Drag reduction for three dimensional wing at transonic speed

The mesh adjoint method has been used as a design tool to aid in the placement and optimisation of flow control devices. For purely geometric optimisations, a by-product of obtaining the gradients of the objective function w.r.t. the design variables is finding the sensitivity of the objective function w.r.t. surface changes. This can be obtained from the solution to the mesh adjoint equation, the mesh adjoint vector, -λmesh .

This test case has focused on the M6 wing as a transonic wing test case, although the methodology can be equially applied to other wing design/optimisation problems. The sensitivity produced from this case is very diverse and therefore shows how the mesh adjoint can aid a designer. The flow over the M6 produces a shock with front and rear shock legs, and shock bumps have been optimised to deal with the production of wave drag in these regions.

An interesting non-shock region of sensitivity was also discovered on the upper surface of the M6 wing. This region was shock free but the sensitivity map indicated that a surface change in the positive z-direction would give a change in the drag. This information is not available from the either the surface pressure or skin friction distributions.

The analysis considered placing bumps in all the sensitivity regions on the M6 wing upper surface and optimising them for minimum drag. In a comparison with the rear-shock region case, using all the sensitivity regions gained an extra reduction in drag by just one drag count. This shows that the most important region for optimisation for the single-point optimisation is the rear shock line. A study of the robustness of the 3D distributed shock indicates that the optimed design shows good robustness near the design conditons in Mach number and lift.