An optimal control approach for design of minimum drag bodies with a turbulent flow model is proposed. The flow is assumed to be governed by steady-state, incompressible Reynolds Averaged Navier-Stokes (RANS) equations. A set of "adjoint" equations is introduced, the solution to which along with the solution to the "direct" RANS equations permit the calculation of the direction and relative magnitude of the change in body profile that leads to a lower drag. Local or global geometry constraints can also be imposed during the optimization process. Each successive shape modification lowers the drag of the body and once this process converges, in principle one would obtain a minimum drag body. The adjoint equations are derived using Dirichlet-type boundary conditions at far field. The numerical computations however are carried out with far field conditions obtained by examination of the characteristics of the equations in the absence of viscous terms. Two-dimensional minimum drag bodies at Reynolds numbers of 6×10{sup}6 and 8×10{sup}6 are obtained using this approach. A geometrical constraint of fixed sectional area is imposed in these calculations.
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