Transition length in turbine/compressor blade flows

Abstract

High Reynolds number mathematical models for convected vortex impinging against a local hump and sound scattering into Tollmien–Schlichting eigenmodes are introduced to simulate basic mechanisms of the disturbance excitation typical of turbomachinery environments. The streamwise dimension of the transitional flow on the suction side of a blade is evaluated on the assumption that the transition length is of equal order with the extent of viscous/inviscid interaction controlling the boundary-layer response. The triple-deck theory gives a simple power law correlation to express a value of the Reynolds number based on the transition length in terms of the Reynolds number calculated with the blade cord. Precisely the same correlation stems from processing experimental data for both smooth and rough surfaces. The computation shows the explosive development of highly modulated wave packets and their rapid breakdown brought about by erratic short-scaled wiggles riding on the primary long-scaled oscillation cycles. The filling-up of distant parts of the wavenumber spectrum is at the heart of the signal distortion. This process heralds the start of deep transition terminating in fully developed turbulent flow well before reaching the upper stability branch. With the time-harmonic excitation broadly used in experiments, transition requires a much longer distance to complete. An agreement between theoretical predictions based on the assumption of indefinitely large Reynolds numbers and experimental findings from wind-tunnel observations at finite Reynolds numbers is encouraging.