Large-Eddy Simulation With Zonal Near Wall Treatment of Flow and Heat Transfer in a Ribbed Duct for the Internal Cooling of Turbine Blades

Abstract

Large eddy simulations of flow and heat transfer in a square ribbed duct with rib height to hydraulic diameter of 0.1 and 0.05 and rib pitch to rib height ratio of 10 and 20 are carried out with the near wall region being modeled with a zonal two layer model. A novel formulation is used for solving the turbulent boundary layer equation for the effective tangential velocity in a generalized co-ordinate system in the near wall zonal treatment. A methodology to model the heat transfer in the zonal near wall layer in the LES framework is presented. This general approach is explained for both Dirichlet and Neumann wall boundary conditions. Reynolds numbers of 20,000 and 60,000 are investigated. Predictions with wall modeled LES are compared with the hydrodynamic and heat transfer experimental data of Rau et al. [1], and Han et al. [2], and wall resolved LES data of Tafti [3]. Friction factor, heat transfer coefficient, mean flow as well as turbulent statistics match available data closely with very good accuracy. Wall modeled LES at high Reynolds numbers as presented in this paper reduces the overall computational complexity by factors of 60–140 compared to resolved LES, without any significant loss in accuracy.