The goal of this work is to propose a new methodology to simulate turbulent thermal wall flows using the classical κ - ε model. The focus of this approach is based on the manner used to implement heat flux boundary conditions on the solid walls. In order to explain and to validate this new algorithm, several test cases are presented, testing a great range of flows in order to analyze the numerical response on different physical aspects of the fluid flow. The proposed approach uses simultaneously a thermal wall law, an analogy between fluid friction and heat transfer and an interpolating polynomial relation that is constructed with a data base generated on experimental research and numerical simulation. The algorithm used to execute the numerical simulations applies the classical κ - ε model with a consolidate Reynolds and Favre averaging process for the turbulent variables. The turbulent inner layer can be modeled by four distinct velocity wall laws and by one temperature wall law. Spacial discretization is done by P1 and P1/isoP2 finite elements and the temporal discretization is implemented using a semi-implicit sequential scheme of finite differences. The pressure-velocity coupling is numerically solved by a variation of Uzawa's algorithm. To filter the numerical noises, originated by the symmetric treatment of the convective fluxes, it is adopted a balance dissipation method. The remaining non-linearities, due to explicit calculations of boundary conditions by wall laws, are treated by a minimal residual method.
turbulence; finite element method; wall laws; analogies; turbulent heat flux
