Shock tube flows past partially opened diaphragms

Abstract

Unsteady compressible flows resulting from the incomplete burst of the shock tube diaphragm are investigated both experimentally and numerically for different initial pressure ratios and opening diameters. The intensity of the shock wave is found to be lower than that corresponding to a complete opening. A heuristic relation is proposed to compute the shock strength as a function of the relative area of the open portion of the diaphragm. Strong pressure oscillations past the shock front are also observed. These multi-dimensional disturbances are generated when the initially normal shock wave diffracts from the diaphragm edges and reflects on the shock tube walls, resulting in a complex unsteady flow field behind the leading shock wave. The limiting local frequency of the pressure oscillations is found to be very close to the ratio of acoustic wave speed in the perturbed region to the shock tube diameter. The power associated with these pressure oscillations decreases with increasing distance from the diaphragm since the diffracted and reflected shocks partially coalesce into a single normal shock front. A simple analytical model is devised to explain the reduction of the local frequency of the disturbances as the distance from the leading shock increases.

The effects that changes in the diaphragm aperture have on the resulting shock tube flow

“…It should be noted here that it takes a distance of 10-20 tube diameters downstream from the diaphragm before a well-formed shock wave is evident. It is, therefore, surprising that in the numerical study presented in [12] a shock is seen diffracted over the open diaphragm (see Fig. 4 in [12]).…”

“…Recently Gaetani et al [12] conducted an experimental and numerical study regarding the effect of incomplete burst of the shock tube diaphragm on the resulting flow. They offered a heuristic relation for estimating the resulting shock wave strength as a function of the relative area of the open portion of the diaphragm.…”

“…They offered a heuristic relation for estimating the resulting shock wave strength as a function of the relative area of the open portion of the diaphragm. In [12], all diaphragms had similar open geometry, a circular shape. For the numerical part, an Euler solver was employed neglecting flow viscosity and thermal conductivity.…”

Finite element modelling of metallic diaphragm rupture in hypersonic shock tube

“…The net result of this process is the weakening of shock intensity and an increase in shock formation distance. Houas et al [23] studied the effect of the ratio between ruptured area and shock tube area and found similar results to Gaetani et al [13]. They found that as this area ratio decreased, the shock formation distance increased, whilst the pressure ratio across the shock decreased.…”

“…Gaetani et al [13] employed experimental and numerical techniques to investigate the resulting flow field from incomplete diaphragm rupture. A complex flow field was described where the leading shock diffracted around the diaphragm orifice.…”