Calculation of Transitional Boundary Layers With an Improved Low-Reynolds Number Version of the k-ε Turbulence Model

Abstract

Several well known low-Reynolds version of the k-ε models are analyzed critically for laminar to turbulent transtional flows as well as near wall turbulent flows from theoretical and numerical standpoint. After examining apparent problems associated with the modelling of low-Reynolds number wall damping functions used in these models, an improved version of k-ε model is proposed by defining the wall damping factors as a function of some quantity (turbulence Reynolds number Rt) which is only a rather general indicator of the degree of turbulent activity at any location in the flow rather than a specific function of the location itself, and by considering the wall limiting behavior, the free-stream asyptotic behavior, and the balnce between production and destruction of turbulence. This new model is applied to the prediction of 1) transitional boundary layers influenced by the free-stream turbulence, pressure gradient and heat transfer; 2) external heat transfer distribution on the gas turbine rotor and stator blade under different inlet Reynolds number and free-stream turbulence conditions. It is demonstrated that the present model yield improved predictions.