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 theory (LST) is unable to accurately describe the unstable flow over crossflow-dominated configurations. In recent years the development of nonlinear parabolized stability equations (NPSE) has opened new pathways toward understanding unstable boundary-layer flows. This is because the elegant inclusion of nonlinear and non-parallel effects in the NPSE allows accurate stability analyses to be performed without the difficulties and overhead associated with direct numerical simulations (DNS). NPSE results are presented here and compared with experimental results obtained at the Arizona State University Unsteady Wind Tunnel. The comparison shows that the saturation of crossflow disturbances is responsible for the discrepancy between LST and experimental results for cases with strong favourable pressure gradient. However, for cases with a weak favourable pressure gradient the stationary crossflow disturbances are damped and nonlinearity is unimportant. The results presented here clearly show that for the latter case curvature and non-parallel effects are responsible for the previously observed discrepancies between LST and experiment. The comparison of NPSE and experimental results shows excellent agreement for both configurations. Through this work, a detailed quantitative comparison and validation of NPSE with a careful experiment has now been provided for three-dimensional boundary layers. Moreover, the results validate the experiments of Reibert et al . (1996), and Radeztsky et al . (1993, 1994) suggesting that their databases can be used by future researchers to verify theories and numerical schemes. The results show the inadequacy of linear theories for modelling these flows for significant crossflow amplitude and demonstrate the effects of weak curvature to be more significant than slight changes in basic state, especially near neutral-stability locations.