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.
Highlights
Transitional flow past a blade in a compressor passage has been thoroughly investigated owing to its rich dynamics associated with pressure gradients, free-stream noise, leading-edge effects and surface curvature (Gostelow, Blunden & Walker 1994; Spalart & Strelets 2000)
The transition to turbulence is initiated by the distortion or secondary instabilities, of the streaks around the top of the boundary layer, activated by high-frequency noise in the free stream (Jacobs & Durbin 2001)
The main objective of the present work is to examine the linear mechanisms behind the laminar–turbulent transition on various regions of the compressor blade, with a focus on bypass transition triggered by noise upstream of the leading edge
Summary
Transitional flow past a blade in a compressor passage has been thoroughly investigated owing to its rich dynamics associated with pressure gradients, free-stream noise, leading-edge effects and surface curvature (Gostelow, Blunden & Walker 1994; Spalart & Strelets 2000). Both orderly and bypass transition scenarios have been observed to occur on various sections of the blade (Zaki et al 2010). The linear perturbation growth that triggers transition is studied
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