Developing a Scalar Flux Model Solely Based on Mean Flow Quantities for the Film Cooling Jet Flow

Abstract

Previous studies showed that the Reynolds-averaged Navier Stokes simulation (RANS) which used gradient diffusion hypothesis (GDH) severely under-predicts the scalar diffusion downstream the film cooling jet flow. Scalar flux models of different types have been developed throughout the years. Of particular interest is the algebraic model, which is easy to implement and has a low computational cost. Well-known algebraic models include the generalized gradient diffusion hypothesis (GGDH) and the high-order generalized gradient diffusion hypothesis (HOGGDH). However, due to the dependence on the Reynolds stress, GGDH and HOGGDH may suffer from a lack of scalar prediction along with RANS, because the Boussinesq core of which will lead to a loss of anisotropy. In a previous study [1], we revealed the mechanism of turbulent scalar transport in the shear layers of the film cooling jet based on the analysis of the flow and scalar field predicted by the large eddy simulation (LES). Upon the mechanism revealed, this paper aims to develop a scalar model that only depend on mean flow quantities, including mean velocity, turbulent kinetic energy and turbulent viscosity. It is our hope that the model can be comparable or surpass the GGDH and HOGGDH concerning the ability of scalar prediction, while not be dependent on the Reynolds stress. Scalar transport equation was solved with the mean flow data provided by the previous LES. The prediction of an inclined cylindrical hole with VR = 0.46 using GGDH, HOGGDH and current model (namely SLR) were compared and analyzed.