Conjugate Heat Transfer Simulation of Internally Cooled Gas Turbine Vane V. Esfahanian 1, A. Shahbazi 1 and G. Ahmadi 2 1 Department of Mechanical Engineering, University of Tehran, Tehran, Iran 2 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 turbine vane is performed using Fluent and the temperature and heat transfer coefficient distribution over its surface are obtained. The study focused on the linear NASA-C3X cascade, for which experimental data are available. Three full turbulence models and two transitional models are studied, namely, Spalart- Allmaras (SA) model, Shear stress transport k ω (sstkw) model, v 2 f (V2F) model, Transition SST (trans-sst) model and k kl ω (k-kl-w) model. Unstructured prism meshes generated with y + of less than 1 for all of turbulence models. Two turbulence intensities of 0.5% and 20% are studied to see the turbulence models performance at both high and low turbulence intensities. For low turbulence intensity, thev2f model can predict heat transfer coefficient distribution very well while for high turbulence intensity, the trans-sst turbulence model is working better. Comparing the results of both high and low turbulence intensities show that V2F model can be used as a reliable model for simulation of gas turbine vane. 1 INTRODUCTION A critical problem in high pressure turbine of modern gas turbines is the vane and blade reliability as it is subjected to high thermal constraints. Actually the flow entering the turbine presents high level of stagnation temperature as well as great radial and circumferential temperature gradients. Considering that a small variation of the blade temperature leads to a strong reduction of its life duration, accurate numerical tools are required 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 temperature and heat transfer distribution in blades: decoupled and coupled. In decoupled approach, the governing equations of fluid zones and conduction equation in solid zones are solved separately. Thermal boundary conditions of the interface used in this approach, are obtained from experimental or numerical correlations and may need some iterations to correct them. In the other approach flow solver and conduction solver coupled with each other by equating temperature and heat flux on both sides of interface wall. This is known as conjugate heat transfer (CHT) simulation. The word conjugate referred to considering the two modes of heat transfer (conduction and convection) simultaneously. Unlike the decoupled approach in which external and internal heat transfer coefficients need to be assigned on the walls, the conjugate heat transfer method requires flow boundary conditions only at the inlet and exit of the gas and coolant passages. 1.1 Experimental works There is two well documented experimental works in CHT analyzing of gas turbine vane that report the heat transfer coefficient and temperature distribution at the midspan of vane. The first experiment was done by Hylton et al. (1983) [1] on C3X vane that consists of simple circular tube as cooling channels (Figure 1). They use temperature close to real gas turbine vane condition in their experiments and use 310 Stainless Steel for vane, but the cooling channels shape in a realistic vane is more complicated including serpentine passages, rib tabulators, 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 geometry of gas turbine vanes, 2) The geometry must be as simple as possible for using in CFD validation. So he perfomed five separate experiment on C3X vane. In this paper, the first experiment of Dees (2010) is selected for simulation. Figure 2 shows the vane and cooling passages. It consists of a U-bend and a radial cooling channel. Dimentionless temperature distribu- Figure 3: tion [4]. Figure 1: C3X vane of Hylton et al. experiment [1]. these two models can not predict transition occurrence on the suction side (Figure 3). York (2006) [4] developed a nonlinear eddy viscosity turbulence model (ACRL-EVRC) and get better results than ske and rke models (Figure 3). Since York does not present heat transfer distribution, one can not see the cause of improvement but as the authors knowledge, by using nonlinear eddy viscosity, one can overcome to stagnation point anomaly problem (Ref. [5]), so the capability of transition prediction of the model is still questionable. Figure 2: U-bend and radial cooling channels of first experiment of (Dees, 2010) [2]. 1.2 Numerical studies Usually bypass transition occur over a gas turbine vane and also there is a stagnation point in leading edge. Turbulence models has great difficulties with these two phenomena, so turbulence models performance over gas turbine blade must be evaluated with experimental works. York and Leylek (2003) [3] simulate C3X vane of Hylton et al. (1983) experiment with Fluent using standard k ε (ske) and realizable k ε (rke) models. Results of temperature distribution show that Luo and Razinsky (2007) [6] simulate C3X vane of Hylton et al. (1983) experiment using three turbulence models: k ε (KE) model, Quadratic k ε (QKE) model and V2F model. Figure 4 show the Luo s results. KE model obviously shows stagnation point anomaly and can not predict transition. V2F model predict the transition but its length is not true. QKE model is nonlinear eddy viscosity model and do not show stagnation point anomaly but it can not predict the transition location and its length with acceptable precision. Dees et al. (2010) [7] simulate C3X vane of Dees (2010) with Fluent using only k ω turbulence model and 21 million mesh volumes. Figure 5 shows the heat transfer distribution obtained by them. This model also shows the stagnation point anomaly and can not predict the transition. Literatures studies show that most of the numerical works have simulated Hylton et al. (1983) C3X vane and there is not any comprehensive simulation of Dees (2010) experiment. The present paper simulates the first experiment of Dees using different turbulence models and their performances are evaluated.
Figure 4: Heat transfer distribution coefficient [6]. Figure 6: Experimental setup of (Dees, 2010) [2]. Figure 5: Heat transfer distribution coefficient [7]. 2 COMPUTATIONAL METHODOLOGY Steady-state solutions of the governing equations of fluid zones and conduction equation in solid zones are solved simultaneously using Fluent. Three full turbulence models and two transitional models are studied, namely, Spalart-Allmaras (SA) model, Shear stress transport k ω (sstkw) model, v 2 f (V2F) model, Transition SST (trans-sst) model and k kl ω (k-kl-w) model. The air is modeled as a incompressible ideal gas with constant specific heat and thermal conductivity while viscosity is modeled using Sutherlands formula. The vane is constructed out of castable epoxy resin (Polycast PC-287) with conductivity k = 1.03 W/mK and its thickness is t = 1.27 cm. The experimental setup of Dees (2010) [2] is shown in Figure 6. According to this setup, translational periodic boundary condition can be used in numerical simulation. Figure 7 shows computational domain and the boundary conditions. There are four zones, namely, hot section gas path, solid vane, forward U-bend cool- Figure 7: Computational domain and boundary conditions [7]. ing and aft radial cooling. To enable coupled boundary condition in Fluent, the wall interface between fluid and solid zones must be common and the meshes should be linked with each other. The boundary conditions for hot gas path and coolant flows are listed in Table 1. As it is shown two turbulence intensities studied. At low turbulence intensities (lower than 1%) the natural transition and at higher turbulence intensities bypass transition are occurred [8]. Although in realistic condition inlet turbulence intensities are much higher than 1% but it is useful to study the turbulence models performance at low turbulence intensities too. For both
Figure 8: Grid independency result for trans-sst model. Table 1: Boundary conditions [2]. Coarse grid Fine Grid Zone Elements Nodes Elements Nodes 1 2.326 1.672 2.953 1.974 2 0.269 0.159 0.539 0.595 3 0.264 0.141 0.69 0.404 4 0.071 0.04 0.175 0.118 Total 2.929 2.011 4.357 3.091 y + 0.08 0.828 0.102 0.822 Table 2: Detailed information of grides. Figure 9: model. Grid independency result for V2F coolant channels, the hydraulic diameter is determined from the Re = 20000, given in the experiment. The grid independency of results is investigated for 2.92 million and 4.36 million unstructured prism meshes by comparison of heat transfer coefficient distribution. Detailed grid information is presented in Table 2. Figures 8 and 9 show the heat transfer coefficient distribution for trans-sst and V2F models at high turbulence intensity. It can be seen that the results are independent of grids, so the coarser grid is selected. Figure 10 shows the generated grid and Figure 11 shows the boundary layer mesh around airfoil. 3 RESULTS The difference between high and low turbulence intensity depends on the mode of transition occurred in each one. For turbulence intensity above and below 1%, the mode of transition occurred are bypass transition and natural transition, respectively. In this section, the results of experiment and simulation for pressure coefficient, heat transfer coefficient and dimensionless tem- Figure 10: Computational domain grid. perature (overall effectiveness) are compared for various turbulence models. 3.1 Low turbulence intensity Figure 12 shows pressure coefficient distribution. All turbulence models predict the C p distribution very well. Heat transfer coefficient distribution presented in Figure 13. Experimental results show that at s/c 0.4,
Figure 11: Boundary layer mesh around airfoil. Figure 12: Pressure coefficient distribution (LTI). the transition from laminar to turbulence occurs at suction side. As it can be seen, the V2F model has the best performance among the others. It predicts the transition onset location and the transition length with very well accuracy. The trans-sst and k-kl-w models predict the location of transition onset lately and they do not 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 turbulence models do not overpredict the heat transfer coefficient at leading edge, so one can conclude the stagnation point anomaly occurs at high turbulence intensities. Overall effectiveness determines the cooling channels effectiveness, defined by relation: Figure 13: Heat transfer coefficient distribution (LTI). ϕ = T T T T c (1) Figure 14 shows overall effectiveness distribution. The CFD simulation of standard k ω of Dees et al. (2010) [7] are included for comparison. The SA, V2F and sstkw turbulence models results better than trans-sst and k-kl-w models. Deviation of tran-sst and k-kl-w models from experimental results is due to poor estimation of heat transfer coefficient on the suction side. Experimental data shows a maximum in ϕ at s/c 0.4 where the channels baffle located. Turbulence models do not works well around this region. This poor performance is not due to mesh size because Ref. [7] use 21 million mesh volumes but its results does not either match with experiment at this region. 3.2 High turbulence intensity Figure 15 shows pressure coefficient distribution. As it is seen all turbulence models predict the C p distribution very well. Figure 14: (LTI). Overall effectiveness distribution Figure 16 shows heat transfer coefficient distribution for TI = 20%. The CFD simulation of standard k ω of Dees et al. (2010) are included for comparison. Experimental results show that at s/c 0.4, the transition from laminar to turbulence occurs. Among the turbulence models trans-sst model could predict the transition onset location and the transition length very well. The models sstkw and V2F overpredict the heat transfer distribution at the leading edge due to overprediction of production term in turbulent kinetic energy
equation. The V2F model also finds transition with the onset location and the transition length close to the experiment but with an offset. This shows that transition predictability of V2F model is very well. The authors of this paper believe that this offset is due to overprediction of production term in turbulent kinetic energy equation and it could be redefined to get better results. The poor prediction of heat transfer coefficient on pressure side supports this statement. The trans-sst and k-kl-w models do not show stagnation point anomaly because unlike the the full turbulence models, they do not treat with laminar zones as turbulence region. Figure 17 shows overall effectiveness distribution forti = 20%. At s/c 0.4 and s/c 0.8, where the baffle between channels located, all of turbulence models underpredict the overall effectiveness. Figure 16: Heat transfer coefficient distribution (HTI). Figure 17: (HTI). Overall effectiveness distribution Figure 15: Pressure coefficient distribution (HTI). 4 CONCLUSIONS Conjugate heat transfer simulation of C3X gas turbine vane is performed and different turbulence models performance are evaluated. Two turbulence intensities of 0.5% and 20% are studied to see the turbulence models performance at both high and low turbulence intensities. For low turbulence intensity, the V2F model can predict heat transfer coefficient distribution very well. This model predicted transition onset and transition length very close to experiment. Trans-sst model also predict the transition onset with acceptable accuracy but it does not agree with experimental results after the transition. For high turbulence intensity trans-sst model working better than other turbulence models and produce results close to experiment. V2F model at high turbulence intensity overpredict the heat transfer coefficient distribution but again the predicted transition onset location and transition length is near the experimental data. The results of the present simulation show that V2F model can predict the transition with acceptable accuracy and by using nonlinear eddy viscosity V2F models one can resolve the stagnation point anomaly problem of this model. Trans-sst and k- kl-w models do not have stagnation point anomaly but they do not produce good results. The authors believe that these two models are in primary steps and must be developed more. ACKNOWLEDGEMENTS The authors would like to thank Vehicle, Fuel and Environment Research Institute (VFERI) of university of Tehran. REFERENCES [1] L. Hylton, M. Mihelc, E. Turner, D. Nealy and R. York. Analytical and experimental evaluation of the heat transfer distribution over the surfaces of turbine vanes. National Aeronautics and Space Administration NASA Lewis Research Center, 1983. [2] J. Dees. Experimental Measurements of Con-
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