Stability and energy balance analysis of axisymmetric boundary layer: effects of oblique non-uniform suction and injection

Abstract

This paper discusses the modal global stability analysis of the boundary layer formed over a circular cylinder subjected to oblique non-uniform suction and injection. The linearized stability equations governing the system are obtained using a standard procedure in the cylindrical coordinate system, followed by discretization using the spectral method. The discretized equations, accompanied by suitable boundary conditions, constitute an eigenvalue problem that is solved using the ARPACK with a shift-and-invert approach. The stability computations are performed for different inclination angles (θ = 30°, 60°, 90°, 120°, and 150°), transpiration velocities (I = 0.5%, 1.5%, and 2.5% of U∞), Reynolds numbers (Reδ* = 195, 285, and 411), and different azimuthal wavenumbers (N = 0 – 10) for both uniform and non-uniform profiles of suction and injection. The results reveal that instability modes, such as Tollmien-Schlichting waves, are damped due to suction and amplified due to injection. The T-S branch of the eigenspectra shifts towards the damped region as the suction angle increases, while it moves towards the upper half-plane as injection angle increases, specifically from δ = 0° to 90°. The uniform suction profile is found to be modally more stable than the non-uniform profiles, while non-uniform injection profiles are found to be more stable than the uniform profile. The energy balance analysis is also performed corresponding to leading non-stationary eigenmodes, and the results reveal that suction has a strong damping viscous dissipation effect, while injection has a strong amplifying energy production effect.