Verification of RANS Turbulence Models in Loci-CHEM using the Method of Manufactured Solutions

An approach for verifying Reynolds-Averaged Navier-Stokes (RANS) turbulence models in Computational Fluid Dynamics (CFD) codes is presented. This approach relies on smooth, non-physical Manufactured Solutions which are chosen so as to provide contributions from all of the terms in the turbulence transport equations including convection, diffusion, production, and destruction. The Loci-CHEM CFD code is employed to solve the steady-state, compressible RANS equations in two-dimensions. The turbulence model verified is the baseline version of Menter's k-ω model. Special attention is paid to the blending function which allows the model to switch between a k-ω and a transformed k-e model. Results are presented for the observed order of accuracy on families of Cartesian structured grids, skewed curvilinear structured grids, and unstructured triangular grids. The Manufactured Solutions clearly identify problems on skewed meshes which cause the diffusion operator to become inconsistent (i.e., the discretization error does not decrease with mesh refinement). An alternative formulation for the diffusion operator is implemented and the Manufactured Solutions are shown to converge in a second-order manner with mesh refinement for the structured grids. Preliminary investigations on the unstructured meshes indicate that while the code is still consistent, the observed order of accuracy is reduced to first order. Nomenclature ω k CD cross-diffusion term in the turbulence frequency transport equation p c specific heat at constant pressure v c specific heat at constant volume k DE discretization error on mesh level k; k=1,2,3,… d normal distance to the nearest no-slip wall e Favre-averaged internal energy t e Favre-averaged total energy F Menter blending function 1 F Menter blending function for the baseline model exact f exact solution to the partial differential equations k f numerical solution to the partial differential equations on mesh level k; k=1,2,3,… h Favre-averaged enthalpy f h heat of formation

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