Excitation and stability of nonlinear compressible Görtler vortices and streaks induced by free-stream vortical disturbances
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arXiv
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| Natura: | Preprint |
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2024
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| author | Xu, Dongdong Ricco, Pierre Marensi, Elena |
| author_facet | Xu, Dongdong Ricco, Pierre Marensi, Elena |
| contents | 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-frequencymodes, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15478 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Excitation and stability of nonlinear compressible Görtler vortices and streaks induced by free-stream vortical disturbances Xu, Dongdong Ricco, Pierre Marensi, Elena Fluid Dynamics 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-frequencymodes, 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. |
| title | Excitation and stability of nonlinear compressible Görtler vortices and streaks induced by free-stream vortical disturbances |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2411.15478 |