Skin friction reduction in fully developed turbulent channel flow based on DNS and adjoint shape optimization

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 improved wall shape. With the modified channel geometry the DNS is continued until a new fully developed state is reached. Time-averaging of the obtained instantaneous wall shapes will finally provide a steady wall shape which interacts with the flow according to a prescribed objective function. Prescribing the turbulence kinetic energy (T KE) as the objective function to be minimized, the approach reduced the T KE by ≈ 11.5% and the driving mean pressure gradient by ≈ 9.7%. The mean pressure drop serves as indicator for the skin friction. Different objective functions are tested to identify flow parameters which are suitable to effectively reduce the skin friction in turbulent channel flow