Streaming effect of wall oscillation on boundary layer separation

The response of boundary layer separation from smooth surface to a periodic vortical excitation imposed locally near the separation point is studied. The emphasis is on the time-averaged streaming effect of the unsteady excitation to the separating flow. The problem is formulated as a small periodic perturbation to a basic steady separating flow which is assumed given. Two types of separation model are studied, the breakaway separation model based on the numerical triple-deck solution of F.T.Smith, and the bubble separation model, which is calculated based on boundary layer equations with prescribed displacement thickness. First and second order perturbation equations are derived and simplified to ordinary differential equations near the separation point by using the triple-deck analysis. The perturbation equations are solved both analytically and numerically. It is found that the ratio of the Strouhal number St and Reynolds number Re, α = St/Re^¼, is an important parameter which determines the nature of the excited flow. For proper value of α, the streaming effect is quite strong which may delay or suppress separation. The numerical results show that there exists an optimum forcing frequency corresponding to a maximum streaming effect for each streamwise location.