Nonlinear eddy viscosity modelling for turbulence and heat transfer near wall and shear-free boundaries

Abstract

Abstract New turbulence and turbulent heat flux models are proposed for capturing flow and thermal fields bounded by walls or free surfaces. The models are constructed using locally definable quantities only, without any recourse to topographical parameters. For the flow field, the proposed model is a cubic nonlinear k–e–A three equation eddy viscosity model. It employs dependence on Lumley's stress flatness parameter A, by solving its modelled transport equation as the third variable. Since A vanishes at two-component turbulence boundaries, introducing its dependency enables a turbulence model to capture the structure of turbulence near shear-free surfaces as well as wall boundaries. To close the modelled A equation, an up-to-date second-moment closure is applied. For the thermal field, an explicit algebraic second-moment closure for turbulent heat flux is proposed. The new aspect of this heat flux model is the use of nonlinear Reynolds stress terms in the eddy diffusivity tensor. This model complies with the linearity and independence principles for passive scalar. The proposed models are tested in fully developed plane channel, open channel and plane Couette–Poiseuille flows at several fluid Prandtl numbers. The results show the very encouraging performance of the present proposals in capturing anisotropic turbulence and thermal fields near both wall and shear-free boundaries in the range of 0.025⩽Pr⩽95.