Effect of turbulent Prandtl number on the computation of film-cooling effectiveness

Abstract

This paper presents a method to improve the accuracy of computed film cooling effectiveness spanwise distribution. The effect of turbulent Prandtl number in the flow field outside the near-wall region on the computation is studied. Realizable k – ε model with a one-equation model in near-wall region is employed. The results show that the variation of turbulent Prandtl number has great influence on the computation. Reducing turbulent Prandtl number increases film cooling effectiveness of the whole spanwise region remarkably under large blowing ratios. Under small blowing ratios, the reduction of turbulent Prandtl number decreases the cooling effectiveness of the center region, and increases the effectiveness of the lateral region off the centerline. Compared with the single value turbulent Prandtl number computation the agreement between computation and measured results is improved notably with varied one in different spanwise regions. A new laterally varying turbulent Prandtl number (LV- Pr t) model dependent on lateral location and blowing ratio has been suggested. Computation accuracy is improved greatly by LV- Pr t model. Compared with the TLVA- Pr model of Lakehal [D. Lakehal, Near-wall modeling of turbulent convective heat transport in film cooling of turbine blades with the aid of direct numerical simulation data, ASME J. Turbomach. 124 (2002) 485–498] which provides the best results in the calculated cases LV- Pr t model is an effective way to improve computation accuracy in the frame of the traditional isotropic turbulence models. More work on the information of the turbulent Prandtl number has to be done for the further development of the LV- Pr t model.