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Viscous flux and turbulence models linearization for aerodynamic shape optimization for turbomachineries

Chi-Tuân Pham
Abstract : The computation of derivatives of aerodynamic functions, with respect to design parameters of the solid shape is now a branch of computational fluid dynamics. This differentiation with respect to two dependent variables, the flow field and the mesh, bound by the discrete fluid dynamics equations, needs the resolution of a linear system. Its matrix is the Jacobian matrix of the fluid dynamics equations with respect to the flow field (direct differentiation method) or the tranposate of this Jacobian matrix (adjoint method). The accuracy of the computation of this Jacobian matrix is discussed when the RANS equations are used. The aim of this PhD thesis is to determine the level of accuracy for the linearization of a discrete viscous flux and the discrete equations of some turbulence models, needed to reach accurate gradients of functions used by the conceptors of turbomachineries, with respect to some design parameters of a blade. Approximate viscous flux linearizations (with or without a thin layer approach) and the linearization of two turbulence models (algebraic Michel et al. model and Launder-Sharma k-e two-equation model)are described. Several approximations for the linearization of Michel et al.'s model are tested and compared. Results (values of gradients of aerodynamic functions, flow sensibilities for the direct differentiation method) are shown for Déléry's C nozzle, ONERA M6 wing and two turbine isolated blades. Recommendations for the computation of derivatives are given for turbomachinery flows with RANS equations.
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Contributor : Ecole Arts Et Métiers Paristech <>
Submitted on : Friday, January 5, 2007 - 8:00:00 AM
Last modification on : Friday, January 5, 2007 - 8:00:00 AM
Long-term archiving on: : Thursday, September 30, 2010 - 7:57:22 PM


  • HAL Id : pastel-00002058, version 1



Chi-Tuân Pham. Viscous flux and turbulence models linearization for aerodynamic shape optimization for turbomachineries. Engineering Sciences [physics]. Arts et Métiers ParisTech, 2006. English. ⟨NNT : 2006ENAM0030⟩. ⟨pastel-00002058⟩



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