Experimental and numerical study of the interaction between a planar shock wave and a square cavity

Abstract

The interaction of a planar shock wave with a square cavity is studied experimentally and numerically. It is shown that such a complex, time-dependent, process can be modelled in a relatively simple manner. The proposed physical model is the Euler equations which are solved numerically, using the second-order-accurate high-resolution GRP scheme, resulting in very good agreement with experimentally obtained findings. Specifically, the wave pattern is numerically simulated throughout the entire interaction process. Excellent agreement is found between the experimentally obtained shadowgraphs and numerical simulations of the various flow discontinuities inside and around the cavity at all times. As could be expected, it is confirmed that the highest pressure acts on the cavity wall which experiences a head-on collision with the incident shock wave while the lowest pressures are encountered on the wall along which the incident shock wave diffracts. The proposed physical model and the numerical simulation used in the present work can be employed in solving shock wave interactions with other complex boundaries.

Shock wave diffraction by a square cavity filled with dusty gas

“…Therefore, for the time period covered in the present computations the flow is practically frozen as is apparent from comparing the results shown in Fig. 8 with those of the pure gas case, (Igra et al 1996). The wave pattern shown in Fig.…”

“…This is clearly noticed in Fig. 7 where all the shock waves which were observed in the pure gas case (see Igra et al 1996) are significantly weakened now and eventually reduce to compression or Mach waves. On the other hand, the large particles (d = 50 µm) require a much longer time for reaching equilibrium with the carrying gas.…”

“…The suspension is modeled as a perfect gas seeded with tiny identical particles uniformly distributed throughout the cavity. As is known from previous numerical and experimental studies in pure air (e.g., see Igra et al 1996), the shock-induced cavity flow involves diffracted shock waves, reflected shock waves, expansion waves, as well as shear layer and vortex regions accompanied by pressure-matching shocks. This array of complex shock wave phenomena will obviously be affected by the particles suspended in the cavity, to an extent commensurate with the dust mass loading ratio and the other physical characteristics of the particles.…”

“…In all cases the dust particles had a material density of 2500 kg/m 3 . The resulting post-shock flow and wave patterns are shown in Figs Igra et al (1996). Results shown in Figs.…”

“…Here, based on the observation in Igra et al (1996), the simplified splitting given in Eq. (4) is adopted since it is more efficient and yields virtually indistinguishable results compared with the more accurate splitting given by Strang (1968).…”