Perturbation Analysis of “k—ω” and “k—ε” Turbulent Models. Wall Functions

Abstract

Presented article shows rigorous method how derive non-stationary turbulent boundary layer equations by perturbation analysis. The same method is used for analysing behaviour of “k-omega” and “k-epsilon” turbulent models. The analysis is divided into two parts: near wall behaviour – boundary conditions, and behaviour in “log-layer” – wall functions. Both parts have important place in CFD. Boundary conditions are important part of CFD. “k-omega” and “k-epsilon” are related by one simple formula, but they yield to different solutions. Exact values for k, omega and epsilon on a wall are evaluated and all theoretical results are compared with numerical solutions. Special treatment is dedicated to “k-epsilon” model and Dirichlet boundary condition for “epsilon, instead of standard Neumann boundary condition. “Log-Layer” is well known from experiments and it is used for setting constants in turbulent models. Standard equations are derived by perturbation analysis. In presented article are these equations derived with 3 more terms, than in standard case. This yields to sharper approximation. These new equations are solved and solution is a bit different, than in standard case. Due to 3 extra terms is possible to get better approximation for k and new view into problematic..