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.