Near-Wall Modeling of Turbulent Convective Heat Transport in Film Cooling of Turbine Blades With the Aid of Direct Numerical Simulation Data

Abstract

The paper presents novel developments in the DNS-based, turbulence modeling strategy of Lakehal et al. developed for calculating jets in crossflow. The particular features of the model include: 1) dynamic coupling of the high-Re k−ε with a one-equation model resolving the near-wall viscosity-affected layer; 2) inclusion of the anisotropy of turbulent transport coefficients for all transport equations; 3) near-wall variation of the turbulent Prandtl number as a function of the local Reynolds number. Most of the important aspects of the proposed model are based on known DNS statistics of channel and boundary layer flows. The model is validated against experiments for the case of film cooling of a flat plate, where coolant air is injected from a row of streamwise inclined jets. Excellent results were obtained for this configuration as compared to earlier numerical investigations reported in the open literature. The model is then extended to calculate film cooling of a symmetrical turbine blade by a row of laterally injected jets for various blowing rates. Comparison of the calculated and measured wall-temperature distributions show that only with this anisotropy eddy-viscosity/diffusivity model can the spanwise spreading of the temperature field be well predicted and the strength of the secondary vortices reduced. Furthermore, results of additional calculations show that combining the anisotropy eddy viscosity model with the DNS-based relation for turbulent Prandtl number promotes the eddy diffusivity of heat vis-à-vis that of momentum further, leading to an enhanced spanwise spreading of the jet. The performance of this new approach improves with increasing blowing rate.