Adjoint shape optimization based on DNS of Turbulent Channel Flow

Abstract

Direct Numerical Simulations (DNS) of turbulent channel flow are performed with the aim to reduce the skin friction by controlling the near-wall transport processes based on surface modifications. The latter are determined based on the solution of the adjoint Navier-Stokes equations which provides surface sensitivities indicating an optimal wall shape. With the modified geometry the DNS is continued until a new fully developed state is reached. Time-averaging of the instantaneous wall shapes produced with this approach will finally lead to a steady wall shape which controls the flow according to a prescribed objective function. Considering that the objective function turbulence kinetic energy (TKE) is minimized, the approach produced a reduction of 9.3% and a mean pressure gradient, required to drive the flow, which is reduced by 7.5%. Currently, different objective functions are tested to identify flow parameters which are suitable to effectively reduce the skin friction in turbulent channel flow.