Abstract
Using a mathematical theory, we show that the optimality condition of a turbulent diffuser with maximum pressure recovery at the exit is zero shear stress along the wall. The optimal diffuser shape is designed through iterative procedures by using the $k-{\varepsilon}-{\nu}^{2}-f$ turbulence model for flow simulation. The Reynolds number based on the bulk mean velocity and the channel height at the diffuser entrance is 18,000. We also perform large eddy simulation to validate the shape design results and investigate the flow characteristics near the zero-skin friction wall. Results from large eddy simulation show that the skin friction is slightly higher than zero but is still very small as compared to that of the flat plate boundary layer flow Although the time-averaged wall shear stress is slightly above zero along the diffuser wall, instantaneous flow reversals occur intermittently. The streamwise mein velocity shows an asymptotic behavior of the half-power-law near the wall where the skin friction is close to zero.
