Evaluation of an alternative algebraic turbulence model in the CFD Software by ONERA, DLR and Airbus (CODA)

Kurzfassung

The CFD Software developed by ONERA, DLR and Airbus (CODA) was extended to allow the use of the algebraic model proposed by C. C. Rossow. In this report, the implementation was compared with the results obtained by C. C. Rossow and with the Spalart-Allmaras Model, using CODA. Two test cases were chosen for the comparison: the first case is the flow around the RAE 2822 air-foil in transonic conditions and the second case is the trailing edge separation for the NACA 4412 air-foil. Using coarse meshes, the model showed consistent and similar behaviour of drag coefficients, lift coefficients, pressure coefficient, and tangential skin friction distributions. For medium and finer meshes the model presented stagnation of residuals and not-a-number values at advanced iteration steps. The oscillatory behaviour of the residuals, caused by the constant redefinition of the wall variables, incremented the number of iterations for convergence as the size of the mesh increased. In addition, the theory involving the equations of turbulence modelling is presented: First, the thermodynamic relation for ideal gases between the specific internal energy and the specific enthalpy is derived. This thermodynamic equation is used in the equation of energy conservation of the Compressible Navier-Stokes equations to get an equation in terms of the specific total enthalpy. The mass, momentum and energy equations of the compressible Navier-Stokes equations are presented to derive the Favre-Reynolds Averaged Navier-Stokes equations for ideal gases. Then, a closed form of the Favre-Reynolds Averaged Navier-Stokes equations is presented, after introducing the Boussinesq eddy viscosity assumption, and common assumptions for the unknown terms arising from the Reynolds averaging. Finally, the Finite Volume Method discretization for the Favre-Averaged Navier Stokes equations is derived, using the discontinuous Galerkin method and the indicator function as test function.