Airfoil Design on Unstructured Grids for Turbulent Flows

Abstract

An aerodynamic design algorithm for turbulent e ows using unstructured grids is described. The current approachusesadjoint (costate)variablestoobtainderivativesofthecostfunction.Thesolutionoftheadjointequations is obtained by using an implicit formulation in which the turbulence model is fully coupled with the e ow equations when solving for the costate variables. The accuracy of the derivatives is demonstrated by comparison with e nite difference gradients, and a few sample computations are shown. Recommendations on directions of further research into the Navier ‐Stokes design process are made. Nomenclature A = area of control volume a = speed of sound C ¤ = constant used in Sutherland’ s law for viscosity cb1;cb2;cv1; = constants used in Spalart ‐Allmaras cw1;cw2;cw3 turbulence model cd = drag cl = lift c1