Transient energy growth analysis of flat-plate boundary layer with an oblique and non-uniform wall suction and injection

Abstract

This paper presents a non-modal bi-global linear stability analysis of an incompressible flat-plate boundary layer under the effects of oblique and non-uniform wall suction and injection. The base flow velocity profile is two-dimensional and fully non-parallel. The flow is laminar at the inflow boundary, and no reverse flow occurs in the flow domain. The Chebyshev spectral collocation method has been used for the discretization of the governing stability equations. The discretized stability equations along with appropriate boundary conditions form an initial value problem (IVP). The transient energy growth (G(t)) and associated optimal perturbations are computed for different oblique angles (θ = 30°, 60°, 90°, 120°, and 150°), suction and injection intensities (I = 0.5%, 1.5%, and 2.5% of U∞), Reynolds numbers (Re = 195, 284 and 411), and different spanwise wavenumbers (β = 0 - 2) for uniform and non-uniform profiles of wall suction and injection. The behaviour of the boundary layer is found to be approximately similar but opposite in nature for θ = 90° to 180° and θ = 0° to 90° due to lower transpiration intensity. The G (t) decreases with the increase in θ from to 0° to 90° for wall suction due to the damping of T–S modes. However, an opposite trend has been observed for injection due to the amplification of T–S modes. The uniform profile is found to be more effective than the non-uniform profiles of suction and injection in terms of their impact on the stability of the boundary layer. The 2D spatial structures of the optimal perturbations are damped and flow becomes modally stable as the spanwise wavenumber (β) is increased.