cfd effects of mach number and reynolds number.pdf

8/10/2019 CFD Effects of Mach number and Reynolds number.pdf

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spacing, hole spacing, and jet Reynolds number. The influ-ences of cross-flow on a single line of jets is examined byMetzger and Korstad[7], showing that target spacing, jetReynolds number, and the relative strengths of the jet flowand the cross-flow influence heat transfer on the targetwall. In another paper, Metzger et al.[8]present heat trans-fer characteristics measured on a target surface beneath atwo-dimensional array of impinging jets also in low-speedflow that indicate in-line jet impingement hole patternsprovide better heat transfer than staggered arrangements.Florschuetz et al. [9] includes data on channel cross-flowmass velocity and jet mass velocity (where ratios rangefrom 0 to 0.8), in addition to a correlation with gives Nus-selt number dependence on these parameters, as well as onjet impingement plate geometry, Prandtl number, andReynolds number. Different cross-flow schemes on

impingement heat transfer in low-speed flows are consid-

ered by Obot and Trabold[10]who arrive at the conclusionthat for a given cross-flow scheme and constant jet diame-ter d, higher heat transfer coefficients are obtained as thenumber of jets over a fixed target area increases and thatprogressively lower performance is obtained as the cross-flow is restricted to exit through two opposite sides, andthen, through one side of the passage between the impinge-ment hole plate and the target plate. Bunker and Metzger[11] present detailed local heat transfer distributions dueto line jet impingement for leading edge regions, both withand without film extraction effects. Fox et al. [12]examinethe effects of unsteady vortical structures on the adiabaticwall temperature distribution produced by a single imping-ing jet. Bailey and Bunker [13] investigate impingementarrays with inline jets in a square array, with differentaxial and lateral jet spacings and relatively low Mach num-

bers. Included are correlations developed from these data

Nomenclature

A impingement hole areaAht heat transfer area on the target plateca impingement air flow sonic velocity

ci impingement air flow ideal sonic velocityCD discharge coefficientD diameter of an individual impingement holehloss heat transfer coefficient to account for convec-

tion and radiation loss from back side of targetplate

k ratio of specific heats_m impingement air mass flow rate

Ma impingement air flow Mach numberMi impingement air flow ideal Mach numberNu local Nusselt numberNuc corrected local Nusselt numberNu line-averaged Nusselt number

Nuc corrected line-averaged Nusselt numberNu spatially averaged Nusselt numberNuF spatially averaged Nusselt number from Flor-

schuetz et al.[9] correlationPa impingement air static pressurePi impingement air ideal static pressureP0j impingement air stagnation pressureQ total power provided to the thermofoil heaterqrf radiation heat flux from front side (or impinge-

ment side) of the target plateqrb radiation heat flux from back side of the target

plate

qcf convection heat flux from front side (orimpingement side) of the target plateqcb convection heat flux from back side of the target

plateR ideal gas constantRej impingement air flow Reynolds numberRF recovery factor

Tambient ambient static temperatureTb local temperature on the back surface of the

polystyrene target plate

TW local target surface temperature on the surfaceof the heater adjacent impingement airTAW local adiabatic target surface temperatureTi impingement air ideal static temperatureTj impingement air static temperatureT0j impingement air stagnation temperatureT0j corrected impingement air stagnation tempera-

ture to give zero spatially averaged surface heatflux

Ttc local thermocouple temperature between theheater and the polystyrene target plate

ua impingement air velocityui impingement air ideal velocity

x streamwise coordinatey spanwise coordinatez normal coordinateX streamwise distance between centerlines of adja-

cent impingement holesY spanwise distance between centerlines of adja-

cent impingement holesZ distance between target plate and impingement

hole plate

Greek symbols

a air thermal conductivity

qa impingement air static densityqi impingement air ideal static densityl absolute viscosityr Boltzman constantef emissivity of the front surface of the target plateeinf emissivity of a plate located opposite to the

target plate

368 M. Goodro et al. / International Journal of Heat and Mass Transfer 50 (2007) 367380


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which extend the range of applicability of the correlationspresented by Florschuetz et al. [9]. Other recent studiesconsidered the effects of jet impingement on a leadingedge/concave wall with roughness [14], and the effects ofjets with mist and steam on a concave target surface[15].Parsons et al. [16,17], Parsons and Han [18], Epstein

et al.[19], and Mattern and Hennecke[20]show that rota-tional effects are important for jets impinging on flat sur-faces at relatively low Reynolds numbers. However, thereis little or no information available at higher jet Reynoldsnumbers and jet rotation numbers on concave surfaces rel-evant to engine conditions. Thus, it is evident that, asidefrom a few investigations, most of the impingement datafrom the open literature are obtained on flat, smooth sur-faces. Brevet et al. [21] employ flat plates to consider onerow of impinging jets in a test section with low speed flowin which the spent air is again constrained to exit in onedirection. Effects of impingement distance, Reynolds num-ber, and spanwise hole spacing on Nusselt number distri-

butions lead to recommendations for optimal Z/d valuesof 25, and optimal spanwise hole spacings of 45 holediameters. Brevet et al. [22] describe recovery factors andNusselt numbers measured on a flat target surface beneatha single, compressible impingement jet. These authors havethe distinction of separating the effects of Mach numberand Reynolds number. Data sets with different Mach num-bers and constant Reynolds number are obtained usingdifferent impingement hole plates with different hole diam-eters. They conclude that, increasing the Mach number (asthe Reynolds number is constant) improves impingementheat transfer significantly for jet Mach numbers greater

than 0.2.Other recent studies by Lee et al. [23], Garimella and

Nenaydykh [24], and Shuja et al. [25] address the effectsof nozzle geometry on heat transfer and fluid flow, whereasSiba et al.[26], Chung and Luo[27], and Abdon and Sun-den [28] use experimental and numerical approaches toconsider the influences of turbulent impingement jets. Inanother numerical investigation, Yong [29] investigatesthe hydrodynamic and heat transfer behavior of circularliquid jets. Laschefski et al. [30] also uses a numericalapproach to investigate of heat transfer produced by rowsof rectangular impinging jets. Seyedein et al. [31] reportheat transfer characteristics from confined multiple turbu-lent impinging slot jets, and Rhee et al. [32] describe heattransfer, mass transfer, and flow characteristics from arraysof effusion holes.

Although the number of existing impingement coolingstudies is considerable, new innovative cooling configura-tions are being used in gas turbines, which require addi-tional investigation to account for a number of currentlyunexplored effects and their influence on impingement heattransfer. Two of the most important of these unexploredareas are the independent effects of Mach number and Rey-nolds number for an array of impinging jets. The presentstudy provides data on these effects for an array of imping-

ing jets in the form of discharge coefficients, local and spa-

tially averaged Nusselt numbers, and local and spatiallyaveraged recovery factors. The data are unique, not onlybecause data are given for impingement jet Mach numbersas high as 0.74 and impingement jet Reynolds numbers ashigh as 60,000, but also because the effects of Reynoldsnumber and Mach number are separated by providing data

at constant Reynolds number as the Mach number is var-ied, and data at constant Mach number as the Reynoldsnumber is varied. As such, the present impingement jetarray study can considered a continuation of the investiga-tion of Brevet et al. [22]wherein Mach number influencesare investigated for a single impingement jet.

2. Experimental apparatus and procedures

2.1. Impingement flow facility, and impingement plate

Schematic diagrams of the facility used for heat transfermeasurements are presented inFigs. 1 and 2. The facility is

constructed of 6.1 mm thick ASTM A38 steel plates,and A53 Grade B ARW steel piping, and is open to the

Fig. 1. Impingement flow facility.

Fig. 2. Impingement flow facility test section, including impingement

plenum, and impingement channel.

M. Goodro et al. / International Journal of Heat and Mass Transfer 50 (2007) 367380 369


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laboratory air at its inlet and exit. Depending upon therequired flow conditions, one of two blowers is employed.For the lower Reynolds numbers investigated, a New YorkBlower Co. 7.5 HP, size 1808 pressure blower is employed.For higher Reynolds numbers, a DRUM Industries, 50HP, D807 pressure blower is employed. In each case, the

air mass flow rate provided to the test section is measured(downstream of whichever blower is employed) using anASME standard orifice plate, flow-mounted calibratedcopperconstantan thermocouples, and Validyne DP15pressure transducers (with diaphragms rated at 13.8 or34.5 kPa) connected to DP10D Carrier Demodulators.The blower exits into a series of two plenums arranged inseries (the upstream plenum is 0.63 m to a side and thedownstream plenum measures 0.63 m0.77 m0.77 m).A Bonneville cross-flow heat exchanger is located withinthe plenum which is farther downstream. As the air exitsthe heat exchanger, and the second plenum, the air passesinto a 0.22 m outer diameter pipe, which contains

the ASME Standard orifice plate employed to measurethe air mass flow rate. This pipe then connects to the0.635 m 0.635 m side of a plenum. Upon entering thisplenum, the air first encounters a flow baffle used to distrib-ute the flow, a honeycomb, and other flow straighteningdevices. These are followed by the impingement plenum(or upper plenum, located below the honeycomb and flowstraightening devices) whose top dimensions are 0.635 mand 0.635 m, and whose height is 0.40 m.

Individual plates with holes used to produce theimpingement jets are located at the bottom of this ple-num, as shown in Fig. 2. A list of the impingement test

plate configurations employed is given in Table 1. Theplenum is thus designed so that different impingementplates can be installed at this location using a 9.5 mmthick polyurethane gasket and 1/4 in SAE J429 Grade5 bolts. Fig. 3 shows that each impingement plate isarranged with 10 rows of holes in the streamwise direc-tion, arranged so that holes in adjacent rows arestaggered with respect to each other. With this arrange-ment, either 9 or 10 holes are located in each streamwiserow. The spacing between holes in the streamwise direc-tion X is then 8D, and the spanwise spacing betweenholes in a given streamwise row Y is also 8D. The thick-ness of each impingement plate is 1D. The spacingbetween the hole exit planes and the target plate isdenoted Z and is equal to 3D. Note that the coordinate

system employed is also shown in Fig. 3. The impinge-ment cooling flow which issues from these holes iscontained within the channel formed by the impingementjet plate and the target surface, and is constrained to exitin a single direction, which here, is denoted as the x-direction. This channel is called the lower plenum. Asdifferent plates are employed with different sized impinge-ment holes, this is accomplished using different polycar-bonate spacers which are exactly 3D in height, and aresealed in place around three sides of the impingement

channel. Plates with different impingement hole diametersare used to provide data at a variety of Mach numbersand Reynolds numbers. Specific hole sizes, mass flowrates, and pressure levels are employed so that data areobtained at different Mach numbers as the Reynoldsnumber is constant, and at different Reynolds numbersas the Mach number is constant.

2.2. Target plate test surfaces for measurements of surface

recovery factors and surface Nusselt numbers

Two different types of target plates are employed. Poly-carbonate target plates are used for measurement of spa-tially resolved distributions of surface adiabatic surfacetemperature and surface recovery factor. Polycarbonate ischosen because of its strength, its low thermal conductivity(0.16 W/mK at 20 C), and to minimize streamwise andspanwise conduction along the test surface, and thus, min-imize smearing of spatially varying temperature gradi-ents along the test surface. Each plate is 1.58 mm thick,and is mounted on the bottom surface of the plenum usinggrey cloth tape with PVC cement, a solvent containingmethyl ethyl ketone, tetrahydrofuran, and acetone to sealthe edges so that no leaks are present along the flow pas-sage. A mounting frame is also employed to hold the target

plate in place, to keep it smooth (without bending or wrin-

Table 1Impingement test plate configurations

Hole diameter(mm)

Plate thickness(mm)

Hole spacing, X, Y(mm)

X/D, Y/D

3 3 24.0 83.5 3.5 28.0 84.5 4.5 36.0 88 8 64.0 815 15 120.0 8

20 20 160.0 8

Fig. 3. Impingement test plate configuration.



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kles), and normal to the impingement jets, as testing isunderway. Ten calibrated, copperconstantan thermocou-ples are placed at different streamwise and spanwise loca-tions within the polycarbonate so that each senses adifferent temperature as data are acquired. Each one ofthese thermocouples is mounted approximately 0.02 cm

just below the surface adjacent to the air containing theimpingement fluid, to provide measurements of local sur-face temperatures, after correction for thermal contactresistance and temperature drop through the 0.16 cm thick-ness of polycarbonate. Thermocouple lead wires are placedin grooves along the polycarbonate, and bonded into placewith epoxy, to minimize thermal disturbances resultingfrom their presence.

Spatially resolved distributions of surface heat transfercoefficients and Nusselt numbers are measured on poly-styrene target plates with heaters and thermocouplesattached. The custom-made HK5184R26 thermofoil heat-ers employed are manufactured by Minco Products Inc.,

and have a temperature rating of 100 C. The etched-foilheating element within this device is encased between twolayers of DuPont Kapton polyimide film, and is used toprovide a constant surface heat flux boundary condition.This heater is located adjacent to the air stream withthe impinging air jets. Its thermal conductivity is 0.2 W/mK at 20 C. Polystyrene is chosen for the target platebecause of its strength, and because it does not deformin shape at temperatures as high as 80 C. It is also suit-able because of its low thermal conductivity (0.09 W/mKat 20 C), which results in minimal streamwise and span-wise conduction along the test surface. The back side of

this polystyrene plate is viewed by the infrared cameraas spatially resolved measurements of surface temperatureare obtained. Each polystyrene target plate is 1.27 mmthick and each heater is approximately 0.3 mm thick, giv-ing a total target plate thickness of 1.57 mm. Like therecovery factor target test plates, and these plates aremounted on the bottom surface of the plenum using greycloth tape with PVC cement to seal the edges so that noleaks are present along the flow passage. A mountingframe is also again employed to hold the target plate inplace, to keep it smooth (without bending or wrinkles),and normal to the impingement jets, as testing is under-way. In order to detect different surface temperatures astesting is underway, nine calibrated, copperconstantanthermocouples are placed at different streamwise andspanwise locations within the polystyrene. Each one ofthese is mounted just below the surface adjacent to theair containing the impingement fluid, between the thermo-foil heater and the polystyrene portion of the target plate.As each thermocouple is used to measure local surfacetemperature, corrections are made for thermal contactresistance and local temperature drop through the ther-mofoil heater. Thermocouple lead wires are placed ingrooves in the polystyrene, and bonded into place withepoxy, to minimize thermal disturbances resulting from

their presence. Because of the wear and degradation

which results from exposure to different temperature lev-els as tests are conducted, these target plates are replacedwith all new components after about 3 or 4 individual testsequences.

2.3. Local impingement air pressure and temperature

measurements

As shown inFig. 2, three wall pressure taps are locatedon the surface of the upper plenum, and eight wall pres-sure taps are located on the surface of the lower plenumfor measurement of local static pressures. As tests are con-ducted, Validyne Model DP15-46 pressure transducers(with diaphragms rated at 13.8 or 34.5 kPa) driven byDP10D Carrier Demodulators are used to sense pressuresfrom these static pressure tappings. Local airflow recoverytemperatures are measured using two calibrated copperconstantan thermocouples located in the central part ofthe lower plenum, and three calibrated copperconstantan

thermocouples located in the central part of the upper ple-num. In each case, readings from either multiple thermo-couples or multiple pressure taps are used to obtainaverage values of measured quantities for a given plenum.In some cases, additional surface pressure taps are locatedon exit side of the plate with the impingement holes. Volt-ages from the carrier demodulators and all thermocouplesemployed in the study are read sequentially using Hewlett-Packard HP44222T and HP44222A relay multiplexer cardassemblies, installed in a Hewlett-Packard HP3497A low-speed data acquisition/control unit. This system providesthermocouple compensation electronically such that volt-

ages for type T copperconstantan thermocouples aregiven relative to 0 C. The voltage outputs from this unitare acquired by the Dell Precision 530 PC workstationthrough its USB port, using LABVIEW 7.0 softwareand a GPIB-USB-B adaptor made by National Ins-truments.

Because the overall volume and cross-sectional area ofthe upper plenum are large compared to the area of theimpingement holes, the velocity of the air in this plenumis near zero. As a result, the static pressure measured atthe wall static pressure taps is the same as the stagnationpressure, and is denoted P0j, the impingement air stagna-tion pressure. The measured air recovery temperature inthe upper plenum is then the same as the upper plenumstatic temperature and upper plenum stagnation tempera-ture. This resulting value is denoted T0j, the impingementstagnation temperature. After measurement of theimpingement air mass flow rate at the pipe orifice plate,the impingement air mass flux is determined using qaua_m=A.

An iterative procedure is then used to determine theimpingement static temperature Tj, and the impingementflow Mach number Ma. The first step in this procedureis estimation of the value ofTj. The local recovery temper-ature, which is measured in the lower plenum, is used

for this estimation. The impingement static density, and



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spatially averaged impingement jet velocity are then deter-mined using qa= Pa/RTj, and ua _m=qaA, respectively.Because the impingement flow vents to the laboratory,the local atmospheric pressure is used for Pa. Measure-ments of lower plenum static pressures using wall pressuretaps confirm this approach. Next, the impingement air

sonic velocity and Mach number are given by ca=(kRTj)1/2 and Ma= ua/ca, respectively. Iterations using

these analysis steps are then continued until the impinge-ment static temperature and impingement Mach numberare consistent with the isentropic equation given by

Tj T0j=1M2ak1=2 1

With impingement static temperatureTj, impingement flowMach number Ma, and other parameters known, theimpingement Reynolds number is subsequently given byan equation of the form

Rej qauaD=l 2

A Kiel-type stagnation pressure probe is used to mea-sure the total pressure in the pipe at a position which islocated upstream of the orifice plate employed to measuremass flow rate. A wall pressure tap located on the surfaceof the pipe, and a calibrated copperconstantan thermo-couple positioned within the air stream are used to sensestatic pressure and flow recovery temperature, respectively,at the same streamwise location. Pressures and tempera-tures measured using the thermocouple, probe, and tapare sensed and processed using the same types of instru-mentation mentioned earlier. The velocities deduced fromthis arrangement are used to provide a cross-check on thevelocities deduced from mass flow rates, which are mea-sured using the ASME standard orifice plate.

2.4. Discharge coefficient determination

The discharge coefficient is determined using

CD qaua=qiui 3

The first step in determining the ideal impingement massflux qiui is obtaining an ideal impingement Mach numberMi using

P0j=Pa 1M2ik1=2

k=k1 4

Next, impingement ideal static temperature Ti is deter-mined usingT0j, the ideal Mach number Mi, and the appro-priate ideal gas isentropic relationship. Impingement idealstatic density is given by qi=Pa/RTi, and impingementideal velocity is given by ui= Mi(kRTi)

1/2. Note that, inmost cases, discharge coefficients are determined whichare based on Pa, the spatially averaged static pressure atthe exits of the impingement holes. In some other cases,local discharge coefficients for different impingement holeslocated along the length of the plate are determined, which

are based on measurements of local static pressure mea-

sured at different surface pressure taps located along theexit side of the impingement plate.

2.5. Local recovery factor measurement

After the static temperature and stagnation tempera-

tures of the impingement air are determined, the local sur-face recovery factor is determined at different target surfacelocations using

RF TAW Tj=T0j Tj 5

Here, TAW represents the local adiabatic surface tempera-ture which is present with zero heat flux on the target sur-face. Note that some small variations of local adiabaticsurface temperature TAW and local recovery factor RFare present due to streamwise and spanwise conductionalong the test surface, but these are minimized by theuse of the polycarbonate target plate, and are includedin the estimates of experimental uncertainty values forthese two quantities. As tests are conducted and dataare acquired, the impingement air jet stagnation tempera-ture is maintained at or very near to the laboratory ambi-ent temperature level T0j=Tambient. This is accomplishedusing liquid nitrogen in the Bonneville heat exchanger tocool the impingement air to the appropriate level as itpasses through the facility. This thermal condition,T0j= Tambient, is then maintained for both the Nusseltnumber experiments and the recovery factor experimentsto provide an appropriate basis of comparison betweenthe data obtained from these two different types ofexperiments.

2.6. Local Nusselt number measurement

The power to the thermofoil heater, mounted on the tar-get plate, is controlled and regulated using a variac powersupply. Energy balances, and analysis to determine temper-ature values on the two surfaces of the target plate, thenallow determination of the magnitude of the total convec-tive power (due to impingement cooling) for a particulartest. To determine the surface heat flux (used to calculateheat transfer coefficients and local Nusselt numbers), thetotal convective power level, provided by the particularthermofoil heater employed, is divided by the single surfacearea of this heater, denoted Aht.

One step in this procedure utilizes a one-dimensionalconduction analysis, which is applied between the surfacewithinthe target plate where the thermocouples are located(between the heater and the polystyrene target plate), andthe ambient air environment behind the target plate. Thisis used to determine Tb, the local temperature on the backsurface of the polystyrene target plate, adjacent to the sur-rounding ambient air environment. Also required for thisanalysis isTtc, the local temperature within the target platebetween the heater and the polystyrene plate, which is

determined from thermocouple measurements. With these



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temperatures known, the radiation heat flux and the con-vection heat flux from the back side of the target plate,qrb and qcb, respectively, are determined together using anequation of the form

qrb qcb hlossTb Tambient 6

where h loss is assumed to be equal to 15 W/m

2

K[21]. Theradiation heat fluxqrfon the front (or impingement side) ofthe target plate is determined using

qrf r1=einf 1=ef 11T4W T

4ambient 7

With this approach, the radiation heat flux is determinedfor an arrangement with multi-reflection between two infi-nite plates where each has a uniform temperature. efandeinfare assumed to be equal to 0.9 for all conditions inves-tigated. This approximate approach works well sinceqrfAht is generally only 36 percent ofQ, the total amountof power provided to the thermofoil heater. Note that

TW, the local target surface temperature on the surfaceof the heater adjacent impingement air, must be knownto determine qrf. Because of the inter-dependence of TW,qrf, and qcf(the convection heat flux from the front sideor impingement side of the target plate), an iterative pro-cedure is required to determine these quantities. The nextpart of this procedure uses a one-dimensional conductionmodel for the heater, which includes source generation ofthermal energy, to provide a relation between TW, Ttc,and qcf. Also included in the analysis is thermal contactresistance between the internal thermocouples and theadjacent heater.

The convection heat flux from the front side (or

impingement side) of the target plate is then given by

qcfQ=Aht qrf qrbqcb 8

The local Nusselt number is then given as

Nu qcfD=TW T0ja 9

Modified local Nusselt numbers are also determined, whichare based on the (TW T

0j) and the (TWTAW) tempera-

ture differences. The determination of these parameters isdiscussed later in the paper.

Spatially resolved temperature distributions along thetarget test surface are determined using infrared imagingin conjunction with thermocouples, energy balances, digi-tal image processing, and in situ calibration procedures.These are then used to determine spatially resolved sur-face Nusselt numbers. To accomplish this, the infraredradiation emitted by the heated interior surface of thechannel is captured using a Thermacam PM390 InfraredImaging Camera, which operates at infrared wavelengthsfrom 3.4 lm to 5.0 lm. Temperatures, measured usingthe calibrated, copperconstantan thermocouples distrib-uted along the test surface adjacent to the flow, are usedto perform the in situ calibrations simultaneously as theradiation contours from surface temperature variations

are recorded.

This is accomplished as the camera views the test surfacefrom behind, as shown inFig. 2. In general, six thermocou-ple junction locations are present in the infrared fieldviewed by the camera. The exact spatial locations and pixellocations of these thermocouple junctions and the coordi-nates of the field of view are known from calibration maps

obtained prior to measurements. During this procedure,the camera is focused, and rigidly mounted and orientedrelative to the test surface in the same way as when radia-tion contours are recorded. Voltages from the thermocou-ples are acquired using the apparatus mentioned earlier.With these data, gray scale values at pixel locations withinvideo taped images from the infrared imaging camera arereadily converted to local Nusselt number values. Becausesuch calibration data depend strongly on camera adjust-ment, the same brightness, contrast, and aperture camerasettings are used to obtain the experimental data. Thein situ calibration approach rigorously and accuratelyaccounts for these variations.

Images from the infrared camera are recorded as 8-bitgray scale directly into the memory of a Dell DimensionXPS T800r PC computer using a Scion Image CorporationFrame grabber video card, and Scion image v.1.9.2 soft-ware. One set of 1520 frames is recorded at a rate of aboutone frame per second. All of the resulting images are thenensemble averaged to obtain the final gray scale dataimage. This final data set is then imported into Matlab ver-sion 6.1.0.450 (Release 12.1) software to convert each of256 possible gray scale values to local Nusselt number ateach pixel location using calibration data. Each individualimage covers a 256256 pixel area.

2.7. Experimental uncertainty estimates

Uncertainty estimates are based on 95% confidence lev-els and are determined using methods described by Klineand McClintock[33]and Moffat[34]. Uncertainty of tem-peratures measured with thermocouples is 0.15 C. Spa-tial and temperature resolutions achieved with infraredimaging are about 0.10.2 mm, and 0.4C, respectively.This magnitude of temperature resolution is due to uncer-tainty in determining the exact locations of thermocoupleswith respect to pixel values used for thein situcalibrations.Local Nusselt number uncertainty is then about 4.8%.Uncertainty magnitudes of local recovery factors and adia-batic surface temperatures are approximately 2.4%, and0.5 C, respectively. Note that uncertainties of local Nus-selt numbers, adiabatic surface temperatures, and recoveryfactors all include the effects of very small amounts ofstreamwise and spanwise conduction along the test surfacesemployed. Reynolds number uncertainty is about 2.0%for an Rejvalue of 20,000.

3. Experimental results and discussion

Table 2gives a summary of the experimental conditions

covered by the present investigation.



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3.1. Impingement hole discharge coefficients

Discharge coefficient data for the present experimentalconditions, which represent average values for all of theimpingement holes at a particular experimental condition,are presented inFig. 4. Here, all discharge coefficients arebased on Pa equal to the ambient pressure measured at

the exit of the impingement flow facility. The data pre-sented here are measured at different impingement Machnumbers and a constant Reynolds number Rejof 60,000,and at different impingement Reynolds numbers and a con-stant Mach numberMaof 0.1. Discharge coefficient valuesrange between 0.73 and 0.90 with a general trend ofdecreasing discharge coefficients with increasing Reynoldsnumber (as the impingement Mach number is heldconstant).

3.2. Determination of spatially averaged adiabatic surface

temperature T0j

To determine an appropriate reference temperature forthe determination of heat transfer coefficients and Nusseltnumbers, the convective heat power from the impingementside of the target plate qcfis determined as it varies with(TWT0j). Data are obtained at three different tempera-ture differences. The largest temperature differenceemployed is always less than 30 C to avoid variations of

measured Nusselt numbers with variable property effects.Such convective heat power data then vary linearly with(TWT0j). Such linear data are extrapolated to theqcf= 0 axis to determine TWT

0j. Note that the convec-

tive power is the value for the entire target plate. Conse-quently, the magnitude of T0j is spatially averaged over

the target plate heat transfer area, and as such, is the spa-tially averaged adiabatic surface temperature for the entireheated portion of the target plate at a particular experimen-tal condition. Consequently, all Nusselt number data areobtained at three different values of (TW T0j) to providea means to determine T0j for each experimental condition.All Nusselt numbers are then determined using

Nu qcfD=AhtTW T0ja 10

3.3. Baseline Nusselt numbers

Baseline Nusselt numbers are measured to provide

checks on measurement apparatus and procedures. Thebaseline test plate and flow conditions employed for thispurpose match ones used by Florschuetz et al. [9] withRej= 34,500, Ma approximately equal to 0, and an arrayof jets with X= 5D, Y= 4D, and Z= 3D. Like the inves-tigation of Florschuetz et al. [9], the passage between theimpingement plate and the target plate in the presentarrangement is closed on three sides so that the effects ofspent air cross-flow are considered.Fig. 5shows a compar-ison of the results from the two investigations. The goodagreement of the area-averaged data from the two sourcesvalidates the experimental procedures and apparatus

employed in the present study. The present data are area-averaged over y/Dfrom8.0 to +8.0, and over 5Dlengthsegments in the streamwise direction. Also presented in thisfigure are local Nu data from the present investigation asthey vary with x/Dfor y/D= 4 andy/D= 8, and Nu datawhich are line-averaged over y/Dfrom 8.0 to +8.0.

The effect of the unheated starting length locatedupstream of the heated target plate is also investigated.This is done by adding an additional heater upstream of

Table 2Experimental conditions employed in the present investigation

Experiment number Rej Ma D (mm)

1 59,900 0.16 202 59,700 0.21 153 59,300 0.38 84 5200 0.092 3

5 6400 0.1 3.55.5 8200 0.1 4.514 58,600 0.63 4.515 56,300 0.74 3.5

0.4

0.5

0.6

0.7

0.8

0.9

1

0 20000 40000 60000 80000

Rej

CD

Ma=0.1 Rej=60,000

Fig. 4. Discharge coefficient data for Rej = 60,000 and different Mach

numbers, and forMa= 0.1 and different impingement Reynolds numbers.

Fig. 5. Comparison of baseline Nusselt number data with correlation ofFlorschuetz et al.[9] for Rej= 34,500, Ma approximately equal to 0, and

an array of jets with X= 5D, Y= 4D, and Z= 3D.



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the heater used on the target plate. Local and spatiallyaveraged Nusselt numbers are then measured on the targetplate, both with and without upstream heating, forRej= 34,500 and Ma= 0.12 with the same impingementhole plate as used for the other baseline data checks. Thevariation of local and spatially averaged Nusselt numbers

between the two tests is only about 2%, at most, indicatingminimal effect of thermal entry length on impingement heattransfer (for these particular experimental conditions).

3.4. Nusselt number variations with Reynolds number

Surface Nusselt number distributions are presented inFig. 6 for Ma= 0.10, and Rej values of 5200, 6400, and8200. The different views of the test surface in the differentparts of this figure are due to different infrared camera

views of the target plate as impingement plates with differ-ent sized holes are employed on the opposite side. Notethat, regardless of the Reynolds number, the qualitativedistributions of local Nusselt number produced by eachimpingement jet are similar, with good periodic repeatabil-ity in the spanwise direction for each streamwise row of

impact locations. This spanwise periodicity is also illus-trated by the local Nu data presented in Fig. 7a forx/D= 32, and the same Rejvalues.

Fig. 6also shows that only one local maximum value ispresent in the Nu distribution underneath each jet. In gen-eral, magnitudes of these local jet maxima underneath thedifferent impingement jets decrease as the flow developsin the streamwise direction and x/Dincreases, for particu-larMaand Rejvalues. This trend is also illustrated by localNusselt number data presented as they vary with x/D inFig. 7b for y/D = 8. Here, the smaller peak values nearx/D= 32 and x/D= 48, which are positioned betweenthe larger peak values, are due to local Nusselt number

increases at spanwise locations approximately halfwaybetween the impact points of nearby impinging jets.Another important conclusion apparent from Figs. 6, 7aand b is that local maximum Nuvalues generally increaseat eachx/Dand y/Dsurface location as the Reynolds num-ber increases.

Fig. 8presents Nusselt numbers as they vary with x/Dfor the same experimental conditions, which are line-aver-aged over y/D from 8.0 to +8.0. Here, local maximumvalues are apparent, which are spaced approximately 8Dapart, and are due to the impact of impingement jets fromeach different streamwise row of holes. Here, line-averaged

Fig. 6. Spatially resolved distributions of surface Nusselt number for

Ma= 0.10, and Rejvalues of (a) 5200, (b) 6400, and (c) 8200.

0

20

40

60

80

0 20 40 60 80

x/D

Nu

0

20

40

60

80

-10 -5 0 10

y/D

Nu

Re=5200

Re=6400

Re=8200

5

a

b

Fig. 7. Local surface Nusselt number variations for Ma= 0.10, and Rejvalues of 5200, 6400, and 8200. (a) Variations with y/Dfor x/D= 32. (b)

Variations with x/Dfor y/D= 8.



10/14

Nu data generally increase with Rejat each x/D location

(provided Ma is constant at 0.1). Local peak line-averagedNusselt numbers then consistently decrease at successivex/D locations for particular values ofRejand Ma (whichis consistent with the data presented in the previous twofigures).

3.5. Nusselt number variations with Mach number

Local spatially resolved surface Nusselt number distri-butions for Rej= 60,000 and Ma values from 0.16 to 0.74are given inFig. 9. Like the results in Fig. 6, the differentviews of the test surface shown by the data in the different

parts ofFig. 9 are due to different infrared camera viewsof the target plate as impingement plates with differentsized holes are employed on the opposite side. The localNusselt number distributions which are produced by eachimpingement jet are qualitatively similar to each otherand to the distributions shown in Fig. 6. This includeslocal distributions associated with each impingementimpact area at different spanwise locations in each stream-wise row.

This spanwise periodicity asy/Dvaries is also shown bythe local Nusselt number data which are presented inFig. 10b. These data are given for the same impingementMach numbers at several different x/D values. Streamwisevariations of local Nusselt numbers are then given inFig. 10a fory/D= 0. For each x/Dand y/Dlocation, localNusselt numbers are either invariant as the impingementMach number increases, or increase with impingementMach number. The smaller peak values present in eachdistribution in Fig. 10a near x/D= 16, x/D= 32, andx/D= 48, and x/D= 64 (which are positioned betweenthe larger peak values) are due to local Nusselt numberincreases at spanwise locations approximately halfwaybetween target surface impact regions of nearby impingingjets.

Corresponding line-averaged Nusselt number data as

they vary with x/D are given in Fig. 11, also for

Rej= 60,000 and Ma= 0.16, 0.21, 0.38, 0.63, and 0.74.Like the data presented in Fig. 8, these data are alsoobtained by line-averaging over y/D values from 8.0 to+8.0. Fig. 11 shows that local maximum Nu values havethe same approximate streamwise spacing as the stream-wise spacing of the holes located on the impingement jetplate. Associated local maximum values here generally

decrease at successive x/D locations for each value of

0

10

20

30

40

50

0 20 40 60 80

X/D

Nu

Re=5200

Re=6400

Re=8200

Fig. 8. Surface Nusselt number variations with x/D, which are line-averaged over y/D from 8.0 to +8.0, for Ma= 0.10, and Rejvalues of5200, 6400, and 8200.

Fig. 9. Spatially resolved distributions of surface Nusselt number forRej= 60,000 and Mavalues of (a) 0.16, (b) 0.21, (c) 0.38, (d) 0.63 and (e)0.74.



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impingement Mach number, Ma. In most cases, line-aver-aged Nu values increase at each x/D location as Maincreases. Exceptions to this trend are exhibited by theMa= 0.21 data which show higher peak values (comparedto data measured at lower Mach numbers) near the x/D=16, x/D= 24, and x/D= 32 locations.

3.6. Comparisons of spatially averaged Nusselt numbers with

existing correlations, and development of a new correlation

Spatially averaged Nusselt numbers are compared to thecorrelation of Florschuetz et al.[9] in Fig. 12a and b. Eachdata point in these figures from the present investigation isdetermined by averaging local Nusselt number data overy/D values from 8.0 to +8.0, and over an x/D range of8.0 (or x/D=4.0 to x/D= +4.0) relative to the centersof the nominal jet impact locations (which correspond tothe x/D centers of the impingement plate holes). The first

of these figures shows Ma= 0.10 data for Rej values of5200, 6400, and 8200. Here, data from the present studyshow reasonably good matches to the correlation valuesfrom Florschuetz et al.[9]for all of these experimental con-ditions. Fig. 12b presents the present spatially averageddata for Rej= 60,000, and Ma values of 0.16, 0.21, 0.38,0.63, and 0.74. In this figure, the experimental data associ-ated with Ma= 0.16 and Ma= 0.21 are in good agreement

with the Florschuetz et al.[9] correlation. The present datathen deviate from this correlation by larger amounts as theimpingement Mach number increases further, with the larg-est deviation evident for Ma= 0.74. In general, the trendsshown by the data in Fig. 12b are qualitatively consistentwith results from Brevet et al.[22]for a single impingementjet.

The variation of spatially averaged Nusselt numberswith Mach number is shown in Fig. 12c. These data aregiven for specific x/D values, and for specific values of

0

50

100

150

200

250

300

0 20 40 60 80

x/D

Nu

0

100

200

300

400

-10 -5 0 5 10

y/D

Nu

a

b

Fig. 10. Local surface Nusselt number variations forRej= 60,000 and Mavalues of 0.16, 0.21, 0.38, 0.63, and 0.74. (a) Variations withx/Dfor y/D= 0.(b) Variations with y/D for x/D= 8, 32, 32, 32, and 32.

60

80

100

120

140

160

180

200

0 20 40 60 80

x/D

Nu

Fig. 11. Surface Nusselt number variations withx/D, which are line-averaged overy/Dfrom8.0 to +8.0, for Rej= 60,000 and Mavalues of 0.16, 0.21,

0.38, 0.63, and 0.74.



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the impingement Mach number. The correlation equationwhich best represents these data is given by

Nu=NuF 1:00:325M1:55a 11

As such, this correlation equation is valid for Rej= 60,000,0.21 6 Ma 6 0.74, X/D= 8, Y/D= 8, Z/D= 3, and20 6 x/D 6 60.

3.7. Recovery factor data

Recovery factor data provide information on the varia-tion of adiabatic surface temperature over the test surface.Examples are shown in Fig. 13ac for Rej= 60,000 andMa= 0.74. The contour plot data inFig. 13a show highervalues of recovery factor RF beneath and in the vicinity ofimpact locations of the impingement jets. This is becauseT0j= 23.27 C, which is approximately equal to Tambient

for these tests which givesTjequal to6.16 C. As a result,

there is heat transfer to the impinging air streams from thesurrounding air, an effect which is enhanced by the familiesof vortices associated with the jet, and the enhanced mixingand entrainment they produce of surrounding fluid to thejets [12]. Nearby jet impact locations, values of RF con-tinue to be relatively high and in general, greater than

1.0, especially on the spanwise sides of impact locations.However, values are occasionally less than one at upstreamand downstream locations. Such local variations and thequantitative variations associated with them are furtherillustrated by the local RF data presented as it varies withx/D for y/D= 0, 4, and 8 in Fig. 13b, and as RF varieswith y/D for x/D= 32, 48, and 56 in Fig. 13c. Note thatvalues of TAW, determined from RF data and spatiallyaveraged over the test surface, approximately match mag-nitudes ofT0j for most all experimental conditions wherethese data are measured.

Fig. 12. Comparison of spatially averaged Nusselt numbers with corre-lation of Florschuetz et al. [9]. (a) Data for Ma= 0.10, and Rejvalues of5200, 6400, and 8200. (b) Data for Rej= 60,000 and Ma values of 0.16,0.21, 0.38, 0.63, and 0.74. (c) Nusselt number data at specific x/dlocationscorrelated with respect to Mach number.

b

0.98

1

1.02

1.04

35 40 45 50 55 60

x/D

RF

y/D=0.0

y/D=4.0

y/D=8.0

c

0.98

1

1.02

1.04

-15 -5 5 15y/D

RF

x/D=32

x/D=48

x/D=56

a

x/D

Y/D

Fig. 13. Recovery factor data for Rej= 60,000 and Ma= 0.74. (a) Localsurface recovery factor distribution. (b) Local surface recovery factor dataas it varies with x/D for y/D= 0, 4, and 8. (c) Local surface recovery

factor data as it varies with y/Dfor x/D= 32, 48, and 56.



13/14

3.8. Nusselt number data corrected using local recovery

factors

The local and line-averaged Nusselt number data pre-sented in Fig. 14ac are based on the difference betweenthe local, spatially varying measured surface temperatureTW, and the local adiabatic surface temperature TAW,

determined from recovery factor data given in Fig. 13a.This is accomplished by correcting local Nusselt numbervalues using the equation given by

Nuc NuTW T0j=TWTAW 12

Recall that T0j represents the adiabatic surface tempera-ture, spatially averaged over the test plate. The results inFig. 14ac are given for Rej= 60,000 and Ma= 0.74. Acomparison of Fig. 14a with results presented in Fig. 9dthen shows that local corrected Nusselt numbers Nucbasedon local (TW TAW) (i.e. Fig. 14a) have slightly higherpeaks than local Nuvalues based on TW T

0j (Fig. 9d).

This trend is also illustrated by the local Nusselt number

data presented as it varies with x/D (for y/D= 0) inFig. 14b, as well as by the line-averaged Nusselt numberdata given inFig. 14c. The relative differences between cor-rected and uncorrected data in these figures are generallyquite small because recovery factors in Fig. 13ac are closeto 1.00 with the largest values in the vicinity of 1.03. As a

result, spatially averaged Nusselt numbers are approxi-mately the same regardless of whether they are based upon(TW TAW) or TWT

0j.

4. Summary and conclusions

In the present investigation, data are given for anarray of impinging jets in the form of discharge coeffi-cients, local and spatially averaged Nusselt numbers,and local and spatially averaged recovery factors. Thespacing between holes in the streamwise direction X isthen 8D, and the spanwise spacing between holes in a

given streamwise row Y is also 8D. The thickness of eachimpingement plate is 1D, and the spacing between thehole exit planes and the target plate is denoted Z andis equal to 3D.

Experimental spatially averaged, surface Nusselt num-ber data obtained for a constant impingement Mach num-ber Ma of 0.1, and different Reynolds numbers Rej from5200 to 8200 show good agreement with the correlationof Florschuetz et al. [9]. Nusselt number data obtained ata constant Reynolds number of 60,000 and differentimpingement Mach numbers also shows good agreementwith the Florschuetz et al. [9] correlation, provided

Ma= 0.16 and Ma= 0.21. Measured spatially averagedresults for Rej= 60,000 then deviate from this correlationby larger amounts as the impingement Mach numberincreases further, with the largest deviation evident forMa= 0.74. A new correlation equation for spatially aver-aged Nusselt numbers is then presented for this range ofMach numbers. The variations represented by this correla-tion are due to local Nusselt numbers and line-averagedNusselt numbers, which generally increase with Machnumber at different x/D and y/D locations, providedRej= 60,000 and impingement Mach number Mais greaterthan 0.21. Local, spatially resolved Nusselt number dataalso show that only one local maximum value is presentunderneath each jet, with local peak line-averaged Nu val-ues, which generally decrease with streamwise developmentat successive x/D locations.

Local spatially resolved Nusselt number data obtained aMach number Ma of 0.74, and Rej= 60,000 are alsocorrected to account for local variations of the adiabaticsurface temperature, which are determined from localrecovery factor data. Local corrected Nusselt numbersNuc based on local (TWTAW) then have higher peaksthan local Nuvalues based on TW T

0j. This is because

local recovery factor RF data are higher beneath and inthe vicinity of impact locations of the impingement jets,

with values as large as 1.03.

b

0

50

100

150

200

250

300

30 40 50 60 70

x/D

Nu

y/D=0.0 uncorrected

y/D=0.0 corrected

c

0

50

100

150

200

250

30 40 50 60 70

x/D

Nu

uncorrected

corrected

NuC

NuC

a

Fig. 14. Corrected and uncorrected surface Nusselt number data forRej= 60,000 and Ma= 0.74. (a) Local corrected surface Nusselt numberdistribution. (b) Local surface Nusselt number data as it varies with x/Dfor y/D= 0. (c) Surface Nusselt number variations with x/D which areline-averaged over y/Dfrom8.0 to +8.0.



14/14

Acknowledgments

The present investigation is supported by Solar TurbinesInc of San Diego, California, USA.

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