Hypersonic limit for steady compressible Euler flows passing straight cones
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910411874369536 |
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| author | Li, Qianfeng Qu, Aifang Su, Xueying Yuan, Hairong |
| author_facet | Li, Qianfeng Qu, Aifang Su, Xueying Yuan, Hairong |
| contents | We investigate the hypersonic limit for steady, uniform, and compressible polytropic gas passing a symmetric straight cone. By considering Radon measure solutions, we show that as the Mach number of the upstream flow tends to infinity, the measures associated with the weak entropy solution containing an attached shock ahead of the cone converge vaguely to the measures associated with a Radon measure solution to the conical hypersonic-limit flow. This justifies the Newtonian sine-squared pressure law for cones in hypersonic aerodynamics. For Chaplygin gas, assuming that the Mach number of the incoming flow is less than a finite critical value, we demonstrate that the vertex angle of the leading shock is independent of the conical body's vertex angle and is totally determined by the incoming flow's Mach number. If the Mach number exceeds the critical value, we explicitly construct a Radon measure solution with a concentration boundary layer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10219 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hypersonic limit for steady compressible Euler flows passing straight cones Li, Qianfeng Qu, Aifang Su, Xueying Yuan, Hairong Analysis of PDEs Mathematical Physics Fluid Dynamics 35L50, 35L65, 35Q31, 35R06, 76K05 We investigate the hypersonic limit for steady, uniform, and compressible polytropic gas passing a symmetric straight cone. By considering Radon measure solutions, we show that as the Mach number of the upstream flow tends to infinity, the measures associated with the weak entropy solution containing an attached shock ahead of the cone converge vaguely to the measures associated with a Radon measure solution to the conical hypersonic-limit flow. This justifies the Newtonian sine-squared pressure law for cones in hypersonic aerodynamics. For Chaplygin gas, assuming that the Mach number of the incoming flow is less than a finite critical value, we demonstrate that the vertex angle of the leading shock is independent of the conical body's vertex angle and is totally determined by the incoming flow's Mach number. If the Mach number exceeds the critical value, we explicitly construct a Radon measure solution with a concentration boundary layer. |
| title | Hypersonic limit for steady compressible Euler flows passing straight cones |
| topic | Analysis of PDEs Mathematical Physics Fluid Dynamics 35L50, 35L65, 35Q31, 35R06, 76K05 |
| url | https://arxiv.org/abs/2404.10219 |