Assessment of URANS and DES for Prediction of Leading Edge...

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Toshihiko TakahashiResearch Scientist

Energy Engineering Research Laboratory,Central Research Institute of Electric Power

Industry,2-6-1 Nagasaka,

Yokosuka, Kanagawa 240-0196, Japane-mail: [email protected]

Ken-ichi FunazakiProfessor

Iwate University,4-3-5, Ueda,

Morioka, Iwate 020-8551, Japane-mail: [email protected]

Hamidon Bin SallehLecturer

University Tun Hussein Onn Malaysia,86400 Parit Raja, Batu Pahat, Johor, Malaysia

e-mail: [email protected]

Eiji SakaiResearch Scientist

Energy Engineering Research Laboratory,Central Research Institute of Electric Power

Industry,2-6-1 Nagasaka,

Yokosuka, Kanagawa 240-0196, Japane-mail: [email protected]

Kazunori WatanabeManager

Planning Group,Central Research Institute of Electric Power

Industry,1-6-1 Ohtemachi,

Chiyoda-ku, Tokyo 100-8126, Japane-mail: [email protected]

Assessment of URANS and DESfor Prediction of Leading EdgeFilm CoolingThis paper describes the assessment of CFD simulations for the film cooling on the bladeleading edge with circular cooling holes in order to contribute durability assessment ofthe turbine blades. Unsteady RANS applying a k-�-v2-f turbulence model and the Spalartand Allmaras turbulence model and detached-eddy simulation (DES) based on the Spal-art and Allmaras turbulence model are addressed to solve thermal convection. The CFDcalculations were conducted by simulating a semicircular model in the wind tunnel ex-periments. The DES and also the k-�-v2-f model evaluate explicitly the unsteady fluc-tuation of local temperature by the vortex structures, so that the predicted film coolingeffectiveness is comparatively in agreement with the measurements. On the other hand,the predicted temperature fields by the Spalart and Allmaras model are less diffusive thanthe DES and the k-�-v2-f model. In the present turbulence modeling, the DES onlypredicts the penetration of main flow into the film cooling hole but the Spalart andAllmaras model is not able to evaluate the unsteadiness and the vortex structures clearly,and overpredict film cooling effectiveness on the partial surface.�DOI: 10.1115/1.4003054�

Introduction

Application of film cooling technology to gas turbinesrogresses in combined power generation plants increasing ther-al efficiency with rise in turbine inlet gas temperature. In order

o assess the durability of the gas turbine blades, it is essential tostimate the temperature distributions of the blades. Accordingly,he prediction of film cooling by CFD is important for the assess-

ent of the durability. It is necessary for the durability assessmento estimate the cooling performance, especially on the leadingdge region, where flow impinges and heavy thermal load ap-ears. Hence, the present study focuses on the CFD prediction ofhe leading edge film cooling performance.

Experimental investigations of the leading edge film coolingave been previously done and clarified a lot of important char-cteristics of the performances. Mick and Mayle �1� measuredlm cooling effectiveness and heat transfer on the semicircular

eading edge with three rows of cooling holes. They presented thathe effectiveness is decreased as the blowing ratio is increased.

ehendale and Han �2� studied the influences of the blowing ratio

Contributed by the International Gas Turbine Institute �IGTI� of ASME for pub-ication in the JOURNAL OF TURBOMACHINERY. Manuscript received June 28, 2010; final

anuscript received July 23, 2010; published online July 14, 2011. Editor: David
isler.
ournal of Turbomachinery Copyright © 20

aded 16 Jul 2011 to 160.29.81.159. Redistribution subject to ASME

and the inlet turbulence intensity by using the same model as thatof Mick and Mayle �1�. Furthermore, Ou et al. �3�, Ekkad et al.�4�, and Johnston et al. �5� investigated the influences of inletturbulence on the cooling performance. Funazaki et al. �6� studiedinfluences of the incoming periodic turbulence by wakes on thefilm cooling of the semicircular leading edge model. Cruse et al.�7� studied the effect of leading edge shapes on the film coolingeffectiveness by using an infrared camera with circular and ellipticleading edge geometries. Reiss and Bölcs �8� examined the influ-ence of the cooling hole geometry on film cooling performance.The authors presented fan-shaped holes’ increased film coolingperformance due to the reduced tendency of “lift off” at highblowing ratios. Ou and Rivir �9� employed liquid crystal image tomeasure the film cooling heat transfer. Ahn et al. �10� measuredthe effectiveness on a rotating blade leading edge by using pres-sure sensitive paints. More recently, Lu et al. �11� conducted adetailed investigation of the hole angle and shape effects by usingtransient infrared thermography techniques. Falcoz et al. �12� pre-sented detailed measurements of the film cooling effectivenesswith thermochromatic liquid crystal.

With regard to the numerical approaches for film cooling, start-ing with flat plate configurations, a number of the investigations�e.g., Refs. �13–24� for flat plate configurations and Refs. �25–36�for leading edge configurations� have been conducted in order to
predict the cooling performance and to clarify the physics of the
MAY 2012, Vol. 134 / 031008-112 by ASME

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hermal flow field, so far. In terms of the leading edge film cool-ng, the CFD studies also presented useful knowledge. The Unitedechnology Pratt and Whitney organized the blind test of filmooling calculation on cylindrical leading edge experiments ofruse et al. �7�. On this blind test, Lin et al. �25�, Martin andhole �26�, and Thakur et al. �27� calculated the same thermofloweld by applying different mesh types with discretization schemesnd turbulence modeling including a k-� model and a k-� modelith wall functions. Chernobrovkin and Lakshminarayana �28�

lso ran simulations for the same flow by a low Reynolds number-� model, later. All those computations correctly predicted theendencies of lateral-averaged effectiveness but included discrep-ncies in local effectiveness. Lin et al. �25� and their extendedork �29� with the SST model clarified how hot spots can form on

he stagnation region due to the flow induced by coolant jets. Onhe other hand, they also indicated that the simulations underpre-icted the spread of the coolant in the wall-normal direction. Yorknd Leylek �30–32� applied the realizable k-� turbulence modelnto the leading edge film cooling in order to investigate the filmooling effectiveness, heat transfer coefficient and the effects ofole shapes, respectively. The authors showed that the predictionsre generally in good agreement with the experiments but discrep-ncies increases with the blowing ratio. All the numerical studiesor the leading edge cooling mentioned above had been conductedased on the steady RANS modeling. Those outcomes demon-trate that CFD is able to serve useful information for the estima-ion of the leading edge film cooling.

However, it is fundamentally difficult in principle for the eddyiscosity models in the steady RANS simulations to correctly re-olve anisotropic behavior induced by large scale structures thatre probably the primal mechanisms of the mixing of the filmoolant with the free stream. A large-eddy simulation �LES� and,f course, DNS are essential to finely resolve turbulence scales.ue to this, the LES has been applied to the calculation of the film

ooling, Tyagi and Acharya �23� and Guo et al. �24� for the flatlate configuration and Rozati and Tafti �34,35� and Sreedharannd Tafti �36� for the leading edge configuration. Those studiesave clarified the detailed physics of the film cooling flow. On thether hand, it is supposed to be difficult for the near future envi-onment of high-performance computing, at least for industrialimulations, to estimate the convective heat transfer of cooledlades in a hot section �e.g., HPT blades� by the LES. Thoseonvective heat transfer calculations need a considerably fineesh similar to the DNS to resolve turbulence scales to be close

o the near wall region. High speed computing and massive re-ources required make it difficult to apply the full LES to real

Fig. 1 Lead

onfigurations and conditions of actual cooled blades.

31008-2 / Vol. 134, MAY 2012


On the above background, this study investigates performancesof unsteady CFD calculations by applying RANS modeling to theleading edge film cooling. Taking practicable simulations for in-dustrial problems in the near future into consideration, calcula-tions of unsteady RANS �URANS� and a detached-eddy simula-tion �DES� are conducted from a view of time-averagedestimation of the cooling performance, which is firstly importantfor the durability assessment of the cooled blade with a largematrix of parameters. The URANS employing the k-�-v2-f turbu-lence model �37,38� and the Spalart and Allmaras turbulencemodel �39�, and the DES �40�, which is a LES with the Spalartand Allmaras turbulence model in the near wall region, are ad-dressed to solve thermal convection. In the unsteady calculations,RANS modeling was possibly expected to work as a filter to ex-tract structures having impacts on the cooling performance. Thepresent authors previously calculated the film cooling mainly forflat plate configurations with steady modeling using the k-� typeturbulence model �chiefly by the SST model� and the DES �33�.The authors presented that the DES could predict secondary vor-tices counter-rotating against the primary vortex pair in the flatplate cooling, which is supposed to enhance the lateral spreadingof the film coolant. The authors also tried to calculate the leadingedge film cooling, in addition, but acquired little information forthe CFD capability for the leading edge film cooling. The presentcalculations were conducted by simulating an experiment of thesemicircular leading edge model. Distributions of film coolingeffectiveness on the model surface and temperatures distributionsin the flow field are compared with the measurements with a ther-moprobe consisting of thermocouples and thermochromatic liquidcrystal. Thermoflow characteristics predicted by the present un-steady calculations were investigated.

2 Leading Edge ModelFigure 1 shows the leading edge model used in the numerical

calculations and experimental measurements. The leading edgemodel consists of a semicircular geometry of 80 mm diameter anda flat after-body. The model has plenum inside to supply the sec-ondary air as film coolant through film cooling holes. On the wallof the model, the film cooling holes of 8 mm diameter are peri-odically placed with staggered arrangement in the three rows.Hole angle is 30 deg to the model surface in the heightwise direc-tion, and the pitch of the periodic holes is 62 mm �7.72d�. Tworows of the film cooling holes, hole 1 �row 1� and hole 2 �row 2�,are located at 15 deg on both sides from the stagnation line in thecase without film cooling. The other row of the film cooling hole,

edge model

hole 3 �row 3�, is placed at 50 deg from the stagnation. As shown

Transactions of the ASME


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n Fig. 2�a�, the computational domain simulating the experimen-al setups is composed of the primary domain, the secondaryhamber, and the connecting duct between the primary domainnd the chamber. The primary domain is a pitch of the periodicalrrangement of the film cooling holes in the heightwise direction,onsisting of the main stream region, the film cooling holes �hole, hole 2, and hole 3�, and the plenum, as shown in Fig. 2�b�.

Descriptions of Numerical CalculationThe “FLUENT” code based on the finite volume method was

sed in the numerical calculations. Unsteady Reynolds-averagednd filtered Navier–Stokes equations were solved with theRANS models and the DES, respectively. The discretized equa-

ions are solved by the SIMPLE algorithm �41� with time integra-ion. The second order implicit scheme is utilized for the timentegral of both the URANS and the DES with a nondimensionalime step of 4.05�10−4 D /Um. Time-averaged statistics were ac-

ig. 2 Computational domain: „a… whole domain and „b… pri-ary domain „extracted from the whole domain…

umulated over the period of about 8D /Um.

ournal of Turbomachinery


3.1 URANS. Unsteady Reynolds-averaged Navier–Stokesequations were solved with the k-�-v2-f model �37,38� �V2F� andthe Spalart and Allmaras model �39� �SA�. The V2F was em-ployed to attempt to correctly treat wall asymptotic behaviors ofthe turbulent properties and to avoid production of anomalousturbulent energy in the flow around the leading edge by a two-equation eddy viscosity model. Regarding this point for the SA,the turbulence production is evaluated based on the antisymmetriccomponents of the velocity gradient tensor �the vorticity tensor�.The convective terms of the momentum equations were dis-cretized by the third order MUSCL scheme �42� and the otherterms are solved with the second order central difference scheme.

3.2 DES. The DES modeling �40� based on the Spalart–Allmaras model �39� was applied. The DES model replaces thelength scale dw in the SA, which is the distance to the closest wall,with the length scale defined as

l = min�dw,Cdes�� 1�

where � is based on the largest grid space in the x, y, or z direc-tions forming the computational cell, and Cdes�=0.65� is the em-pirical constant. The second order central difference scheme isapplied into all the spatial discretizations of the momentum equa-tions.

3.3 Computational Mesh and Conditions. Figure 3 showsthe outline of the computational mesh �surface mesh� employed inthe calculations. Unstructured grid system, which consists ofhexahedral cells and tetra cells, was employed to solve the dis-cretized equations. Except in the plenum and the secondary airchamber, the hexahedral cells are generated in the main streamregion and the film cooling holes.

It is supposed to be some challenge to search grid convergencefor the DES switching the modeling from the LES to the SA closeto the wall, as indicated by Eq. �1�. The present study, however,just focused on the leading edge portion with a very thin boundary

(a) Mesh of the primary domain

(b) Mesh around leading edge (expanded)

Fig. 3 Outlines of CFD mesh „surface mesh…: „a… mesh of theprimary domain and „b… mesh around the leading edge„expanded…

layer in the whole domain, near wall mesh is fined by using hang-

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ng nodes in order to secure resolution. The total number of theells is 3,995,322, 1,898,260 cells in the main stream regionround the leading edge model, 1,783,376 cells in the film coolingoles, 271,830 cells in the plenum, and 41,856 cells in the sec-ndary air chamber. The cells on the model surface are formedayered-structure in the near wall regions. The value of y+ for theomputational point of the first cell above the wall is less thannity so that the wall function approach is not applied on the wall.or a reference of mesh dependency in the solutions, Fig. 4 showsomparisons of spanwise-averaged film cooling effectiveness onhe model between the DES calculations with the primary mesh

entioned above and a coarse mesh. The computational condi-ions will be shown later. The total cell number of the coarse meshs 1,422,738, 587,748 cells in the main stream region, 521,304ells in the film cooling holes, and 313,686 cells in the otheregions. The coarse mesh results show only a small differencerom the primary mesh ones. In the present study, the primaryesh had been employed for all the calculations of the DES andRANS.Table 1 shows inlet conditions for the numerical calculations. In

his study, the temperature of the second air was set at higher thanhe main flow temperature, according to experimental conditions,s presented below. All the calculations were performed for Rey-olds number ReD of 8.55�104, based on the model diameter Dnd inlet flow conditions. Two cases for the mean blowing ratioBR�1,2� of the three holes, hole 1, hole 2, and hole 3, arealculated for each of the turbulence model. Adiabatic conditionsere imposed on the wall of the model. Mass flow rate, total

emperature and turbulent quantities were imposed at the inlets ofhe main stream region and the secondary air chamber, and thetatic pressure is set at both the outlets of the main stream regionnd the plenum. The static pressure at the plenum outlet waspecified to balance a mean mass flow in film cooling holes,hich is determined by the prescribed mean blowing ratio BR.ith regard to the inlet turbulence quantities in each turbulenceodel, steady component is set at constant on the basis of the

urbulence intensity of 0.1%, referred to the wind tunnel experi-ent. Unsteady components of the flow primitives are not given

t the inlets in the calculations.All the computations were executed with a PC cluster of eight

PUs. The process time per CPU for the DES and the SA is

ave

DES Primary meshDES Coarse meshExperiment LQ

deg.

BR= 1.031.021.06

-90 -60 -30 0 30 60 900

0.1

0.2

0.3

0.4

0.5

Fig. 4 Variations of predicted effectiveness with mesh

Table 1 Compu

�mUm�kg / �m2 s�� Tm ,K

��kg /

BR�1 19.29 291.17 19.8219.8720.0

BR�2 19.28 290.57 41.0641.6041.8

31008-4 / Vol. 134, MAY 2012


approximately 5 s per iteration in the SIMPLE algorithm, and theprocess for the V2F took about 20% longer than for the SA be-cause of the number of the equations.

4 Experimental MeasurementsLocal temperatures on and around the leading edge model,

which is installed in a test section of a low speed wind tunnel,were measured with thermocouples and thermochromatic liquidcrystal applied on the model surface. Turbulence intensity of themain stream into the test section of the wind tunnel is less than0.5%.

Locations of the temperature measurement by the thermo-couples are shown with dotted lines in Fig. 5. The temperaturedistributions on four traverse planes normal to the model surface,shown in Fig. 5�a�, were measured by a probe of a K-type ther-mocouple. On each of the plane of 5d�7.72d �a pitch of theperiodic hole arrangement�, temperatures are measured on 17�9 crossing points of the grid lines shown in Fig. 5�b� by travers-ing the probe. Local temperature profile of very near wall fields isalso measured on the half surface of the model at the same side asthe above flow field measurements, as a surface temperature byusing the thermocouple probe. Wall temperature profile on thewhole surface of the model was also measured by the transientmethod using thermochromatic liquid crystal with two video cam-eras set at each side of the model, which is referred to in Ref. �33�.Those temperatures measured were converted to film cooling ef-fectiveness. The experimental details were described in Refs.�43–45� including information for uncertainties in the measure-ment of the thermochromatic liquid crystal. Table 2 presents theexperimental condition for each of the measurement.

5 Results and Discussion

5.1 Blowing Ratio of Each Film Cooling Hole. Figure 6shows the time-averaged fraction of blowing ratio for each filmcooling hole to mean blowing ratio BR for the three holes. All theturbulence models estimate nearly the same blowing ratio frac-tions for each of the cooling hole. The blowing ratio of hole 1 andhole 2 located close to the stagnation region is smaller than hole 3.In the case of the small mean blowing ratio �BR�1�, the blowing

onal conditions

s�� T2 ,KSecond air chamber supply

�kg/s�

ES� 321.15 0.0302F�A�ES� 329.15 0.0302F�A�

Fig. 5 Locations of temperature measurement by TC: „a… mea-sured planes and „b… measurement points in each plane

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atio fraction of hole 2, as which hole 3 is located in the same sidef the semicircular model, is larger than hole 1 located on thepposite side at the same angle from the stagnation line withoutlm holes as hole 2. Those differences of the blowing ratio frac-

ions are due to static pressure distribution around the leadingdge model, and decreases with the increase of the mean blowingatio BR because of the increase of the dynamic pressure of theecondary flow ejecting. Hereinafter, the mean blowing ratio BRs designated as a “blowing ratio.”

5.2 Film Cooling Effectiveness on the Model Surface. Fig-re 7 shows predicted distributions of time-averaged local filmooling effectiveness on the model surface, and Figs. 8�a� and�b� show measured distributions of the film cooling effectivenessith �a� the thermocouple probe and �b� the thermochromatic liq-id crystal, respectively. The black area in Fig. 8�b� is owing toone reaction of the thermochromatic liquid crystal in the tran-ient method. The measured distribution agrees with each other

Table 2 Experimental conditions: measuremments with thermochromatic liquid crystal „LQ


�2�kg / �

BR�1 19.87 291.17 21BR�2 19.75 290.57 40


�2�kg / �

BR�1 20.10 292.75 21BR�2 20.15 291.45 41

Hole1 Hole2 Hole3

BR

BRH

ole

/BR

DESV2FS A

1 2

0.8

1

1.2

Fig. 6 Fraction of blowing ratio for each cooling hole

(a) DES

BR=1.03

BR=2.13

HoleHole3

Hole2

Hole1

Hole3

Hole2

Hole1Hol

6.0

4.0

2.0

0.0

6.0

4.0

2.0

0.09090 0 -90

deg.

Fig. 7 Time-averaged local adiabatic
SA


for the angle ��0 deg, and the numerical distributions and theirvariations with the blowing ratio BR are generally similar as theexperimental measurements. Both of the measurements and thepredictions indicate that local effectiveness decreases and filmcoverage get worse with the increase of the blowing ratio BR,owing to the increase of penetration of the ejected secondary airinto the main flow. All the results also show that the film coverageregion leans downward of the model as the blowing ratio BRincreases.

The CFD calculations, however, predict local higher effective-ness than the measurements in regions downstream of the trailingedges of the film cooling holes, as shown in Fig. 7. This local higheffectiveness in the prediction is more remarkable and concen-trated spatially in the predictions by the SA than in the otherpredictions, especially in the region downstream of hole 3. Fur-thermore, the distribution by the SA in the case of the smallerblowing ratio �BR=1.04� shows a peak area �a plateau� of higheffectiveness down hole 1 ��30 deg�, which is not found in theexperimental measurement by the thermochromatic liquid crystalof Fig. 8�b� �BR=1.06� and in other numerical predictions.

Figure 9 shows time-averaged distributions of the spanwise-averaged film cooling effectiveness. In this figure, previous resultsby steady calculations using the SST model �33� are also included.The figure indicates that all the CFD calculations have reasonablecapabilities to predict the spatial-averaged profiles of the leadingedge film cooling. The DES and the V2F results are comparativelyin agreement with the measurements. However, the SA of BR=1.04, as shown in Fig. 7, and also the previous steady calculationby the SST model of BR=2.05 predict high effectiveness in thedownstream region of hole 1 ��30 deg�, which appear to bequalitatively different from the measurement.

5.3 Local Temperature Distribution Around the Model.Figure 10 shows time-averaged distributions of measured and pre-dicted local temperatures on transverse planes normal to themodel surface, at each angle of �=−30 deg, −40 deg, −70 deg,

ts with thermocouples „TCs… and measure-


�kg/s�

340.15 0.038345.15 0.041


�kg/s�318.15 0.036327.15 0.042

2F (c) SA

BR=1.03

BR=2.16

BR=1.04

BR=2.17

ole2

Hole1Hole3

Hole2

Hole1

Hole2

Hole1Hole3

Hole2

Hole1

-90deg.

90 0 -90deg.

ectiveness: „a… DES, „b… V2F, and „c…

en…

U2m2

.06

.29

U2m2

.30

.10

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nd −90 deg, which is downstream of hole 2 and hole 3. In Fig.0, time-averaged spanwise profiles of the local film cooling ef-ectiveness on the model surface are also presented at the samengles � as those normal planes in the flow field. The CFD resultshown in these figures are time-averaged, and the measurementata are acquired by traversing the thermocouples. The local tem-erature on the normal plane is nondimensionalized by the sameefinition as the film cooling effectiveness . The previous steadyalculations using the SST model �33� are also included in thegures of the spanwise profiles on the model surface.Every turbulence model shows relatively good performance for

redicting the location of bulk of the secondary air ejected into theain flow on the normal planes, and simulates departures of the

econdary air from the surface with the increase of the blowingatio BR. The V2F, especially, as shown in Fig. 10�b�, in the casef BR�1, appears to have advantage in the prediction of theocation of the bulk secondary air on the normal plane. Distributedatterns of the local temperature are supposed to be affected by a

(a)Measurementswith thermocouples(TC) (b

-20-90 deg.

BR=1.09

Hole3

Hole2

6.0

4.0

2.0

0.0

-20-90 deg.

BR=1.89

Hole3

Hole2

6.0

4.0

2.0

0.0

Fig. 8 Measured distributions of adiwith TCs and „b… measurements with tnonreaction of the liquid crystal…

(a) BR~1

(b) BR~2

ave

Exp., TC, BR=LC,

DESV2FSASST(Steady)[33]

deg.

1.091.061.031.031.041.00

-90 -60 -30 0 30 60 900

0.1

0.2

0.3

0.4

0.5

ave

Exp., TC, BR=LC,

DESV2FSASST(Steady)[33]

deg.

1.892.042.132.162.172.05

-90 -60 -30 0 30 60 900

0.1

0.2

0.3

0.4

0.5

ig. 9 Time-averaged distributions of spanwise-averaged film
ooling effectiveness: „a… BRÈ1 and „b… BRÈ2
31008-6 / Vol. 134, MAY 2012


so-called kidney-shape vortex pairs, which are found clearly in theresults by the SA at the angles �=−30 deg of BR=1.04 and �=−30 deg and −40 deg of BR=2.17. Those predicted patterns ofthe local temperature indicate that the vortices, such as thekidney-shape, do not have a symmetric structure with respect tothe center of the cooling holes as found in the flat plate cooling. Inthis leading edge film cooling, the entrainment of the main flowby the vortex appears to be larger on the upper side �the leadingedge side of the hole� than on the lower side �the trailing edge sideof the hole�, so that the film cooling effectiveness is higher on thetrailing edge side of the hole, as shown in Fig. 7.

Regarding those structures on the local temperature in the flowfield, all the CFD calculations predict similar aspects but the SAestimates higher nondimensional temperature in their core regionsthan the V2F and the DES. These local distributions predicted bythe V2F and the DES appear to be more diffusive and are consis-tent with aspects in the measurements, and as shown in Fig. 10�b�of the higher blowing ratio �BR�2�, the V2F and the DES esti-mate the same extent of the normal spreading of the secondary airas the measurements but the SA underestimates that. In Fig. 10�a�of the lower blowing ratio �BR�1�, the normal spreading pre-dicted by the V2F is a little larger than the DES but the spreadingof the secondary air in every calculation shows similar extent toeach other.

Furthermore, in Fig. 11, presenting the predicted time-averagedlocal temperature distributions on normal planes to the model sur-face downstream of hole 1 �at angles �=30 deg and 60 deg�, theSA evaluates the bulk of the secondary air to be remarkably closerto the wall, shown in Fig. 11�a� of BR=1.04 and the normalspreading of the secondary air in the SA is also smaller than theother models. As a result, as shown previously in Figs. 7�c� and9�a�, the plateau of the high film cooling effectiveness down-stream of hole 1 is estimated in the SA than in the others. Thislocal high wall effectiveness is also presented in the right handand lower figure of the spanwise profile of Fig. 11�b�. In terms ofprediction of peak in the local film cooling effectiveness on thesurface shown in the right hand figures of the spanwise wall pro-files of Fig. 10, the DES and the V2F show better performanceand the DES appears to be the best coincident with the measure-ments in the present. However, there are discrepancies betweenthe predictions and the measurements. The present unsteady SAeven shows equal performance to the steady calculations by theSST model �33� and has larger divergences in the location and the

asurementswith thermochromatic liquid crystal (LQ)

lack area is due to no reaction of liquid crystal)

BR=1.06

BR=2.04

Hole3

Hole2

Hole1

Hole3

Hole2

Hole1

BR=1.06

BR=2.04

9020 deg.-20-90 deg.

9020 deg.-20-90 deg.

6.0

4.0

2.0

0.0

6.0

4.0

2.0

0.0

tic effectiveness: „a… measurementsmochromatic LQ „black area is due to

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Figure 12 shows predicted instantaneous distributions of theocal nondimensional temperature on the cross-sectional planesormal to the model surface at the hole 2 center �at the angle �−15 deg� of BR�1. In the present turbulence models, the DESredicts the smallest scales around the interface between the mainow and the secondary air. The V2F also shows the wave patternround there but in the SA, the interface did not find any fluctua-ion. Here, the DES could only predict the instantaneous penetra-ion of the main flow into the film hole. That is useful for thessessment of the blade durability on the safe side.

5.4 Thermoflow Structure. Figure 13 presents predicted in-tantaneous views of vortex structures, colored by the local non-imensional temperature. These vortex structures are represented

(a) BR~ 1

(formeasurements)0.0 1.0

=-30°

=-40°

=-70°

=-90°

TC DES V2F SABR=1.09 1.03 1.03 1.04

2d 0 2d 0 2d 0 2d 0nnnn

DESV2FS ASteady SST[33Exp. TC

z/d

0

2

4

z/d

0

2

4

6

z/d

0

2

4

6

z/d

0 0.5 10

2

4

6

Fig. 10 Time-averaged local temperaand spanwise profiles of film coolingand „b… BRÈ2

(a) BR~ 1 (b) BR~ 2

0.0 1.0

= 30°

= 60°

DES V2F SABR=1.03 1.03 1.04

= 30°

= 60°

DES V2F SABR=2.13 2.16 2.17

2d 0 2d 0 2d 0nnn2d 0 2d 0 2d 0nnn

DESV2FS A

z/d

0

2

4

z/d

0 0.5 10

2

4

6

DESV2FS A

z/d

0

2

4

z/d

0 0.50

2

4

6

ig. 11 Time-averaged local temperature on normal planes toodel surfaces and spanwise profiles of film cooling effective-

ess on the surfaces „a… BRÈ1 and „b… BRÈ2



by iso-surfaces of second invariant of gradient of velocity tensorQ. The nondimensional temperature is evaluated by the same defi-nition as the film cooling effectiveness .

The predictable flow scales depend on the turbulence model,and there are large differences between the SA and the others.Those result from differences in estimations of the eddy viscosityamong the turbulence models. The DES and the V2F predict vor-tex structures representing anisotropic motions, and the DES pre-sents smaller scales resolved than the V2F. The extracted vortexstructures from the DES results are found in slightly longer areasdownstream of the holes than the V2F results. On the contrary, theSA evaluates the markedly short area where the vortices are founddownstream of the holes. Those aspects indicate that the predictedflows by the DES and the V2F promote mixing by the vortexstructures more than the flow predicted by the SA.

What the “Reynolds averaging” in the unsteady problem actu-ally represents is not supposed to be well known. In this study,however, both the V2F and the SA based Reynolds averaging areconducted with the same mesh resolution and the same temporalintegration as the DES. It is important at least that those dis-

(b) BR~2

(for CFD)0.0 1.0

=-30°

=-40°

=-70°

=-90°

C DES V2F SA=1.89 2.13 2.16 2.17

2d 0 2d 0 2d 0 2d 0nnnn

DESV2FS ASteady SST[33]Exp. TC

z/d

0

2

4

z/d

0

2

4

6

z/d

0

2

4

6

z/d

0 0.5 10

2

4

6

on normal planes to model surfacesctiveness on the surfaces „a… BRÈ1

0.0 1.0

Penetrationof main flow

DES V2F SABR=1.03 1.03 1.04

Hole2 Hole2 Hole2

Fig. 12 Instantaneous local temperature on normal planes to

TBR

]

tureeffe

the surface BRÈ1

MAY 2012, Vol. 134 / 031008-7


cetrfiawttt

abshcs=Dtctttpfi

n

Fp

0

Downlo

retized equations appropriately evaluate the eddy viscosity atach cell and each time step. The present numerical results showhat the SA of the one-equation model, which is not able to cor-ectly take the “turbulence length scale,” yields a stronger spatiallter than the others. On the other hand, the V2F, which takes intoccount the wall asymptotic behaviors of the turbulence propertiesith four constitutive equations, appears to reasonably estimate

he eddy viscosity. However, in the RANS, especially the V2F,here must also be influences of the MUSCL �up-wind� scheme onhe predictions.

The DES and V2F similarly predict distinctive vortex structurest around envelopes of the bulk structures, which are shear-layersetween the main flow and the ejected secondary air. Inside thesehear-layer vortices in the DES and the V2F, other structures withigher nondimensional temperature are found. However, in the SAalculations, the shear-layer vortex structures are not found. Ashown in predicted instantaneous iso-temperature surfaces �0.4� of Fig. 14 �at the same angle of depression as Fig. 13�, theES and also the V2F predict fluctuations of the local tempera-

ure. These pictures for the DES and the V2F in Fig. 14 exhibithiefly that the structures in the shear-layers influence the fluctua-ions of the local temperature. On the other hand, the SA estimateshe smooth iso-surfaces, indicating a small fluctuation of the localemperature field. These aspects are consistent with the local tem-erature distributions on the cross-sectional planes in the floweld, presented in Fig. 12.Figure 15 views predicted �a� time-averaged and �b� instanta-

eous iso-temperature surfaces �=0.4� from the bottom of the

1.0

0.0

DES V2FBR=1.03 BR=1.03

DES V2FBR=2.13 BR=2.16

Fig. 13 Instantaneous vortex structumensional temperature

DES V2F SABR=1.03 BR=1.03 BR=1.04

DES V2F SABR=2.13 BR=2.16 BR=2.17

ig. 14 Instantaneous iso-surfaces of nondimensional tem-
erature �=0.4
31008-8 / Vol. 134, MAY 2012


model for the blowing ratio BR�1. In every instantaneous picturein Fig. 15�b�, the volumes wrapped by the temperature iso-surfaces are seen to remain downstream of the film cooling holesalong the surface curvature of the model. The SA only predicts thecontinuous volumes along the model surface in the instantaneouspicture. As shown in Fig. 15�a� for the time-averaged views, how-ever, the DES and the V2F present the volumes shorter down-stream of the holes �clearly for downstream of hole 1� than theSA. These are supposed to be due to the fact that the DES and alsothe V2F evaluate the mixing by the unsteady vortex structures. Onthe contrary, the SA distinctively estimates the long time-averagedvolumes of the temperature that are similar to the instantaneous

SABR=1.04

SABR=2.17

„Q=−3Ã106…, colored by local nondi-

DESBR=1.03

V2FBR=1.03

SABR=1.04

Model surfaceModel surfaceModel surfaceHole1

Hole3

Hole2

Hole1

Hole3

Hole2

Hole1

Hole3

Hole2

(b) Instantaneous view

(a) Time-averaged view

DESBR=1.03

Model surfaceModel surfaceModel surfaceHole1

Hole3

Hole2

Hole1

Hole3

Hole2

Hole1

Hole3

Hole2

V2FBR=1.03

SABR=1.04

Fig. 15 Iso-surfaces of nondimensional temperature �=0.4,BRÈ1, views from the bottom of the model: „a… time-averaged

res

view and „b… instantaneous view



oef

�atctissssras

tasfi

6

utplbwtp

iccttstltpaws

usripaiDwa

npatAs

J

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ne. Those characteristics of the predicted flow structures differ-nt from each turbulence modeling give information for the dif-usion behavior of the local temperature field.

The high film cooling effectiveness downstream of hole 1 ��30 deg� at BR=1.04 in the SA, presented before in Figs. 7�c�

nd 9�a�, is relevant to the predicted characteristics of the localemperature field mentioned above. It seems that the stable andontinuous volume of higher temperature above the surface thanhe main flow temperature could be brought closer to the surfacen the flow accelerated along the curvature of the leading edge, ashown in Fig. 11�a�. This disadvantage found in the present un-teady simulation of the SA model would be also true with theteady RANS simulations, as presented in Fig. 9�c� for thepanwise-averaged effectiveness by the SST model. The presentesults illustrate a risk, wherein the steady simulation that is notble to evaluate unsteady vortices also fails to predict even apatial-averaged performance of film cooling on a curved surface.

In this regard, however, in the present study, the temperature ofhe second air was set higher than the main flow temperatureccording to the experimental conditions. Consequently, the oppo-ite influence to the present result would be found in the inherentlm cooling.

ConclusionsIn order to horizontally assess unsteady CFD calculations by

sing RANS modeling for the prediction of the film cooling onhe semicircular leading edge model, the URANS simulations em-loying the k-�-v2-f model and the Spalart and Allmaras turbu-ence model and the DES based on the Spalart and Allmaras tur-ulence model were performed and those results were comparedith the temperature measurements with the thermocouples and

hermochromatic liquid crystal. As a result, some aspects for theerformances of those CFD simulations were brought out.

The DES and the k-�-v2-f model presented good performancesn estimations of time-averaged, spanwise-averaged film and localooling effectiveness on the leading edge surface. Overall, it wasoncluded that the predicted temperature fields by these simula-ions were more diffusive and comparatively in agreement withhe measurements than the Spalart and Allmaras model and theteady calculation by the SST model done previously. However,here were some quantitative discrepancies in the time-averagedocal peak of the effectiveness on the surface in the predictions byhe DES and the k-�-v2-f model. The Spalart and Allmaras modelredicted the high film cooling effectiveness on the partial surfacet angle ��30 deg in the case of the blowing ratio BR�1, whichas not found in the measurement. That was also similar with the

teady calculations by the SST model.The DES and also the k-�-v2-f model evaluated explicitly the

nsteady fluctuation of local temperature induced by the vortextructures �anisotropic motions�. However, the Spalart and Allma-as model could not clearly predict the unsteadiness and the an-sotropic motions despite of the unsteady simulation. In theresent turbulence modeling, the DES resolved the smallest scale,nd only predicted the penetration of main flow into the film cool-ng hole. The k-�-v2-f model predicted similar structures to theES but did not show that penetration of the main flow. Thoseere due to the differences in the evaluations of the eddy viscosity

mong the models.The partial overestimation of the local film cooling effective-

ess by the Spalart and Allmaras model mentioned above is sup-osed to be due to the lack of the unsteady vortex structures in theccelerated flow along the leading edge curvature. This disadvan-age found in the present unsteady simulation of the Spalart andllmaras model would be also true with ordinary steady RANS

imulations.



NomenclatureBR mean blowing ratio for all film cooling holes,

�2U2 /�mUmD diameter of the leading edge model, md diameter of film cooling holes, mh heat transfer coefficient, W / �m2 K�

LQ thermochromatic liquid crystaln wall-normal distance, mQ second invariant of gradient of velocityq heat flux, W /m2

ReD Reynolds number, �UmD /�T temperature, K

TC thermocouplest time, s

U mean velocity, m/sx ,y ,z Cartesian coordinates, m

� angle, deg film cooling effectiveness, �Tm−Taw� / �Tm−T2�� viscosity, Pa s� density, kg /m3

Subscriptsaw adiabatic wallave average in the pitchwise direction of the model

hole relative to each cooling holeM relative to main flowW wall2 relative to film flow

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