Statistical behavior of post-shock overpressure past grid turbulence

When a shock wave ejected from the exit of a 5.4-mm inner diameter, stainless steel tube propagated through grid turbulence across a distance of 215 mm, which is 5–15 times larger than its integral length scale \(L_{u}\) , and was normally incident onto a flat surface; the peak value of post-shock overpressure, \(\Delta P_{\mathrm{peak}}\) , at a shock Mach number of 1.0009 on the flat surface experienced a standard deviation of up to about 9 % of its ensemble average. This value was more than 40 times larger than the dynamic pressure fluctuation corresponding to the maximum value of the root-mean-square velocity fluctuation, \(u^{\prime }= 1.2~\hbox {m}/\hbox {s}\) . By varying \(u^{\prime }\) and \(L_{u}\) , the statistical behavior of \(\Delta P_{\mathrm{peak}}\) was obtained after at least 500 runs were performed for each condition. The standard deviation of \(\Delta P_{\mathrm{peak}}\) due to the turbulence was almost proportional to \(u^{{\prime }}\) . Although the overpressure modulations at two points 200 mm apart were independent of each other, we observed a weak positive correlation between the peak overpressure difference and the relative arrival time difference.