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| Steady Compressible Euler Equations of Concentration Layers for Hypersonic-limit Flows Passing Three-dimensional Bodies and Generalized Newton-Busemann Pressure Law* |
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Citation： |
Aifang QU,Hairong YUAN.Steady Compressible Euler Equations of Concentration Layers for Hypersonic-limit Flows Passing Three-dimensional Bodies and Generalized Newton-Busemann Pressure Law*[J].Chinese Annals of Mathematics B,2023,44(4):561~576 |
| Page view： 1283
Net amount： 703 |
Authors： |
Aifang QU; Hairong YUAN |
Foundation： |
This work was supported by the National Natural Science Foundation of China (Nos. 11871218,12071298) and the Science and Technology Commission of Shanghai Municipality (No. 18dz2271000). |
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| Abstract： |
For stationary hypersonic-limit Euler flows passing a solid body in three-dimensional space, the shock-front coincides with the upwind surface of the body, hence there is an infinite-thin layer of concentrated mass, in which all particles hitting the body move along its upwind surface. By proposing a concept of Radon measure solutions of boundary value problems of the multi-dimensional compressible Euler equations, which incorporates the large-scale of three-dimensional distributions of upcoming hypersonic flows and the small-scale of particles moving on two-dimensional surfaces, the authors derive the compressible Euler equations for flows in concentration layers, which is a stationary pressureless compressible Euler system with source terms and independent variables on curved surface. As a by-product, they obtain a formula for pressure distribution on surfaces of general obstacles in hypersonic flows, which is a generalization of the classical Newton-Busemann law for drag/lift in hypersonic aerodynamics. |
Keywords： |
Compressible Euler equations, Hypersonic flow, Concentration layer,Ramp, Cone, Radon measure solution, Newton-Busemann law |
Classification： |
35L50, 35L65, 35L67, 35Q31, 35R01, 35R06, 58J32,58J45, 76K05 |
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