Effect Of Hole Shapes, Orientation And Hole Arrangements On Film

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Sep 15, 2016 - mass consumption, Semi-elliptic hole came out to give best results. Key words: ... based on the free-stream velocity and hole diameter, and the.
Paper Int’l J. of Aeronautical & Space Sci. 17(3), 341–351 (2016) DOI: http://dx.doi.org/10.5139/IJASS.2016.17.3.341

Effect Of Hole Shapes, Orientation And Hole Arrangements On Film Cooling Effectiveness Effect Of Hole Shapes, Orientation And Hole Arrangements On Film Cooling Effectiveness Effect Of Hole Shapes, Orientation And Hole Arrangements On Department of Mechanical Engineering, Birla Institute of Technology, Mesra, Ranchi, JH 835215, India. Film Cooling Effectiveness 1 2 3 Prakhar Jindal*, A.K. Roy** and R.P. Sharma*** Prakhar Jindal , A.K. Roy and R.P. Sharma

Department of Mechanical Engineering, Birla Institute of Technology, Mesra, Ranchi, JH 835215, India. Abstract 1 2 3

Prakhar Jindal , A.K. Roy and R.P. Sharma In this present work, the effectEngineering, of hole shapes, orientation and hole arrangements on film cooling effectiveness has been Department of Mechanical Birla Institute of Technology, Mesra, Ranchi, JH 835215, India. ABSTRACT carried out.InFor this work a flat plate has been considered for the computational model. Computational analysis of film this present work, the effect of hole shapes, orientation and hole arrangements on film cooling ABSTRACT coolingeffectiveness effectiveness using different hole shapes with no streamwise inclination has been carried out. Initially, the model has been carried out. For this work a flat plate has been considered for the computational model. In this present work, the effect of hole shapes, orientation and hole arrangements on film cooling with an inclination of 30° has been verified with the experimental data. The validation results are well in agreement with the Computational analysis of film cooling effectiveness using different hole shapes with no streamwise inclination effectiveness has been carried out. For this work a flat plate has been considered for the computational model. results taken from literature. Five different hole shapes viz. Cylindrical, Elliptic, Triangular, Semi-Cylindrical and Semi-Elliptic has been carried out. Initially, the model with an inclination of 30 ° has been verified with the experimental Computational of film cooling using different hole shapes no streamwise inclination have been compared analysis and validated over aeffectiveness wide range of blowing ratios. Thewith blowing ratios ranged from 0.67 to 1.67. Later, data. The validation results are well in agreement with the results taken from literature. Five different hole has of been carried Initially, modelalong with an inclination of 30 of ° has been verified the experimental orientation holes haveout. also been the varied with the number rows and hole with arrangements in rows. The performance shapes viz. Cylindrical, Elliptic, Triangular, Semi-Cylindrical and Semi-Elliptic have been compared and data. The validation are well agreement with the results taken from literature. Five different hole of film cooling scheme has results been given in in terms of centerline and laterally averaged adiabatic effectiveness. Semi-elliptic hole validated over a wide range of blowing ratios. The blowing ratios ranged from 0.67 to 1.67. Later, orientation of shapes viz. Cylindrical, Elliptic, Triangular, Semi-Cylindrical and Semi-Elliptic have been compared and utilizes half of the mass flow as in other hole shapes and gives nominal values of effectiveness. The triangular hole geometry holes have also been varied along with the number of rows and hole arrangements in rows. The performance of validated overof a wide range of blowing ratios.hole The blowing ratios ranged fromcompared 0.67 to 1.67.on Later, of shows higher values effectiveness than other geometries. But when theorientation basis of effectiveness and coolant film cooling scheme has been given in termsout of centerline andresults. laterally averaged adiabatic effectiveness. Semimass consumption, Semi-elliptic hole with came to give best holes have also been varied along the number of rows and hole arrangements in rows. The performance of elliptic hole utilizes half of the mass flow as in other hole shapes and gives nominal values of effectiveness. The film cooling scheme has been given in terms of centerline and laterally averaged adiabatic effectiveness. Semitriangular hole geometry shows higher values of effectiveness than other hole geometries. But when compared Key words:  CFD, Film cooling, shapes, effectiveness, elliptic hole utilizes half ofhole the mass flow blowing as in otherratio, hole shapes and givesOrientation. nominal values of effectiveness. The on the basis of effectiveness and coolant mass consumption, Semi-elliptic hole came out to give best results. triangular hole geometry shows higher values of effectiveness than other hole geometries. But when compared on the basis of effectiveness and coolant mass consumption, Semi-elliptic hole came out to give best results.

Keywords: CFD, Film cooling, hole shapes, blowing ratio, effectiveness, Orientation.

Nomenclature

designers. Film cooling is an active cooling strategy, which

Keywords: CFD, Film cooling, hole shapes, blowing ratio, effectiveness, involvesOrientation. the continuous injection of a thin layer of protective

NOMENCLATURE

fluid (coolant) near a wall or boundary to insulate it from rapidly flowing hot propellant gases. Its main advantages are that it allows for the use of much lighter-weight nozzle Adiabatic wall temperature, K Taw assemblies and it is relatively simple to implement from a 𝑇𝑇𝑇𝑇∞ − 𝑇𝑇𝑇𝑇𝑤𝑤𝑤𝑤 Adiabatic cooling effectiveness, η η TcAdiabatic cooling effectiveness, Coolant temperature, K 𝑇𝑇𝑇𝑇∞ − 𝑇𝑇𝑇𝑇𝑐𝑐𝑐𝑐 fabrication standpoint. 𝑇𝑇𝑇𝑇∞ − 𝑇𝑇𝑇𝑇𝑤𝑤𝑤𝑤 Film cooling usually measured in dimensionless form Mη MassMass flux ratio blowing ratio (defined (defined asas ratio of mass coolant to the is mainstream) Adiabatic cooling effectiveness, M  flux ratio or or blowing ratio ratio of flux of 𝑇𝑇𝑇𝑇∞ − 𝑇𝑇𝑇𝑇𝑐𝑐𝑐𝑐 𝑇𝑇𝑇𝑇𝐻𝐻𝐻𝐻 − 𝑇𝑇𝑇𝑇𝑤𝑤𝑤𝑤 known as “film cooling effectiveness” , and defined mass flux of coolant to the mainstream) θM Non-dimensional Temperature, Film cooling is usually measured in dimensionless known "film cooling effectiveness", andas: defined as: Mass flux ratio or blowing ratio as ratio of mass flux ofform coolant to the as mainstream) 𝑇𝑇𝑇𝑇 (defined − 𝑇𝑇𝑇𝑇 T∞ T∞ Free Free stream temperature, stream temperature, K NOMENCLATURE Taw Taw Adiabatic wallwall temperature, Adiabatic temperature, K K Free stream temperature, K T∞ Tc Tc Coolant temperature, Coolant temperature,KK

θ

θ Non-dimensional Non-dimensional Temperature, Temperature, INTRODUCTION

𝐻𝐻𝐻𝐻

𝑐𝑐𝑐𝑐

𝑇𝑇𝑇𝑇𝐻𝐻𝐻𝐻 − 𝑇𝑇𝑇𝑇𝑤𝑤𝑤𝑤 𝑇𝑇𝑇𝑇𝐻𝐻𝐻𝐻 − 𝑇𝑇𝑇𝑇𝑐𝑐𝑐𝑐

η=

𝑇𝑇𝑇𝑇∞ − 𝑇𝑇𝑇𝑇𝑤𝑤𝑤𝑤 𝑇𝑇𝑇𝑇∞ − 𝑇𝑇𝑇𝑇𝑐𝑐𝑐𝑐

(1)

(1)

T∞ is freestream temperature = 600 K, & Tc is coolant inlet INTRODUCTION where, Tw is adiabatic wall temperature, Tw isin adiabatic wall temperature, T∞ is freestream The thermal management and protection of the components where, and surfaces rocket engine combustion

temperature =300 K temperature = 600 K, is coolant inlet temperature =300 K 1. Introduction chambers presents one of the most challenging problems for designers. Film cooling is & anTcactive cooling The thermal management and protection of the components and surfaces in rocket engine combustion

To study fluid film cooling strategy, which involves the continuous injection of a thin layer of protective (coolant) phenomena, near a wall or investigators have been chambers presents one the most challenging problems for investigators designers. Filmhave cooling is an activesimple coolinggeometries to reduce the Toofstudy cooling phenomena, been using The thermal management andfilmprotection of the using simple geometries to reduce the complexity of the flow boundary to insulate it from rapidly flowing hot propellant gases. Its main advantages are that it allows for the strategy, which involves the continuous injection of a thin layer of protective fluid (coolant) near a wall complexity of the flow affecting the heat exchange between the test surface between and theor mainstream gas flow. The components and surfaces in rocket engine combustion affecting the heat exchange the test surface and use of much lighter-weight nozzle assemblies and it is relatively simple to implement from a fabrication boundary to insulate it from rapidly flowing hot propellant gases. Its main advantages are that it allows for the chambers presents one of the most challenging gasfilm flow.cooling The geometrically simplea form of geometrically simple formproblems of a flat for plate the withmainstream one or more holes often offers sufficient standpoint. use of much lighter-weight nozzle assemblies and it is relatively simple to implement from a fabrication

approximation of the reality for a lot of research interests. A better understanding of the mechanisms involved in

standpoint. Ph. D Student, ,Corresponding author: [email protected] 2 This is an Open Access article film distributed under is theneeded terms of the cooling to Creative achieveComan optimized and film cooling with a minimum amount of coolant. Ph. D Student, Corresponding author: [email protected] * effective Ph. D. mons Attribution Non-Commercial License (http://creativecommons.org/licenses/by3 1 Associate Professor ** Ph. D. Ph. D Student, ,Corresponding author: [email protected] However, the effectiveness film cooling is *** very much dependent on the shape of the injection hole, layout nc/3.0/) which non-commercial use, distribution,ofand reproduc2 permits unrestricted Professor Received: December 14, 2015 Revised: September 15, 2016 Accepted: September 19, 2016 Ph. D.provided tion in any medium, the original work is properly cited. 3 Ph. D. geometry and injection angle [1]. 1

Received: December 14, 2015 Revised: September 15, 2016 Accepted: September 19, 2016

Many researchers have conducted computational and experimental work on film cooling, some of which

Received: December 14, 2015 Revised: September 15, 2016 Accepted: September 19, 2016 Copyright ⓒ The Korean Society & Space Sciences canfor beAeronautical found here. Bunker [2] in his comprehensive 341

review paper on film cooling from shapedeISSN: holes2093-2480 has pointed http://ijass.org pISSN: 2093-274x

out that no single shaping of film hole stands as an optimal geometry for all applications. He also concluded that hole shape maintains the cooling jets closer to surface, enhances film coverage and reduces mixing. Goldstein et al. [3-4] reported the effectiveness resulting from a single cylindrical hole and row of holes. They considered a (341~351)15-180.indd 341

2016-10-04 오후 3:21:10

blowing ratio (M) of 0.5 for maximum effectiveness at coolant to freestream DR (Density Ratio) around 1.0.

Int’l J. of Aeronautical & Space Sci. 17(3), 341–351 (2016)

a flat plate with one or more film cooling holes often offers 2. Computational Modelling a sufficient approximation of the reality for a lot of research interests. A better understanding of the mechanisms 2.1 Physical Model involved in film cooling is needed to achieve an optimized GAMBIT 2.4.6 has been used to model the computational and effective film cooling with a minimum amount of domain and also to generate mesh. In the present study, k–ε coolant. However, the effectiveness of film cooling is very turbulence model has been used. The hot combustion gases much dependent on the shape of the injection hole, layout are passing over the surface of a flat plate and the coolant geometry and injection angle [1]. is being injected to create a film above it. The inclination of Many researchers have conducted computational and coolant injection is 30° and the compound angle is varied experimental work on film cooling, some of which can be from 0° to 90°. Validation of the model has been done using found here. Bunker [2] in his comprehensive review paper the results of cylindrical cooling hole with the experimental on film cooling from shaped holes has pointed out that no study of Yuen et al. [5].The geometrical conditions have been single shaping of film hole stands as an optimal geometry kept in coordination with the literature work so as to achieve for all applications. He also concluded that hole shape better validation results. In the later part of the study, three maintains the cooling jets closer to surface, enhances film different shaped holes (semi-cylindrical, semi-elliptic and coverage and reduces mixing. Goldstein et al. [3-4] reported COMPUTATIONAL MODELLING triangular) have been investigated. The cross-sectional the effectiveness resulting from a single cylindrical hole 1. PHYSICAL MODEL area of other hole configurations used in this work has and row of holes. They considered a blowing ratio (M) of COMPUTATIONAL MODELLING kept thattheofcomputational cylindrical hole.andFig. 0.5 for maximum effectiveness at coolant to freestream GAMBITbeen 2.4.6 has beensame used toas model domain also1toshows generate the mesh. In the present 1. PHYSICAL MODEL computational the dimensions study, k – ε turbulence model has domain been used. along The hot with combustion gases are passingand over the the surface of a flat DR (Density Ratio) around 1.0. Film cooling effectiveness is being injected toGAMBIT create film above it. The inclination of angles coolant injection is 30°and andalso to generat boundary conditions. Fig.a 22.4.6 shows the compound of domain using a cylindrical hole at an angle of 30°, 60° and 90°plate wasand the coolant has been used to model the computational compoundthe angle is varied from 0° tok 90°. Validation of the thehas model been using the results hole shapes while 3 shows geometry ofdone all studied by Yuen and Martinez [5]. They considered a the hole study, –Fig. ε turbulence model beenhas used. The hot the combustion gases of are passing ove cylindrical cooling hole with the experimental study of Yuen et al. [5].The geometrical conditions have been plate and the coolant is being injected to create a film above it. The inclination of coolan hole shapes used. length of L=4D, the free-stream Reynolds number of 8563

work so asangle to achieve better validation results. In the later partmodel of thehas been done the compound is varied from 0° to 90°. Validation of the based on the free-stream velocity and hole diameter, andkept thein coordination with the literature study, three different shaped holes cylindrical (semi-cylindrical, semi-elliptic and triangular) have been investigated. The geometrical cooling hole with the experimental study of Yuen et al. [5].The 2.2 Boundary Conditions blowing ratio was varied from 0.33-2. For a single 30° hole, cross-sectional area of other hole configurations used in this work has been kept same as that of cylindrical hole. kept in coordination with the literature work so as to achieve better validation results. In the maximum effectiveness increased up to a blowing ratio Fig. 1 shows the For computational domain with the consists dimensions the boundary conditions. Fig. and 2 shows validation, thealong geometry ofand a(semi-cylindrical, single cylindrical study, three different shaped holes semi-elliptic triangular) have b of 0.5, then decreased with increasing blowing ratio due to the compound angles of the hole shapes while Fig. 3 shows the geometry of all the hole shapes used. cross-sectional area of other hole configurations used in this work has been kept same as th jet penetration into the free stream. Yuen and Martinez [6] Fig. 1 shows the computational domain along with the dimensions and the boundary con in their another paper studied the film cooling effectiveness the compound angles of the hole shapes while Fig. 3 shows the geometry of all the hole sha and heat transfer coefficients for a rows of round holes with different hole inclinations. To study the effect of injecting a small amount of water into the cooling air for film cooling performance, FLUENT was used by T. Wang and X. Li [7]. Their operating conditions were a pressure of 15 atm and a temperature of 1561K. The result showed that 5-10% cooling effectiveness was achieved by 10-20% mist. Influence of different hole shapes on film cooling with CO2 was investigated by G. Li et al. [8]. Figure 1: Geometry of Computational Domain Fig. 1. Geometry of Computational Domain Concluding from the literatures, film cooling effectiveness mainly depends on certain factors such as blowing ratio, Figure 1: Geometry of Computational Domain injection angle, compound angle/orientation, L/D ratio etc. Hence, the present work aims to further investigate the effects of different coolant hole geometries with varying lateral orientations of the holes on the flow structure for a flat plate in FLUENT using k-ε turbulence model. To achieve this objective, multiple computations has been conducted for different hole geometries and for more number of rows with aligned and staggered hole configurations at several Figure 3: Geometry of Each Hole Shapes Figure 2: Compound Angles used for the Hole Shapes blowing ratios ranging from 0.67 to 1.67. Compound angles of the holes have also been varied from 0° to 90°. Fig. 2. Compound Angles used for the Hole Shapes Figure 3: Geometry of Each Hole Shap 2. BOUNDARY CONDITIONS

Figure 2: Compound Angles used for the Hole Shapes

For validation, the geometry consists of a single cylindrical hole inclined at an angle of 30° streamwise

DOI: http://dx.doi.org/10.5139/IJASS.2016.17.3.341

having hole diameter 10mm. The L/D ratio is 7. Reynolds number based on freestream velocity and hole 2. BOUNDARY CONDITIONS diameter342 is 10364. Blowing ratios ranging 0.67 - the 1.67geometry have been investigated whichcylindrical corresponds the Forfrom validation, consists of a single holeto inclined at an ang

having hole diameter 10mm. The L/D ratio is 7. Reynolds number based on freestrea

diameter is 10364. Blowing ratios ranging from 0.67 - 1.67 have been investigated whic

(341~351)15-180.indd 342

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GAMBIT 2.4.6 has been used to model the computational domain and also to generate mesh. In the present study, k – ε turbulence model has been used. The hot combustion gases are passing over the surface of a flat plate and the coolant is being injected to create a film above it. The inclination of coolant injection is 30° and the compound angle is varied from 0° to 90°. Validation of the model has been done using the results of cylindrical cooling hole with the experimental study of Yuen et al. [5].The geometrical conditions have been

Jindal results. Effect Shapes, kept in coordination with the literature work so as to achieve Prakhar better validation In Of the Hole later part of the Orientation And Hole Arrangements On Film Cooling Effectiveness study, three different shaped holes (semi-cylindrical, semi-elliptic and triangular) have been investigated. The cross-sectional area of other hole configurations used in this work has been kept same as that of cylindrical hole.

hole inclined at an angle of 30° streamwise having hole diameter 10mm. The L/D ratio isof7. number the compound angles of the hole shapes while Fig. 3 shows the geometry allReynolds the hole shapes used. based on freestream velocity and hole diameter is 10364. Blowing ratios ranging from 0.67 - 1.67 have been investigated which corresponds to the coolant inlet velocities (Table 2). Table 1 gives the values of boundary conditions used. For grid dependency, the cylindrical hole case for blowing ratio M=0.33 is selected. Different meshes have been tried. Fig. 4 shows the mesh dependency for centerline effectiveness. The different grid size for various meshes is tabulated in the Table 3. From Fig. 4 it is clear that the result in case of medium 2 and fine meshes are almost similar but still fine mesh is

Fig. 1 shows the computational domain along with the dimensions and the boundary conditions. Fig. 2 shows

Figure 1: Geometry of Computational Domain

used for analysis to achieve more accurate results. 2.2.1. Solver A 3D segregated, steady state solver was used. For linearization of governing equations implicit method was used. For turbulence modeling k-ε model with standard wall functions was used. To avoid use of enhanced wall treatment mesh was kept fine enough to have wall Y+ in the range 0-5.Discretization scheme used was in 2nd order upwind for momentum, turbulence kinetic energy, turbulence dissipation rate and energy, whereas for pressure standard discretization scheme was used [9]. For pressurevelocity coupling SIMPLE algorithm was used. A UDF was used for plotting the centerline effectiveness in all the cases. Convergence is considered to be achieved when the residual values are less than 10-5 for continuity equation, 10-7 for momentum and 10-8 for energy. 2.2.2. Governing Equations The continuity (2) and momentum (3) equations for the present case of steady state, incompressible, segregated 3D solver and standard k-ε (without viscous heating) turbulence model are:

Fig. 3. Geometry of Each Shapesof Each Hole Shapes FigureHole 3: Geometry Figure 2: Compound Angles used for the Hole Shapes

coolant inlet velocities (Table 2). Table 1 gives the values of boundary conditions used. ∂u i Table 1. Boundary Conditions TABLE 1: Boundary Conditions TABLE 2: Coolant = 0Inlet Velocities with blowing ratios 2. BOUNDARY CONDITIONS

∂x ∂u i used. coolant inlet velocities (Table 2). Table 1 gives thei values of boundary conditions =0 For validation, the geometry consists of a single cylindrical hole inclined at an angle of 30° streamwise S.No. Blowing Ratio (M) Coolant Inlet Velocity

(2)

(2) (2)

xi  ∂∂Inlet Values u Coolant 2 ∂2: ∂ 1: Boundary Conditions ∂p ∂   ∂u i ∂u j TABLE TABLE Velocities with blowing ratios (3) (−∂ρuu ′ i u ′ j ) u i u j ) =and − hole+ − δ ij l  + having hole diameter 10mm. The L/D ratio is 7. Reynolds number based on freestream( ρvelocity µ  ∂ + u ∂  2 ∂u l  ∂ p ∂ ∂ 1. 0.67 m/s j ∂ 3− ∂+xl  µ ∂xuji10 ∂x j the values of∂xboundary ∂x j  conditions ∂x j ( ρu∂uxused. i + i i (3) (2) − ρ u ′i u ′ j ) ) − δ ijCoolant =  +Inlet(Velocity  = 0 (3) coolant inlet velocities (Table 2). Table 1 gives Mainstream Inlet Velocity 15m/s i j S.No. Blowing Ratio (M) diameter is 10364. Blowing ratios ranging from 0.67 - 1.67 have been investigated which corresponds to the Values ∂x   Conditions ∂xi ∂x j   ∂∂xxj i ∂xi 3 ∂xl  ∂x j j where, 2. 1.00 15 m/s TABLE 1: Boundary Conditions 2: Coolant Inlet Velocities with blowing 1. 0.67 ∂ratios where, u j 2 ∂u  10 ∂m/s Mainstream Inlet Temperature 600 K Inlet Velocity TABLE ∂p ∂   ∂u Mainstream ∂u j  2∂ (1.33 ∂u 15m/s (3) (− ρ u ′ i u ′ j ) ρu i u j ) = ∂−u i  + ∂u µ  i20 + m/s − δ ij l  + where, u ∂ 2 2. 1.00 j µ δ − −∂xρj uρκ + − ρ u ′ i u ′ j = µ t  i 3. + x x x xiµ ∂3u i δ∂xl  15∂m/s x j (4) ∂ ∂ ∂ ∂ i j ρκ +  i ij j  − Inlet (4) i u ′ j = tµ Blowing (M) Velocity  3  ′Ratio  ∂S.No. t x  +Coolant t ij Mainstream Inlet Temperature 600 K Density Ratio 1 (approx.) x x ∂ ∂    Conditions Values j i j x x x ∂ ∂ ∂ 3  1.67   i  1.33 j  4. where, 25 m/s 3. j 20 m/s The two additional (for turbulence kinetic k, the turbulence dissipation rate, 1. 1 The 0.67transport twothe additional theand turbulence kinetic k, and the turbulence dissipation rate, Density Ratio transport equations (approx.)  m/s  equations ∂u(for ∂u i  energy, ∂u i energy, 210 Coolant Inlet Temperature 300 K j  Mainstream Inlet Velocity 15m/s 4. 1.67 25 εm/s    u ′ i uμ′tas (4) − ρand =a µfunction +of k and is − computed as: ε, areissolved, computed as:ρκ +asµa tfunctionδ ijof k and ε, are solved, and μt (turbulent viscosity) j(turbulent (4) t  viscosity)  m/s ∂x   ε315 x x ∂ ∂ 1.00 j i j Coolant Inlet Temperature 2. 300 K  µ t  ∂k  ∂   ∂additional ble 2). Table 1 gives the values of boundary conditions µ ttwo k ∂ (kutransport ∂  The Mainstream Inletused. Temperature 600 K ∂   ) G + − ρ µ ρε (5) = + equations (for the turbulence kinetic energy, k, and the(5) turbulence dissipation rate,   k  ∂x1.33 (kui for ) = blowing + Gik − ∂ρε ρhole case  µ +ε, areM=0.33 x j viscosity) x20 σ kis computed ∂meshes For gridVelocities dependency, cylindrical (turbulent a function of k and ε as: μtselected. j is j  Different  m/sashave xj x j and σ k solved, ∂ratios ∂x j 3. ratio Table 2.TABLE Coolant withthe blowing ratios dary Conditions 2: Inlet Coolant blowing  ∂The two additional transport equations (for the turbulence Density RatioInlet Velocities withFor 1 (approx.) grid dependency, the cylindrical hole case for blowing ratio M=0.33 is selected. Different meshes have 2  m/s kfor 2∂∂ε25 µµ tsize ε ∂∂1.67 ∂∂  µgrid 4.effectiveness. been tried. Fig. 4 shows the mesh dependency for centerline The ku G1εk ε− G +Cvarious ρεk − Cdissipation (5)  (6) µand ((εenergy, u i i))different =ε= ++ t εthe +different µ  ∂ρεfor∂xxcenterline ∂4Velocity ∂  dependency 2ε ρ rate, ε, are been tried. Fig. shows grid size for S.No.Coolant Blowing (M) Coolant xj j k, σk k∂The ∂xeffectiveness. ∂xxj turbulence σ κ k various ∂G    µ + t kinetic j (6)  InletRatio Temperature 300Inlet K ( ρ ε ρ + − u i ) =the mesh C  i j C1ε    Values    ε k 2and meshes is tabulated in the Table 3. From Fig. 4 it is clear that the result in case of medium 2 fine meshes are κμthe k viscosity) ∂x ∂x  FromσFig. 2 solved, and computed as k  meshes is10 tabulated 4∂xitj is∂clear that in fine meshes area function k 2isand result t∂(turbulent   ∂µεof=medium µ tcase 1. 0.67 m/s i in the Tablej 3. (7) C µ ε2G − C ρ ε  t  +ρC (6) (results. ρ εu i ) =k city 15m/s  µ + 1ε ε k 2ε almost similar but still fine mesh is used for but analysis to mesh achieve more σ κ x x x k ∂ ∂ ∂ of k and ε as: almost similar still fine is used for accurate analysis to achieve more accurate results.  Prandtl number for k is taken(7)as σ = 1.0 and the model  as the i ρC j  k  j  = µ t µ The model constants known turbulent 2. For grid dependency, 1.00 15 m/s 2 the cylindrical hole case for blowing ratio M=0.33 is selected. Different meshes have k ε k perature 600 K model constant C1ε, C2ε(7) and known asPrandtl turbulentnumber Prandtl number for =ε is µ t taken ρCused 1.0along and with the the model The constants known asconstant the turbulent for k is σ σε==1.3 µ as2as 3. tried. 20 model m/s been Fig.3:1.33 4Different shows the dependency for centerline effectiveness. TABLE gridmesh size for various TABLE 3: meshes Different grid size for various meshes The different grid size for various ε k the default (C1ε=1.44, Cµ=0.09) in FLUENT. these model constant values µ taken 2ε=1.92 and = 1.0 and the model The as model asalong the Cturbulent number for kC1ε is, taken as σ 1 (approx.) k with thePrandtl model constant CAs and constant known as turbulent Prandtl Cnumber for ε isconstants usedvalues asknown σε=1.3 2ε Grid Nodes meshes is tabulated the Table 3.Faces From25 Fig. 4Nodes it Cells is clear thatFaces the result in case medium 2found andtofine meshes are 4. Grid 1.67inCells m/s are standard oneof andturbulent have been workfor fairly with range of wall bounded and free shear flows, constant Prandtl ε iswell as σwide ε=1.3 along with the model constant C1ε, C2ε and C2εknown =1.92asand Cµ=0.09) in number FLUENT. Asused these model constant values Cµ taken as the default values (C1ε=1.44, ature 300 K hence the same results. are used for the present computational model [10]. 153459 477210 165291 almost similar but still fine mesh isCoarse used for1 analysis to achieve more accurate

Conditions

Coarse 1

153459

Cµ taken as the default values (C1ε=1.44, C2ε=1.92 and Cµ=0.09) in FLUENT. As these model constant values 477210 are standard 165291 one and have been found to work fairly well with wide range of wall bounded and free shear flows,

are standard one and have been found to work fairly well with wide range of wall bounded and free shear flows, 328161 1012327RESULTS 347496 Coarse 2 AND DISCUSSION Table 3. Different grid for various meshes hence the same are used for the present computational model [10]. 1012327 347496 Coarse 2 size 328161 hence the same are used for the present computational model [10]. TABLE 3: Different gridDifferent size for various meshes the cylindrical hole case for blowing ratio M=0.33 is selected. meshes have Medium 1 634220 1946355 a.664793 VALIDATION - CYLINDRICAL HOLE (SINGLE)

634220 1946355 664793 Medium 1 TheCells Grid Faces Nodes he mesh dependency for centerline effectiveness. different grid size for various For theAND validation of the turbulence model used, the computational results obtained for the case of RESULTS DISCUSSION DISCUSSION 1218504 3722716RESULTS 1265080 Medium 2AND cylindrical holes have been verified by the experimental 1218504 3722716 1265080 Medium 2 a. VALIDATION HOLE (SINGLE)data of Yuen et al. [5]. The performance of different VALIDATION - CYLINDRICAL HOLE (SINGLE)CYLINDRICAL Table 3. From Fig. 4 it is clear that theCoarse result in1case of medium 2 477210 andFine finea.meshes are 153459 165291 3818610 11548110 3911869 hole shapes (Semi-cylindrical, semi-elliptic and

id size for various meshes

4

0

triangular)

for

film cooling effectiveness has been

For model the validation of the turbulence model used,obtained the computational For the validation of the turbulence used, the computational results for the results case ofobtained for the case of mesh is used for analysis to achieve more results. 3818610 1012327 11548110 3911869 Fineaccurate 328161 347496 Coarse 2 measured terms of been centerline andbyspatially averaged data adiabatic filmetcooling Also noncylindricalinholes have verified the experimental of Yuen al. [5]. effectiveness. The performance of the different

Medium 1

634220

cylindrical holes have been verified by the experimental data of Yuen et al. [5]. The performance of different

1946355 hole shapes664793 (Semi-cylindrical,

Faces

Nodes

Medium 2

1218504

477210

165291

Fine

dimensional temperature 3818610 11548110 3911869

1012327

347496

measured 1265080 in terms of 3722716

dimensional temperature profiles have beenand plotted for all thefor cases. film Figure 5 shows the validation of hole shapes (Semi-cylindrical, semi-elliptic triangular) cooling effectiveness has been

semi-elliptic andresults triangular) for film has been computational with the experimental data. cooling The giveneffectiveness Fig. 5 shows validation for all the blowing ratios.

measured in terms of centerline and spatially averaged adiabatic film cooling effectiveness. Also the non-

centerline and spatially averaged filmbeen cooling effectiveness. Alsoin the nonAs can be seen from the adiabatic Fig. 5, thehave centerline effectiveness is very much agreement with the the validation experimental dimensional temperature profiles plotted for all the cases. Figure 5 shows of

results throughout the with length the near hole region (x/D