Design of Minimum Drag Bodies in Incompressible Laminar Flow

An optimal control approach based on perturbation analysis for modifying the shape of a body in laminar flow to reduce its drag is presented. With certain geometrical constraints, repeatedly modifying the body shape in this approach, which needs to solve one direct problem and one adjoint problem, would lead to a body of minimum drag. Dirichlet-type far-field conditions are required in the analysis. In the actual numerical computation, the far field boundary conditions are obtained from examination of the characteristics of the equations. A series two-dimensional minimum drag bodies are obtained for a range of Reynolds numbers varying from 20 to 105. A geometrical constraint of fixed sectional area was imposed in these calculations. The optimization process monotonically reduces total drag along with an associated reduction in flow separation. It is shown that a minimum drag body obtained for near transition albeit laminar flow Reynolds number demonstrates low drag characteristics even under turbulent flow conditions.