Reynolds stresses and turbulent heat fluxes in fan-shaped and cylindrical film cooling holes

Abstract

Large eddy simulation (LES) is carried out to predict the thermal performance, unsteady flow patterns, and turbulence characteristics of the fan-shaped hole and the cylindrical hole cooling films. Velocity fields, Reynolds stresses, and turbulent heat flux distributions are the factors that ultimately determine the film cooling effectiveness by deciding the concentration of coolant and heat near the surface. Accurate prediction of these processes can provide a reliable data set for the design of film cooling systems. It can also help solve difficulties of improving RANS-based simulations in terms of their inaccuracies in matching measured flow rates for a given pressure drop across the film and the mixing process once the coolant is ejected from the film. Credible estimates and modest costs of the current LES originate from the multiblock hexahedra meshing, the turbulence inflow generator, and the numerical schemes implemented. Multiblock hexahedra meshes are adopted and generated by a quasi-automatic mesh generation algorithm utilizing template-based multi-block construction followed by elliptic smoothing. Computational resources are utilized in a way that mesh refinement exists only near cooling decorations of small size and wall boundaries, without the need for associated clustering in the far field which is commonly used in commercial packages. The high orthogonality and continuous smoothness throughout the computational domain are maintained to facilitate turbulence capturing. The synthetic inflow generator produces a random field matching a realistic set of two-point statistics based on eigen-reconstruction in a computationally inexpensive processing step. To prove that the current LES simulations of modest cost can reproduce with high accuracy, the discharge characteristics, velocity, and turbulence intensity profiles of cylindrical and fan-shaped cooling films are compared with published measured data on the same flow configurations. Results reveal that the set of modeling methodologies is valid for calculating film-cooling performance within an acceptable range of accuracy. The energy-carrying turbulence structures in and near the cooling holes are shown and their behaviors are linked to turbulent Reynolds stresses. Reynolds stresses and turbulent heat fluxes are compared for different blowing ratios and two types of cooling holes in the parametric study. Similarity patterns of velocity profiles, non-dimensional temperature profiles, Reynolds stress and turbulent heat flux profiles are discussed.