Simulation of swept-wing vortices using nonlinear parabolized stability equations

The nonlinear development of stationary crossflow vortices over a 45 degree s swept NLF(2)-0415 airfoil is studied. Previous investigations indicate th at the linear stability theory (LST) is unable to accurately describe the u nstable flow over crossflow-dominated configurations. In recent years the d evelopment of nonlinear parabolized stability equations (NPSE) has opened n ew pathways toward understanding unstable boundary-layer flows. This is bec ause the elegant inclusion of nonlinear and nonparallel effects in the NPSE allows accurate stability analyses to be performed without the difficultie s and overhead associated with direct numerical simulations (DNS). NPSE res ults are presented here and compared with experimental results obtained at the Arizona State University Unsteady Wind Tunnel. The comparison shows tha t the saturation of crossflow disturbances is responsible for the discrepan cy between LST and experimental results for cases with strong favourable pr essure gradient. However, for cases with a weak favourable pressure gradien t the stationary crossflow disturbances are damped and nonlinearity is unim portant. The results presented here clearly show that for the latter case c urvature and non-parallel effects are responsible for the previously observ ed discrepancies between LST and experiment. The comparison of NPSE and exp erimental results shows excellent agreement for both configurations. Through this work, a detailed quantitative comparison and validation of NPS E with a careful experiment has now been provided for three-dimensional bou ndary layers. Moreover, the results validate the experiments of Reibert et al. (1996), and Radeztsky et al. (1993, 1994) suggesting that their databas es can be used by future researchers to verify theories and numerical schem es. The results show the inadequacy of linear theories for modelling these flows for significant crossflow amplitude and demonstrate the effects of we ak curvature to be more significant than slight changes in basic state, esp ecially near neutral-stability locations.