Overall Effectiveness and Flowfield Measurements for an

Amy Mensch12

Department of Mechanical

and Nuclear Engineering

The Pennsylvania State University

University Park PA 16802

e-mail amymenschnistgov

Karen A TholeDepartment of Mechanical

and Nuclear Engineering

The Pennsylvania State University

University Park PA 16802

e-mail ktholepsuedu

Overall Effectivenessand Flowfield Measurementsfor an Endwall WithNonaxisymmetric ContouringEndwall contouring is a technique used to reduce the strength and development ofthree-dimensional secondary flows in a turbine vane or blade passage in a gas turbineThe secondary flows locally affect the external heat transfer particularly on the endwallsurface The combination of external and internal convective heat transfer along withsolid conduction determines component temperatures which affect the service life of tur-bine components A conjugate heat transfer model is used to measure the nondimensionalexternal surface temperature known as overall effectiveness of an endwall with nonaxi-symmetric contouring The endwall cooling methods include internal impingement cool-ing and external film cooling Measured values of overall effectiveness show that endwallcontouring reduces the effectiveness of impingement alone but increases the effective-ness of film cooling alone Given the combined case of both impingement and film cool-ing the laterally averaged overall effectiveness is not significantly changed between theflat and the contoured endwalls Flowfield measurements indicate that the size and loca-tion of the passage vortex changes as film cooling is added and as the blowing ratioincreases Because endwall contouring can produce local effects on internal cooling andfilm cooling performance the implications for heat transfer should be considered inendwall contour designs [DOI 10111514031962]

Introduction

The gas turbine industry continues to require higher overallengine efficiency and therefore more effective and efficient tur-bine component designs Turbine cooling performance continuesto be important in order to maintain component life and reliabilityas well It may be possible to improve both efficiency and coolingperformance with three-dimensional endwall contouring Endwallcontouring can reduce the strength of the passage vortex and othersecondary flows which causes increased heat transfer on the end-wall surface Although contouring reduces secondary flows theimpact of contouring on the heat transfer and cooling performanceis not straightforward

The overall cooling performance of a contoured endwall rela-tive to a flat endwall depends on the local change of heat transfercoefficients as well as the changes in film coolant distribution Itis important to understand how traditional cooling methods willperform when applied to contoured endwalls In the case of filmcooling jets the changing gradient of the surface may increase ordecrease film cooling attachment and effectiveness For internalimpingement cooling the impingement plate to target spacingwill vary leading to a range of impingement cooling effects

The current study examines the thermal performance of a con-toured endwall with a typical endwall cooling configuration thatincludes impingement cooling and angled film cooling holesBoth surface thermal measurements and flowfield measurementsare used to learn how the passage secondary flows and film cool-ing interact to influence the cooling performance of contouredendwalls These types of data will allow turbine designers to

generate cooling arrangements and methods that are optimized forcontoured endwalls

Relevant Literature

A conjugate heat transfer approach can be applied inexperiments and computational simulations to determine the non-dimensional external metal temperature also known as overalleffectiveness Overall effectiveness is defined as the differencebetween the mainstream temperature and the external metal tem-perature divided by the overall mainstream-to-coolant tempera-ture difference The definition along with its relationship to theimportant nondimensional parameters will be described in thenext section Albert et al [1] were the first to derive an equationfor by considering one-dimensional heat transfer The equationdemonstrated that it is necessary to match the Biot number Bi aswell as the ratio of internal-to-external heat transfer coefficientsh1hi to acquire relevant scaled data in a conjugate simulation orexperiment

The practice of reporting the values of these nondimensionalparameters only exists for more recent studies However conju-gate studies without matched Bi and h1hi still provide conjugateresults to compare to computational predictions for model valida-tion The first conjugate heat transfer experiments for turbineapplications by Hylton et al [23] and Turner et al [4] provideda benchmark for computational work and improved understandingof the thermal fields of a conducting vane Papanicolaou et al [5]and Panda and Prasad [6] compared computational predictions toexperimental measurements of conjugate heat transfer for a film-cooled flat plate Panda and Prasad [6] also studied a configurationthat included internal impingement cooling The qualitativeeffects of heat conduction within the wall were apparent in bothstudies but quantitatively the temperature distribution and gra-dients require a matched Bi and h1hi configuration

Properly scaled conjugate heat transfer models have been usedto determine the relative importance of impingement and film

1Corresponding author2Present address National Institute of Standards and Technology Gaithersburg

MD 20899Contributed by the International Gas Turbine Institute (IGTI) of ASME for

publication in the JOURNAL OF TURBOMACHINERY Manuscript received October 72015 final manuscript received October 21 2015 published online December 222015 Editor Kenneth C Hall

Journal of Turbomachinery MARCH 2016 Vol 138 031007-1Copyright VC 2016 by ASME

Downloaded From httpturbomachineryasmedigitalcollectionasmeorg on 12222015 Terms of Use httpwwwasmeorgabout-asmeterms-of-use

cooling to overall effectiveness The first experiments to usean engine-matched Bi experimental model were completed bySweeney and Rhodes [7] for a three-dimensional flat plate with in-ternal impingement and film cooling Between the impingementplate and the wall were heat transfer enhancement features in aLamilloy

snowflake design Their results showed that impinge-ment cooling dominated over film cooling in the distribution ofexternal wall temperatures A series of matched Bi experimentsand simulations studied a vane leading edge model with internaljet impingement and external film cooling [8ndash11] There wasslight difference between the cases with and without impingementdue to the high effectiveness of the showerhead film coolingAnother series of engine-matched Bi studies [12ndash14] measuredthe effectiveness and thermal fields above a vane suction side withfilm cooling and impingement Williams et al [12] showed thatfor this part of the vane the impingement cooling contributed sig-nificantly to the overall effectiveness even more than the contri-bution from film cooling They concluded that as the blowingratio increased the improvement in impingement cooling com-pensated for the reduction in film cooling effectiveness As withthe flat plate and the vane the importance of impingementcooling for the endwall of an airfoil was observed by Mensch andThole [15]

Unlike a flat plate or vane surface endwall external heat trans-fer coefficients are influenced by three-dimensional secondaryflow structures including the horseshoe and passage vortices[16ndash19] Endwall heat transfer increases near the leading edgepressure side and wake of the Pack-B blade used in the presentstudy as shown in Fig 1(a) with contours of Nusselt number Nufor a flat endwall [16] Figure 1(b) gives the heat transfer augmen-tation due to nonaxisymmetric endwall contouring designed byPraisner et al [20] to minimize passage aerodynamic losses [16]

Endwall contouring can reduce aerodynamic losses by reducingthe cross-passage pressure gradient and the strength of the passagevortex compared to a flat endwall [21] The effect of endwall con-touring on the Pack-B passage vortex was measured by Lynch[22] using laser Doppler velocimetry From the three-dimensionalaverage flow measurements it was found that contouring slightlyreduced the strength of the passage vortex and delayed its progres-sion to the suction side of the passage Although Lynch [22] andothers have measured the passage flowfield in detail with andwithout endwall contouring the effects of film cooling on thepassage vortex development and strength have not been measuredConsidering that the film cooling jets at high blowing ratiosdetach from the endwall the interactions between the passagevortex and film cooling are investigated in the current study

Contouring can also reduce overall endwall heat transfer by thesame mechanism as the reduction in losses [1623] Figure 1(b)shows that the Pack-B endwall contouring increased heat transfer

at the leading edge and upstream portions of the passage How-ever the overall area-averaged heat transfer coefficient across theentire passage was reduced by 3 [16] Also contouring was ableto reduce heat transfer in the regions with the highest heat transfernear the pressure side Although the metric of heat transfer aug-mentation conveys the heat transfer performance due to endwallcontouring the primary metric for cooling performance is theoverall effectiveness which is obtained with a conjugate model inthe current study

Conjugate Endwall Model

The conjugate heat transfer in the contoured endwall is approxi-mated as one-dimensional using the conjugate endwall model asdepicted in Fig 2 The endwall model includes the combinedeffects of the internal and external convective heat transfer as wellas the solid heat conduction to obtain the scaled endwall tempera-tures The data are engine relevant if the appropriate physicalparameters are matched between the experimental model andengine conditions

The relevant nondimensional parameters can be found from thefollowing equation

frac14 T1 Tw

T1 Tcinfrac14 1 vg

1thorn Bithorn h1=hi

thorn vg (1)

which is derived from a one-dimensional heat transfer circuit usingFig 2 Equation (1) reveals that the endwall overall effectiveness isa function of the Bi h1hi and the product vg which representsan estimate for the nondimensional film temperature [12] Thedimensionless film temperature is approximated by the adiabaticeffectiveness g and a scale factor v which is defined as

v frac14 T1 Tcexit

T1 Tcin(2)

The coolant warming factor v corrects g for the warming of thecoolant during impingement and flow through the film coolingholes [12] Adiabatic effectiveness and the coolant warming factorare assumed to be functions of the geometry the mainstream flowparameters and the film cooling flow parameters such as the filmcooling blowing ratio M

Table 1 lists the nondimensional parameters matched to anengine for both the experiments and simulations in this studyEngine-matched Bi is achieved by thermoforming the contouredendwall from Corian

The contoured endwall heat transfer h1

is obtained from heat transfer measurements by Lynch et al [16]

Fig 1 Heat transfer measurements for the Pack-B cascade atReexit of 2 3 105 (Ref [16]) (a) Nusselt number contours for theflat endwall and (b) heat transfer augmentation contours due toendwall contouring with box for area-averaging

Fig 2 One-dimensional conjugate model of a conducting end-wall with impingement and film cooling

031007-2 Vol 138 MARCH 2016 Transactions of the ASME

A Nu correlation for an impingement array with staggered coolantextraction [24] is used to estimate the range of hi for each blowingratio The blowing ratio Mavg affects vg and defines the averageratio of coolant to mainstream mass flux

Experimental and Computational Methods

Experimental Methods Experiments to measure the con-toured endwall overall effectiveness and the passage flowfieldwere completed using a large-scale low-speed closed-loop windtunnel as shown in Fig 3(a) In this facility the flow was splitupstream of the test section into a mainstream section in thecenter and into coolant streams above and below the mainstreamsection The mainstream flow passed through a heater bank andflow conditioning elements including a turbulence grid 11Cax

upstream of the test section More details about the wind tunneland flow conditioning can be found in Ref [16]

The corner test section contained seven blades in a linearcascade as shown in Fig 3(b) The low-pressure turbine Pack-Bairfoil was used in the cascade because it has been used in severalother studies particularly studies of contoured endwall perform-ance [1516202125ndash27] The nonaxisymmetric contouringdesigned by Praisner et al [20] was implemented for the endwallThe darker portion of the endwall in Fig 3(b) was conducting and

contained the contoured geometry The rest of the endwall outsideof the passages was made from insulating medium density fiber-board Passages 3 and 4 were cooled by both internal impinge-ment cooling and film cooling Passages 1 and 2 had film coolingbut no impingement cooling Passages 5 and 6 had only impinge-ment cooling and the coolant was exhausted laterally from theside of the impingement channel There was good periodicitybetween the blades in the cascade as shown in Fig 4 which givesthe pressure distribution measured at the midspan of each blade asa function of axial distance The computational prediction of pres-sure distribution from two previous studies [2526] is shown forcomparison

The inlet conditions to the passage were measured at multiplespanwise and pitchwise locations at 052Cax upstream of theblades in the axial direction A thermocouple rake was used tomeasure the incoming flow temperature The variation in tempera-ture at different locations was less than 606 C from the averageT1 The incoming flow velocity was measured using a Pitot probeat midspan of the test section The mainstream inlet velocityU1in had a standard deviation of less than 1 Table 2 providesa summary of the blade geometry and mainstream flow condi-tions Additionally the inlet boundary layer was characterized at285Cax upstream of the center blade to have dSfrac14 0061 and 6freestream turbulence [16]

The coolant stream was extracted by a blower at the top of thewind tunnel as shown in Fig 3(a) The coolant was dried toremove any humidity cooled and then diverted to separate ple-nums below the endwall as shown in Fig 3(c) The coolant flowrate was adjusted to achieve the required blowing ratio and meas-ured using a laminar flow element The blowing ratio reportedwas an average of the local blowing ratio for each film coolinghole The coolant flow rate uncertainty was estimated withsequential perturbation [28] to be 63 for a 95 confidenceinterval The coolant temperature Tcin was measured with twothermocouples suspended in each plenum 87D below thecooling holes in the impingement plate or 87D below the endwallwhen no impingement plate is used The mainstream-to-coolant

Table 1 Conjugate contoured endwall parameters

Parameter Model Typical engine

Mavg 06 10 20 10ndash20kw (Wm K) 099ndash106 22tw (cm) 127 020Bifrac14 h1twkw 03ndash07 [16] 027h1hi Mfrac14 06 10ndash23 [1624] 10

Mfrac14 10 06ndash14 [1624]Mfrac14 20 04ndash10 [1624]

Fig 3 Depiction of (a) the large-scale low-speed wind tunnel(b) the test section containing the Pack-B linear blade cascadeand conjugate endwall and (c) the side view of the plenum andimpingement channel for the flat endwall

Fig 4 Pack-B cascade static pressure distribution at the blademidspan compared to CFD predictions

Table 2 Flow conditions and blade geometry

Scale factor 86 Inlet U1in 105 ms

Cax 0218 m Inlet flow angle 35 degpCax 0826 Exit flow angle 60 degSCax 250 Inlet Ma 0029Inlet Re 122 105 Exit Ma 0047Exit Re 198 105

Journal of Turbomachinery MARCH 2016 Vol 138 031007-3

temperature difference was typically 40 C which yielded acoolant-to-mainstream density ratio of about 115

The contoured endwall was cooled by an impingement and filmcooling configuration designed for comparison to the impinge-ment and film-cooled flat endwall used by Mensch et al[152529] A flat impingement plate with an array of 28 staggeredholes was located below the endwall as shown in Fig 3(c) Thecoolant exited the impingement channel through ten film coolingholes angled at 30 deg to the endwall surface at the hole exit Asmentioned previously the coolant exited through a slot on theside of the impingement channel when film cooling was not usedThe impingement holes and film cooling holes all had a diameterof Dfrac14 44 mm The spacing between the impingement holes was465D

Special attention was given to the location of the film coolingholes for both the flat and the contoured endwall designs For theflat endwall the inlets to the film cooling holes were locatedbetween the rows of impingement holes The 30 deg angled filmcooling holes were aligned in the xndashy plane to match the directionof the qualitative endwall streaklines The endwall streaklines andfilm cooling hole locations for both flat and contoured endwallsare shown in Figs 5(a) and 5(b) [16] In the contoured endwallthe film cooling exit locations were at the same location as the flatendwall configuration in order to compare the film cooling behav-ior at the same location Since the endwall streaklines differbetween the flat and the contoured endwalls the orientation of thefilm cooling holes changed between the two designs especially inthe row that extended downstream across the passage Because ofthe changing hole orientation as well as the contour itself the sizeand location of the film cooling hole inlets are different betweenthe flat and the contoured endwalls For the case of the contouredendwall a few of the film cooling hole inlets are larger and closerto the impingement hole locations than the flat endwall film cool-ing holes The length of the film cooling holes L also variesbetween 42D and 80D for the contoured endwall while all of theflat endwall film cooling holes have Lfrac14 58D

A qualitative representation of the hills and valleys of the end-wall contouring is given in Fig 5(c) The design incorporated ahill on the pressure side and a valley on the suction side in theupstream half of the passage to reduce cross-passage pressuregradients [20] A ridge and valley in the downstream half of thepassage helped displace the passage vortex and reduce exit flowangle deviation as shown by the streaklines in Fig 5(b) comparedto Fig 5(a) The contoured endwall in this study was constructedwith a constant thickness to retain a relatively uniform Bi acrossthe passage which was similar to the flat endwall A consequenceof the constant thickness endwall was a varying distance betweenthe flat impingement plate and the endwall H The nominal H at

the inlet and exit of the passage was the same H used for the flatendwall 29D For the contoured endwall however H variedbetween 06D and 34D

Temperatures on the surface were measured with infrared (IR)thermography using an FLIR P20 IR camera The ceiling of thetest section contained removable viewing ports to allow directoptical access and achieve an image resolution of 57 pixelsD Atleast two thermocouples per image area were embedded in theendwall with the bead at the surface When the thermocouplesindicated that steady-state was achieved five images wereacquired from each port The images at each location were cali-brated for emissivity and reflected temperature by minimizing thedifference between the thermocouple measurements and theimage temperatures at the thermocouple locations The emissivitywas typically 092 from the flat black paint on the surface Thecalibrated images at each location were averaged together andassembled into a complete endwall temperature map The uncer-tainty in the external effectiveness was estimated as 6002 for a95 confidence interval [15]

Computational Methods Conjugate RANS simulations forthe contoured endwall were performed using the commercialsoftware FLUENT [30] which uses the segregated pressure-basedSIMPLE algorithm The SST kndashx turbulence model [31] wasused for closure with second-order spatial discretization schemesThe computational grid is depicted in Fig 6(a) which shows theboundary conditions Periodic boundaries extending through thedomain were used to simulate a single blade passage The speci-fied velocity and boundary layer profile at the inlet were bench-marked to the measurements by Lynch et al [16] An outflowboundary condition was applied at the outlet and a symmetryboundary condition was applied at the top of the domain A massflow inlet boundary condition was applied at the bottom of theplenum to correspond to the flow and temperature conditions asso-ciated with each blowing ratio Conjugate interfaces were ther-mally coupled and all other surfaces were adiabatic Convergenceof a simulation was achieved when the normalized residuals wereless than 1 104 and the area-averaged endwall changed byless than 00015 over 500 iterations Additional details regardingthe solution methods and boundary conditions can be found inRef [25]

Unstructured grids were generated for the endwall and flowdomains using Pointwise [32] The flow domain grid containedwall-normal prism layers to resolve the boundary layers such thatthe ythorn of the first grid point was less than one Figure 6(b) showsa slice of the grid in the impingement channel impingement holeand film cooling hole The grid size was 106 106 cells for the

Fig 5 Comparison of oil flow visualization of endwall streaklines [16] with film cooling holeinlet and outlet locations for the (a) flat and (b) contoured endwalls and (c) qualitative repre-sentation of the contoured endwall height

flow domain and 18 106 cells for the endwall domain A gridsensitivity study was conducted for the case of the flat endwallmesh generated in the same manner as the contoured endwallmesh [25]

Flowfield Measurement Methods Time-resolved particleimage velocimetry (PIV) was used to measure the flowfield inthree two-dimensional planes near the trailing edge of the passagesuction side as shown in Fig 7 Planes A and B were parallel tothe exit flow direction 5D and 3D from the center of the center-line of the blade trailing edge respectively Plane C was parallelto the trailing edge of the passage at an axial location of 108Cax

from the leading edge Plane C was at an angle of 30 deg fromplanes A and B and crossed the other planes near the trailingedge as shown in Fig 7(a) Figure 7(b) shows the approximatelocations where planes A and B cross plane C while viewing theflat endwall predicted contours of turbulent kinetic energy inplane C Figure 7(a) also shows the relative locations of the filmand impingement holes in the endwall

During the PIV measurements the flow was seeded with atom-ized liquid di-ethyl-hexyl-sebacat resulting in an average Stokes

number much less than one The particles in the measurementplanes were illuminated with an NdYLF laser sheet and imagedwith a high-speed CMOS camera oriented normal to each mea-surement plane Images at planes A and B were taken for a win-dow size of 1024 1024 at 1 kHz and a resolution of 22 pixelsDImages at plane C were taken for a window size of 1024 512 at2 kHz and a resolution of 16 pixelsD The total number of imagepairs recorded was 3000 at planes A and B and 6000 at plane CThe total data acquisition time for all three planes was 3 s Theflow crossed the domain at least 90 times in the data acquisitionperiod The time delay between laser pulses was chosen based onan estimated bulk movement of 10 pixels about 16 the initialinterrogation window size

Image processing and vector calculation were performed withLAVISION software [33] To increase the contrast of the raw imagesthe sliding minimum of the surrounding three images was sub-tracted from each image prior to vector calculation The vectorcalculation was performed using a cross-correlation over fourpasses with a decreasing interrogation window at each pass Vec-tor postprocessing evaluated possible spurious vectors throughtwo passes of a median filter using universal outlier detection fora 3 3 pixel region [33] Empty spaces surrounded by at least twocalculated vectors were filled by interpolating between thesurrounding vectors

Results and Discussion

Effects of Contouring on Overall Effectiveness Measurementsand computational predictions of the contoured endwall overalleffectiveness are shown in Fig 8 for blowing ratios of Mfrac14 10and 20 Overlaid on the contour plots are the locations of the filmcooling holes impingement holes and plenum boundaries as wellas an elevation map for the height of the contoured endwall Dot-ted lines indicate negative height values where there is a valleyThe measured results are shown for passage 4 The area used foraveraging is shown by the box in Fig 1(b)

In general there is good agreement between the predictions andthe measurements of contoured endwall effectiveness except forthe common failure of RANS to accurately predict film cooling

Fig 6 Depiction of (a) the computational domain and bound-ary conditions and (b) the prism layer volume grid in the holesand impingement channel

Fig 7 Planes measured with PIV (a) shown from above and (b)shown from the view of plane C overlaid with flat endwall CFDtke contours for Mavg 5 20

Fig 8 Contoured endwall overall effectiveness for (a)Mavg 5 10 measured (b) Mavg 5 10 predicted (c) Mavg 5 20measured and (d) Mavg 5 20 predicted

jet mixing and attachment [131434] A similar overprediction offilm jet attachment was found for the flat endwall simulation byMensch et al [25] Downstream in the passage the predicted isabout 005 less than the measurements This difference betweenthe measured and predicted downstream was also observedfor the flat endwall and was attributed to heat losses in theexperiments from boundaries assigned as adiabatic in the simula-tions [25]

Figure 9 compares the overall effectiveness with film andimpingement cooling of the flat endwall to the contoured endwallThe locations of the cooling holes and plenum boundaries areshown for all cases The change in height of the contoured end-wall is also shown with elevation lines in Figs 9(d)ndash9(f) Figure10 shows the laterally averaged effectiveness as a function of theaxial distance across the passage for both flat and contoured end-walls The data in Fig 10(a) for the cases with film and impinge-ment cooling correspond to the contour plots in Fig 9 Figures10(b) and 10(c) compare the effectiveness for the cases with filmcooling only and impingement only respectively The overall

effectiveness peaks around the first row of film cooling holes andincreases with blowing ratio as discussed in Ref [15]

Generally the results for the contoured endwall are similar tothose for the flat endwall as shown in Figs 9 and 10 One differ-ence seen in Fig 9 is that there is slightly increased effectivenessdue to film cooling with contouring especially for the upstreamrow of film cooling holes at Mavgfrac14 10 Improved film coolingeffectiveness can also been seen in Fig 10(b) where the peakeffectiveness is higher for the contoured endwall than for the flatendwall

Endwall contouring reduces the effect of the passage vortex onthe endwall flow as can be seen in the oil flow visualization of theendwall streaklines in Figs 5(a) and 5(b) With a contoured end-wall the film cooling jets are less disturbed by the weaker passagevortex Additionally it is observed in Fig 9 that the holes in thefirst row are near a valley of the contour and may experience amore favorable pressure distribution coming out of the valleywhich promotes jet attachment

When comparing the contoured endwall to the flat endwall in aconjugate analysis one must consider both the change in filmcooling (local fluid driving temperature) and the change in theexternal heat transfer coefficient For the case in which the exter-nal heat transfer coefficient increases due to endwall contouringand the film coolant stays along the surface one would expect alower wall temperature (higher effectiveness value) For the casein which the external heat transfer coefficient increases but thefilm coolant is separated from the surface one would expect ahigher wall temperature (lower effectiveness value) There arealso possibilities in between that give competing effects

In reviewing the effectiveness results in Figs 9 and 10 it canbe seen that the film cooling effectiveness improves with contour-ing Because the external h1 is higher with contouring in theupstream half of the passage (Fig 1(b)) there is an overall reduc-tion of the wall temperature (higher effectiveness value) Theboxed area in Fig 1(b) surrounds the region containing theimpingement and film cooling holes Within this area the averageheat transfer augmentation isthorn 4 with contouring Along thepressure side of the blade there is a 20ndash30 reduction in h1Although this area has no external cooling the contoured endwallincreases the by 01ndash012 for Mavgfrac14 20 in Fig 9(f) whichresults in lower wall temperatures

Although contouring improves the effectiveness of the externalcooling the internal cooling appears to be less effective with con-touring The contoured endwall laterally averaged effectiveness

with impingement only o in Fig 10(c) is similar qualitativelyto the flat endwall but the level of effectiveness is considerablyless for the contoured endwall compared to the flat endwall Sincethe endwall thickness is uniform and the same as the flat endwall

Fig 9 Measured endwall overall effectiveness for the flatendwall [15] at (a) Mavg 5 06 (b) 10 and (c) 20 and for the con-toured endwall at (d) Mavg 5 06 (e) 10 and (f) 20

Fig 10 Laterally averaged overall effectiveness for (a) film and impingement (b) film cooling only and (c) impingementonly measured for the flat and contoured endwalls

the differences arise from the changes that the contoured endwallhas on the internal and external heat transfer coefficients The in-ternal hi is affected by the contouring because the HD variesacross the passage which locally reduces hi from its peak per-formance at HD 3 [29] Although the variation in HD contrib-

utes to lower o the HD effect does not fully account for thereduction because the area-averaged o with contouring is lessthan the area-averaged o for a flat endwall with nonoptimal HD

which was measured by Mensch and Thole [29] Reduced o isalso caused by the 4 increase in external h1 for the area sur-rounding the cooling features For impingement cooling only theexternal driving temperature is T1 and a higher h1 results inhigher wall temperatures In the other configurations with filmcooling the presence of cooler fluid in the film jets reduces theexternal driving temperature Therefore with film cooling theincrease in h1 does not result in lower effectiveness

Effects of Film Cooling on Contoured Flowfield The aver-age velocity vector field and turbulent kinetic energy (tke) fieldsare obtained with time-resolved PIV for the planes in Fig 7 Thethree trailing edge planes are of interest because the passage vor-tex causes an increase in endwall heat transfer in this region [16]The time-averaged in-plane streamlines are given in Fig 11 for nofilm cooling and for two blowing ratios Mavgfrac14 10 and 20 Themain component of velocity is in-plane for planes A and Bwhereas plane C has a significant out-of-plane component

The line of sight location of the blade trailing edge is shown ineach image for reference The background of each image is coloredby the measured velocity magnitude normalized by the inlet U1in

The low-velocity region in planes A and B in Fig 11 isassumed to be the location of the top of the passage vortex as itcirculates through the measurement planes which are approxi-mately aligned with the inviscid flow direction The streamlineswithin the low-velocity region converge downstream of the trail-ing edge line indicating a significant out-of-plane velocity com-ponent associated with the rotating vortex The top of the vortex ismoving away from the endwall as the streamlines below the topof the vortex are turned upward The passage vortex appears to bevery close to the blade since the velocities in plane B are muchlower than in plane A In plane C the passage vortex appearsslightly to the right of the line of sight location of the trailing edgebecause the flow is exiting the passage at a 30 deg angle to planeC and the flow exiting the passage is 69D to the right of its loca-tion at the blade trailing edge (see Fig 7(a))

The approximate z (spanwise) location of the top of thepassage vortex or the center of the low-velocity area is labeledin Fig 10(a) as Zp As film cooling is introduced inFigs 11(d)ndash11(i) Zp increases Table 3 reports the nondimen-sional ZpS for all nine images in Fig 11 The endwall film cool-ing not only increases the height of the passage vortex but alsoappears to fill some of the velocity deficit especially with thehighest blowing ratio The low-velocity region shrinks in plane Awith each increase in blowing ratio In planes B and C the

Fig 11 In-plane time-averaged streamlines measured with PIV with contours of magnitude for the contoured endwall for(a)ndash(c) no film cooling (d)ndash(f) Mavg 5 10 and (g)ndash(i) Mavg 5 20

velocity increase is more significant for the change fromMavgfrac14 10ndash20 There are other small changes in the shape of thelow-velocity region with film cooling for all three planes In planeC although the height of the passage vortex from the endwall isnot significantly changed with blowing ratio the width of the pas-sage vortex grows as blowing ratio increases

Contours of normalized turbulent kinetic energy (tke) are givenin Fig 12 for no film cooling (a)ndash(c) for Mavgfrac14 10 (d)ndash(f) andfor Mavgfrac14 20 (g)ndash(i) The line of sight location of the blade trail-ing edge is shown in each image for reference For a two-

dimensional velocity field tke is defined as 3=4eth u02 thorn v02THORN whichassumes the root mean square of the out-of-plane velocity fluctua-tions is an average of the other two components [33] The tke isnondimensionalized by the inlet velocity U1in

2 The contours of tke characterize the turbulence generated by

shear layers as well as the unsteadiness of large flow structuressuch as the passage vortex and film cooling jets In the mainstream

flow outside of the boundary layer tkeU1in2 is quite low and

only reflects the level entering from the upstream grid as expectedConsistent with the average velocity data the shear layer at thetop of the passage vortex clearly rises moving downstream InFig 12(c) without film cooling there are two distinct regions ofmaximum tke indicating there is a counter-rotating vortex locatedabove the passage vortex Figure 12(b) indicates the presence ofanother vortex with two bands of maximum tke on top of oneanother With the addition of film cooling these bands becomeclearer in the upstream half of Figs 12(e) and 12(h) The presenceof a second vortex also explains the elongated region of low ve-locity observed in the average velocity contours of Figs 11(c)11(f) and 11(i) This vortex originates from the suction-side legof the horseshoe vortex [35] or the second vortex could be a vor-tex induced by the passage vortex [36] Goldstein and Spores [35]noted that both this second vortex and the passage vortex moveaway from the endwall along the blade on the suction side of thepassage because the pressure is lower away from the endwall

Film cooling has a significant impact on the tke at the upstreamside of the images in Figs 12(d) and 12(g) The levels of tke atthe upstream side of plane A approximately double with eachincrease in blowing ratio The peak level of tke in Fig 12(g) is019 For both blowing ratios tested the film cooling jets are notwell attached and mix into the passage vortex Although the lastfilm cooling hole in the diagonal row exits at approximately 40Dupstream of the plane A images film cooling has a significantimpact on the turbulence levels downstream Film cooling also

Table 3 Distance from the endwall of the center of the low-velocity region ZpS

Plane A Plane B Plane C

No film cooling 013 013 016Mavgfrac14 10 015 015 016Mavgfrac14 20 016 016 016

Fig 12 Turbulent kinetic energy measured with PIV for the contoured endwall for (a)ndash(c) no film cooling (d)ndash(f) Mavg 5 10and (g)ndash(i) Mavg 5 20

increases the tke levels of the passage vortex in the upstream halfof plane B The other vortex is weakened with film cooling asseen on the downstream half of plane B and at the trailing edgeline in plane C With film cooling plane C also has a third peak intke located to the left of the trailing edge line and below the peaksassociated with the vortices This peak appears for Mavgfrac14 10 andbecomes more pronounced at Mavgfrac14 20 This region is also justbelow the extended region of low velocity in Fig 11(i)

Under the regions of peak tke in Fig 12 the tke levels increaseas the blowing ratio increases in all three measurement planesFilm cooling causes increased mixing near the wall which pro-motes heat transfer The thermal effect of this mixing can be seenin the nondimensional wall temperature contours of Fig 9 As thesecondary flows cross the passage they entrain cooler flow fromthe film cooling as well as from the endwall thermal boundarylayer The cooler secondary flow cools the endwall along thesuction-side trailing edge of the passage in Fig 9 The coolingeffect increases as the blowing ratio increases because there ismore coolant injected into the mainstream having two effects Asthe blowing ratio increases the temperature of the secondary flowis cooler and there is increased near-wall mixing downstreamfrom the film cooling as demonstrated in Fig 12

Conclusions

The current study examines the effects of endwall contouringon the overall effectiveness Previous research has shown thatendwall contouring reduces the area-averaged heat transfer coeffi-cient by delaying the development of the passage vortex and otherpassage secondary flows However the effects of contouring onthermal performance are more complicated than the effect on theaverage heat transfer coefficient The overall cooling effectivenessdepends on the local heat transfer coefficients and on the sur-rounding thermal fields which are determined by the effective-ness of the cooling methods with endwall contouring

Film cooling effectiveness improves with endwall contouringbecause the weakened passage vortex has less effect on the nearendwall flow and on cooling jet mixing with contouring Theflowfield measurements of the passage vortex show that the pas-sage vortex convects away from the endwall toward the midspanFilm cooling significantly affects the trajectory of the passage vor-tex by increasing the convective motion toward the midspanFrom the overall effectiveness measurements it can also be seenthat the influence of the passage vortex on the cooling of the end-wall near the trailing edge is diminished for the contoured endwallcompared to the flat endwall Another reason for improved filmcooling effectiveness with contouring is that the film cooling jetscan have better attachment to the surface compared to a flat end-wall if there is a local favorable pressure gradient due to the localsurface gradient in the contouring Although the conjugate heattransfer simulations can satisfactorily predict area-averaged over-all effectiveness their failure to accurately predict local film cool-ing effectiveness limits the benefit of RANS predictions for whenfilm cooling is important Although film cooling effectivenessimproves with contouring the internal impingement effectivenessworsens with contouring because the varying HD for thecontoured endwall causes a reduction in the impingementperformance

Local changes in the external heat transfer coefficient with end-wall contouring can either increase or decrease the local coolingperformance depending on the presence or lack of film coolantabove the endwall Increased h1 improves the overall effective-ness when film cooling is present but decreases the overall effec-tiveness (raises the wall temperature) when there is no filmcooling The increased h1 in the upstream half of the contouredpassage relative to the flat endwall can improve cooling becausethe presence of the film coolant lowers the effective external driv-ing temperature However an endwall with only impingementcooling and no film cooling has worse performance with contour-ing due to increased h1 Conversely decreased h1 improves the

overall effectiveness when film cooling is not present but internalcooling is present An example is the improved overall effective-ness along the pressure side where there is no film cooling and h1is reduced with contouring

For the current contoured endwall cooling geometry the per-formance for the flat and contoured endwalls is mostly the samewhen comparing the laterally averaged results although local var-iations are present In general the cooling performance with con-touring could increase or decrease depending on the local effectsIn order to optimize contoured endwall performance film coolingand internal cooling should be fully integrated into the design forcontoured endwalls

Acknowledgment

The authors would like to acknowledge the support from theUS Department of Energy (DOE) National Energy TechnologyLaboratory (NETL) through the University Turbine SystemsResearch (UTSR) program The authors also would like to thankDr Brent Craven currently with the FDA Mark Zelesky ofPratt amp Whitney Dr David Bogard of the University of Texasand Robin Ames of DOE-NETL for their communication andsupport regarding this research

Nomenclature

Bi frac14 Biot number (h1tkw)Cax frac14 axial chord lengthCp frac14 pressure coefficientD frac14 hole diameterh frac14 convective heat transfer coefficientH frac14 impingement gap heightk frac14 turbulent kinetic energy or thermal conductivityL frac14 length

M frac14 blowing ratio (qcUcq1U1)Ma frac14 Mach numberNu frac14 Nusselt number (hDkfluid)

p frac14 pitch lengthP frac14 pressure

PIV frac14 particle image velocimetryq frac14 heat flux

Re frac14 Reynolds number (q1U1inCaxl1)s frac14 streamwise coordinate for flow measurementsS frac14 blade spant frac14 thickness

T frac14 temperaturetke frac14 turbulent kinetic energy (34[(u0)2thorn (v0)2])

U frac14 velocityu0 frac14 fluctuating velocity

x y z frac14 global coordinates where x is blade axial direction

Greek Symbols

d99 frac14 boundary layer thickness (99)g frac14 adiabatic effectiveness (T1 Taw)(T1Tcexit)h frac14 momentum thicknessl frac14 dynamic viscosityq frac14 density frac14 overall effectiveness (T1Tw)(T1 Tcin)v frac14 internal coolant warming factor for g(T1Tcexit)

(T1 Tcin)

Subscripts and Accents

avg frac14 averageaw frac14 adiabatic wall

cexit frac14 coolant at film cooling hole exitcin frac14 coolant upstream of impingement plate

f frac14 film cooling onlyi frac14 internal

meas frac14 measured

o frac14 impingement cooling onlys frac14 static

w frac14 wall or external wall surface1frac14 external

1in frac14 mainstream conditions at the cascade inletethTHORN frac14 laterally averagedethTHORN frac14 area-averaged

References[1] Albert J E Bogard D G and Cunha F 2004 ldquoAdiabatic and Overall Effec-

tiveness for a Film Cooled Bladerdquo ASME Paper No GT2004-53998[2] Hylton L D Mihelc M S Turner E R Nealy D A and York R E

1983 ldquoAnalytical and Experimental Evaluation of the Heat Transfer Distribu-tion Over the Surfaces of Turbine Vanesrdquo NASA Lewis Research CenterCleveland OH Report No NASA-CR-168015

[3] Hylton L D Nirmalan V Sultanian B K and Kauffman R M 1988 ldquoTheEffects of Leading Edge and Downstream Film Cooling on Turbine Vane HeatTransferrdquo NASA Lewis Research Center Cleveland OH Report No NASA-CR-182133

[4] Turner E R Wilson M D Hylton L D and Kauffman R M 1985ldquoTurbine Vane External Heat Transfer Volume 1 Analytical and ExperimentalEvaluation of Surface Heat Transfer Distributions With Leading Edge Shower-head Film Coolingrdquo NASA Lewis Research Center Cleveland OH ReportNo NASA-CR-174827

[5] Papanicolaou E Giebert D Koch R and Schulz A 2001 ldquoAConservation-Based Discretization Approach for Conjugate Heat Transfer Cal-culations in Hot-Gas Ducting Turbomachinery Componentsrdquo Int J Heat MassTransfer 44(18) pp 3413ndash3429

[6] Panda R K and Prasad B V S S S 2012 ldquoConjugate Heat Transfer Froma Flat Plate With Combined Impingement and Film Coolingrdquo ASME Paper NoGT2012-68830

[7] Sweeney P C and Rhodes J F 2000 ldquoAn Infrared Technique for EvaluatingTurbine Airfoil Cooling Designsrdquo ASME J Turbomach 122(1) pp 170ndash177

[8] Maikell J Bogard D Piggush J and Kohli A 2011 ldquoExperimental Simu-lation of a Film Cooled Turbine Blade Leading Edge Including Thermal BarrierCoating Effectsrdquo ASME J Turbomach 133(1) p 011014

[9] Dobrowolski L D Bogard D G Piggush J and Kohli A 2009ldquoNumerical Simulation of a Simulated Film Cooled Turbine Blade LeadingEdge Including Conjugate Heat Transfer Effectsrdquo ASME Paper NoIMECE2009-11670

[10] Mouzon B D Terrell E J Albert J E and Bogard D G 2005 ldquoNet HeatFlux Reduction and Overall Effectiveness for a Turbine Blade Leading EdgerdquoASME Paper No GT2005-69002

[11] Ravelli S Dobrowolski L and Bogard D G 2010 ldquoEvaluating the Effectsof Internal Impingement Cooling on a Film Cooled Turbine Blade LeadingEdgerdquo ASME Paper No GT2010-23002

[12] Williams R P Dyson T E Bogard D G and Bradshaw S D 2014ldquoSensitivity of the Overall Effectiveness to Film Cooling and Internal Coolingon a Turbine Vane Suction Siderdquo ASME J Turbomach 136(3) p 031006

[13] Dyson T E Bogard D G and Bradshaw S D 2012 ldquoEvaluation of CFDSimulations of Film Cooling Performance on a Turbine Vane Including Conju-gate Heat Transfer Effectsrdquo ASME Paper No GT2012-69107

[14] Stewart W R and Bogard D G 2014 ldquoExperimental Thermal Field Meas-urements of Film Cooling Above the Suction Surface of a Turbine VanerdquoASME Paper No GT2014-27111

[15] Mensch A and Thole K A 2014 ldquoOverall Effectiveness of a Blade EndwallWith Jet Impingement and Film Coolingrdquo ASME J Eng Gas Turbines Power136(3) p 031901

[16] Lynch S P Thole K A Kohli A and Lehane C 2011 ldquoHeat Transfer fora Turbine Blade With Nonaxisymmetric Endwall Contouringrdquo ASME JTurbomach 133(1) p 011019

[17] Kang M B Kohli A and Thole K A 1999 ldquoHeat Transfer and FlowfieldMeasurements in the Leading Edge Region of a Stator Vane Endwallrdquo ASMEJ Turbomach 121(3) pp 558ndash568

[18] Radomsky R W and Thole K A 2000 ldquoHigh Free-Steam TurbulenceEffects on Endwall Heat Transfer for a Gas Turbine Stator Vanerdquo ASME JTurbomach 122(4) pp 699ndash708

[19] Kang M B and Thole K A 2000 ldquoFlowfield Measurements inthe Endwall Region of a Stator Vanerdquo ASME J Turbomach 122(3) pp 458ndash466

[20] Praisner T J Allen-Bradley E Grover E A Knezevici D C and SjolanderS A 2007 ldquoApplication of Non-Axisymmetric Endwall Contouring to Conven-tional and High-Lift Turbine Airfoilsrdquo ASME Paper No GT2007-27579

[21] Knezevici D C Sjolander S A Praisner T J Allen-Bradley E andGrover E A 2010 ldquoMeasurements of Secondary Losses in a Turbine CascadeWith the Implementation of Nonaxisymmetric Endwall Contouringrdquo ASME JTurbomach 132(1) p 011013

[22] Lynch S P 2011 ldquoThe Effect of Endwall Contouring on Boundary LayerDevelopment in a Turbine Blade Passagerdquo PhD thesis Virginia PolytechnicInstitute and State University Blacksburg VA

[23] Saha A K and Acharya S 2008 ldquoComputations of Turbulent Flow and HeatTransfer Through a Three-Dimensional Nonaxisymmetric Blade PassagerdquoASME J Turbomach 130(3) p 031008

[24] Hollworth B R and Dagan L 1980 ldquoArrays of Impinging Jets With SpentFluid Removal Through Vent Holes on the Target SurfacemdashPart 1 AverageHeat Transferrdquo J Eng Power 102(4) pp 994ndash999

[25] Mensch A Thole K A and Craven B A 2014 ldquoConjugate Heat TransferMeasurements and Predictions of a Blade Endwall With a Thermal BarrierCoatingrdquo ASME J Turbomach 136(12) p 121003

[26] Lynch S P Thole K A Kohli A and Lehane C 2011 ldquoComputational Predic-tions of Heat Transfer and Film-Cooling for a Turbine Blade With NonaxisymmetricEndwall Contouringrdquo ASME J Turbomach 133(4) p 041003

[27] Lawson S A Lynch S P and Thole K A 2013 ldquoSimulations of Multi-phase Particle Deposition on a Nonaxisymmetric Contoured Endwall WithFilm-Coolingrdquo ASME J Turbomach 135(3) p 031032

[28] Moffat R J 1988 ldquoDescribing the Uncertainties in Experimental ResultsrdquoExp Therm Fluid Sci 1(1) pp 3ndash17

[29] Mensch A and Thole K A 2015 ldquoConjugate Heat Transfer Analysis of theEffects of Impingement Channel Height for a Turbine Blade Endwallrdquo Int JHeat Mass Transfer 82 pp 66ndash77

[30] ANSYS 2010 FLUENT 1300 ANSYS Inc Cannonsburg PA[31] Menter F R 1994 ldquoTwo-Equation Eddy-Viscosity Turbulence Models for

Engineering Applicationsrdquo AIAA J 32(8) pp 1598ndash1605[32] Pointwise 2013 Pointwise 171r3 Pointwise Fort Worth TX[33] LaVision 2012 DaVis 814 LaVision Ypsilanti MI[34] Foroutan H and Yavuzkurt S 2014 ldquoSimulation of the Near-Field Region of

Film Cooling Jets Using RANS and Hybrid URANSLES Modelsrdquo ASMEPaper No GT2014-25959

[35] Goldstein R J and Spores R A 1988 ldquoTurbulent Transport on the Endwallin the Region Between Adjacent Turbine Bladesrdquo ASME J Heat Transfer110(4a) pp 862ndash869

[36] Wang H P Olson S J Goldstein R J and Eckert E R G 1997 ldquoFlowVisualization in a Linear Turbine Cascade of High Performance TurbineBladesrdquo ASME J Turbomach 119(1) pp 1ndash8

cooling to overall effectiveness The first experiments to usean engine-matched Bi experimental model were completed bySweeney and Rhodes [7] for a three-dimensional flat plate with in-ternal impingement and film cooling Between the impingementplate and the wall were heat transfer enhancement features in aLamilloy

snowflake design Their results showed that impinge-ment cooling dominated over film cooling in the distribution ofexternal wall temperatures A series of matched Bi experimentsand simulations studied a vane leading edge model with internaljet impingement and external film cooling [8ndash11] There wasslight difference between the cases with and without impingementdue to the high effectiveness of the showerhead film coolingAnother series of engine-matched Bi studies [12ndash14] measuredthe effectiveness and thermal fields above a vane suction side withfilm cooling and impingement Williams et al [12] showed thatfor this part of the vane the impingement cooling contributed sig-nificantly to the overall effectiveness even more than the contri-bution from film cooling They concluded that as the blowingratio increased the improvement in impingement cooling com-pensated for the reduction in film cooling effectiveness As withthe flat plate and the vane the importance of impingementcooling for the endwall of an airfoil was observed by Mensch andThole [15]

Unlike a flat plate or vane surface endwall external heat trans-fer coefficients are influenced by three-dimensional secondaryflow structures including the horseshoe and passage vortices[16ndash19] Endwall heat transfer increases near the leading edgepressure side and wake of the Pack-B blade used in the presentstudy as shown in Fig 1(a) with contours of Nusselt number Nufor a flat endwall [16] Figure 1(b) gives the heat transfer augmen-tation due to nonaxisymmetric endwall contouring designed byPraisner et al [20] to minimize passage aerodynamic losses [16]

Endwall contouring can reduce aerodynamic losses by reducingthe cross-passage pressure gradient and the strength of the passagevortex compared to a flat endwall [21] The effect of endwall con-touring on the Pack-B passage vortex was measured by Lynch[22] using laser Doppler velocimetry From the three-dimensionalaverage flow measurements it was found that contouring slightlyreduced the strength of the passage vortex and delayed its progres-sion to the suction side of the passage Although Lynch [22] andothers have measured the passage flowfield in detail with andwithout endwall contouring the effects of film cooling on thepassage vortex development and strength have not been measuredConsidering that the film cooling jets at high blowing ratiosdetach from the endwall the interactions between the passagevortex and film cooling are investigated in the current study

Contouring can also reduce overall endwall heat transfer by thesame mechanism as the reduction in losses [1623] Figure 1(b)shows that the Pack-B endwall contouring increased heat transfer

at the leading edge and upstream portions of the passage How-ever the overall area-averaged heat transfer coefficient across theentire passage was reduced by 3 [16] Also contouring was ableto reduce heat transfer in the regions with the highest heat transfernear the pressure side Although the metric of heat transfer aug-mentation conveys the heat transfer performance due to endwallcontouring the primary metric for cooling performance is theoverall effectiveness which is obtained with a conjugate model inthe current study

Conjugate Endwall Model

The conjugate heat transfer in the contoured endwall is approxi-mated as one-dimensional using the conjugate endwall model asdepicted in Fig 2 The endwall model includes the combinedeffects of the internal and external convective heat transfer as wellas the solid heat conduction to obtain the scaled endwall tempera-tures The data are engine relevant if the appropriate physicalparameters are matched between the experimental model andengine conditions

The relevant nondimensional parameters can be found from thefollowing equation

frac14 T1 Tw

T1 Tcinfrac14 1 vg

1thorn Bithorn h1=hi

thorn vg (1)

which is derived from a one-dimensional heat transfer circuit usingFig 2 Equation (1) reveals that the endwall overall effectiveness isa function of the Bi h1hi and the product vg which representsan estimate for the nondimensional film temperature [12] Thedimensionless film temperature is approximated by the adiabaticeffectiveness g and a scale factor v which is defined as

v frac14 T1 Tcexit

T1 Tcin(2)

The coolant warming factor v corrects g for the warming of thecoolant during impingement and flow through the film coolingholes [12] Adiabatic effectiveness and the coolant warming factorare assumed to be functions of the geometry the mainstream flowparameters and the film cooling flow parameters such as the filmcooling blowing ratio M

Table 1 lists the nondimensional parameters matched to anengine for both the experiments and simulations in this studyEngine-matched Bi is achieved by thermoforming the contouredendwall from Corian

The contoured endwall heat transfer h1

is obtained from heat transfer measurements by Lynch et al [16]

Fig 1 Heat transfer measurements for the Pack-B cascade atReexit of 2 3 105 (Ref [16]) (a) Nusselt number contours for theflat endwall and (b) heat transfer augmentation contours due toendwall contouring with box for area-averaging

Fig 2 One-dimensional conjugate model of a conducting end-wall with impingement and film cooling

Conclusions

Acknowledgment

Nomenclature

Greek Symbols

(T1 Tcin)

Conclusions

Acknowledgment

Nomenclature

Greek Symbols

(T1 Tcin)

Conclusions

Acknowledgment

Nomenclature

Greek Symbols

(T1 Tcin)

Conclusions

Acknowledgment

Nomenclature

Greek Symbols

(T1 Tcin)

Conclusions

Acknowledgment

Nomenclature

Greek Symbols

(T1 Tcin)

Conclusions

Acknowledgment

Nomenclature

Greek Symbols

(T1 Tcin)

Conclusions

Acknowledgment

Nomenclature

Greek Symbols

(T1 Tcin)

Conclusions

Acknowledgment

Nomenclature

Greek Symbols

(T1 Tcin)

Documents

Overall Effectiveness and Flowfield Measurements for an