On the practical application of the PSE approach to linear stability analysis

Abstract

The transition to turbulence of the laminar boundary layer plays an important role in airfoil design. The new PSE approach is more accurate and consistent than the classical Orr-Sommerfeld theory. The aim of this paper is to prove that this approach can be routinely used in practical applications to study instabilities and to predict the onset of laminar-turbulent transition. The main difficulty in its intensive use concerns the initialisation. However, systematic studies can be conducted and the results presented show that the non-parallel effects are negligible for streamwise instabilities and strengthen n factor values for crossflow instabilities. In some intermediate cases, the PSE results exhibit large crossflow amplification for low frequencies as well as large streamwise amplification at higher frequencies, whereas only the latter one is dominant according to the Orr-Sommerfeld theory. In these particular cases, the fluctuation spectra present two relative maxima (with the PSE) and the instability type and the most amplified frequencies can therefore be very different from those predicted by the Orr-Sommerfeld theory.