New numerical and experimental results on the transition between regular and Mach reflections of steady shock waves are presented.
The influence of flow three-dimensionality on transition between steady regular and Mach reflection has been studied in detail
both numerically and experimentally. Characteristic features of 3D shock wave configuration, such as peripheral Mach reflection,
non-monotonous Mach stem variation in transverse direction, the existence of combined Mach-regular-peripheral Mach shock wave
configuration, have been found in the numerical simulations. The application of laser sheet imaging technique in streamwise
direction allowed us to confirm all the details of shock wave configuration in the experiments. Close agreement of the numerical
and experimental data on Mach stem heights is shown.
Received 23 November 2000 / Accepted 25 April 2001 相似文献
This paper is devoted to studying the local structure of Mach reflection, which occurs in the problem of the shock front hitting a ramp. The compressible flow is described by the full unsteady Euler system of gas dynamics. Because of the special geometry, the motion of the fluid can be described by self-similar coordinates, so that the unsteady flow becomes a pseudo-stationary flow in this coordinate system. When the slope of the ramp is less than a critical value, the Mach reflection occurs. The wave configuration in Mach reflection is composed of three shock fronts and a slip line bearing contact discontinuity. The local existence of a flow field with such a configuration under some assumptions is proved in this paper. Our result confirms the reasonableness of the corresponding physical observations and numerical computations in Mach reflection.
In order to prove the result, we formulate the problem to a free boundary value problem of a pseudo-stationary Euler system. In this problem two unknown shock fronts are the free boundary, and the slip line is also an unknown curve inside the flow field. The proof contains some crucial ingredients. The slip line will be transformed to a fixed straight line by a generalized Lagrange transformation. The whole free boundary value problem will be decomposed to a fixed boundary value problem of the Euler system and a problem to updating the location of the shock front. The Euler system in the subsonic region is an elliptic-hyperbolic composite system, which will be decoupled to the elliptic part and the hyperbolic part at the level of principal parts. Then some sophisticated estimates and a suitable iterative scheme are established. The proof leads to the existence and stability of the local structure of Mach reflection.
In this paper, RR→MR transition of asymmetric shock waves has been theoretically studied. The transition can occur between
the sonic-point and maximum-deflection criteria due to the the effects of expansion fans which are inherent flow structures.
Comparison shows a better agreement among experiments and the analytical results. Some discrepancies reported in previous
studies among experiments and theory have also been explained based on the threshold for RR→MR transition.
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