nearly the same for square and circular ori-fices. However, a square orifice is found to perform better at largeraxial distance while a rectangular is found to be more effective atlower axial distances, when compared with their circular counter-parts. The heat transfer coefficient is found to reduce with an in-crease in the aspect ratio and a decrease in hydraulic diameter.Lastly, a correlation has been proposed to estimate the Nusseltnumber for different shapes of orifice having the same hydraulicdiameter.

2. Experimental setup and measurement procedure

Fig. 1 shows the schematic of heat transfer experimental setup.For the current study, an electromagnetically operated diaphragmof diameter 50 mm is used as the actuator for creating the syn-thetic jet. The input voltage to the actuator is fixed at 4 V (rms)throughout this work. The frequency of excitation is controlledby a signal generator and monitored with an oscilloscope (Tek-tronix, TDS 2022B). The cavity dimensions of the synthetic jetassembly are given in Table 1. Note that owing to the modular de-sign, most of the cavity parameters can be adjusted according tothe requirement [18]. In particular, the cover plate with differentorifice shapes can be easily changed. The experiments are con-ducted for different orifices, as given in Table 2. The synthetic jetassembly is attached to a two-dimensional traverse stand so thatthe distance between the jet orifice and the heated surface canbe controlled using a fine pitch traversing mechanism.

The heater block is constructed from a copper block of dimen-sions ð40� 40� 5Þmm3, and is heated by a nichrome foil heaterof the same size attached underneath [2]. The heater is supported

Copper PlateHeater

Bakellite

Glass-wool

Speaker with cavity

2-d Traverse Stand

Perpex

(a)

line 0o

Slot orifice

(b)

z

line 45o

w

line 90o

R

lL

t

H

Fig. 1. (a) Schematic of heat transfer experimental setup. (b) Dimensional parameters relevant for the study.

Table 1Parameters for study of heat transfer, see Fig. 1 for definition of the parameters.

Parameter Value Dimension

t 2.4 mmL 110 mmR 20 mmH 6.3 mm

Table 2Different configurations of orifices employed in the present study.

S.no.

w ðmmÞ � l ðmmÞ Hydraulic diameter(mm)

Aspectratio

Re at200 Hz

1 8� 8 8 1 39502 5:45� 15 7.99 2.75 40003 5� 20 8 4 33004 4:76� 25 7.99 5.25 30005 4:4� 40 7.94 9.09 23006 3� 40 5.58 13.33 19007 2� 40 3.8 20 1400

248 M. Chaudhari et al. / Experimental Thermal and Fluid Science 34 (2010) 246–256

by a bakelite plate to provide a proper contact between the heaterand copper block. The copper block is insulated by glass-wool (sizeof 180� 180� 40 mm3Þ to minimize the heat loss through thesides and bottom. The heater surface provides a constant heat flux,as the driving power input is constant. The surface temperature ismeasured with pre-calibrated K-type thermocouples, which aresoldered at the two sides of the copper block, 4 mm from the sidesurface (r-direction), thus providing a spatially averaged tempera-ture measurement over the exposed surface of the copper block. It

is noticed that the spatial variation in temperature is less than0.05%. An identical thermocouple located approximately 200 mmaway from the heated surface is used for ambient air temperaturemeasurement. The calibration of the thermocouple has been doneagainst a thermometer placed in a stirred hot water tank. The

(Ts - Tinf)

Qlo

ss

0 10 20 30 40 500

0.5

1

1.5

2

2.5

3

Heat lossCurve fit

Qloss = 0.0696 (Ts - Tinf) -0.0636

(W)

( o C)

Fig. 2. Heat loss curve.

Table 3Maximum uncertainty in measurements of different parameters.

Parameter Error in measurement

L 1 mmd; t 0.25 mmR; H 0.5 mmz 0.5 mmDT 0:5�CV 0.001 VI 0.01 AUo ±3%

havg 4%Nuavg 7.5%


power supplied to the heater is measured with a multi-meter andcontrolled by a rheostat.

The jet issuing from the orifice, impinges vertically onto the plateat a distance of z from the orifice (Fig. 1b). The working fluid is air. Theeffect of synthetic jet impingement cooling is investigated by mea-suring the surface and ambient temperatures for different syntheticjet operating frequencies (Reynolds numbers) for a constant powersupplied to the heater and the speaker. The variation of the averageNusselt number as a function of z=d for different Reynolds numbershas been studied. The temperature difference between the copperblock surface and the ambient is maintained above 15 �C in all cases,so that the error in measurement of temperature is reasonably small.All measurements are performed at steady state.

2.1. Data reduction

The Reynolds number is calculated by the procedure given bySmith and Glezer [1]

Re ¼ U0dm

ð1Þ

where d is the hydraulic diameter, m is the kinematic viscosity, andU0 is the average orifice velocity during the blowing part of the cy-cle. The average velocity is calculated as:

U0 ¼ L0f ð2Þ

where f is the excitation frequency (or inverse of time period s) andL0 is the stroke length. The stroke length is calculated over the ejec-tion part of the total cycle as

L0 ¼Z s=2

0uðtÞdt ð3Þ

where uðtÞ is the instantaneous velocity acquired using hot-wireanemometer. The Reynolds number varies between 950 and 4000in the present experiments based on the average velocity. The Rey-nolds number based on the peak velocity is in the range of 2500–12,000.

The procedure for calculation of Nu is as follows:

Nuavg ¼havgd

kð4Þ

where havg is calculated from

havg ¼qconv

ðTs � T inf Þð5Þ

The issue of recirculation of the fluid at lower axial distanceswhich raises the temperature of the air inside the cavity and the re-duces the temperature difference (between the surface tempera-ture and temperature of fluid inside the cavity) has been lookedat by Gillespie et al. [13], and in our other work [17]. However, herewe follow Pavlova and Amitay [12] and define the temperature dif-ference of the heated copper surface with respect to the ambientair. Due to an over estimate in temperature difference at small dis-tances, the heat transfer coefficient is underpredicted by about 20%in such cases. However, the present definition is relatively simpleto apply and therefore more relevant from practical viewpoint.Now,

qconv ¼ qjoule � qloss ð6Þ

and

qjoule ¼VIA

ð7Þ

The heat dissipated by all means other than that removed by airis termed as heat loss and is typically estimated to be 22% of theinput power. The heat loss depends on the surface temperature

of copper block and the atmospheric temperature; therefore itcan be expressed as a function of temperature differenceðTs � Tinf Þ. In order to obtain the relation between heat loss andtemperature difference ðTs � Tinf Þ, known electrical power wassupplied to the heater and the surface temperatures are recordedunder steady-state condition. The heat loss curve is shown inFig. 2. This experimental data was then used to obtain Eq. (8) forheat loss from the setup:

qloss ¼ Q loss=A 0:0696� ðTs � Tinf Þ � 0:0636 ð8Þ

The value of natural heat transfer is estimated to be about 14 W/m2 K. The radiation losses are found to be less than 0.5% for the pol-ished copper block used in the experiments; these losses are there-fore neglected in the calculations.

The uncertainty in the reported values of the average Nusseltnumber is 7.5%. The uncertainties in the other relevant parametersare given in Table 3. Note that the characteristic length scale is thehydraulic diameter in the calculation of both the Reynolds andNusselt numbers.

2.2. Validation of experimental setup

The validation of the experimental setup has been presented inour earlier work [2,18]. Nonetheless, these are recalled here, in or-der to enhance confidence in the results presented in the subse-quent sections. The synthetic jet assembly has beenbenchmarked in Chaudhari et al. [18]. There the centerline velocity

z/d

Nu av

g

2 4 6 8 1060

70

80

90

100

110

Present resultsLytle and Webb

Fig. 3. Validation of experimental setup with continuous jet at Re ¼ 12; 000.z (mm)

h(W

/m2 K

)

0 30 60 90 120 150 1800

25

50

75

100

125

150

175

200

55 Hz100 Hz200 Hz250 Hz

Fig. 4. Variation of average heat transfer coefficient with the axial distance fordifferent excitation frequencies with 8 mm square orifice hydraulic diameter.


decay of synthetic jet has been compared against experimental re-sults available in the literature and the similarity analysis of Agra-wal and Verma [19].

Since there are relatively few studies on impingement coolingwith synthetic jets, validation of the experimental setup has beendone by employing a continuous axisymmetric jet under an other-wise same set of conditions [2]. Lytle and Webb [20] presented lo-cal heat transfer data for different nozzle-plate spacing ðz=dÞ anddifferent Reynolds numbers for a continuous axisymmetric uncon-fined jet. The present experimental setup has been validated bycomparing for the average Nu obtained upon suitable integration.The comparison in Fig. 3 is for a Reynolds number of 12,000 atthree nozzle-plate spacing. The difference between the two setsof measurements is within ±3%, which is well within the uncer-tainty of the measurements. The repeatability of the results hasbeen systematically checked and is found to be within �1.7% as gi-ven in our earlier work [2]. Therefore, the entire setup can be con-sidered to have been validated and the results to be repeatable.

3. Measurement of heat transfer coefficient

This section presents the results of impingement of synthetic jeton a copper block, for different shapes and sizes of the synthetic jetorifice. The behavior of the heat transfer coefficient as a function ofaxial distance, for square, rectangular and slit orifices is presented.

3.1. Square orifice

As mentioned earlier, synthetic jet with a square orifice hasrarely been studied. The Reynolds number is expected to have asignificant impact on the Nusselt number in the forced convectionregime. Here, the Reynolds number is varied by changing the exci-tation frequency of the actuator. The dimensional results (h versusz) are first presented, followed by the non-dimensional results (Nuversus z=d). The dimensional results, presented only in this subsec-tion, give an idea of the value of the heat transfer coefficient thatcan be obtained with synthetic jets.

Fig. 4 shows the variation of the average heat transfer coeffi-cient ðhÞwith distance between the orifice plate and heated copperblock ðzÞ, for square orifice of 8 mm hydraulic diameter. The abovesets of experiments are conducted for four different excitation fre-quencies in the range of 55–250 Hz, while all other parameters areheld constant. It is observed that the average heat transfer coeffi-cient ðhÞ increases rapidly up to some axial distance

ðz ¼ 48—50 mmÞ and then decreases gradually with an increasein axial distance, for all frequencies. Also, it is observed that theaverage heat transfer coefficient increases with an increase in fre-quency up to 200 Hz, beyond which it reduces. The resonant fre-quency of the cavity is 200 Hz [18]; the average heat transfercoefficient is therefore maximum at the resonance frequency.The maximum value of average heat transfer coefficient is179 W=m2 K at 200 Hz, which is larger than most of the reportedvalues of heat transfer coefficient with synthetic jet.

Fig. 5 shows the variation of the average Nusselt number withthe normalized axial distance, for 8 mm square orifice for differentReynolds numbers. It is observed that the average Nusselt numbergets maximized at z=d ¼ 6 irrespective of the Reynolds number.Also, on the whole the average Nusselt number is higher at largerReynolds number for all z=d except the last few data points forRe ¼ 2000, which may be due to experimental error. The maximumvalue of the average Nusselt number is 55 for a Reynolds numberof 3900. While the qualitative trend of the average Nusselt numberwith axial distance and Reynolds number is similar to that for cir-cular orifice, a quantitative comparison of the two cases is pre-sented in Section 4.

3.2. Rectangular orifice of different aspect ratios

In this subsection, the results of the heat transfer coefficient fordifferent aspect ratios of orifice, having the same hydraulic diame-ter are presented. The length and width of the orifice are appropri-ately varied to achieve this (orifices 1–4 in Table 2). The objective isto see if certain rectangular orifices perform better than theirsquare counterparts.

Fig. 6 shows the variation of the average Nusselt number versusthe normalized axial distance, for different aspect ratio of the ori-fice. Note that the hydraulic diameter at 8 mm is identical for allorifices and the excitation frequency is maintained constant at200 Hz for these set of measurements. It is observed that the qual-itative behavior of the average Nusselt number (increase and thendecrease with the axial distance) is same for all aspect ratios. How-ever, there is a leftward (and slight downward) shift of the curveswith an increase in the aspect ratio. Therefore, at lower axial dis-tances ðz < zmaxÞ, the average Nusselt number is higher for large as-pect ratio. Similarly, at larger axial distances ðz > zmaxÞ, the average

z/d

Nu av

g

0 5 10 15 20 250

10

20

30

40

50

60Re = 1050Re = 2000Re = 3100Re = 3950

Fig. 5. Variation of average Nusselt number with the normalized axial distance fordifferent Reynolds numbers with 8 mm square orifice hydraulic diameter.

z/d

Nu av

g

0 5 10 15 20 250

10

20

30

40

50

60

70

AR = 1AR = 2.75AR = 4AR = 5.25

Fig. 6. Variation of average Nusselt number with the normalized axial distance fordifferent aspect ratios of the rectangular orifice. Note that the excitation frequencyhas been maintained constant at 200 Hz (Reynolds number range 3000–4000;Table 2).

z/d

Nu av

g

0 5 10 15 20 250

5

10

15

20

25

30

35AR = 1AR = 2.75AR = 4AR = 5.25

Fig. 7. Variation of average Nusselt number with the normalized axial distance fordifferent aspect ratios of the rectangular orifice. Note that the excitation frequencyhas been maintained constant at 55 Hz (the Reynolds number in the range of 950–1500).


Nusselt number is higher for aspect ratio of one and the curvesshift almost parallelly downward with an increase in aspect ratio.Note that both the maximum Nusselt number and the location cor-responding to the maximum Nusselt number decrease with an in-crease in aspect ratio ðzmax=d ¼ 6 for AR = 1 and zmax=d ¼ 3 forAR = 5.25). While the reduction in the maximum Nusselt numbercan be attributed to some extent to a reduction in the Reynoldsnumber (Table 2), the movement of the location of the maximais attributed to the aspect ratio. Note that, while an increase in Rey-nolds number shifts the entire Nusselt number curve upwards (i.e.for all z=d; see Fig. 5), it is observed that a change in AR moves thecurve towards left/right. Therefore, we believe that while the in-crease in Nusselt number is due to a corresponding increase inReynolds number, the change in the location of maximum Nusseltnumber is due to a change in AR.

To check for the repeatability of these characteristics with re-spect to aspect ratio, another set of experiments is conducted ata different excitation frequency (55 Hz). The Nusselt number at55 Hz is approximately half of that at 200 Hz excitation, and a sim-ilar observation applies (Fig. 7).

3.3. Slit of different hydraulic diameter

A large aspect ratio (>8, say) rectangular orifice can be regardedas a slit, and the flow can be regarded as two-dimensional in suchcases. Slit and circular orifice are the two most commonly used ori-fice shapes. This section presents the heat transfer results for dif-ferent hydraulic diameters of the slit. The measurements are forthe same length (=40 mm) but different widths of the slit orifice(orifices 5–7 in Table 2). The Nusselt number and the normalizedaxial distance are calculated using the hydraulic diameter of theorifice, as noted earlier.

There seems to be a distinct change in behavior with slit whencompared with square and rectangular orifices (Fig. 8). For hydrau-lic diameter of 8 mm slit, an almost monotonic decrease in theNusselt number with the normalized axial distance is observed.On the other hand, the average Nusselt number remains approxi-mately the same (up to z=d ¼ 15) for slit of hydraulic diameter of3.8 mm. It is observed that an increase in the hydraulic diameterincreases the Reynolds number (Table 2) and the average Nusseltnumber (Fig. 8), especially at smaller axial distances. The maxi-mum Nusselt number occurs close to the heated surface with theslit but the value is much smaller as compared to that in case ofthe square and rectangular orifices (Table 4).

4. Effect of shape of the orifice

In this section the effect of shape of orifice on the average Nus-selt number is presented. The shapes considered are square, rect-angular (AR = 4), slit and circle. The data for the circular orifice istaken from Chaudhari et al. [2]. Note that this comparison is donefor a hydraulic diameter of 8 mm, maintaining all other dimen-sional parameters constant.

z/d

Nu av

g

0 5 10 15 20 25 300

5

10

15

20

25

30

35

4.4 X 40 (d = 8)3 X 40 (d = 5.6)2 X 40 (d = 3.8)

Fig. 8. Variation of average Nusselt number with the normalized axial distance for aslit orifice of different hydraulic diameters. Note the excitation frequency is keptconstant at 200 Hz (Reynolds number range 1400–2300; Table 2).

Table 4Summary of results.

Shape Numax zmax=d

Square 55 6Rectangular (AR = 2.75) 52 4Rectangular (AR = 4) 52 4Rectangular (AR = 5.25) 52 4Slit 37 3Circle 43 6

.

.

. ..

.

..

.

.

.

z/d

Nu av

g

0 5 10 15 20 25 300

10

20

30

40

50

60

70

8 mm Circular8 mm Square8 mm Rect (5*20)7.95 mm Slit (4.4*40)

.

Fig. 9. Variation of average Nusselt number with the normalized axial distance fordifferent shapes of orifice having same hydraulic diameter. Note the excitationfrequency is kept constant at 200 Hz (Reynolds number range 2300–3950; Table 2).


Fig. 9 presents the variation of the average Nusselt number ver-sus the normalized axial distance. At lower axial distances theaverage Nusselt number is higher for rectangular shape orifice ascompared to that for circular and square shapes. However, at largeraxial distances, the square orifice outperforms the other shapes.Also the circular and rectangular orifices give approximately thesame Nusselt number at larger axial distances but not at smallerones. The average Nusselt numbers are smallest with the slitorifice.

The maximum Nusselt numbers for the square, rectangular, slitand circular orifices are 56, 52, 34 and 43 respectively. The corre-sponding zmax=d values are 6, 6, 4 and 3 respectively. Based onthe above result, we recommend using a rectangular orifice (ofAR between 4 and 6) to obtain optimal performance, in applica-tions with limitation of space.

4.1. Velocity measurements

Some velocity measurements are also performed with rectan-gular and circular orifices, so as to obtain an idea of the radial var-iation of mean and rms velocity over the heated surface. Thesemeasurements lead to a better understanding of the behavior ofthe heat transfer coefficient for different configurations.

The radial velocities (both mean and fluctuations) are measuredwith a constant temperature hot-wire anemometry system (TSI,IFA-300). A tungsten–platinum coated single wire probe (Model1210-T1.5 with temperature coefficient of resistance of 0:0042=�C,diameter of wire = 3:8 lm, length of sensing element = 1.27 mm) isused for the measurements. The hot-wire probe is mounted on a

two-dimensional traversing stand. During calibration of the hot-wire probe, the reference velocity is measured with a pitot tubeconnected to a differential pressure transducer (Furness Control,FCO332, least count = 0.01 mm water, full range = 20 mm water).The measurement points are fitted with King’s law, with a maxi-mum uncertainty of 3%. The velocity measurements are donealong different radial positions in the jet, starting at a fixed dis-tance of 2.5 mm (y=d ¼ 0:3125, where y is the co-ordinate normalto the plate) from the copper block. The measurements are alongboth the minor and major axis, as well as along the diagonal, ofthe rectangular orifice from the center of the copper block. Thevelocity measurements with the hot-wire are at the atmospherictemperature (i.e., with power to heater below the copper blockswitched off).

Figs. 10 and 11 show the normalized mean velocity ðUmean=UexitÞalong the normalized radial distance, for rectangular orifice and cir-cular orifices, respectively. Note that the measurements are for sev-eral normalized axial distances between the jet and the block. InFig. 10a–c the mean velocity measurements are for minor axis, majoraxis, and along the diagonal of the rectangular orifice, respectively. Itis observed that the maximum value of normalized mean velocity isat z=d ¼ 1 for minor axis and diagonal, whereas it is at z=d ¼ 2 formajor axis Fig. 10b. Gillespie et al. [13] also noted difference in flowbehavior along major and minor axis for a rectangular orifice. Noticethat the rectangular orifice shows a single peak whereas two peaksare observed for the circular orifice. The two figures differ qualita-tively, especially for z=d < 4. Whereas the mean velocity increasesup to r=d ¼ 1:25 and then reduces with rectangular orifice forz=d ¼ 1 (Fig. 10a), the corresponding curve with circular orificeexhibits two peaks and is highly non-monotonic. However, at largeraxial distances, the velocity is only a weak function of radial positionfor both the cases.

Figs. 12 and 13 show the radial distribution of the normalizedrms velocity for rectangular orifice and circular orifice, respec-tively. The normalization has been done using the exit velocity atthe centerline of the orifice. It is noticed that the rms velocitiesare maximum at the lower axial distances but the variation isnon-monotonic for the measurements along different axis asshown in Fig. 12a–c. The rms velocity monotonically decreaseswith increase in the normalized axial distance for the circular

r/d

Um

ean

/Uex

it

0 0.5 1 1.5 2 2.5 30

0.25

0.5

0.75

1

1.25

1.5

z/d = 1z/d = 2z/d = 4z/d = 8

(a)

r/d

Um

ean

/Uex

it

0 0.5 1 1.5 2 2.5 30

0.25

0.5

0.75

1

1.25

1.5

z/d = 1z/d = 2z/d = 4z/d = 8

(b)

r/d

Um

ean

/Uex

it

0 0.5 1 1.5 2 2.5 30

0.25

0.5

0.75

1

1.25

1.5

z/d = 1z/d = 2z/d = 4z/d = 8

(c)

Fig. 10. Normalized mean velocity with normalized radial distance for rectangularð5� 20Þ orifice (Re = 3300) along the (a) minor axis, (b) major axis, and (c) diagonal.

r/d

Um

ean

/Uex

it

0 0.5 1 1.5 2 2.5 30

0.5

1

1.5z/d = 1z/d = 3z/d = 6z/d = 8z/d = 12

Fig. 11. Normalized mean velocity with normalized radial distance for 8 mmcircular orifice (Re = 3950).


orifice, as shown in Fig. 13. At lower axial distances (z=d 6 4) therms velocities are higher and at larger axial distances the rmsvelocities are nearly constant along the radial distance. Overall,the trends are similar to their corresponding mean velocities.

4.2. Correlation

Correlations for different cases are developed from the experi-mental data using multiple regression analysis. In our earlier work[2], a correlation for a circular orifice was proposed in terms ofRe; Pr; L=d; R=d, and z=d. This correlation was first used to esti-mate the value of the Nusselt number for square and rectangularorifices. It was noticed that the proposed correlation for circularorifice substantially underpredicts the value of the Nusselt num-ber. Hence, an attempt is made to develop a new correlation fordifferent shapes of the orifice.

Using the experimental data in this work, the following correla-tion is proposed for square and rectangular orifices:

Nuavg

Pr0:333 ¼ 0:494 ðReÞ0:912 Ld

� ��0:494 Rd

� ��0:498 zd

� ��0:559ð9Þ

The above correlation is valid for the following set of parameters:L=d ¼ 13:75; R=d ¼ 2:5, and Re ¼ 600—4000. Also, the above corre-lation is valid only in the region where Nu reduces with an increasein z=d (i.e z=d ¼ 4—25). As shown in Fig. 14, the estimated valuesfrom the present correlation fall within ±20% of the experimentaldata with approximately 85% of the data points lying within thisrange.

An attempt has also been made to give a single correlation forall shapes of orifice investigated and the following correlation isproposed:

Nuavg

Pr0:333 ¼ 0:014 ðReÞ0:841 Ld

� �1:514 Rd

� ��1:725 zd

� ��0:607: ð10Þ

The above correlation is based on 176 data points and validfor the following range of parameters: L=d ¼ 7:86—22; R=d ¼1:5—4; z=d J 3; Re ¼ 600—4180, and for circular, square, rectan-gular, and slit orifices. A comparison of predicted and measured

r/d

Urm

s/U

exit

0 0.5 1 1.5 2 2.5 30

0.25

0.5

0.75

1

z/d = 1z/d = 2z/d = 4z/d = 8

(a)

r/d

Urm

s/U

exit

0 0.5 1 1.5 2 2.5 30

0.25

0.5

0.75

(b)

r/d

Urm

s/U

exit

0 0.5 1 1.5 2 2.5 30

0.25

0.5

0.75

(c)

z/d = 1z/d = 2z/d = 4z/d = 8

z/d = 1z/d = 2z/d = 4z/d = 8

Fig. 12. Normalized rms velocity with normalized radial distance for rectangularð5� 20Þ orifice (Re = 3300) along the (a) minor axis, (b) major axis, and (c) diagonal.

r/d

Urm

s/U

exit

0 0.5 1 1.5 2 2.5 30

0.25

0.5

0.75

1z/d = 1z/d = 3z/d = 6z/d = 8z/d = 12

Fig. 13. Normalized rms velocity with normalized radial distance for 8 mm circularorifice (Re = 3950).

Nuexp

Nu c

0 10 20 30 40 50 60 700

10

20

30

40

50

60

70

45%+ 20%

- 20%

Fig. 14. Comparison of Nuexp versus Nuc for square and rectangular orifices.


Nusselt number is presented in Fig. 15. The predicted value for 90%of the data points fall within �20% of the experimentally deter-mined value.

5. Discussion

The behavior of the average Nusselt number with the normal-ized axial distance observed here is similar to that for a continuousimpinging jet – the heat transfer coefficient increases up to a cer-tain axial distance and then reduces. For circular (and square) ori-fice, at small axial distances ðz=d < 6Þ, recirculation of fluid occursdue to confinement, owing to the presence of the orifice plate. Thisis apparent from appearance of double peaks in the mean and rmsvelocities (Figs. 11 and 13) and supported by preliminary flow

Nuexp

Nu c

0 10 20 30 40 50 60 700

10

20

30

40

50

60

70

CircularSquareRect (5 X 20)Rect (5.4 X 15)Rect (4.75 X 25)Rect (4.4 X 40)+20%-20%

45o

Fig. 15. Nuexp versus Nuc for square, rectangular, and circular orifices.


visualization performed using the smoke-wire technique as shownin Fig. 16. However, a single peak is obtained with rectangular ori-fice (Figs. 10 and 12) indicating absence of recirculation even at thesmallest distance for which the data is available. With an increasein the axial distance, the amount and strength of the recirculationdecreases, due to decrease in confinement effect, leading to an in-crease in the heat transfer coefficient. However, at large axial dis-tances, the jet velocity reduces due to entrainment of still ambientair, which again reduces the heat transfer coefficient. Besides ab-sence of recirculation, another probable reason for the higher heattransfer coefficient with rectangular orifice at small distances isthat the Nusselt number contours retain the shape of the orificefrom which the flow emerges at lower axial distances [9]. There-fore, a larger surface area is covered by the flow with a rectangularorifice at smaller axial distances. The heat transfer coefficient in-creases with an increase in the exit velocity (or an increase inthe Reynolds number), as expected in the forced convection re-gime. Grinstein and DeVore [21] note that the entrainment ratefor the square orifice is significantly larger than those for circularorifice. Due to a large entrainment, square orifice attains a largermass flux at the same distance from the nozzle. The mass fluxhas a direct bearing on momentum and heat transport betweenjet and surrounding. This is a possible reason of square orifice syn-thetic jet outperforming its circular orifice counterpart as observedin Fig. 9.

Fig. 16. Flow visualization using

The above explanations are based on the average flow behavior,while the following discussion is with respect to near-field coher-ent structures in the flow. Grienstein and deVore [21], Hart et al.[22], among others, have studied the near-field characteristics ofrectangular free jets, and found them to be substantially differentthan their circular counterparts. Whereas curvature is constantfor circular vortex rings, difference in curvature exists betweenedge and corner of vortex ring exiting from a rectangular orifice.This leads to difference in the self-induced velocity and increaseddeformation of the vortex ring in the latter case. Grienstein and de-Vore [21] show that the corner region of an initially planar ringmoves ahead of the plane containing the ring and towards the jetaxis; the straight section remains behind and away from the axis,due to difference in the self-induced velocity. Hart [22] mentionedthat the entrainment rate from the straight side can become great-er than that from the corners beyond three times the orifice diam-eter. Assuming that the above process applies for a synthetic jetand in presence of a wall, a higher heat transfer coefficient for rect-angular orifice can be attributed to the enhanced amount ofentrainment. Furthermore, we expect the vortex ring from a rect-angular orifice to be less stable than that from a square orifice(some evidence of this is provided in Zhang and Tan [14]). Accord-ing to Zhang and Tan [14], for rectangular orifice, a pair of counter-rotating vortices is formed along the minor axis which dissipatesdownstream. Along the major axis, due to long length of the orificecompared to the vortex size, a narrow strip vortex is formed in-stead of a pair of vortices. The narrow strip vortex moves awayfrom the slot and breaks into a series of vortices. The number ofvortices increases with an increase in the length of the rectangularorifice. These vortices create a high turbulence level after imping-ing on the heated block surface which leads to higher extraction ofheat at lower axial distance. The heat transfer coefficient increasesdue to fluctuations which are created between the wall jet andambient air after impingement. The heat transfer coefficient there-fore increases with an increase in aspect ratio, as seen in Figs. 6 and7.

From the above results and discussion it is concluded that asynthetic jet with a rectangular orifice having a large Reynoldsnumber can be effectively used for cooling of hot surfaces at loweraxial distances. Also, with the availability of space in a device,square orifice can be used instead of rectangular for cooling withthe same set of boundary conditions.

6. Conclusion

The heat transfer experiments are conducted using synthetic jetwith square, rectangular and slit shapes of orifices. The variation ofaverage Nusselt number for different aspect ratios having the samehydraulic diameter is discussed in the present work. Also, the ef-

smoke at 200 Hz and z=d = 6.


fect of higher aspect ratio with different hydraulic diameters of theorifice on heat transfer has been discussed. Finally, the wall turbu-lence intensity measurements are presented.

It is noticed that the square and circular orifices behave qualita-tively similarly, while the behavior of the rectangular orifice is dif-ferent. The square orifice gives the maximum heat transfercoefficient for given set of boundary conditions at larger axial dis-tances. The rectangular orifice having small aspect ratio (1–5.25)and same hydraulic diameter performs better at the lower axialdistances for the given geometric and flow parameters. With an in-crease in aspect ratio the cooling performance decreases at largeraxial distances. The rate of decrease of heat transfer coefficientalong the axial distance is very small for a rectangular orifice withlarger aspect ratio and smaller hydraulic diameter. A rectangularorifice with larger hydraulic diameter and smaller aspect ratio isthe best option for space constrained systems as far as impinge-ment cooling of heated surface is concerned.

Acknowledgements

The first author is thankful to Vishwakarma Institute of Tech-nology, Pune for sponsoring him during the course of this work.This project is funded by the Department of Information Technol-ogy, New Delhi.

References

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effect of orifice shape in synthetic jet based impingement cooling

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