Numerical Simulation of Swept-Wing Vortices Using Nonlinear Parabolized Stability Equations

The nonlinear development of stationary crossflow vortices over a 45° swept NLF(2)-0415 airfoil is studied. Previous investigations indicate that the linear stability theories are unable to accurately describe the transitional flow over crossflow-dominated configurations. In recent years the development of nonlinear parabolized stability equations (NPSE) has opened new pathways toward understanding transitional boundary-layer flows. This is because the elegant inclusion of nonlinear and nonparallel effects in the NPSE allows accurate stability analyses to be performed without the difficulties and overhead associated with direct numerical simulations (DNS). Numerical (NPSE) results are presented here and compared with experimental results obtained at the Arizona State University Unsteady Wind Tunnel (ASUUWT) for the same configurations. The comparison shows that the saturation of crossflow disturbances is responsible for the discrepancy between linear stability theories and experimental results for cases with strong favorable pressure gradient. However, for cases with a weak favorable pressure gradient the stationary crossflow disturbances are damped and nonlinearity is unimportant. For the latter case curvature and nonparallel effects are responsible for the previously observed discrepancies between linear stability theory and experiment. The comparison of computational (NPSE) and experimental results show excellent agreement for both configurations.