Computation of shock wave reflection by circular cylinders

Abstract

The nonstationary shock wave diffraction patterns generated by a blast wave impinging on a circular cylinder are numerically simulated using a second-order hybrid upwind method for solving the two-dimensional inviscid compressible Euler equations of gasdynamics. The diffraction was followed through about 6 radii of travel of the incident shock past the cylinder. A broad range of incident shock Mach numbers are covered. The complete diffraction patterns, including the transition from regular to Mach reflection, trajectory of the Mach triple point, and the complex shock-on-shock interaction at the wake region resulting from the Mach shocks collision behind the cylinder are reported in detail. Pressure-time history and various contour plots are also included. Comparison between the work of Bryson and Gross, which included both experimental schlieren pictures and theoretical calculations using Whitham's ray/shock theory, and results of the present finite-difference computation indicate good agreement in every aspect except for some nonideal gas and viscous effects that are not accounted for by the Euler equations.

Shallow flow simulation on dynamically adaptive cut cell quadtree grids

“…Excellent agreement is also achieved with the results of Yang et al [29], who solved the gas dynamics equations using finite differences. Of course, the shallow water equations can be viewed as a special version of the compressible gas dynamics equations with the ratio of the specific heats ( = 2).…”

“…Considering the upper part of the flow, when the angle between the front stagnation point and the shock collision point increases to about 45 • at t = 0.025s, the collision point separates from the cylinder surface and changes into a triple point. A diffracted shock appears and a three-shock system is developed together with the incident and reflected shocks, indicating the flow dynamics regime changing from regular reflection to Mach reflection [29]. Later, the diffracted shock fronts from upper and lower sides of the cylinder curl up and meet at the rear stagnation point behind the cylinder, creating vortices, and resulting in an instantaneous increase of water depth in the wake that is then transported downstream.…”

“…The interaction of a shock-like bore with a circular cylinder has been intensively investigated (see References [3,28,29]). In the present work, the calculation is carried out in a 5 m × 5 m domain, with a horizontal, frictionless bed.…”

Simulation of shock wave diffraction by a square cylinder in gases of arbitrary statistics using a semiclassical Boltzmann–Bhatnagar–Gross–Krook equation solver

“…In the past, many experimental and numerical studies for such shock wave diffraction problems have been reported for the classical gases (e.g. Bryson & Gross (1961) and Yang et al (1987)) and they serve as good examples for testing the capability of a numerical method for solving gas dynamical problems. The total variation diminishing (TVD) scheme is adopted in this paper to describe the evolution of these equations.…”

Interaction of a Spherical Shock Wave and a Submerged Fluid-Filled Circular Cylindrical Shell

“…Innumerous numerical codes have been produced, from relatively simple ones aimed at analyzing a particular problem, to universal supercomputer-oriented industrial codes. Some researchers have been focused on the study of the shock waves propagation and di!raction over a rigid "xed cylindrical structure (e.g., references [12,13]), while others have been addressing a &hydroelastical' aspect of #uid}shell interaction, developing e$cient solvers for coupled equations of a shell and #uid(s).…”