Numerical Solutions of Spherical Blast Waves

Abstract

The strong-shock, point-source solution and spherical isothermal distributions were used as initial conditions for a numerical integration of the differential equations of gas motion in Lagrangean form. The von Neumann-Richtmyer artificial viscosity was employed to avoid shock discontinuities. The solutions were carried from two thousand atmospheres to less than one-tenth atmospheres peak overpressure. Results include overpressure, density, particle velocity, and position as functions of time and space. The dynamic pressure, the positive and negative impulses of both dynamic pressure and static overpressure, positive and negative durations of pressure and velocity, and shock values of all quantities are also described for various times and radial distances. Analytical approximations to the numerical results are provided.

Blast Wave Simulations with a Runge-Kutta Discontinuous Galerkin Method

“…Figure 14 contained loci of resulting primary shock, contact surface and secondary shock. Predictions were also compared with numerical solutions by Brode [41]. In this figure horizontal axis represented distance from the center normalized by the initial sphere radius, r0 and vertical axis represented time normalized by r0 and ambient speed of sound, a0.…”

Prediction of blast wave effects on a developed site

“…Figures (10) and (11) present the distribution of the Mach number and the relative overpressure on the ground and on the concrete blocks for a simulation time varying from 1 ms to 25 ms. At the blast onset, a rarefaction happens in the explosive charge volume, because of the rapid fluid expansion [16]. This rarefaction is followed by an inbound compression wave propagating from the hot gases/air contact surface.…”

“…It is actually possible to consider the wave as propagating isotropically at the onset of the explosion. This spherical one-dimensional approach has proven to be valid as long as the blast wave propagates in an open area [3,16]. In this case, the simplified approach represents a good alternative to fully three-dimensional approaches.…”

“…The smaller α, the higher the level of damage. In the case of a rigid-perfectly plastic response of the element (i.e., α < 1 and q m ≫ 1), solving the ordinary differential system (15)(16) gives the following iso-damage curves equation [10]:…”

Estimating safe scaled distances for columns subjected to blast

“…In columns that are free to clear, the net load on the column (see the shaded area in Figure 3(c)) is the front-side load (Figure 3(a)) minus the rear-side load (Figure 3(b)). Various graphs to estimate air blast loads are available (Brode, 1955;Henrych, 1979;Kingery and Bulmash, 1984). In the present investigation, blast wave parameters were based on the equations developed by Kingery and Bulmash (1984).…”