Numerical study of shock-wave mitigation through matrices of solid obstacles

Shock-wave propagation through different arrays of solid obstacles and its attenuation are analyzed by means of numerical simulations. The two-dimensional compressible Navier-Stokes equations are solved using a fifth-order weighted essentially non-oscillatory scheme, in conjunction with an immersed-boundary method to treat the embedded solids within a cartesian grid. The present study focuses on the geometrical aspects of the solid obstacles, particularly at lower effective flow area, where the frictional forces are expected to be important. The main objective is to analyze the controlling mechanism for shock propagation and attenuation in complex inhomogeneous and porous medium. Different parameters are investigated such as the geometry of the obstacles, their orientation in space as well as the relaxation lengths between two consecutive columns. The study highlights a number of interesting phenomena such as compressible vortices and shock-vortex interactions that are produced in the post-shock region. This also includes shock interactions, hydrodynamic instabilities and non-linear growth of the mixing. Ultimately, the Kelvin-Helmholtz instability invokes transition to a turbulent mixing region across the matrix columns and eddies of different length scales are generated in the wake region downstream of the solid blocks. The power spectrum of instantaneous dynamic pressure shows the existence of a wide range of frequencies which scales nearly with f^-5/3. In terms of shock attenuation, the results indicate that the staggered matrix of reversed triangular prism (where the base of the triangular prism is facing the incoming shock) is the most efficient arrangement. In this case, both static and dynamic pressure impulses show significant reduction compared to the other studied configurations, which confirms the effectiveness of this type of barrier configuration. Furthermore, the use of combination of reverse-reverse arrangement of triangular prism obstacle maze is found more effective compared to the forward-reverse or forward-forward arrangements.