Turbulent mixing driven by spherical implosions. Part 1. Flow description and mixing-layer growth

Abstract

We present large-eddy si mulations (LES) of turbulent mixing at a perturbed, spherical interface separating two fluids of differing densities and subsequently impacted by a spherically imploding shock wave. This paper focuses on the differences between two fundamental configurations, keeping fixed the initial s hock Mach number ~1.2, the density ratio (precisely IAol ~ 0.67) and the perturbation shape (dominant spherical wavenumber .f 0 = 40 and amplitude-to-initial radius of 3 %): the incident shock travels from the lighter fluid to the heavy fluid or, inversely, from the heavy to the light fluid. After describing the computational problem we present results on the radially symmetric flow, the mean flow, and the growth of the mixing layer. , vol. 748, 2014, pp. 113-142). A wave-diagram analysis of the radially symmetric flow highlights that the light-heavy mixing layer is processed by consecutive reshocks, and not by reverberating rarefaction waves as is usually observed in planar geometry. Less surprisingly, reshocks process the heavy-light mixing layer as in the planar case. In both configurations, the incident imploding shock and the reshocks induce Richtmyer-Meshkov (RM ) instabilities at the density layer. However, we observe differences in the mixing-layer growth because the RM instability occurrences, Rayleigh-Taylor (RT) unstable scenarios (due to the radially accelerated motion of the layer) and phase inversion events are different.A small-amplitude stability analysis along the lines of Be ll (Los Alamos Scientific Laboratory Report, LA-132 L, 1951 ) and Plesset (J. Appl. Phys., vol. 25, 1954, pp. 96-98) helps quantify the effects of the mean flow on the mixing-layer growth by decoupling the effects of RT/RM instabilities from Be ll-Plessel effects associated with geometric convergence and compressibility for arbitrary convergence ratios. The analysis indicates that baroclinic instabilities are the dominant effect, considering the low convergence ratio (~2) and rather high ce > 10) mode numbers considered.

Experimental investigation of cylindrical converging shock waves interacting with a polygonal heavy gas cylinder

“…It should be noted that a secondary, inward-facing shock forms at the tail of the rrw (Lombardini et al 2014a). This only appears in spherical and cylindrical flows, and does not arise in planar geometries such as flows in a constant-cross-section shock tube with an endwall.…”

Effects of magnetic fields on magnetohydrodynamic cylindrical and spherical Richtmyer-Meshkov instability

“…We follow the work of Lombardini et al 24 in their creation of a distribution of wavenumbers centred at a dominant wavenumber, with an expansion of ζ 0 (θ, φ) using the real spherical harmonics basis,…”

“…[23][24][25] Here we investigate the light-to-heavy (that is, the incident shock travels from the light fluid to the heavy) RM instability in the presence of seed fields in cylindrical and spherical implosions under two promising seed field configurations; these configurations are chosen from Mostert et al 18 for their relative ability to minimize asymmetry in imploding MHD flows of this nature. We characterize the shock refraction processes, examine perturbation growth along the RM interface, and study the degree of asymmetry in interface geometry and perturbation growth.…”

Magnetohydrodynamic implosion symmetry and suppression of Richtmyer-Meshkov instability in an octahedrally symmetric field

“…Equation (7) differs from that of Lombardini et al [22] and Mostert et al [20] by selecting only even l and m, with m 0. This ensures that the density interface is normal to the boundaries at φ = 0,π/2 and θ = 0,π/2, so that the principal planes x,y,z are true symmetry planes for the initial density interface.…”

“…The fast shocks generated by the Riemann problem will accelerate the DI, provoking the RM instability. We define the DI by a spherical harmonic formulation similar to that of Lombardini et al [22] with the surface ζ 0 (θ,φ) according to the expansion…”