Transition induced by linear and nonlinear perturbation growth in flow past a compressor blade

Abstract

Flow past a NACA 65 blade at chord-based Reynolds number 138 500 is studied using stability analysis, generalized (spatially weighted) transient growth analysis and direct numerical simulations (DNS). The mechanisms of transition on various sections of the blade observed in previous work by Zaki et al. (J. Fluid Mech., vol. 665, 2010, pp. 57–98) are examined, with a focus on the pressure side around the leading edge. In this region, the linearly most energetic perturbation has spanwise wavenumber $40\unicode[STIX]{x03C0}$ (five boundary-layer thicknesses) and is tilted against the mean shear to take advantage of the Orr mechanism. In a DNS, the nonlinear development of this optimal perturbation induces $\unicode[STIX]{x1D6EC}$ structures, which are further stretched to hairpin vortices before breaking down to turbulence. At higher spanwise wavenumber, e.g. $120\unicode[STIX]{x03C0}$, a free-stream optimal perturbation is obtained upstream of the leading edge, in the form of streamwise vortices. During its nonlinear evolution, this optimal perturbation tilts the mean shear and generates spanwise periodic high- and low-speed streaks. Then through a nonlinear lift-up mechanism, the low-speed streaks are lifted above the high-speed ones. This layout of streaks generates a mean shear with two inflectional points and activates secondary instabilities, namely inner and outer instabilities previously reported in the literature.