Numerical Investigation of Cross-Flow Instability for a Supersonic Swept Wing with a Biconvex Airfoil

The linear and nonlinear disturbance development for a supersonic (infinite) swept wing with a biconvex airfoil are investigated using a linear/nonlinear disturbance flow formulation solver based on the compressible Navier-Stokes equations. In addition, a biglobal stability solver was developed and is employed here to allow linear stability investigations for baseflows strongly dependent on two spatial directions. Results for M = 2 and a chord based Reynolds number R_e = 1.45 · 10⁶ obtained from the linear disturbance flow computations are compared with conventional linear stability theory. The nonlinear development of steady cross-flow modes were computed with the nonlinear disturbance flow formulation solver to reach the nonlinear saturation of the cross-flow mode. The nonlinearly saturated, new baseflow (for secondary instability analysis) is strongly dependent on the wall normal and wave propagation direction and therefore requires a biglobal stability analysis, while the primary cross-flow vortex direction can be considered homogeneous. The biglobal baseflow was constructed using the original baseflow and Fourier transformed disturbance flow data from the nonlinear disturbance flow computation. In addition, preliminary temporal biglobal stability computations are presented.