Fluid dynamic design problems require the calculation of many computationally expensive flow analyses. One impediment to the use of CFD in the conceptual design process is the need to determine detailed body-fitted grids over wide classes of different geometric topologies. The grid generation process is often laborious and is not always as automated as desired. For conceptual design, where inviscid methods may be adequate, procedures involving Cartesian grid methods, particularly in combination with grid adaptation have proved to be effective. This paper presents an efficient formulation for the robust design optimisation of two-dimensional transonic inviscid fluid flow problems on Cartesian grids. Cartesian grid methods are particularly well-suited for rapid, conceptual-design tools. The methodology has several essential ingredients. First, the procedure utilises an accurate flow solver tailored for use on Cartesian grids. Approximate but efficient design sensitivities are obtained using a discrete adjoint formulation. This adjoint problem is based on an artificially dissipative flow solver in order to obtain robust sensitivity derivatives. We solve the quasi-time-dependent adjoint equations in conjunction with what we term progressive optimisation, whereby a sequence of operations, controlling a partially converged flow solution, followed by a partially converged adjoint solution followed by an optimisation step is perfonned. Finally, we use progressively finer grids for the progressive solution of the flow field, while using a reduced domain for the solution of the adjoint equations. The methodology is shown to be accurate, robust and highly efficient, with converged inverse design optimisations of airfoils produced in no more than the amount of computational work to perform one flow analysis and direct design of airfoils in no more than the amount of computational work to perform eight flow analyses.
Efficient fluid dynamic design optimization using Cartesian grids
Effiziente strömungsmechanische Optimierung basierend auf kartesischen Koordinaten
AIAA Computational Fluid Dynamics Conference, 16 ; 1130-1140
2003
11 Seiten, 8 Bilder, 1 Tabelle, 11 Quellen
Aufsatz (Konferenz)
Englisch
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