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Enhanced Transient Heat Transfer From Arrays of JetsImpinging on a Moving PlateJihad Badra a , Assaad R. Masri a & Masud Behnia aa University of Sydney, Sydney, Australia

Accepted author version posted online: 06 Aug 2012.Version of record first published: 15 Oct2012.

To cite this article: Jihad Badra, Assaad R. Masri & Masud Behnia (2013): Enhanced Transient Heat Transfer From Arrays ofJets Impinging on a Moving Plate, Heat Transfer Engineering, 34:4, 361-371

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Heat Transfer Engineering, 34(4):361–371, 2013Copyright C©© Taylor and Francis Group, LLCISSN: 0145-7632 print / 1521-0537 onlineDOI: 10.1080/01457632.2013.717046

Enhanced Transient Heat TransferFrom Arrays of Jets Impingingon a Moving Plate

JIHAD BADRA, ASSAAD R. MASRI, and MASUD BEHNIAUniversity of Sydney, Sydney, Australia

This article addresses the numerical analysis of single and multiple circular jets impinging perpendicularly on a flat platefor heating and cooling purposes. Computational fluid dynamics (CFD) is used to evaluate heat transfer calculations fordifferent configurations and different flow boundary conditions. The commercial CFD package FLUENT is employed withvarious turbulence models. Results for a single jet are validated against experimental data. The SST k − ω turbulencemodel is compared with the elliptic V 2F model, and both were validated against experimental data. Results were obtainedfor a range of jet Reynolds numbers and jet-to-target distances. Optimization results for the single jet case are validatedagainst experimental data. The SST k − ω and V 2F turbulence models succeeded with a reasonable accuracy (within 20%error) in reproducing experimental results. The heat transfer rates from the use of multijet configurations are discussed inthe article. Transient heat transfer between multiple jets and a moving plate is more difficult to study due to the changingboundaries but is also very relevant in engineering applications. This article presents full CFD calculations of the transientheat transfer between a bank of circular jets and a moving plate. Design optimization has also been achieved for the single-and multiple-jet configurations.

INTRODUCTION

In the last two decades, there has been a lot of work doneon turbulent jets impinging on a flat plate. Impinging jets areused in many engineering applications to enhance heat transferin cooling or heating modes, with typical applications beingelectronics cooling, paper drying, metal annealing, and glassmanufacturing. They are also used to enhance and control masstransfer in vapor deposition of chemicals. For example, the flowfield generated by fan-powered vertical take-off and landingvehicles can be simulated and studied by considering impingingjet flows [1]. In electronic chip cooling, jet impingement is ofinterest due to high heat transfer rates generated close to theimpingement region. The method of cooling based on turbulentjet impingement is also widely used on the inner surface of vanesin modern gas turbines in order to prevent the metal temperaturefrom overheating [2]. Furthermore, jet impingement is also usedas an effective method of drying film and textile [3]. In most

We acknowledge partial support from Fitch Metals Engineering Pty., Ltd.,to carry out this project.

Address correspondence to Masud Behnia, School of Aerospace, Mechan-ical and Mechatronic Engineering, The University of Sydney, Building J07,Sydney, NSW, 2006, Australia. E-mail: m.behnia@usyd.edu.au

of these applications, array of jets rather than a single jet areused in a range of configurations and shapes to optimize the heator mass transfer rates. The optimization process is complicatedby the wide range of parameters that affect the heat or masstransfer rates, making it time-consuming and costly to achieveexperimentally.

The standard configuration of jets of various cross sectionsperpendicular to a plate has been analyzed extensively and isnow available in textbooks [4]. The simple case of a single jetimpinging on a flat plate has been widely studied both experi-mentally and numerically and hence forms a good platform fornumerical model validation. Despite its simplicity, this flow hassome complex heat transfer features that are not easy to predict,so it forms a good turbulence test case due to the impingingflow exhibiting severe streamline curvature and high pressureand velocity gradients around the stagnation region. The dis-tance of the jet exit plane from the plate is a key controllingparameter, and when this distance is larger than the potentialcore, measurements [5–13] have shown that the Nusselt numberdecreases monotonically with increasing radial distance awayfrom the jet axis. However, with shorter jet-to-plate distances, adouble peak in the Nusselt number develops, with the first oneforming close to the centerline of the jet and the second one at

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larger radial distances. This feature is not easy to reproduce andforms a good test for the robustness of the models used in thecalculations. Behnia et al. [6, 7] have reproduced such behav-ior numerically only with the elliptic V 2F turbulence model.Park and Sung [14] performed some numerical studies using theRANS turbulence models. The investigations conducted thus farhave only attempted steady simulations of the mean flow fieldand heat transfer. More recently, unsteady simulations of a slotjet impinging normally onto a flat surface have been performedby Chung et al. [15] and Cziesla et al. [16] using the large eddysimulation (LES) approach. The accuracy of these simulationshas been verified by comparing them with the experimentalstudies previously reported by Sparrow and Wong [17].

With arrays of jets, the situation is much more complex dueto the multitude of additional parameters that affect the fluiddynamics and heat transfer. Interactions between adjacent jetsalso become an issue, imposing more severe requirements onthe computations. Reliable measurements of heat transfer frommultiple impinging jets are not abundant and the data providedby Goldstein and Timmers [18] are useful, as they form a goodplatform for model validation. Huber and Viskanta [19] per-formed a study pertaining to an array of axis-symmetric jets andthey pointed out that the important difference between the flowcharacteristics of various arrangements of impinging jets arisesdue to the flow resistance offered by neighboring jets. Investiga-tions by Brevet et al. [2] and San and Lai [20] have consideredthe influence of jet-to-jet spacing, Reynolds number, and jetheight on the stagnation point Nusselt number. The numericalstudy of such a configuration has also been carried out by Ald-abbagh and Sezai [21]. The transient case of jets impinging on amoving target is even more complex, and reliable experimentaldata for such configurations are scarce. This article extends thesingle-jet heat transfer calculations to cover such cases.

The objective of this work is to analyze and optimize thelayout of arrays of jets impinging on a moving plate for a spe-cific engineering application, which includes annealing of metalsheets. Initially, we have demonstrated that accurate heat trans-fer calculations can be obtained from single and multiple jetsusing an optimum turbulence model. Such calculations are vali-dated against experimental data from Lee and Lee [10] for singlejet and Goldstein and Timmers [18] for multiple jets impingingon a stationary plate. They are compared with the numerical cal-culations of Behnia et al. [6] using the V 2F turbulence model,and the complex heat transfer features associated with both flowconfigurations are faithfully reproduced. The validation of theturbulence model includes the optimization of the jet-to-platedistance (H/D) for the single jet impinging on a stable plate,and comparison with available experimental and numerical datahas been performed. A good agreement, within 20% error, withexperimental and numerical data has been achieved and the opti-mum H/D value has been used throughout the three-dimensional(3D) optimization tests of the plate moving under arrays of jets.Subsequently, computations are performed for the more generaland widely used engineering application of arrays of round jetsimpinging on a moving flat plate. Three-dimensional simula-

tions for the plate moving under an array of round jets haveallowed the optimization of two design parameters: jet-to-platedistance (H/D) and spacings between jets (S/D).

NUMERICAL SIMULATION

The FLUENT-6.3.26 [22] commercial CFD package is usedhere to perform three-dimensional calculations of transient heattransfer from both single and multiple jets impinging on a plate.A necessary prerequisite for good calculations of heat transferis the accurate prediction of the flow and turbulent fields, partic-ularly in the boundary layer, across which heat is transferred. Tothis end, a second-order upwind discretization scheme is usedfor momentum, turbulent kinetic energy, dissipation rate, and en-ergy. Flow, turbulence, and energy equations have been solvedusing a nonuniform grid. The standard SIMPLE algorithm isadopted for the pressure-velocity coupling. All calculations pre-sented here for single- and multiple-jet cases are initiated twopipe diameters upstream of the jet exit plane. This, however, isnot sufficient to allow the development of the flow, and hencefully developed turbulent velocity profiles are imposed at theoutset.

Validating the Model for Single Impinging Jet

The experimental data available for single impinging jets areemployed here to validate calculations that use a range of turbu-lence models with the objective of selecting an optimum modelfor subsequent calculations. The results are also compared withthose of Behnia et al. [6] for similar flow geometry. The com-putational domain consists of a quarter of the entire pipe-plateassembly with two planes of symmetry as shown in Figure 1.The grid consists of 93,000 quadratic cells. The details of ge-ometry, physical properties and boundary conditions are shownin Table 1. The boundary conditions are representative of theexperimental conditions with respect to the temperature and ve-locity of the impinging jet as well as the temperature of theambient air and the plate.

Six different turbulence models which are available withinthe FLUENT package are tested here: (i) standard k − ε model,(ii) RNG k − ε model, (iii) realizable k − ε model, (iv) standard

Table 1 Geometrical, flow, and physical properties

D 25 mmH 50, 200, 300 mmRe 5,000–30,000Tj 20◦CPlate Aluminumρair 1.20147 kg/m3

kair 0.0242 W/m-Kµair 1.17894 × 10−5 kg/m-sSpecific heat ratio 1.4

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Figure 1 The numerical domain (H/D = 2) and the boundary conditions.

k − ω model, (v) shear stress transport (SST) k − ω model,and (vi) the Reynolds stress model (RSM). Results from thesecalculations are also compared with those of Behnia et al. [6]using the accurate V 2F turbulence model, which is based on afull second moment closure (SMC) model [23]. It introduces anew velocity variance scale, v2 (instead of k), for the evaluationof turbulence viscosity [6]. It is noted that the V 2F model is notpart of the standard suite of models in FLUENT. More detaileddescription of the governing equations and turbulence modelsis given in Behnia et al. [5].

Special care has been taken with the treatment of the bound-ary layer on the plate. The k − ε and RSM models have theoption to use enhanced wall treatment (EWT), which combinesa blended law-of-the-wall and a two-layer zonal model. EWT issuitable for low-Reynolds-number flows or flows with complexnear-wall phenomena. Using EWT as an option for the turbu-lence models mentioned earlier will modify those turbulencemodels for the inner layer. The use of EWT generally requiresa fine near-wall mesh capable of resolving the viscous sublayer(at least 10 cells within the “inner layer”). The mesh near thewall should be refined enough to match y+ ≈ 1. The k−ω fam-ily of models does not have the option of using enhanced walltreatment, but SST k − ω combines the original Wilcox model[24] for near the walls and the standard k − ε model away fromthe walls using a blending function. Grid-independent solutionsare obtained for all the flow configurations presented here. Testsfor grid independency have been performed and an error of lessthan 3% for the average Nusselt number along the plate has beenachieved for two consecutive grid refinements. The importantparameter in the impinging jet configurations is the first cellheight, which describes the wall y+ values along the top surfaceof the plate. When the jet flow impinges on the top surface ofthe plate severe pressure and velocity gradients appear in the

Figure 2 Nusselt number distribution for different first cell heights.

stagnation region and in the wall jet region. Several tests havebeen completed using different grid sizes and the Nusseltnumber distribution along the plate has been monitored to reachthe grid independent solution (Figure 2 shows the local Nusseltnumber distribution along the top plate surface for differentgrid sizes). As can be seen from Figure 2, the first cell heightof 0.01 mm results in a grid-independent solution. This value isused in all the calculations in this article as the first cell heightwith a 10% increase in grid size upon moving away from thestagnation point where the pressure and velocity gradients aresmaller.

Numerically, the method of calculating the local and averageNusselt number at the surface involves the local (h) and aver-age heat transfer coefficient (h), the jet diameter (D), and thetemperature difference between the jet and surface (�T). Thefollowing equation is used to obtain the surface heat transfercoefficient:

h = q

Tw − Tre f(1)

where q is the convective heat flux, Tw is the wall temperature,and Tre f is the reference temperature. Tref is a constant value thatshould be representative of the problem. There are two methodsfor definingTre f . It can be the local adiabatic wall temperature,as used by Gardon and Cobonque [25] and Goldstein et al. [26],or it can be the jet exit temperature. In experiments [10], the heat-ing and cooling effects of the jet due to thermal entrainment ofambient air were minimized by maintaining the impinging air jettemperature close to ambient temperature, Ta−Tj = ±0.1◦C. Inthe present study, the jet exit temperature was used to calculatethe local heat transfer coefficient instead of the local adiabaticwall temperature. Note that an isoflux thermal boundary con-dition was utilized to match the experimental conditions [10].The plate Nusselt number is then calculated using the followingequation:

Nu = hL

k(2)

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where h is the heat transfer coefficient, L is the reference length,which is set to be the jet exit diameter, and k is the thermalconductivity of the air exiting from the jet.

Jet impingement heat transfer has been known to be stronglydependent on the jet exit conditions (both velocity profile andturbulence intensity), and an extensive study on the effect ofthe jet exit conditions on the heat transfer features for a singlejet impinging on a flat plate can be found in Behnia et al. [5].Comparison of our numerical results is made with experimentalmeasurements for single impinging jet configuration by Lee andLee [10], who used a very long jet pipe (78D) to ensure a jet fullydeveloped turbulent velocity profile. To reproduce the velocityand turbulence profiles at the jet exit plane, an initial simulationof a long pipe (78D) was performed and the profile at the exitplane was employed for all jet simulations.

Details of the computational domain are shown in Table 1and Figure 1. The first case was performed for H/D = 6. TheReynolds number was chosen to be 25,000 following Lee andLee [10], who compared their results with data from Baughn andShimizu [9], who used Re = 23,750 with very good agreement,within 1 to 5% error, between the two sets of measurements(see Figure 8 in [10]). Figure 3 shows the Nusselt number dis-tribution using various turbulence models. The features of theexperimental and numerical simulations are similar with the lo-cal Nusselt number peaking at the stagnation region and thendecreasing monotonically downstream.

It is noticed that the experimental stagnation Nusselt numberfor this case is 160 and the predicted numerical values rangefrom 140 to 203. The best models to predict the stagnationNusselt number are the SST k − ω and the realizable k−ε mod-els. The numerical Nusselt number distribution differs from theexperimental data near the stagnation region regardless of theturbulence model used (0 < R/D < 0.5). The SST k − ω resultsare in good agreement with experiments, within 1 to 10% errormargin, for 0.5 < R/D < 2; however, the agreement deterioratessomewhat past R/D of 2.

Figure 3 Nusselt number distribution for the single jet impinging on a flatplate at H/D = 6 and Re = 25,000.

The numerical results are compared with the empirical corre-lations of Lee and Lee [10]. Their least-square estimations of theaverage Nusselt number were evaluated for R/D = 0 → 2 andR/D = 0 → 4 for the nozzle-to-plate spacing of 2 ≤ H/D ≤ 10and the jet Reynolds number ranging from 5,000 to 30,000 asfollows:

Nu R/D=0→2 = 0.203Re0.635

(H

D

)−0.0968

(3)

and

Nu R/D=0→4 = 0.083Re0.708

(H

D

)−0.144

(4)

Lee and Lee [10] reported that the two correlations (Eq.(3) and Eq. (4)) have a standard deviation of 2.4% and 2.7%,respectively. The difference between the correlation results andthe simulations is shown in Table 2. It is clear that the averageNusselt number is best determined by the SST k − ω model,with an error of just 14.8% have been achieved for the averageNusselt number for R/D between 0 and 4.

Calculations are performed for H/D = 2 and Re = 25,000.The Nusselt number distribution using different turbulence mod-els are plotted in Figure 4a against experimental data for H/D =2. The local Nusselt number peaks at two locations for H/D = 2.Reproducing these peaks is a challenge that is only achieved byone of the turbulence models, namely, the SST k−ω along withthe V 2F model used by Behnia et al. [6]. Some investigators[11] have attributed the secondary maximum Nusselt number toa transition from laminar to turbulent boundary layer in the walljet region. This is not supported by the measurements of Lytleand Webb [13], who note that there are relatively high levelsof turbulence even in the stagnation region. It is believed thata radial increase in the turbulent kinetic energy away from thestagnation point is responsible for this local increase of Nu (seeFigure 8 of [7]). The comparison is reasonable, and both tur-bulence models reproduced the second peak in agreement withthe experimental data. For 0 ≤ R/D ≤ 1.5, SST k − ω is betterthan the V 2F model. The opposite is true for R/D > 1.5. TheV 2F model is computationally expensive and it requires a largenumber of mesh points, whereas the SST k − ω is availablein FLUENT and requires less computational resources. Moretests have been performed using the SST k − ω model to checkthe effect of Reynolds number on the distribution of the localNusselt number and the behavior of the first and second peaks.

Table 2 Average Nusselt number using different turbulence models forR/D = 0 → 2 and 4 against correlation data

NuR/D=0→2 Error (%) NuR/D=0→4 Error (%)

Correlation 105.9 83.3Standard k − ε 94.8 10.5 57.7 30.7RNG k − ε 94.5 10.7 57.5 30.9Realizable k − ε 95.6 9.7 57.3 31.2Standard k − w 109.3 3.2 65 21.9SST k − w 110.9 4.7 70.9 14.8

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Figure 4 Local Nusselt number versus R/D (a) for H/D = 2 and Re = 25,000using different turbulence models and (b) for different Reynolds numbers.

Figure 4b shows the distribution of the Nusselt number for dif-ferent Reynolds numbers using the same turbulence model andthey are validated against the experimental data from Lee andLee [10].

Measurements show that at H/D = 2, the second peak inthe Nusselt number begins to form at Reynolds numbers wellabove 5,000, and this trend is faithfully reproduced by the SSTk − ω model, with the second peak becoming more distinct ata Reynolds number of 30,000. The location of the peak doesnot seem to change with increasing Reynolds number, and thisaspect is also loosely reproduced numerically. It is worth notinghere that at R/D between 0 and 2 and Reynolds number of 15,000the error in the SST k − ω predictions for the average Nusseltnumber is just 2.3%.

More validation tests for a single jet issuing on a stagnantflat plate have been performed, where the numerical data usingthe SST k − ω turbulence model have been compared with theavailable experimental and numerical data. The optimizationparameter selected here for the single-jet case is the jet-to-targetplate distance H/D with the objective of maximizing the heattransfer rate. Calculations are repeated here using the SST k−ω

turbulence model for a range of H/D, and for a Reynolds numberof 23,000 for comparison with the experimental data of Baughnand Shimizu [9].

Figure 5 Nusselt number variation with H/D for Re = 23,000 (a) stagnationNusselt number and (b) area-weighted average Nusselt number.

Figure 5a shows the stagnation Nusselt number plottedagainst H/D for the current calculation using the SST k − ω

model as well as for the V 2F and the k − ε model calculationsof Behnia et al. [6]. The experimental data set is also shownon Figure 5a. It is evident from the results published by Behniaet al. [6] that the k − ε model is overpredicting the Nu num-ber significantly. However, the V 2F results are in agreementwith experiments, yielding a maximum stagnation heat trans-fer rate at H/D = 6–7. This optimal value has already beenreported in numerous experimental studies [27, 28]. The simu-lations did not predict the second local maximum of the stag-nation Nusselt number at H/D = 1, and these results could notbe reproduced using either the SST k − ω or V 2F turbulencemodels.

Another parameter of practical interest is the area-weightedaverage Nusselt number. This is calculated here over an areaof a circle of radius R/D = 10 drawn by the rotation of a lineunder the jet axis and has been plotted against H/D; the resultsare shown in Figure 5b. The area-weighted average Nusseltnumber decreases with increasing H/D. Average Nu is at max-imum for H/D = 1 for the range of H/D examined here (1 <

H/D < 8). It is noted that the variation with H/D is not large(e.g., Nu changes from 60 to 50 with H/D changing from 1to 8).

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Figure 6 Nusselt number on surface along line through geometric centers ofthe three co-linear impinging jets with H/D = 6.

Array of Jets

Goldstein and Timmers [18] have performed an experimentalstudy for two kinds of arrays: three co-linear jets with jet-to-plate spacing of two and six diameters (H/D = 2 and 6) anda single jet surrounded hexagonally by a set of six jets. Thediameter of the jets is 10 mm, the spacing between the jets isfour diameters, and the Reynolds number is 40,000. The threeco-linear jets case with H/D = 6 has been taken as the referencefor comparing the numerical results.

The case of three co-linear jets investigated experimen-tally by Goldstein and Timmers [18] is computed here usinga three-dimensional mesh of 186,040 cells, which yields a grid-independent solution. The mesh consists of a quarter of thewhole domain with two symmetry planes being employed. Spe-cial care has been taken for near-wall treatment and the wall y+

values are less than 1. The computational time for a convergedsolution is 3 h and 15 min on a desktop with 2.40 GHz CPU and1 GB of RAM.

Figure 6 shows the local Nusselt numbers computed along aline parallel to the axis joining the jet centerlines. Also shownon Figure 6 are the measurements reported by Goldstein andTimmers [18] for the same configuration. The arrows on thex-axis indicate the location of the center of the jet. It is evi-dent that near the jet axis, the computed local Nusselt numbersare close to the measurements. However, away from the stag-nation point of each jet the difference between experimentaland numerical data increases, as noted for the single-jet case atH/D = 6. No local maximum Nusselt numbers (i.e., secondarypeaks) are observed between the jets because H/D is high. Thisis consistent with the experimental results of Goldstein andTimmers [18].

IMPINGING JETS ON A MOVING PLATE

The more complex but relevant problem occurs when theflow is transient due to a relative movement between the plateand the jet. The efficiency of the heat exchange becomes ofcritical importance, as this determines the quality of the productbeing processed and the size of the equipment (e.g., a furnace)that is necessary to perform such a task. Computational fluiddynamics (CFD) is now sufficiently advanced to be used herewith a significant degree of confidence. The grid generationfor a domain with a moving section is somewhat complicatedand requires the sliding mesh technique. Two grid interfaces areassigned for the two edges that are going to slide upon each other.The sliding mesh technique and its application to the problemconsidered here are illustrated schematically in Figure 7 fordifferent times during the calculations.

The jets are meshed similarly to the steady 3D case con-sidered earlier in this article. The domain is smoothly meshedusing a rectangular grid where the first cell height can be easilycontrolled. The plate is meshed separately and slides with re-spect to the jets. The mesh in the whole domain will not changeas the plate is sliding under the jet, but additional nodes areforming only as the two overlapping grid interfaces slide uponeach other. The sliding mesh method seems to be working bet-ter than the dynamic mesh for these specific geometries. Therelative velocity between the plate and its surroundings is equalto the plate velocity.

The initial, boundary, and geometrical conditions of the 3Ddomain shown in Figure 7 are listed in Table 3, with the plateproperties. The Reynolds number for the 3D moving plate caseis chosen to be 66,000. The temperature difference between thejet (400◦C) and plate (38◦C) is large, and in order to accountfor changes in thermophysical properties, as is customary, anaverage mean temperature has been used. Also, it should benoted that the jet Reynolds number is quite high and thereforethe viscous forces compared to buoyancy forces are dominant.The time step is 1 s, the domain length is 1.6 m, and twosymmetry planes are employed.

Table 3 Flow, boundary, initial conditions, and plate properties

D 50 mmH 200 mmS 300 mmU 45 m/sTj 400◦CTw 38◦Cρair 0.5244034 kg/m3

kair 0.0242 W/m-Kµair 1.7894 × 10−5 kg/m-sSpecific heat ratio 1.4Plate material Aluminumρplate 2719kg/m3

C pplate 871 J/kg-Kkplate 202.4 W/m-KPlate velocity 0.01 m/s

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Figure 7 Three-dimensional (3D) domain with its boundary conditions at two different time steps.

Due to the absence of experimental data, only calculationsare presented here for the temperature history at a point on theplate as it moves under the impinging jets. The monitor pointis selected to be the center point shown in Figure 7. Figure 8shows the temperature versus time at this monitor point, as wellas the rate of temperature change with time. As the monitorpoint moves under the first jet, the rate of heating increases, asexpected, and this rate gradually decreases as the plate movestoward the second and third impinging jet. It is noted that steepertemperature gradients are observed as the center point travels

Figure 8 Temperature and heating rate versus time for the center point shownin Figure 6.

under the first jet because of the larger temperature differencebetween the jet and plate. Smaller temperature gradients can beseen when the same point is crossing the axis of the second jet,due to the smaller temperature difference between the jet andplate. The plate is heating up and its temperature is approachingthat of the jet.

OPTIMIZATION

Optimization techniques are gradually becoming available tosolve multiparameter problems. Those techniques are packagedinto numerical tools such as ModeFRONTIER [29], which maybe coupled with CFD codes such as FLUENT to enable fulloptimization. Such packages are still evolving and are compu-tationally demanding. In this article, the simple approach usedinvolves the selection of a single parameter and the performanceof calculations to find an optimal solution.

Multiple impinging jet configurations are much more com-plicated than the single-jet geometry due to the interactionsbetween the jets. Here we have considered just two key con-trolling design variables, the height of the jet exit plane and thespacing between the jets both normalized by the jet exit diameter(i.e., H/D and S/D). These parameters can play a critical role onthe rate of heat transfer and therefore optimization is requiredfor design purposes. Other parameters, such as jet exit velocityand temperature, are dictated by the heat transfer requirements.However, little research has been found for this type of optimiza-tion, either numerically or experimentally. The only source of in-formation found to form a baseline to start multijet optimization

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was the work done by Martin [27], who derived some formulasbased on experimental work and obtained theoretical optimiza-tion for the already-mentioned two design variables. Martin [27]reported two optimum values for H/D and S/D with respect tothe average Nusselt number for a range of Reynolds numbers:

2,000 < Re < 30,000 (H/D)opt = 5.6

30,000 < Re < 120,000 (H/D)opt = 5

For the whole range of Reynolds number,

(S/D)opt = 5

Several tests have been performed for different geometries,such as the 3D single-jet case as well as two-jet cases but withS/D = 2, 5, 10, and 100. The cases with very large S/D (e.g.,S/D = 10 and 100) are representative of the single-jet case.The boundary conditions, initial conditions, and flow and platematerial properties are kept unchanged from the last case wherethe properties were shown in Table 3.

The stagnation Nusselt number is plotted against H/D for thefive different cases in Figure 9a. As expected, the stagnationNusselt number for the single-jet case and that for the two jetcases with S/D = 10 and 100 are very similar, where the trend isthe same as shown before but the numbers are different becauseof the different boundary conditions. For smaller S/D values

Figure 9 Nusselt number versus H/D for five different geometries: (a) stagna-tion Nusselt number and (b) average Nusselt number.

of 2 and 5 the stagnation Nusselt number versus H/D curvestarts to show a noticeable difference due to the interactionsbetween the two jets. The location of the maximum stagnationNusselt number is moving toward smaller H/D values as S/Ddecreases. The stagnation Nusselt number peaks between 6 and7 for the single jet (also cases with two jets with S/D = 10, andtwo jets with S/D = 100). It peaks between 5 and 6 for the twojets with S/D = 5 and between 4 and 5 for the cases with twojets with S/D = 2. The magnitude of the peak becomes smalleras S/D decreases. This is due to the interactions between thejets, and as they become close enough the flow fields interact.For S/D values higher than 10 the two-jet cases are the sameas the single-jet configuration where the jets are effectively notinteracting with each other. The average Nusselt numbers on top

Figure 10 Nusselt number distribution for two jet cases with (a) S/D = 10,(b) S/D = 5, and (c) S/D = 2.

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of the plate are calculated for each different case and are plottedagainst H/D in Figure 9b for the five different cases. The trendfor the single-jet case is nearly the same as that of the two jetcases with S/D = 10 and 100. The shape of the curve is the sameas for the single-jet optimization tests shown earlier, where theaverage Nusselt number is increasing as H/D decreases. Thiscan be observed from the Nusselt number distribution along a

Figure 11 Temperature history versus time for (a) the center point, (b) the leftpoint, and (c) the right point for different S/D.

line under the jets axis for three different cases (two jets withS/D = 2, S/D = 5, and S/D = 10). Figure 10 shows the Nusseltnumber distribution along a line under the jets axis for the twojets with S/D = 2, 5, and 10 cases.

The symmetric profiles shown in Figure 10a for S/D = 10 in-dicate that the jets are not interacting with each other. However,for S/D = 5 (Figure 10b) the jets start to interact and the sym-metry mentioned starts to disappear. This is because the wallflows of the two jets are impinging upon each other and henceforming a new stagnation region with higher Nusselt numbers.This affects the stagnation and average distribution of Nusseltnumber versus H/D and this interaction is more obvious in thecase of S/D = 2 (Figure 10c); as a result, another Nusselt num-ber peak is formed right at the symmetry plane where the newstagnation region is. This peak and interaction between the jetswill affect the flow and heat transfer characteristics and hencethe optimization of H/D based on the distribution of stagnationand average Nusselt number versus H/D.

Further simulations are performed with a fixed H/D = 5 as perMartin [27] but with S/D between 1 and 8. In these calculationsthe plate is moving and the sliding mesh technique is used. Thedomain with three different points (center, left, and right) wasshown in Figure 7. The temperatures of the three different pointshave been monitored as the plate is moving under the jets foreach different case. The temperature history for each point isshown in Figure 11. The curves for different S/D values arebehaving in the same manner and sharing similar features butwith slightly different magnitude.

CONCLUDING REMARKS

Numerical simulations of impinging jets flows are carriedout and validated against experimental data. Various turbulencemodels are tested. The SST k − ω model shows reasonableagreement and it is comparable in performance to the V 2Fmodel. The second peak in the Nusselt number at low jet-to-plate distances was well predicted by the SST k − ω model,which is subsequently used to evaluate the influence of jet-to-plate distance, the Reynolds number, and multijet cases. TheSST k − ω was shown to perform very well in the range of H/Dand Re tested here. Optimization for the single impinging jetconfiguration has been performed and the optimal value for H/Dbased on the stagnation Nusselt number is found to be between6 and 7. The multijet case has been carried out and evaluatedagainst experimental data as well. It showed good agreementwith the available data set. Optimization for the multiple jetsimpinging on a moving plate has also been performed withrespect to two parameters, namely, H/D and S/D.

NOMENCLATURE

Cp specific heat, J/m-KD nozzle diameter, m

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370 J. BADRA ET AL.

h local heat transfer coefficient, W/m2-Kh average heat transfer coefficient, W/m2-KH distance between nozzle exit and impinging plate, mH/D dimensionless jet-to plate-spacingk thermal conductivity of air, W/m-KL length, mNu local Nusselt number, dimensionlessNu average Nusselt number, dimensionlessq combined convective and radiative heat flux, w/m2

R radial distance from stagnation point, mR/D dimensionless radial distanceRe Reynolds number based on the exit diameter, = ρUD/µ,

dimensionlessS jets spacing, mt time, sT temperature, K or ◦Cτw wall shear stress, kg/m-s2

µτ friction velocity, =√τw/ρw, m/s

U mean velocity at jet exit, m/sy+ dimensionless parameter, = ρµτyp/µ

yp distance from point P to the wall, m

Greek Symbolsρ density of air, kg/m3

µ kinematic viscosity of air, kg/m-s�T temperature difference, K or ◦C

Subscriptsa ambientw wallj jetref reference3D three-dimensional

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Jihad Badra received his B.E. degree from Bala-mand University, Lebanon, in 2006 and his M.E.Sand M.E.R. degrees from Sydney University, Syd-ney, Australia, in 2007 and 2008, both in mechanicalengineering. He is currently a Ph.D. candidate in theDepartment of Aerospace, Mechanical and Mecha-tronic Engineering, Sydney University. His researchinterests include catalysts understanding and micro-combustion applications, both numerically and ex-perimentally.

Assaad R. Masri is a professor in the School ofAerospace, Mechanical and Mechatronic Engineer-ing at the University of Sydney. He received his Ph.D.in 1987 from the University of Sydney. His area ofexpertise includes turbulent combustion, air condi-tioning, and laser diagnostics in combustion. He iscurrently an associate dean (Research and ResearchTraining) in the Faculty of Engineering and Informa-tion Technologies.

Masud Behnia obtained his B.S., M.S., and Ph.D.from Purdue University. Prior to starting his academiccareer he had an extensive period in the power indus-try. He has worked in experimental and numericalfluid mechanics and heat transfer for over 30 years.Results of his research have been widely publishedin journals and conferences, and his career total pub-lications include more than 350 refereed papers. Heis currently the Dean of Graduate Studies and a pro-fessor at the University of Sydney.

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