Investigation on spatial evolutions of two- and three-dimensional modes in a laminar separation bubble over a low-pressure turbine cascade

Abstract

Separation-induced transition under a low level of freestream turbulence is investigated via direct numerical simulation of flow over a low-pressure turbine cascade. The results are comprehensively analyzed in physical and Fourier spaces to elucidate the mechanisms of flow transition in the shear layer and the recirculation region of the separation bubble. It is observed that the instability process in the upstream attached boundary layer provides considerable low-frequency waves to the separated shear layer. As a result, intense nonlinear effects occur in the shear layer leading to the growth of two-dimensional waves with low to high frequencies in sequence and, eventually, giving rise to the most-amplified wave associated with the vortex-shedding frequency. Inside the recirculation region, the corresponding two-dimensional waves are induced showing the evidence for previous research on receptivity. Different from the downstream propagation of two-dimensional waves, the collision and merging of upstream- and downstream-propagating oblique waves contribute to the initiation of three-dimensional fluctuations. The subsequent three-dimensionality of the shear layer is closely associated with the growth of three fundamental oblique waves with large spanwise wavelengths. It is illustrated that these characteristic modes correspond to λ-shaped vortices and continuously developing hairpin vortex chains.