Global Stability Analysis of Spatially Developing Boundary Layer: Effect of Streamwise Pressure Gradients

Аннотация

The paper presents a global stability analysis of the two-dimensional incompressible boundary layer with the effect of streamwise pressure gradient. A symmetric wedge flow is considered at different values of the dimensionless pressure gradient parameter β_H. The pressure gradient dp/dx in the flow direction is zero, when β_H = 0, favorable (negative) for β_H > 0, and adverse (positive) for β_H < 0. The base flow is computed by numerical solution of Falkner—Skan equation. The Reynolds number is based on the displacement thickness δ* at the inflow boundary. The stability equations governing the flow are derived in body-fitted coordinates. The stability equations are discretized using the Chebyshev spectral collocation method. The discretized equations, together with boundary conditions, form a general eigenvalue problem and are solved using Arnoldi’s algorithm. The temporal global modes are computed for β_H = 0.022, 0.044, and 0.066, for favorable and adverse pressure gradients. The temporal growth rate ω_i is found to be negative for all the global modes. The ω_i value is smaller for the favorable pressure gradient (FPG) than for the adverse pressure gradient (APG) at the same Reynolds number (Re = 340). Thus, the FPG has a stabilizing effect on the boundary layer. The comparison of the spatial eigenmodes and spatial amplification rates for FPG and APG show that FPG has a stabilizing effect, whereas APG has a destabilizing effect on the disturbances.