Stability and receptivity analysis of flat-plate boundary layer with suction and blowing

Abstract

The effect of suction and blowing on the local stability of the flat-plate boundary layer is presented using non-normal theory. The 3D governing stability equations are derived using standard procedure in the form of normal velocity and vorticity. The governing stability equations are discretized using the Chebyshev spectral collocation method. The discretized governing equations with grid stretching form an eigenvalue problem, and it is solved using the QZ algorithm with an appropriate boundary conditions. The transient energy growth is computed by the linear superposition of the non-orthogonal eigenvectors. The energy curve is obtained by singular value decomposition (SVD) of the matrix exponential. The receptivity analysis is also considered based on the input output framework to quantify a fluid systems response with external forcing frequencies. The optimal fluid system response corresponding to the optimal initial condition is computed for non-modal and receptivity analysis. The flow is modally stable for suction even at a higher Reynolds number (Re??)(Re??), while a reverse trend is observed for blowing.