Shock Waves from Line Sources. Numerical Solutions and Experimental Measurements

Abstract

The cylindrical pressure wave resulting from instantaneous energy release along a line in a quiescent atmosphere has been studied by numerical integration of the equations of gas dynamics. Atmospheres obeying both the ideal gas law, and a realistic equation of state for air at high temperatures, were employed. The effects of varying the initial distribution of mass and energy in space were also investigated. The computations were carried well into the weak shock region, and agree well with asymptotic solutions for very strong and very weak shock waves. The effects of deviations from the initial assumptions of the strong shock asymptotic solutions are discussed. An approximate equation for the radial dependence of shock strength, applicable to most of the numerical solutions, is presented. Experimental measurements of shock strengths from detonation of long high explosive charges are shown to be in good agreement with the numerical solutions.

Investigating the risk of lightning’s pressure blast wave

“…Previous experimental set-ups were examined [8][9][10] and the 'sixth mechanism experiment' was designed ( Figure 1). …”

Bead lightning formation

“…The minimum pressure on axis is reached when the position of the shock wave nearly equals the characteristic radius R 0 defined in Appendix A, which corresponds to P = 0.838 in Plooster's coordinates. This point indicates the onset of backflow at the channel, which occurs for P = c 0 t b / R P Х 0.44 according to Plooster's results 27 and corresponds to t b / 0 = ͑R P / R 0 ͒c 0 t b / R P Х 0.53. In a second analysis of numerical results, Hill 14 displays a set of curves and tables adapted from Plooster's results.…”

“…Since Hill uses a characteristic radius that is twice the characteristic radius defined by Plooster, 27 one has R H = P /2. Now, according to the results of Appendix B, the channel radius is related to the shock radius by r c ͑t͒ = c r 0 ͑t͒ = 0.526r 0 ͑t͒.…”

“…The distributions ͑A18͒ can be compared with the numerical solutions for cylindrical shock waves obtained by Plooster,27 who used the normalized coordinates P = r / R P and P = c 0 t / R P , where R P = ͓C 4 ͑␥͒E / ͑4␥p 0 ͔͒ 1/2 = ͓ C 4 ͑␥͒ / ͑4␥͑␥ −1͔͒͒ 1/2 R 0 = 1.19R 0 . In Plooster's coordinates, the pressure equilibration on axis calculated from the strong shock solution corresponds to P = 0.660 and P = 0.218.…”

“…In a second analysis of numerical results, Hill 14 displays a set of curves and tables adapted from Plooster's results. 27 From the curves one can estimate the maximum backflow velocity at the channel boundary as…”