Shock wave interaction with obstacles of various geometric shapes has always attracted attention in a large number of experimental and numerical studies. During the interaction of a shock wave with an obstacle a very complex wave pattern is formed which affects the shock-wave induced flow. The interaction reduces the shock-wave strength and generates rotational flow behind the obstacle. The interaction of shock waves with rigid obstacles is of significant importance in aerodynamic science and other engineering applications. Whitham [1] formulated an approximate theory for the dynamics of two- and three-dimensional shock waves and applied this theory to the description of shock diffraction by wedges and corners. Bryson & Gross [2] broadened Whitham’s theory and applied it to two- and three-dimensional bodies such as cylinders and spheres. They carried out theoretical and experimental work to assess the analytical computations that were made by Whitham. One dominant direction in investigation of shock-cylinder interaction is finding the RR→MR transition criterion. When the shock wave strikes a cylinder, it is reflected as an RR and then transforms to a Mach reflection MR. Major RR→MR transition criteria were summarized and discussed in a scientific monograph by Ben-Dor [3]. Since 1970, due to progress in numerical techniques, very accurate simulations of shock wave propagation over obstacles have been achieved. In most of studies efforts to validate the Euler scheme were undertaken. In the numerical study of Drikakis et al. [4] viscous effects were examined at various Mach numbers during of shock-cylinder interaction by comparing the inviscid and viscous calculations. It was found that the flow field in the downstream half of the cylinder is influenced by viscosity. The main objective of the present study is to better understand the physical elements governing the flow induced by the shock wave and the elements affecting the shock wave strength after passing the obstacle. To carry out the overall research plan two different approaches have been utilized - experimental and numerical. In the present study we focused on the investigation of the reflected shock wave from a single cylinder for low Mach numbers (M S ~1 − 1.4) in order to characterize the physical factors affecting its propagation. The first part of a broad investigation of the shock wave interaction with complex geometries is presented.

The interaction of shock waves with rigid obstacles is of significant interest in aerodynamic science and other engineering applications. During the interaction of a shock wave with an obstacle, a very complex wave pattern which affects the shockwave induced flow is formed. The interaction process depends on a variety of physical parameters such as the shape of the obstacle, the shock wave strength and the type of gas in which the interaction occurs. In the present paper, the interaction of a planar shock wave with a cylinder and a sphere is investigated. Our investigation follows closely the recentwork of Sadot et al. [1] which dealt with shock tube experiments with low Mach number shocks, in the range 1.1 to 1.4. An empirical relation was proposed for the trajectory of the reflected wave. This relation was expressed in terms of non-dimensional distance and time and was shown to be applicable for the investigated range of Mach numbers, cylinder diameters and a general ideal gas. The purpose of the present work is to focus on the backward reflected wave, and in particular, on its velocity change as it progresses away from the leading edge of the cylinder/sphere. It is expected that the reflected wave initially propagates at the velocity of shock reflection from a rigid wall, and asymptotically decelerates to the velocity corresponding to that of a sonic wave in the shocked region. This theoretical behavior is born out by fine mesh hydro-code computations of the interaction problem. The paper is organized as follows: in Section 2 a theoretical background for the limiting velocities of the reflected shock is given, followed by a brief description of the numerical codes and the problem setup (Section 3). The results of simulations for various cases by different CFD codes are given in Section 4. We conclude (Section 5) with a summary and suggestion of future work.

Two different approaches are undertaken to investigate the interaction of planar shock waves with circular cylinders. Experiments are conducted in a shock-tube apparatus equipped with a schlieren-based optical system to monitor the interaction, and numerical simulations are carried out using an in-house computer code to simulate similar problems. The incident shock-wave Mach number is varied in the range 1.1-1.4. Excellent agreement is found between the simulations and the experiments in terms of shock patterns, even though the model is based on an inviscid approach. Quantitative comparisons between the experimental results for different initial conditions (shock-wave strength, cylinder diameter, and working gas) are made to find the physical parameters affecting the path of the reflected shock. An approximate universal relation is derived, which predicts the reflected-shock trajectory along the axis of symmetry as a function of the incident-shock Mach, the diameter of the cylinder, and the gas properties. This relation is valid in the vicinity of the cylinder in the range of 0.1-5 D, where D is the cylinder diameter. It is found that the reflected shock from the cylinder evolves as in the case of a reflected-shock wave from a planar wall multiplied by a reduction factor, which depends on the incident-shock Mach number and the ratio of specific heats.

SUMMARYIn this study, an immersed boundary (IB) method based on a direct forcing is coupled with a high‐order weighted‐essentially non‐oscillatory (WENO) scheme to simulate fluid–solid interaction (FSI) problems with complex geometries. The IB is a general simulation method for FSI, whereas the WENO is an efficient scheme for fluid flow simulations and shock waves, and both of them work on regular cartesian grids. The effectiveness and the accuracy of the coupled scheme are first analyzed on well‐documented supersonic test problems for a wide range of Mach numbers. The results are in good agreement with both analytical and experimental data. A comprehensive analysis of the interaction of the moving shock through an array of cylinder matrix is then conducted by varying the number of cylinders in the matrix block while keeping the same opening passage. The relaxation length between two adjacent columns of cylinders is kept identical to study uniquely the effect of surface‐to‐volume ratio of the obstacle matrix. It is shown that the configuration with higher surface‐to‐volume ratio produces more post‐shock flow instabilities downstream of the matrix block. The complex shock/shock and shock/vortex interactions are well resolved by the present computation. It is being observed that after the passage of the shock through the cylinder matrix, eddies of different length scales are generated, but the later stage of shock/vortex and shocklet/vortexlet interactions are different for the two cases. The analysis of the PSD of the total kinetic energy globally conforms to Richardson's inviscid cascade. An intermittent peaked PDF of downstream instantaneous vorticity field is obtained in the limit of Re → ∞ . The baroclinic production of vorticity is found to be feeble as previously founded by Sun and Takayama (J. Fluid Mech. 2003; 478:237–256). Copyright © 2011 John Wiley & Sons, Ltd.