Studies of interactions of a propagating shock wave with decaying grid turbulence: velocity and vorticity fields

Abstract

The unsteady interaction of a moving shock wave with nearly homogeneous and isotropic decaying compressible turbulence has been studied experimentally in a large-scale shock tube facility. Rectangular grids of various mesh sizes were used to generate turbulence with Reynolds numbers based on Taylor's microscale ranging from 260 to 1300. The interaction has been investigated by measuring the three-dimensional velocity and vorticity vectors, the full velocity gradient and rate-of-strain tensors with instrumentation of high temporal and spatial resolution. This allowed estimates of dilatation, compressible dissipation and dilatational stretching to be obtained. The time-dependent signals of enstrophy, vortex stretching/tilting vector and dilatational stretching vector were found to exhibit a rather strong intermittent behaviour which is characterized by high-amplitude bursts with values up to 8 times their r.m.s. within periods of less violent and longer lived events. Several of these bursts are evident in all the signals, suggesting the existence of a dynamical flow phenomenon as a common cause. Fluctuations of all velocity gradients in the longitudinal direction are amplified significantly downstream of the interaction. Fluctuations of the velocity gradients in the lateral directions show no change or a minor reduction through the interaction. Root mean square values of the lateral vorticity components indicate a 25% amplification on average, which appears to be very weakly dependent on the shock strength. The transmission of the longitudinal vorticity fluctuations through the shock appears to be less affected by the interaction than the fluctuations of the lateral components. Non-dissipative vortex tubes and irrotational dissipative motions are more intense in the region downstream of the shock. There is also a significant increase in the number of events with intense rotational and dissipative motions. Integral length scales and Taylor's microscales were reduced after the interaction with the shock in all investigated flow cases. The integral length scales in the lateral direction increase at low Mach numbers and decrease during strong interactions. It appears that in the weakest of the present interactions, turbulent eddies are compressed drastically in the longitudinal direction while their extent in the normal direction remains relatively the same. As the shock strength increases the lateral integral length scales increase while the longitudinal ones decrease. At the strongest interaction of the present flow cases turbulent eddies are compressed in both directions. However, even at the highest Mach number the issue is more complicated since amplification of the lateral scales has been observed in flows with fine grids. Thus the outcome of the interaction strongly depends on the initial conditions.

Reynolds- and Mach-number effects in canonical shock–turbulence interaction

“…They found close agreement with Ribner's linear theory for the amplification of velocity fluctuations, and some discrepancy with earlier experiments for the turbulent energy amplification present at low wavenumbers. In an experiment by Agui, Briassulis & Andreopoulos (2005), an incident shock generated an induced flow behind it that passed later through a grid to obtain a nearly homogeneous and isotropic flow field, which was then processed by the reflected shock. Intense vorticity structures were suggested as the cause of high-amplitude events of time signals of enstrophy, dissipation rate and dilatational stretching; the dissipation seemed to have a more dominant effect on the flow motions than on the enstrophy.…”

Vorticity dynamics after the shock–turbulence interaction

“…This is known as the Linear Interaction Approximation (LIA) [1][2][3]. However, due to the high cost of simulations for the parameter space close to the LIA limit (and practical applications) and difficulties with accurate experimental measurements close to the shock, previous studies have shown only limited agreement with LIA [3][4][5][6][7][8][9][10]. Recently, Ryu and Livescu [11], using high resolution fully resolved Direct Numerical Simulations (DNS) extensively covering the parameter range, have shown that the DNS results converge to the LIA solutions as the ratio δ/η, where δ is the shock width and η is the Kolmogorov microscale of the incoming turbulence, becomes small.…”

Hybrid LES of Detonations in Reacting Multi-Phase Mixtures

“…Such interactions can have a strong impact on the flow evolution, increasing turbulent mixing, but also increasing losses and surface drag and/or heat transfer depending upon the strength of the shock. Many studies of shock / turbulence interactions have been conducted, both numerically and experimentally (see Andreopoulos et al [2000] for a review), and physical insights have been gained from the studies of simple test cases, such as the interaction of shocks with isotropic and/or homogeneous turbulence, studied experimentally (e.g., Jacquin et al [1993], Honkan and Andreopoulos [1992], Barre et al [1996], Agui et al [2005]) and numerically using high-order shock capturing methods (e.g., Lee et al [1993], Hannappel and Friedrich [1995], Lee et al [1997], Mahesh et al [1997], Jamme et al [2002Jamme et al [ , 2005) and, more recently, using a shock-fitting method (Sesterhenn et al [2005]). …”