Optimal perturbations of flat-plate boundary layer with suction and injection

Abstract

This paper presents the effect of suction and injection on the non-modal stability analysis of the boundary layer flow. The base flow solution is obtained by OpenFOAM software. The 3D governing stability equations are derived in terms of normal velocity and vorticity. The spectral collocation method is used for spatial discretization of the stability equations. The QZ algorithm solves the formulated eigenvalue problem with appropriate boundary conditions. Transient amplification is achieved by linear superposition of non-orthogonal eigenvectors. The optimal energy growth and associated perturbations are computed for different parameters such as Reynolds number (Re), streamwise and spanwise wave numbers (α, β), and time horizon (t). A detailed description of it is mentioned in the results and discussion section. A harmonically driven input–output framework is also considered in a general fluid system to study receptivity analysis. In a case of injection, strong resonant peak is detected at resonant frequency, ω ω = 0.07143 and 0.602 for α = 0.15, β = 0.96 and α = 0.86, β = 1.7, respectively. Similarly for suction, peak response in energy is found at ω = 0.1122 and 0.8469 for α = 0.15, β = 0.96 and α = 0.86, β = 1.7, respectively.