Sensitivity Analysis for the RANS Equations coupled with Linearized Turbulence Model

摘要

A method is described for sensitivity analysis with Reynolds-averaged Navier-Stokes equations coupled with a turbulence model. The algebraic model of Michel et al. and the two-equation k-e model of Launder-Sharma are considered for both steady-state computations and sensitivity analysis using discrete direct differentiation method or discrete adjoint vector method. The mean flow and turbulence model equations are analytically differentiated to evaluate the derivatives of the aerodynamic functions with respect to the design parameters. This method is applied to two-dimensional and three-dimensional flows. The influence of classical assumptions on the sensitivity accuracy is explored by comparing results with finite difference evaluations. The application of the thin-layer approximation allows enhancing the robustness and convergence rate of the 3D flow computations without reducing accuracy. The constant turbulent eddy viscosity leads however to inaccurate results.