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Excitation and stability of nonlinear compressible Görtler vortices and streaks induced by free-stream vortical disturbances

Published online by Cambridge University Press:  04 December 2024

Dongdong Xu Open the ORCID record for Dongdong Xu [Opens in a new window] ,
Pierre Ricco Open the ORCID record for Pierre Ricco [Opens in a new window]  and
Elena Marensi Open the ORCID record for Elena Marensi [Opens in a new window]
Dongdong Xu
Affiliation:
School of Mechanical, Aerospace and Civil Engineering, The University of Sheffield, Sheffield S1 3JD, UK
Pierre Ricco*
Affiliation:
School of Mechanical, Aerospace and Civil Engineering, The University of Sheffield, Sheffield S1 3JD, UK
Elena Marensi
Affiliation:
School of Mechanical, Aerospace and Civil Engineering, The University of Sheffield, Sheffield S1 3JD, UK
*
†Email address for correspondence: p.ricco@sheffield.ac.uk
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Abstract

We study the generation, nonlinear development and secondary instability of unsteady Görtler vortices and streaks in compressible boundary layers exposed to free-stream vortical disturbances and evolving over concave, flat and convex walls. The formation and evolution of the disturbances are governed by the compressible nonlinear boundary-region equations, supplemented by initial and boundary conditions that characterise the impact of the free-stream disturbances on the boundary layer. Computations are performed for parameters typical of flows over high-pressure turbine blades, where the Görtler number, a measure of the curvature effects, and the disturbance Reynolds number, a measure of the nonlinear effects, are order-one quantities. At moderate intensities of the free-stream disturbances, increasing the Görtler number renders the boundary layer more unstable, while increasing the Mach number or the frequency stabilises the flow. As the free-stream disturbances become more intense, vortices over concave surfaces no longer develop into the characteristic mushroom-shaped structures, while the flow over convex surfaces is destabilised. An occurrence map identifies Görtler vortices or streaks for different levels of free-stream disturbances and Görtler numbers. Our calculations capture well the experimental measurements of the enhanced skin friction and wall-heat transfer over turbine-blade pressure surfaces. The time-averaged wall-heat transfer modulations, termed hot fingers, are elongated in the streamwise direction and their spanwise wavelength is half of the characteristic wavelength of the free-stream disturbances. Nonlinearly saturated disturbances are unstable to secondary high-frequency modes, whose growth rate increases with the Görtler number. A new varicose even mode is reported, which may promote transition to turbulence at the stem of nonlinear streaks.

JFM classification

Aerodynamics: High-speed flow Boundary Layers: Boundary layer receptivity Instability: Transition to turbulence

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JFM Papers
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Journal of Fluid Mechanics , Volume 1000 , 10 December 2024 , A93
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© The Author(s), 2024. Published by Cambridge University Press

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