Near-Wall Modification of an Explicit Algebraic Reynolds Stress Model Using Elliptic Blending

Abstract

This chapter examines near-wall modification of an explicit algebraic Reynolds that stress model using elliptic blending. Two-equation, linear eddy viscosity turbulence models are widely used for modeling industrial flow problems. However for complex flows, the Boussinesq approximation is not accurate and the linear models do not give satisfactory results especially for the turbulence quantities. In this chapter, the elliptic blending approach is used in order to modify an explicit algebraic Reynolds stress model so as to reproduce the correct near wall behavior of the turbulent stresses. The modification introduces one additional equation compared to the standard k–ɛ model, namely the equation for the elliptic blending parameterγ. The model is used to simulate the turbulent fluid flow and heat transfer between parallel flat plates at 3 Reynolds numbers based on three different values of the friction velocity and the flow in a backward facing step at ReH=28,000. The model does not use the distance from the wall thus it is easily applied to complex geometries. The comparison with DNS data or experimental measurements is found to be satisfactory.