Sonic Eddy Model of the Turbulent Boundary Layer
The effects of Mach number on the skin friction and velocity fluctuations of the turbulent boundary layer are considered through a sonic eddy model. Originally proposed for free shear flows, the model assumes that the eddies responsible for momentum transfer have a rotation Mach number of unity, wit...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-01-01
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| Series: | Fluids |
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| Online Access: | https://www.mdpi.com/2311-5521/7/1/37 |
| _version_ | 1827665552397565952 |
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| author | Paul Dintilhac Robert Breidenthal |
| author_facet | Paul Dintilhac Robert Breidenthal |
| author_sort | Paul Dintilhac |
| collection | DOAJ |
| description | The effects of Mach number on the skin friction and velocity fluctuations of the turbulent boundary layer are considered through a sonic eddy model. Originally proposed for free shear flows, the model assumes that the eddies responsible for momentum transfer have a rotation Mach number of unity, with the entrainment rate limited by acoustic signaling. Under this assumption, the model predicts that the skin friction coefficient should go as the inverse Mach number in a regime where the Mach number is larger than unity but smaller than the square root of the Reynolds number. The velocity fluctuations normalized by the friction velocity should be the inverse square root of the Mach number in the same regime. Turbulent transport is controlled by acoustic signaling. The density field adjusts itself such that the Reynolds stresses correspond to the momentum transport. In contrast, the conventional van Driest–Morkovin view is that the Mach number effects are due to density variations directly. A new experiment or simulation is proposed to test this model using different gases in an incompressible boundary layer, following the example of Brown and Roshko in the free shear layer. |
| first_indexed | 2024-03-10T01:29:37Z |
| format | Article |
| id | doaj.art-5f1e7398a4e24623ad3c4a45d7f02e54 |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-03-10T01:29:37Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj.art-5f1e7398a4e24623ad3c4a45d7f02e542023-11-23T13:44:08ZengMDPI AGFluids2311-55212022-01-01713710.3390/fluids7010037Sonic Eddy Model of the Turbulent Boundary LayerPaul Dintilhac0Robert Breidenthal1William E. Boeing Department of Aeronautics and Astronautics, University of Washington, Seattle, WA 98195-2180, USAWilliam E. Boeing Department of Aeronautics and Astronautics, University of Washington, Seattle, WA 98195-2180, USAThe effects of Mach number on the skin friction and velocity fluctuations of the turbulent boundary layer are considered through a sonic eddy model. Originally proposed for free shear flows, the model assumes that the eddies responsible for momentum transfer have a rotation Mach number of unity, with the entrainment rate limited by acoustic signaling. Under this assumption, the model predicts that the skin friction coefficient should go as the inverse Mach number in a regime where the Mach number is larger than unity but smaller than the square root of the Reynolds number. The velocity fluctuations normalized by the friction velocity should be the inverse square root of the Mach number in the same regime. Turbulent transport is controlled by acoustic signaling. The density field adjusts itself such that the Reynolds stresses correspond to the momentum transport. In contrast, the conventional van Driest–Morkovin view is that the Mach number effects are due to density variations directly. A new experiment or simulation is proposed to test this model using different gases in an incompressible boundary layer, following the example of Brown and Roshko in the free shear layer.https://www.mdpi.com/2311-5521/7/1/37turbulencecompressibleboundary layeracoustic signaling |
| spellingShingle | Paul Dintilhac Robert Breidenthal Sonic Eddy Model of the Turbulent Boundary Layer Fluids turbulence compressible boundary layer acoustic signaling |
| title | Sonic Eddy Model of the Turbulent Boundary Layer |
| title_full | Sonic Eddy Model of the Turbulent Boundary Layer |
| title_fullStr | Sonic Eddy Model of the Turbulent Boundary Layer |
| title_full_unstemmed | Sonic Eddy Model of the Turbulent Boundary Layer |
| title_short | Sonic Eddy Model of the Turbulent Boundary Layer |
| title_sort | sonic eddy model of the turbulent boundary layer |
| topic | turbulence compressible boundary layer acoustic signaling |
| url | https://www.mdpi.com/2311-5521/7/1/37 |
| work_keys_str_mv | AT pauldintilhac soniceddymodeloftheturbulentboundarylayer AT robertbreidenthal soniceddymodeloftheturbulentboundarylayer |