Conjugate Heat Transfer Simulation of Internally CooledGas Turbine Vane

V. Esfahanian1∗, A. Shahbazi1 † and G. Ahmadi2‡

1 Department of Mechanical Engineering, University of Tehran, Tehran, Iran2 Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY, USA

Email: evahid@ut.ac.ir

ABSTRACT

A 3D conjugate heat transfer simulation of a gas tur-bine vane is performed using Fluent and the temper-ature and heat transfer coefficient distribution overits surface are obtained. The study focused on thelinear NASA-C3X cascade, for which experimentaldata are available. Three full turbulence models andtwo transitional models are studied, namely, Spalart-Allmaras (SA) model, Shear stress transport k − ω(sstkw) model, v2 − f (V2F) model, Transition SST(trans-sst) model and k− kl −ω (k-kl-w) model. Un-structured prism meshes generated with y+ of lessthan 1 for all of turbulence models. Two turbulenceintensities of 0.5% and 20% are studied to see theturbulence models performance at both high and lowturbulence intensities. For low turbulence intensity,theV2F model can predict heat transfer coefficient dis-tribution very well while for high turbulence intensity,the trans-sst turbulence model is working better. Com-paring the results of both high and low turbulence in-tensities show that V2F model can be used as a reliablemodel for simulation of gas turbine vane.

1 INTRODUCTION

A critical problem in high pressure turbine of moderngas turbines is the vane and blade reliability as it is sub-jected to high thermal constraints. Actually the flowentering the turbine presents high level of stagnationtemperature as well as great radial and circumferentialtemperature gradients. Considering that a small varia-tion of the blade temperature leads to a strong reduc-tion of its life duration, accurate numerical tools arerequired for prediction of blade temperature. There are

∗Professor of Mechanical Engineering†M.Sc. Student of Mechanical Engineering‡Professor of Mechanical and Aeronautical Engineering

two approaches for analyzing and acquiring tempera-ture and heat transfer distribution in blades: decoupledand coupled. In decoupled approach, the governingequations of fluid zones and conduction equation insolid zones are solved separately. Thermal boundaryconditions of the interface used in this approach, areobtained from experimental or numerical correlationsand may need some iterations to correct them. In theother approach flow solver and conduction solver cou-pled with each other by equating temperature and heatflux on both sides of interface wall. This is known asconjugate heat transfer (CHT) simulation. The wordconjugate referred to considering the two modes ofheat transfer (conduction and convection) simultane-ously. Unlike the decoupled approach in which exter-nal and internal heat transfer coefficients need to be as-signed on the walls, the conjugate heat transfer methodrequires flow boundary conditions only at the inlet andexit of the gas and coolant passages.

1.1 Experimental works

There is two well documented experimental works inCHT analyzing of gas turbine vane that report the heattransfer coefficient and temperature distribution at themidspan of vane.

The first experiment was done by Hylton et al.(1983) [1] on C3X vane that consists of simple circulartube as cooling channels (Figure 1). They use temper-ature close to real gas turbine vane condition in theirexperiments and use 310 Stainless Steel for vane, butthe cooling channels shape in a realistic vane is morecomplicated including serpentine passages, rib tabula-tors, film cooling and so on.

The second experiment was done by Dees (2010) [2].He considers two main purposes in his experiments:

1) The vane geometry must be close to the realistic ge-ometry of gas turbine vanes, 2) The geometry must beas simple as possible for using in CFD validation. Sohe perfomed five separate experiment on C3X vane.In this paper, the first experiment of Dees (2010) isselected for simulation. Figure 2 shows the vane andcooling passages. It consists of a U-bend and a radialcooling channel.

Figure 1: C3X vane of Hylton et al. experiment [1].

Figure 2: U-bend and radial cooling channels offirst experiment of (Dees, 2010) [2].

1.2 Numerical studies

Usually bypass transition occur over a gas turbine vaneand also there is a stagnation point in leading edge.Turbulence models has great difficulties with these twophenomena, so turbulence models performance overgas turbine blade must be evaluated with experimen-tal works. York and Leylek (2003) [3] simulate C3Xvane of Hylton et al. (1983) experiment with Fluentusing standard k − ε (ske) and realizable k − ε (rke)models. Results of temperature distribution show that

Figure 3: Dimentionless temperature distribu-tion [4].

these two models can not predict transition occurrenceon the suction side (Figure 3). York (2006) [4] de-veloped a nonlinear eddy viscosity turbulence model(ACRL-EVRC) and get better results than ske and rkemodels (Figure 3). Since York does not present heattransfer distribution, one can not see the cause of im-provement but as the authors knowledge, by using non-linear eddy viscosity, one can overcome to stagnationpoint anomaly problem (Ref. [5]), so the capability oftransition prediction of the model is still questionable.

Luo and Razinsky (2007) [6] simulate C3X vane ofHylton et al. (1983) experiment using three turbulencemodels: k− ε (KE) model, Quadratic k − ε (QKE)model and V2F model. Figure 4 show the Luo’s re-sults. KE model obviously shows stagnation pointanomaly and can not predict transition. V2F modelpredict the transition but its length is not true. QKEmodel is nonlinear eddy viscosity model and do notshow stagnation point anomaly but it can not predictthe transition location and its length with acceptableprecision.

Dees et al. (2010) [7] simulate C3X vane of Dees(2010) with Fluent using only k−ω turbulence modeland 21 million mesh volumes. Figure 5 shows the heattransfer distribution obtained by them. This model alsoshows the stagnation point anomaly and can not pre-dict the transition.

Literatures studies show that most of the numericalworks have simulated Hylton et al. (1983) C3X vaneand there is not any comprehensive simulation of Dees(2010) experiment. The present paper simulates thefirst experiment of Dees using different turbulencemodels and their performances are evaluated.

Figure 4: Heat transfer distribution coefficient [6].

Figure 5: Heat transfer distribution coefficient [7].

2 COMPUTATIONAL METHODOLOGY

Steady-state solutions of the governing equationsof fluid zones and conduction equation in solidzones are solved simultaneously using Fluent.Three full turbulence models and two transitionalmodels are studied, namely, Spalart-Allmaras (SA)model, Shear stress transport k − ω (sstkw) model,v2 − f (V2F) model, Transition SST (trans-sst) modeland k− kl −ω (k-kl-w) model.

The air is modeled as a incompressible ideal gas withconstant specific heat and thermal conductivity whileviscosity is modeled using Sutherlands formula. Thevane is constructed out of castable epoxy resin (Poly-cast PC-287) with conductivity k = 1.03 W/mK andits thickness is t = 1.27 cm.

The experimental setup of Dees (2010) [2] is shownin Figure 6. According to this setup, translational peri-odic boundary condition can be used in numerical sim-ulation. Figure 7 shows computational domain and theboundary conditions. There are four zones, namely,hot section gas path, solid vane, forward U-bend cool-

Figure 6: Experimental setup of (Dees, 2010) [2].

Figure 7: Computational domain and boundaryconditions [7].

ing and aft radial cooling. To enable coupled bound-ary condition in Fluent, the wall interface betweenfluid and solid zones must be common and the meshesshould be linked with each other. The boundary con-ditions for hot gas path and coolant flows are listed inTable 1.

As it is shown two turbulence intensities studied. Atlow turbulence intensities (lower than 1%) the naturaltransition and at higher turbulence intensities bypasstransition are occurred [8]. Although in realistic con-dition inlet turbulence intensities are much higher than1% but it is useful to study the turbulence models per-formance at low turbulence intensities too. For both

Table 1: Boundary conditions [2].

Coarse grid Fine GridZone Elements Nodes Elements Nodes

1 2.326 1.672 2.953 1.9742 0.269 0.159 0.539 0.5953 0.264 0.141 0.69 0.4044 0.071 0.04 0.175 0.118

Total 2.929 2.011 4.357 3.091y+ 0.08−0.828 0.102−0.822

Table 2: Detailed information of grides.

coolant channels, the hydraulic diameter is determinedfrom the Re = 20000, given in the experiment.

The grid independency of results is investigated for2.92 million and 4.36 million unstructured prismmeshes by comparison of heat transfer coefficient dis-tribution. Detailed grid information is presented in Ta-ble 2. Figures 8 and 9 show the heat transfer coefficientdistribution for trans-sst and V2F models at high tur-bulence intensity. It can be seen that the results are in-dependent of grids, so the coarser grid is selected. Fig-ure 10 shows the generated grid and Figure 11 showsthe boundary layer mesh around airfoil.

3 RESULTS

The difference between high and low turbulence inten-sity depends on the mode of transition occurred in eachone. For turbulence intensity above and below 1%, themode of transition occurred are bypass transition andnatural transition, respectively. In this section, the re-sults of experiment and simulation for pressure coeffi-cient, heat transfer coefficient and dimensionless tem-

Figure 8: Grid independency result for trans-sstmodel.

Figure 9: Grid independency result for V2Fmodel.

Figure 10: Computational domain grid.

perature (overall effectiveness) are compared for vari-ous turbulence models.

3.1 Low turbulence intensity

Figure 12 shows pressure coefficient distribution. Allturbulence models predict the Cp distribution verywell.

Heat transfer coefficient distribution presented in Fig-ure 13. Experimental results show that at s/C ≈ 0.4,

Figure 11: Boundary layer mesh around airfoil.

the transition from laminar to turbulence occurs at suc-tion side. As it can be seen, the V2F model has the bestperformance among the others. It predicts the transi-tion onset location and the transition length with verywell accuracy. The trans-sst and k-kl-w models pre-dict the location of transition onset lately and they donot agree with experimental results after the transition.The SA and sstkw models can not detect the transition.

As it can be seen, at low turbulence intensity turbu-lence models do not overpredict the heat transfer coef-ficient at leading edge, so one can conclude the stag-nation point anomaly occurs at high turbulence inten-sities.

Overall effectiveness determines the cooling channelseffectiveness, defined by relation:

ϕ =T∞ −TT∞ −Tc

(1)

Figure 14 shows overall effectiveness distribution. TheCFD simulation of standard k−ω of Dees et al. (2010)[7] are included for comparison. The SA, V2F andsstkw turbulence models results better than trans-sstand k-kl-w models. Deviation of tran-sst and k-kl-wmodels from experimental results is due to poor es-timation of heat transfer coefficient on the suctionside. Experimental data shows a maximum in ϕ ats/C ≈ −0.4 where the channels baffle located. Tur-bulence models do not works well around this region.This poor performance is not due to mesh size becauseRef. [7] use 21 million mesh volumes but its resultsdoes not either match with experiment at this region.

3.2 High turbulence intensity

Figure 15 shows pressure coefficient distribution. Asit is seen all turbulence models predict the Cp distribu-tion very well.

Figure 12: Pressure coefficient distribution (LTI).

Figure 13: Heat transfer coefficient distribution(LTI).

Figure 14: Overall effectiveness distribution(LTI).

Figure 16 shows heat transfer coefficient distributionfor TI = 20%. The CFD simulation of standard k−ωof Dees et al. (2010) are included for comparison. Ex-perimental results show that at s/C ≈ 0.4, the transi-tion from laminar to turbulence occurs. Among theturbulence models trans-sst model could predict thetransition onset location and the transition length verywell. The models sstkw and V2F overpredict the heattransfer distribution at the leading edge due to overpre-diction of production term in turbulent kinetic energy

equation. The V2F model also finds transition withthe onset location and the transition length close to theexperiment but with an offset. This shows that tran-sition predictability of V2F model is very well. Theauthors of this paper believe that this offset is due tooverprediction of production term in turbulent kineticenergy equation and it could be redefined to get betterresults. The poor prediction of heat transfer coefficienton pressure side supports this statement.

The trans-sst and k-kl-w models do not show stagna-tion point anomaly because unlike the the full turbu-lence models, they do not treat with laminar zones asturbulence region.

Figure 17 shows overall effectiveness distributionforTI = 20%. At s/C ≈ −0.4 and s/C ≈ 0.8, wherethe baffle between channels located, all of turbulencemodels underpredict the overall effectiveness.

Figure 15: Pressure coefficient distribution (HTI).

4 CONCLUSIONS

Conjugate heat transfer simulation of C3X gas tur-bine vane is performed and different turbulence mod-els performance are evaluated. Two turbulence inten-sities of 0.5% and 20% are studied to see the turbu-lence models performance at both high and low turbu-lence intensities. For low turbulence intensity, the V2Fmodel can predict heat transfer coefficient distributionvery well. This model predicted transition onset andtransition length very close to experiment. Trans-sstmodel also predict the transition onset with acceptableaccuracy but it does not agree with experimental re-sults after the transition. For high turbulence intensitytrans-sst model working better than other turbulencemodels and produce results close to experiment. V2Fmodel at high turbulence intensity overpredict the heattransfer coefficient distribution but again the predictedtransition onset location and transition length is nearthe experimental data. The results of the present sim-ulation show that V2F model can predict the transition

Figure 16: Heat transfer coefficient distribution(HTI).

Figure 17: Overall effectiveness distribution(HTI).

with acceptable accuracy and by using nonlinear eddyviscosity V2F models one can resolve the stagnationpoint anomaly problem of this model. Trans-sst and k-kl-w models do not have stagnation point anomaly butthey do not produce good results. The authors believethat these two models are in primary steps and must bedeveloped more.

ACKNOWLEDGEMENTS

The authors would like to thank Vehicle, Fuel and En-vironment Research Institute (VFERI) of university ofTehran.

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