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International Journal of Heat and Mass Transfer 49 (2006) 3045–3059

Heat transfer of impinging jet-array over convex-dimpled surface

Chang Shyy Woei a,*, Jan Yih Jena b, Chang Shuen Fei b

a Thermal Fluids Laboratory, National Kaohsiung Marine University, No. 142, Haijhuan Road, Nanzih District,

Kaohsiung City 81143, Taiwan, ROCb Department of Marine Engineering, National Kaohsiung Marine University, No. 142, Haijhuan Road, Nanzih District,

Kaohsiung City 81143, Taiwan, ROC

Received 31 August 2005; received in revised form 3 February 2006Available online 18 April 2006

Abstract

A detailed heat transfer measurement over a convex-dimpled surface of impinging jet-array with three eccentricities (E/H) between jet-centre and dimple-centre is performed. These surface dimples considerably modify heat transfers from smooth-walled scenarios due todifferent impinging topologies for jet array with modified inter-jet reactions. Heat transfer variations caused by adjusting jet Reynoldsnumber (Re) and separation distance (S/Dj) over the ranges of 5000 6 Re 6 15,000 and 0.5 6 S/Dj 6 11 with three eccentricities ofE/H = 0, 1/4 and 1/2 are examined. A selection of experimental data illustrates the isolated and interactive influences of Re, S/Dj

and E/H on local and spatially averaged heat transfers. In conformity with the experimentally revealed heat transfer physics, a regres-sion-type analysis is performed to generate a set of heat transfer correlations, which permit the evaluations of spatially averaged Nusseltnumbers over central jet region of dimpled impinging surface.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Impinging jet-array; Convex-dimpled impinging surface

1. Introduction

Jet impingement heat transfer provides high local heattransfer rate that serves a variety of applications rangingfrom cooling of gas turbine hot-components to rapid con-vective heating such as annealing of glass and heat treat-ment of metals. There have been numerous experimentaland theoretical studies investigating heat transfers ofimpinging jet and jet array [1–37]. There are fundamentaldifferences in the fluid mechanics between single and multi-ple impinging-jets due to the jet-to-jet interactions prior toand after their impingement on the surface. The factorsthose influence heat transfers of impinging jet-arraysinclude turbulence [2], entrainment [3], nozzle geometry[4–6], separation distance [1–6], jet incidence angle [7], sur-face condition of impinging plate [8–10], wall-jet inter-

0017-9310/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ijheatmasstransfer.2006.02.030

* Corresponding author. Tel.: +886 7 810 0888/5216; fax: +886 7 5721035.

E-mail address: [email protected] (S.W. Chang).

action [11–17], jet spacing [18] and external factors suchas the crossflow [19–23], spent flow condition [24,25],drainage [26,12] and jet pulsation [27]. The impacts of thesefactors on heat transfer are generally described as functionsof separation distance and jet Reynolds number for a setof geometrical specifications. A major disadvantage ofimpinging jet-array is that the spatial heat transfer varia-tions over impinging surface could be highly non-uniform.Therefore, the flow and geometrical parameters of a multi-ple-jet system have to be carefully selected in order to pro-vide the required heat transfer rates with acceptableuniformity over the impinging surface.

Lee and Vafai [28] developed a procedure to determinethe optimal separation distance and nozzle-to-nozzle spac-ing for an impinging jet-array using the previous experi-mental results [3,11,21,23,29]. The maximum convectivecapability of an impinging jet-array is significantly affectedby the manner of treating the spent flow [28]. The spentfluid in the wall-jet region is forced to flow laterally overthe impinging surface. The networks along which the radial

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Nomenclature

A, B coefficientsDj diameter of jet nozzle for baseline array (m)E eccentricity between jet-centre and dimple-

centre (m)kf thermal conductivity of fluid (W/m K)H jet-to-jet space (m)_M total mass flow rate issued from jet array

Nu local Nusselt number = qDj/kf(Tw � Tj)NuC area-averaged Nusselt number of central jet

regionq convective heat flux (W/m2)

Re Reynolds number ¼ 412p

_MDjl

S separation distance (m)Tj fluid temperature at exit of nozzle (�C)Tf film temperature = (Tw + Tj)/2 (�C)Tw wall temperature (�C)X, Y dimensionless location (x/Dj,y/Dj)

Greek symbols

l fluid dynamic viscosity (kg/ms)q fluid density (kg/m3)

3046 S.W. Chang et al. / International Journal of Heat and Mass Transfer 49 (2006) 3045–3059

spent fluid is convected generate the hexagonal and squarewebs on the impinging surface for the staggered and in-linejet arrays, respectively [14,15]. The development of suchradial network is a result of jet-to-jet interaction afterimpingement. With certain flow conditions, the secondaryheat/mass transfer maximum could develop in the interac-tion zone [13,14,18,24,30,31]. A ring of secondary stagna-tion-heat-transfer contour that surrounds the centralconfined jet could appear when jet Reynolds number andseparation distance are, respectively, large and small [14].The secondary stagnation heat transfer level decreases withthe increases of nozzle-to-nozzle spacing [13] and separa-tion distance [14]. This result typifies the influence ofboundary layer transition on heat transfer owing to theradial flow acceleration and deceleration.

When the impinging jet-array is confined, the exit streamof the spent fluid could generate the crossflow that deflectsor diffuses the jet momentum. In general, local heat trans-fers over the impinging surface are deteriorated by thecrossflow but could be enhanced when the separation dis-tance is very small [19,20,23,28]. The crossflow effect isminimized by locating the spent air exits through the open-ings in the impinging surface or in the nozzle plate[18,24,12]. The other measure to assist the transportationof radial spent fluid is to use the grooved orifice plate toeject the multiple jets. The considerable heat transferenhancement over the most confined central jet region ina jet array is attainable by ejecting jets from the groovedsurface [6]. This particular measure not only providesfavourable treatment of spent fluids but the deflected jetsconfined in the groove could also enrich the central jetmomentum via the enhanced entrainment at small separa-tion distance.

Most of the previous studies have being concerned witheither single-jet or jet array impinging on flat surface. Onlya few of recent studies concerns more complex geometriesof impinging surfaces. These impinging surfaces resemblethose of electronic component and pin-fin array [32,33],cylindrical food product [10] and rib-roughened surfaces[34–36]. For an axisymmetric jet impinging on a heatedpedestal [32], the jet-flow develops into a free jet after leav-

ing the nozzle and decelerates as it impinges on top of thepedestal. A very thin boundary layer approaches the sharpcorner of pedestal, where separation occurs. A highly tur-bulent region develops along the separated shear layer,then reattaches to the base plate. The recirculation zonethat forms at the side of pedestal under the separated shearlayer becomes the thermal barrier. Under the recirculationzone, heat transfers reach local minimum on the bottomcorner of pedestal that gradually increase along the baseplate. A local maximum base-plate heat transfer point ispositioned at the location slightly upstream of the reattach-ment point. When the single pedestal is extended to therepeated rectangular ribs [34], the wall-jet stream couldbe trapped into the cavity between neighbouring ribs thatreduces local heat transfer. At the spacing between neigh-bouring rectangular ribs close to the stagnation point, theair bobble that encloses the cavity prevents penetration ofimpinging jet into the cavity and the recirculation zone.This effect also impairs local heat transfers on and aroundthe stagnation point. Nevertheless, by replacing the rectan-gular ribs with triangular ribs that provides a widelyopened spacing between neighbouring ribs [35], the imping-ing or the wall jet is more readily to penetrate into the cav-ity and impinge on the wall. Impingement heat transfersalong the triangular ribbed surface are higher than thosecounterparts along the rectangular ribbed wall. With ajet-flow impinging on a circular cylinder, the flow acceler-ates beyond the stagnation point that follows the curvatureof cylinder up to the separation point, where the flow yieldsto a wall jet [10]. Below the separated shear layer, the flowis reversed that forms a wake, which creates an increase invelocity and heat transfer. For cooling or heating of a largearea, the elements of surface roughness such as the pedestaland the rectangular, triangular and circular protrusions arerepeated and the jet array configuration have to be used. Inthis study, the impinging surface has convex dimplesarranged as the in-lined array. These convex dimples couldaffect the jet-flow structures [10] with weakened jet-to-jetinterference and promote the turbulent mixing by introduc-ing the separation shear layers [10,32]. It is expected thatheat transfer enhancement with improved uniformity could

S.W. Chang et al. / International Journal of Heat and Mass Transfer 49 (2006) 3045–3059 3047

be achieved by impinging the jet array over convex dimpledtarget surface. None of the aforementioned works havestudied this heat transfer configuration.

The present study performs the detailed heat transfermeasurements of an impinging jet-array over the convex-dimpled surface. Three test conditions are performed tounravel the different heat transfer patterns caused by vary-ing the distance between jet-centre and dimple-centre. Thereference condition is referred to as the inline configura-tion. When the jet-centres are inline with the dimple-cen-tres, the jets impinge directly onto the apexes of convexdimples. The remaining two test series allow the jet arrayto be shifted horizontally with distances of 1/4 and 1/2jet-to-jet spacing. The shifting length is referred to as theeccentricity between the jet-centre and dimple-centre. Thedetailed distributions of local Nusselt number contoursand spatially averaged heat transfer data, evaluated from

Fig. 1. Experimen

the infrared thermal images of the impinging dimpled sur-faces, are presented over a range of separation distancesand Reynolds numbers for three test configurations. Anadditional series of tests using the smooth-walled imping-ing surface are performed to generate the heat transfer ref-erences for comparing the heat transfer results acquiredfrom the dimpled surface. The impacts of convex dimplesand eccentricity on heat transfer are subsequently analyzedto assist the derivation of empirical heat transfercorrelations.

2. Experimental details

2.1. Apparatus

The experimental apparatus is shown in Fig. 1. Prior toentering the 200 mm long, 15 mm wide square-sectioned

tal apparatus.


flow-calming-tube (1), the air fed form the IWATA SC175C screw-type compressor unit was dehumidified andcooled to the ambient temperature through a refrigeratingunit that was integrated with the compressor. The dry andcooled airflow was then guided through a set of pressureregulator and filter with the flow rate to be metered andadjusted by a Tokyo Keiso TF-1120 mass flow meter anda needle valve, respectively. The adjusted and metered testfluid was then directed into the flow-settling chamber (2).The divergent flow settling chamber is of 120 mm long withthe orifice plate (3) fitted at the wide end. A 3 · 4 array ofjets was issued from the nozzles through the orifice plate.Twelve in-line jet-nozzles were equally spaced over the ori-fice plate with the jet diameter (Dj) of 3 mm. The jet-diam-eter was selected as the characteristic length for defining theReynolds and Nusselt numbers. As indicated in Fig. 1b, thethickness of orifice plate was two jet diameters. Each nozzlehad abrupt inlet and exit. The dimensionless jet-to-jet spac-ing, H/Dj, was 4. The complete jet array assembly was fixedand centred on a movable clamp (4). The vertical and hor-izontal movements of this clamp were adjusted by twoindependent thread mechanisms, which could be preciselyadjusted in order to position the jet array at the predefinedlocation. The separation distance between the outer-face oforifice plate and the flat-edge of convex-dimpled surface, asindicated in Fig. 1b, could be precisely controlled. An opti-cal micrometer (5) with the precision of 0.01 mm wasmounted on the test frame (6) to measure the separationdistance. The jets issued from the orifice plate impingedhorizontally against a very thin (0.1 mm) and 65 mm widestainless-steel target foil (7). Twelve equal-spaced convexdimples with the identical pitch as that of jet-nozzles wereforged from a continuous thin stainless steel foil. The pho-tograph of dimpled heating foil and the detailed geometri-cal specifications for this convex-dimpled impingingsurface were depicted in Fig. 1b. The check of the dimpledstainless foil indicated that the maximum non-uniformityin thickness was less than 1% so that the electrical resis-tance of the steel foil was approximately uniform. Thecoordinate system adopted by the present study was indi-cated on the impinging surface as shown in Fig. 1b thatthe origin was specified at the centre of dimple-array. Thisconvex dimpled stainless steel foil was stretched tightlybetween two copper bus bars (8) on the test facility. Asindicated in Fig. 1a, these two copper bus bars (8) wereattached with the vertical frames by threads which pro-vided the required stretching force to tighten the heatingfoil fixed on the copper bus bars (8). To perform the testsinvolving eccentricity between jet-centre and dimple-centre,the heating foil was horizontally shifted. For all the testconditions, the foil deflection under the maximum Rey-nolds number tested at the smallest separation distancewas less than 0.02 mm as measured by a precision calipers.The adjustable high current DC electrical power wasdirectly fed into the thin steel foil to generate the basicallyuniform heat flux surface. The temperatures of the heatingsurface under each test condition were imaged by a two-

dimensional NEC TH3101-MR infrared radiometer (9).For this thermal image processing system, it took 0.3 s tocomplete a full-field of 239 · 255 matrix scan. The backsurface of the heating foil was painted black in order tominimize the background reflection and to increase theemission.

2.2. Program and procedures

The experimental program involved two phases. Initiallythe effect of convex dimples on heat transfer was checkedout with a series of baseline tests without eccentricity overa range of separation distances and Reynolds numbers.The results acquired from this series of tests were comparedwith the data obtained from the smooth-walled impingingsurface. This was followed by a similar series of experi-ments for test conditions with eccentricities of 1/4 and1/2H. With the same ranges of flow and geometric param-eters, the heat transfer results from the two phases werecompared to reveal the heat transfer modifications causedby the different eccentricities between the jet-centre anddimple-centre. Finally, the empirical correlations for thespatially averaged heat transfer rates over the centralregion of dimpled surface for three sets of test scenarioswere derived as the strategic aim of the present study.

For each individual test, the apparatus was allowed toachieve steady state. A steady state was assured when sev-eral successive scans of wall temperatures over the imping-ing surface were less than 0.3 �C for each test at thepredefined flow rate and heating power. The percentageof 0.3 �C was in the range of 0.18–0.9% of the wall temper-atures tested. To account for the viscous heating effect overthe dimpled impinging surface, the reference fluid tempera-ture adopted to define the local Nusselt number was ini-tially selected as the adiabatic wall temperature. Over theentire tested conditions performed by the present study,the maximum differences between the adiabatic wall tem-perature and jet temperature were less than 0.1 �C whichwas 0.67% in percentage. Thus, the reference fluid temper-ature for defining local heat transfer rate was replaced byjet temperature. The jet temperature, Tj, was measuredusing a thermocouple penetrated into the plenum chamberas indicated in Fig. 1. The effect of variable properties wasembodied in the film temperature, Tf, defined asTf = (Tw + Tj)/2. All the fluid properties were evaluatedbased on the local film temperature. With tests at eachRe � S/Dj options, the heater power was fixed at 460 Wthat provided the supplied heat flux of 4641.78 W/m2.The electrical heating power was measured by the wattagemeter. The area used to define the total heat flux includedthe surface areas of convex dimples. This heating powerresulted in the wall-to-jet temperature differences in therange of 7–54 �C. Along with the measured heating powerand jet temperature, Tj, the local Nusselt number distribu-tions at the prescribed Reynolds number and separationdistance were evaluated. The local Nusselt number is eval-uated as


Nu ¼ qDj=kfðT w � T jÞ. ð1Þ

In Eq. (1), the convective heat flux, q, was calculated fromthe electrical dissipation measured over the entire heatingsurface with the heat loss to be subtracted. The character-istics of external heat loss at different heating levels weredetermined through a number of heat loss calibration runs.For each set of calibration runs, the flow was blocked offand the impinging surface was fitted with thermal insula-tion. Under such circumstance, the heat supplied to theheating foil was entirely lost into atmosphere from the backof the impinging surface and balanced with the amount ofheat loss at the corresponding steady-state temperature dis-tribution. A review of the temperature data collected fromthe heat-loss calibration test runs showed less than 2.95%of non-uniformity in the wall temperature distributions.Thus, by plotting the heat flux applied for each heat-losscalibration test against the corresponding steady wall-to-ambient temperature difference reveals the proportionalitybetween the heat loss flux and the prevailing wall-to-ambi-ent temperature difference. This proportionality was incor-porated into the data processing program to evaluate thelocal heat-loss flux. The maximum local heat loss fluxwas divided by the total heat flux supplied to define themaximum percentage of the heat loss. The maximum heatloss flux for the entire sets of data generated was 9.6% ofthe total heat flux supplied. It is worth noting that, whenthe jet array is issued from the orifice plate, the pressuredistribution over the impinging surface varies with the flowand geometric parameters such as Reynolds number, sepa-ration distance and the dimpled surface. As a result, therate of mass flow through each nozzle in the orifice plateis different and is functionally related with Re, S/Dj andgeometric features of the impinging surface [25]. Theadjustment of Reynolds number or the geometric parame-ters of the jet-array system provide a unique mass flux dis-tribution for the jets issued from the orifice plate. Thedifferent mass flow rate through each nozzle in an array is-sued from the orifice plate reflects the realistic flow phe-nomena when the jet arrays are issued from an orificeplate during the engineering application, which effect onheat-transfer was also an engineering focus for investiga-tion [24,25,12]. The Reynolds number is specified as4 _M=12pDjl, where _M is the total mass-flow-rate fed tothe 12 jets. The range of Reynolds numbers tested ensuredthe turbulent jets were examined because the jet becameturbulent with Re P 3000 [37]. The Reynolds numberstested were 5000, 7500, 10,000, 12,500 and 15,000. For eachtested Reynolds number, heat transfer coefficients with ele-ven separation distances of 0.5, 1.5, 2, 3, 4, 5, 6, 7, 8, 10 and11 Dj were measured.

The experimental repeatability of temperature measure-ment using NEC TH3101-MR infrared radiometer waspreviously carried out [6]. The maximum uncertainty oftemperature measurement was in the range of ±0.7 �Cfor the present system. This uncertainty of temperaturemeasurement was the major source to attribute the uncer-

tainties for the coolant’s thermal conductivity, fluid densityand viscosity. Following the policy of ASME on reportingthe uncertainties in experimental measurements and results[38], the maximum uncertainty associated with the localNusselt and Reynolds numbers were estimated to be9.7% and 6.5%, respectively.

3. Results and discussion

3.1. General results

To highlight the impact of surface dimples on heattransfer, a set of comparable results obtained from thesmooth-walled and convex-dimpled impinging surfacesare depicted in Fig. 2. Fig. 2a and b shows the distributionsof Nusselt number contour over smooth-walled and con-vex-dimpled surfaces with Re = 7500 and S/Dj = 4. Theboundaries of central-unit-cell and convex-dimple are spec-ified in Fig. 2. The spatially averaged Nusselt numbers overthe entire scanned area and the central-unit-cell are evalu-ated as Nu and NuC, respectively. The values of Nu and NuC

are, respectively, obtained by averaging the local Nusseltnumbers over the regions of entire scanned area and thecentral-unit-cell. The interval between two adjacent Nu

contours in Fig. 2a and b remains identical. As shown inFig. 2a, the Nusselt number contours over the smooth-walled surface distribute symmetrically about X and Y

axes. This observation reveals the free surface like jet-flowin the central jet region at separation distance of 4Dj. Thedistributing pattern of Nu contours depicted in Fig. 2a fol-lows the typical result of impinging jet-array with the max-imum heat transfer rate at each stagnation point. Nine heattransfer humps centred at the stagnation points feature theimpacts of impinging jets on heat transfer augmentation. Incontrast to these improving heat transfer humps, there areregions of concave Nu surfaces developed at the inter-jetregions as shown in Fig. 2a. The locally minimum Nusseltnumbers in these regions generally take place at the geo-metric centres of four surrounding jets that are the intersec-tions of flow paths along which the radial spent fluids areconvected. This type of heat transfer impediment reflectsthe influences of weakened wall-jet flow momentum andthickened boundary layers due to the collision of radialspreading flows, which is referred to as the jet-to-jet inter-ference. The moderation of jet-to-jet interferences and/orthe shrinkage of inter-jet regions could further elevate thevalues of Nu and NuC for an impinging jet-array system.A cross-examination of distributing patterns of Nu con-tours for the two scenarios depicted in Fig. 2a and b high-lights the shrinkage of inter-jet regions and the elevationsof stagnant and spatially averaged Nusselt numbers overthe convex-dimpled surface. The concentric Nu contours,centred at the dimple-centre that corresponds to the stag-nation point when the eccentricity is zero, develop overeach spherical surface-dimple. Nusselt number contoursover these convex dimples are much dense than those coun-terparts over the smooth-walled surface. This is attributed

Fig. 2. Typical heat transfer distributions over smooth-walled and convex-dimpled surfaces.


to the considerable elevation of stagnant Nusselt numberover each dimple. As indicated in Fig. 2a and b, the stag-nant Nusselt number over the convex-dimpled surfacereaches almost twofold stagnant Nu value over thesmooth-walled surface for this set of test condition. Theseconvex dimples also provide considerable heat-transferimpacts over the inter-jet regions. To further probe intothis respect, the X-wise Nusselt number distributions overthe smooth-walled and convex-dimpled surfaces along thehorizontal axis of Y = 2 are compared in Fig. 2c. The hor-izontal axis of Y = 2 traverses the inter-jet region. Asshown in Fig. 2c, the locally minimum heat transfer spotsdevelop at X = ±6 and ±2 that correspond to the intersec-tions of radial flow paths for spent fluids. The degree ofheat transfer reduction due to jet-to-jet interference in theinter-jet region over the dimpled surface is moderated fromthe smooth-walled scenario. The convex-dimpled surfacefor this particular set of test conditions is in favour of mod-erating jet-to-jet interference and reducing inter-jet regions.This impact on heat transfer for jet array could assist toimprove the uniformity of heat transfer distributions over

the impinging surface provided the combination of Re

and S/Dj is adequately selected. In this regard, furtherincrease of Reynolds number and/or decrease of separationdistance could alter the beneficial heat transfer impactsattributed from the surface dimples, which will beaddressed in the latter sections.

3.2. Re, S/Dj and E/H impacts on heat transfer

The Nu distributions over smooth-walled and convex-dimpled surfaces are both symmetrical about X and Y axesas demonstrated in Fig. 2. This symmetry allows one half ofeach Nu plot typified in Fig. 2 to be representative for theheat transfer scenario detected from any set of test condi-tions. In order to highlight the impacts of convex-dimpledsurface on heat transfer, local Nusselt numbers over dim-pled surface are normalized by Nu values detected fromthe smooth-walled surface with identical X and Y coordi-nates. The Nusselt number ratio in terms of Nu/Nusmooth-wall

quantifies the local heat transfer variation from the smooth-walled level. Fig. 3 compares the distributions of Nu and

Fig. 3. Effect of jet Reynolds number on heat transfer distributions over convex-dimpled surface with separation distance of 4Dj.


Nu/Nusmooth-wall over the dimpled surface for Reynoldsnumbers of 5000, 10,000, 12,500 and 15,000 at separationdistance of 4Dj without eccentricity. Each individualplot in Fig. 3 is constructed by the contours of Nu andNu/Nusmooth-wall over the respective regions of 0 6 X 6 6and �6 6 X 6 0. As shown in Fig. 3, the increase ofReynolds number systematically elevates the stagnationheat transfer and NuC without varying the distributingpattern of Nu contours. Local Nusselt numbers over thehump regions and the inter-jet regions, as shown in Fig. 3,are both elevated when Re increases. But the ratios ofNu/Nusmooth-wall over the dimpled surfaces are systemati-cally reduced as Re increases. This data trend unravels thatthe heat transfer augmentation generated by these surfacedimples is reduced as Re increases. Heat transfer augmenta-tion also appears to be spatially dependent. As indicated in

each plot of Fig. 3, the higher ratios of Nu/Nusmooth-wall

consistently develop over the hump regions in comparisonwith those in the inter-jet regions. For the test conditionsof S/Dj = 4 and Re 6 10,000, Fig. 3a and b shows that themost of Nu/Nusmooth-wall ratios are above than unity overthe dimpled surfaces. Further increase of Reynolds numberto 12,500, the ratios of Nu/Nusmooth-wall start to be lessthan unity from the inter-jet region, although the heat trans-fers are still higher than those of smooth-walled counter-parts in the hump regions (see Fig. 3c). At Reynoldsnumber of 15,000 as revealed in Fig. 3d, the areas appearingNu/Nusmooth-wall < 1 are expanded from the inter-jet regionstoward the hump regions. The growing rate of inter-jetimpacts on heat transfer impediments via increasing Re

for convex-dimpled surface appears to be faster than thatfor the smooth-walled surface. In this respect, the decrease

Fig. 4. Effect of separation distance on heat transfer distributions over convex-dimpled surface with jet Reynolds number of 10,000.


(increase) of separation distance could accelerate (deceler-ate) the impeding impacts of jet-to-jet interferences on localheat transfer over the convex-dimpled surface when eccen-tricity is zero. Fig. 4 is constructed in the manner to clarifythis particular heat transfer physic.

Fig. 4 compares the distributions of Nu and Nu/Nusmooth-wall over the convex-dimpled surface at separationdistances of 2, 4, 6 and 8 S/Dj for Reynolds number of10,000. In view of the Nu plots shown in Fig. 4a–d, the dis-tributing pattern of Nu contour remains unaltered but theNuC values are systematically reduced when S/Dj increases.The distributing contours of Nu/Nusmooth-wall shown inFig. 4 indicate a trend of increasing Nu/Nusmooth-wall ratiosas S/Dj increases. The plots of Nu/Nusmooth-wall contoursshown from Fig. 4a–d demonstrate the recovery ofNu/Nusmooth-wall ratios in the inter-jet regions from imped-iments at S/Dj = 1.5 to enhancements at S/Dj P 6. Therecovery of Nu/Nusmooth-wall ratios in the inter-jet regionfrom heat transfer impediment to enhancement as seen in

Fig. 4a–d indicates that the jet-to-jet interferences areweakened at a faster rate over the dimpled surface relativeto the smooth-walled counterpart as S/Dj increases. Thisphysic could lead to the extension of Re ranges withinwhich the NuC values over dimpled surface are higher thanthose over smooth-walled surface as S/Dj increases. Adetailed description in this respect will be discussed whenthe variations of NuC against Re with different eccentricitiesare examined.

To highlight the influences of eccentricity between jet-centre and dimple-centre on heat transfer, the distributionsof Nu contour at eccentricity ratios (E/H) of 0, 1/4 and 1/2are compared in Fig. 5 using three sets of test results withdifferent Re and S/Dj. The comparative results between theplots collected in the first and second columns of Fig. 5indicate the impacts of eccentricity ratio on heat transferwith different Re at a fixed S/Dj of 1.5. When the secondand third columns of Fig. 5 are compared, the differentNu profiles attributed from the E/H impacts are revealed

Fig. 5. Effect of eccentricity on heat transfer distribution over convex-dimpled surface with separation of 1.5 and 4 at jet Reynolds number of 10,000 and15,000.


with different S/Dj at a fixed Re. As a general impact ofdimples on Nu distribution, the oval-shaped Nu contours,which are stretched in the horizontal direction from theconcentric circular shapes over the smooth-walled surface,are observed for test conditions of E/H = 0, 1/4 and 1/2.With test conditions of E/H = 1/4 and 1/2, the locationson impinging surface corresponding to the jet-centre anddimple-centre, which are, respectively, indicated as + and· in Fig. 5, are not overlapping. As shown in Fig. 5, the dis-tributing patterns of Nu contour are considerably modifiedwhen eccentricity ratio varies. It is worth to note that thetopology remains symmetrical about each spot correspond-ing to jet-centre for test conditions of E/H = 0 and 1/2 butis asymmetrical for test conditions of E/H = 1/4. As aresult, the local Nu peaks that correspond to the stagnation

points are consistently developed at jet-centres for all thetest scenarios with E/H = 0 and 1/2. However, for the testresults with E/H = 1/4 as demonstrated in Fig. 5b, e and h,the stagnation heat transfers are not resolved at the jet-cen-tres but at the locations between the jet-centre and dimple-centre. This finding indicates that the jet issued from orificeplate is bend toward the dimple-centre by asymmetricalpressure field developed over the dimpled surface whenthe topology becomes asymmetrical about the jet-centrefor test conditions of E/H = 1/4. With E/H = 1/4, theconcave Nu profiles attributed from the jet-to-jet interfer-ences still occupy a considerable portion of impingingsurface but are off-centred from the counterparts obtainedwith E = 0. Instead of having the local minimum Nu spotdeveloped at the geometric centre between four surrounding

Fig. 6. Nusselt number distribution along the horizontal and verticalcentre-lines with Reynolds number = 15,000 and S/Dj = 2 for the E = 0,E = 1/4H and E = 1/2H.


stagnation points as shown in the test results of E/H = 0and 1/2, the minimum Nu spot in each region with concaveNu profiles is horizontally shifted in the right direction asindicated in Fig. 5b, e and h. The shift of minimum Nu spotindicates the unbalance of radial momentum from four sur-rounding stagnation points as the jointed consequences ofbent-jet and asymmetrical spherical topology. Neverthe-less, NuC values for each comparing pairs of E = 0 andE = 1/4 are in the close agreements. Further increase ofE/H ratio from 1/4 to 1/2, the topology surrounding thestagnation point becomes symmetrical that resolves intoanother form of symmetrical Nu profiles as demonstratedin Fig. 5c, f and i. Once again, each stagnation point coin-cides with the jet-centre at the middle position between twodimple-centres. The minimum Nu spot among each inter-jet region for the test results with E/H = 1/2 also developsat the geometric centre between four surrounding stagna-tion points. A comparison of the Nu plots between the testresults of E/H = 0 and 1/2 unravels that the areas occupiedby heat transfer humps are considerably extended for thescenarios with E/H = 1/2, which effect has led to the con-siderable increase of NuC from the result obtained withE/H = 0.

To examine E/H impacts on heat transfer with the com-parative manner, a set of selective Nu profiles along Y = 0axis and along three X axes corresponding to the verticalaxis that connects three jet-centres for four test scenariosare, respectively, compared in Fig. 6a and b. The locationsof jet-centres are marked in Fig. 6a so that the off-set ofstagnation point from the jet-centre for test conditions ofE/H = 1/4 is highlighted. As seen in Fig. 6a, the smooth-walled Nu profiles follow the typical results of impingingjet-array with Nu peak developed at the stagnation pointthat corresponds to the jet-centre. The locally minimumNu values develop at the locations of X = ±2 and ±6 forsmooth-walled case due to jet-to-jet interferences. In viewof the Nu profiles over dimpled surface with E/H = 0, thelocations of Nu peak and local Nu minimum are identicalwith the smooth-walled counterparts. The Nu values inthe inter-jet regions for smooth-walled and E/H = 0 condi-tions are in the similar levels; but the stagnation heat trans-fer over the dimpled surface with E/H = 0 is consistentlyhigher than the smooth-walled level as shown in Fig. 6a.Nevertheless, the increase of Re at fixed S/Dj or decreaseof S/Dj at fixed Re could moderate such heat transfer aug-mentation at the stagnation point over the dimpled surface.It is worth noting that, for the test conditions ofRe P 10,000 and S/Dj = 1.5, heat transfer rates in theinter-jet regions over dimpled surface with E/H = 0 and1/4 are reduced to be less than the smooth-walled levels.These typical heat transfer results for these particular testconditions (Re P 10,000 and S/Dj = 1.5) could lead theNuC values with E/H = 0 and 1/4 to the levels less thanthe smooth-walled counterparts. Further discussion on thisissue will be addressed when the NuC data is examined.

As described previously, the stagnation point is horizon-tally shifted about 0.5 jet-diameter toward the dimple-

centre due to the asymmetrical surface topology surround-ing the jet-centre for the test result of E/H = 1/4 as shown inFig. 6a. Also the stagnation heat transfer for E/H = 1/4 isfurther elevated from the smooth-walled and E/H = 0 con-ditions. There are heat transfer ripples developed in theinter-jet regions at the locations of ±2X for condition ofE/H = 1/4. These spots of ±2X correspond to the geometriccentres of each four surrounding dimples. With conditionsof E/H = 1/4, the radial momentums of spent flows fromeach four surrounding stagnation points are not equilib-rium due to the asymmetric topology for impinging jets.As a result, the additional flow momentum in radial direc-tion is generated to assist the convection of spent fluidsout of the inter-jet regions. Heat transfer ripples at the loca-tions of ±2X are therefore observed in Fig. 6a for test con-dition of E/H = 1/4. Further increase of E/H value from 1/4to 1/2 resolves into another symmetrical topology conditionfor impinging jet-array. However, the jet-centre locates atthe flat surface between convex dimples when E/H = 1/2.As shown in Fig. 6a for E/H = 1/2, the stagnation pointcoincides with the jet-centre and the Nu minimum developsbetween two adjacent jet-centres where corresponds to theapex of each dimple. Instead of having the heat transferripples developed at the inter-jet regions for E/H = 1/4


condition, the heat transfer ripples consistently develop atthe locations between jet-centre and dimple-centre for thetest conditions with E/H = 1/2. Fig. 6b compares Nu pro-files along Y axes that correspond to three vertical scan-ning-lines connecting three jet-centres for four testconditions. It is worth to mention that the stagnation heattransfers are not developed at the jet-centres for E/H =1/4 condition. As shown in Fig. 6b, all the Nu profiles alongthe vertical scanning-lines follow the heat transfer patternof impinging jet-array over smooth-walled surface irrespec-tive to the eccentricity brought in the horizontal direction.Referring the smooth-walled data to as the comparison ref-erence, heat transfers over convex-dimpled surface areimpeded in the inter-jet regions but augmented over thestagnation regions. In view of the overall Nu levels for all

Re = 10

0

0.5

1

1.5

2

-6 -4 -2 0 2 4 6

dimpled E = 0

dimpled E = 1/4 H

dimpled E = 1/2 H

0

0.5

1

1.5

2

-6 -4 -2 0 2 4 6

dimpled E = 0

dimpled E = 1/4 H

dimpled E = 1/2 H

0

0.5

1

1.5

2

-6 -4 -2 0 2 4 6

dimpled E = 0

dimpled E = 1/4 H

dimpled E = 1/2 H

((a)

(b) (

(c) (

S/Dj = 4

S/Dj = 2

S/Dj = 1.5

Nu/

Nu

Smoo

th-w

all

Nu/

Nu

Smoo

th-w

all

Nu/

Nu

Smoo

th-w

all

x'/Dj

x'/Dj

x'/Dj

Fig. 7. Distributions of Nusselt number ratio along horizontal and vertical stE = 0, 1/4H and 1/2H.

the test results compared in Fig. 6a and b and for all the testresults acquired from the present series of tests, the test con-ditions with E/H = 1/2 consistently provide the highest heattransfer rates relative to the results obtained from thesmooth-walled, E/H = 0 and 1/4 conditions.

Fig. 7 examines the E/H impacts on heat transfer by plot-ting Nu/Nusmooth-wall ratios along Y = 0 axis and alongthree X axes of X = 0 (E = 0), X = 1/4 (E = 1/4H) andX = 1/2 (E = 1/2H) with S/Dj = 1.5, 2 and 4 at Reynoldsnumber of 10,000. Due to the oval-shaped Nu contoursdeveloped over the dimpled surface as demonstrated inFig. 5, the distributions of Nu/Nusmooth-wall ratio along X

and Y axes perform differently. As shown in Fig. 7a–c, theNu/Nusmooth-wall ratios along X axis for three eccentricitiestested are higher than unity. The higher Nu/Nusmooth-wall

000

0

0.5

1

1.5

2

-6 -4 -2 0 2 4 6

dimpled E = 0, x/Dj = 0

dimpled E = 1/4 H, x/Dj = 1/4 H


0

0.5

1

1.5

2

-6 -4 -2 0 2 4 6




0

0.5

1

1.5

2

-6 -4 -2 0 2 4 6




d)

e)

f)

S/Dj = 1.5

S/Dj = 2

S/Dj = 4

Nu/

Nu

Smoo

th-w

all

Nu/

Nu

Smoo

th-w

all

Nu/

Nu

Smoo

th-w

all

y'/Dj

y'/Dj

y'/Dj

agnation-lines at Reynolds number of 10,000 and S/Dj = 1.5, 2 and 4 for

40

50

60

70

80

90

100

110

120

4000 6000 8000 10000 12000 14000 16000

E = 0E = 1/4 HE = 1/2 HSmooth-walledPan and Webb [14]

cN

u

Re(a)

S/Dj = 1.5

20

30

40

50

60

70

4000 6000 8000 10000 12000 14000 16000

E = 0E = 1/4 HE = 1/2 HSmooth-walledPan and Webb [14]

cN

u

(b) Re

S/Dj = 8

Fig. 8. Variation of NuC with jet Reynolds number for E = 0, E = 1/4H,E = 1/2H at S/Dj = 1.5 and S/Dj = 8.


ratios consistently develop at the stagnation points relativeto those over the inter-jet regions. The X-wise heat transferaugmentations for E/H = 1/2 conditions are considerablyhigher than the counterparts with E/H = 0 and 1/4. Fortest conditions with E/H = 1/4, the X-wise profiles ofNu/Nusmooth-wall ratio follow the twin-ripple patterns dueto the heat transfer humps developed at the middlelocations between two adjacent dimple-centres. TheNu/Nusmooth-wall ratios are ranged from 1 to 2 as depictedin Fig. 7a–c. But the Y-wise variations of Nu/Nusmooth-wall

ratio are in the range of 0.8–1.45 as shown in Fig. 7d–f,which are considerably less than the varying range detectedalong X axis. Thus the differences in Nu/Nusmooth-wall ratiosalong Y axis between three eccentricities tested are consid-erably suppressed from the X-wise levels. In particular,the Y-wise heat-transfer ratios for three E/H values testedare less than unity over the inter-jet regions. But the Y-wiseNu/Nusmooth-wall ratios in the stagnation regions are stillabove than unity. Nevertheless, as the jet centres are notcorresponding to the stagnation points for the test condi-tions with E/H = 1/4, the lowest Nu/Nusmooth-wall ratiosconsistently develop for the scenarios with E/H = 1/4 asindicated in Fig. 7d–f. Following the manner of data pre-sentation shown in Fig. 7 but applied to different Reynoldsnumbers tested, it shows that the increase of Reynolds numberreduces the heat transfer augmentation. In view of the S/Dj

impacts for any fixed Reynolds number, the X-wise andY-wise heat transfer enhancements systematically in-crease with the increase of S/Dj ratio as demonstrated inFig. 7.

3.3. Spatially averaged heat transfer correlation

over central jet region

The physics through which the variations of Re, S/Dj

and E/H modify heat transfers involve the various modesof radial spent flows due to different impinging topologiesfor jet array and the modified inter-jet reactions. These flowmechanisms could be inter-correlated with the controllingparameters of Re, S/Dj and E/H. As a result, the spatiallyaveraged Nusselt number over central jet region (NuC)could be inter-correlated with the controlling parametersof Re, S/Dj and E/H. To unravel the functional relation-ship between Re, S/Dj and E/H for evaluating NuC, theNuC data collected from each test condition with smooth-walled, E/H = 0, 1/4 or 1/2 at S/Dj = 1.5 and 8 is plottedagainst Re as shown in Fig. 8. If the limiting condition ofvanishing forced convection is designated as NuC ¼ 0, thefunctional relationship between NuC and Re for each testcondition, justified by the data trend revealed in Fig. 8,could be constructed as

NuC ¼ AfS=Djg � ReBfS=Djg. ð2ÞThe coefficient A and power index B of Eq. (2) are initiallyassumed to be functions of S/Dj for each test condition.Also compared in Fig. 8 are the NuC results evaluated fromthe empirical correlation proposed by Pan and Webb [14]

for the smooth-walled surface. As shown in Fig. 8, the pres-ent smooth-walled NuC values are in good agreements withthe correlative results of Pan and Webb [14]. It is worthnoting that, as indicated in Fig. 8a with S/Dj = 1.5, thesmooth-walled NuC values are higher than those over thedimpled surfaces with E/H = 0 and 1/4 when Reynoldsnumber is greater than 10,000. This particular result im-plies that the B values in Eq. (2) for test conditions ofE/H = 0 and 1/4 are less than the smooth-walled B value.However, further increase of separation distance from 1.5to 8Dj extends the effective Re range within which theNuC values over dimpled surface are higher than thesmooth-walled counterparts. Therefore, the differences ofA values between smooth-walled and dimpled-surface areincreased when separation distance is increased. Neverthe-less, for each option of Re � S/Dj tested, the NuC valuesover dimpled surfaces with E/H = 0 and 1/4 are very close.The dimpled surface with E/H = 1/2 consistently providethe highest NuC values among the four tested scenarios.

The S/Dj impact on NuC for four test conditions is illus-trated in Fig. 9 using the data obtained at Reynolds num-ber of 10,000. The exponential decay of NuC against S/Dj isfollowed by four sets of test results. The data trends ofE/H = 0 and 1/4 decay with the lower rates than thesmooth-walled condition. The variation manners of NuC

against S/Dj as revealed in Fig. 9 are repeated for all theReynolds numbers tested. In order to develop a set of heat

0

20

40

60

80

100

120

0 20 40 60 80 100 120

Experimental measurement ( )

Hea

t-tr

ansf

er c

orre

lati

on (

)

Smooth-walled

E =0

E =1/4 H

E =1/2 H

CNu

CN

u

10% discrepancies

Fig. 11. Comparison of experimental data with heat transfer correlation.

30

40

50

60

70

80

90

100

0 2 4 6 8 10 12S/D j

Smooth-walled

E = 0

E = 1/4 H

E = 1/2 H

Re = 10000

CN

u

Fig. 9. Variation of NuC with S/Dj at Reynolds number of 10,000, forE = 0, E = 1/4H, and E = 1/2H.


transfer correlations for evaluating NuC, each set of NuC

data acquired from four test conditions is individually cor-related using Eq. (2) as the functional structure. Fig. 10depicts the varying trends of A and B coefficients againstS/Dj. The B value, which quotes for the power index ofRe in Eq. (2), tends to be invariant when S/Dj varies.The smooth-walled condition possesses the highest B value.When the eccentricity ratio increases from 0 to 1/2, a sys-tematic increase of B value is obtained that implies theenhanced Re dependency for NuC. Although the B valueappears to be a very weak function of S/Dj for each setof test conditions, the exponential decay of NuC againstS/Dj typified in Fig. 9 is recast by the varying manner ofcoefficient A as shown in Fig. 10a. Justified by the regres-sion-type evidence depicted in Fig. 10, the heat transfercorrelations for evaluating NuC are obtained as

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10 12S/D j

B

Smooth-walledE=0

E=1/4 HE=1/2 H

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 2 4 6 8 10 12S/D j

A

Smooth-walled

E=0

E=1/4 H

E=1/2 H

(b)

(a)

Fig. 10. Variation of coefficients A and B with S/Dj for smooth-walled,E = 0, E = 1/4H, and E = 1/2H.

NuC ¼ 0:228e�0:08S=Dj � Re0:646

ðsmooth-walled surfaceÞ; ð3ÞNuC ¼ 4:028e�0:055S=Dj � Re0:332

ðdimpled surface with E=H ¼ 0Þ; ð4ÞNuC ¼ 3:393e�0:049S=Dj � Re0:348

ðdimpled surface with E=H ¼ 1=4Þ; ð5ÞNuC ¼ 4:148e�0:065S=Dj � Re0:35

ðdimpled surface with E=H ¼ 1=2Þ: ð6Þ

The overall success of the proposed correlations embodiedin Eqs. (3)–(6) for NuC over the smooth-walled and dimpledimpinging surfaces is examined by comparing all the exper-imental measurements with the empirical predictions asindicated in Fig. 11. As shown in Fig. 11, the values ofNuC indicating by the ranges of data spreads with test con-dition of E/H = 1/2 are generally higher. The maximumdiscrepancy of ±10% between the experimental and correl-ative results is achieved for the entire set of data. Even withthe presence of surface-dimple complexities for the jetarray, the experimentally based correlations could still pro-vide the reasonable evaluations for spatially averaged heattransfers over central jet region.

4. Conclusions

The detailed heat transfer measurements of impingingjet-array over smooth-walled and convex-dimpled surfacesare performed to study the combined effects of Re, S/Dj

and E/H on heat transfer. The heat transfer physics areinter-correlated with the controlling parameters of Re,S/Dj and E/H. Several salient points that have been identi-fied are as follows:

1. With adequate selection of Re and S/Dj, the moderatedjet-to-jet interference and shrinkage of inter-jet regionalong with elevated heat transfers over stagnationregions assist to augment heat transfer with improveduniformity over the convex-dimpled surface. Furtherincrease of Re or/and decrease of S/Dj moderate the


improvement of heat transfer performance attributedfrom the surface dimples. For test conditions ofRe P 10,000 and S/Dj = 1.5, Nu levels in the inter-jetregions over convex-dimpled surface with E/H = 0 and1/4 are less than the smooth-walled counterparts so thatthe NuC values for E/H = 0 and 1/4 are less than thesmooth-walled levels.

2. The isolated Re and S/Dj impacts on NuC are, res-pectively, indexed by A and B coefficients in Eq. (2). Asystematic increase of E/H ratio results in the corre-sponding increase of B value that reflects the enhanceddependency of NuC on Re. The exponential decay ofNuC with increased S/Dj is confirmed fro all the testscenarios which is recast by A{S/Dj} function. Ascoefficients A and B both vary with E/H ratio, theuncoupling effects of Re and S/Dj on NuC are inter-correlated with E/H.

3. The symmetrical and asymmetrical surface topologiesfor impinging jet-array are, respectively, generated fortest conditions with E/H = 0, 1/2 and 1/4. Due to theasymmetrical surface topology surrounding the jet-cen-tre for test conditions of E/H = 1/4, each jet issued fromorifice plat is bend toward the dimple-centre so that itsstagnation point is horizontally shifted about 0.5 jet-diameter toward the dimple centre. Among each fourcomparable sets of test scenarios, the highest NuC levelsconsistently develop over the dimpled surface for the testconditions with E/H = 1/2; while the NuC values for testconditions of E/H = 0 and 1/4 are in close agreements.

4. In conformity with the experimental evidences, a regres-sion-type analysis is performed to generate the empiricalheat transfer correlations that permit the evaluations ofNuC values over the smooth-walled and the convex-dim-pled surfaces with E/H = 0, 1/4 and 1/2.

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