Turbulent mixing in a Richtmyer–Meshkov fluid layer after reshock: velocity and density statistics

Abstract

The properties of turbulent mixing in a Richtmyer–Meshkov (RM) unstable fluid layer are studied under the impact of a single shock followed by a reshock wave using simultaneous velocity–density measurements to provide new insights into the physics of RM mixing. The experiments were conducted on a varicose ${\mathrm{SF} }_{6} $ fluid layer (heavy fluid) interposed in air (light fluid) inside a horizontal shock tube at an incident Mach number of 1.21 and a reflected reshock Mach number of 1.14. The light–heavy–light fluid layer is observed to develop a nonlinear growth pattern, with no transition to turbulence upon impact by a single shock (up to $tU/ \lambda = 23. 4$). However, upon reshock, enhanced mixing between the heavy and light fluids along with a transition to a turbulent state characterized by the generation of significant turbulent velocity fluctuations (${\sigma }_{u} / U\ensuremath{\sim} 0. 3$) is observed. The streamwise and spanwise root-mean-squared velocity fluctuation statistics show similar trends across the fluid layer after reshock, with no observable preference for the direction of the shock wave motion. The measured streamwise mass flux ($ \overline{{\rho }^{\ensuremath{\prime} } {u}^{\ensuremath{\prime} } } $) shows opposing signs on either side of the density peak within the fluid layer, consistent with the turbulent material transport being driven along the direction of the density gradient. Measurements of three of the six independent components of the general Reynolds stress tensor (${R}_{ij} = \overline{\rho { u}_{i}^{\ensuremath{\prime} \ensuremath{\prime} } { u}_{j}^{\ensuremath{\prime} \ensuremath{\prime} } } $) show that the self-correlation terms ${R}_{11} $ and ${R}_{22} $ are similar in magnitude across much of the fluid layer, and much larger than the cross-correlation term ${R}_{12} $. Most importantly, the Reynolds stresses (${R}_{ij} $) are dominated by the mean density, cross-velocity product term ($ \overline{\rho } \hspace{0.167em} \overline{{ u}_{i}^{\ensuremath{\prime} } { u}_{j}^{\ensuremath{\prime} } } $), with the mass flux product and triple correlation terms being negligibly smaller in comparison. A lack of homogeneous mixing (and, possibly, a long-term imprint of the initial conditions) is observed in the spanwise turbulent mass flux measurements, with important implications for the simulation and modelling of RM mixing flows.

Evolution of the density self-correlation in developing Richtmyer–Meshkov turbulence

“…Both the PIV and PLIF cameras were equipped with sharp cut-off filters to prevent image cross-contamination. Further experimental details are provided elsewhere, including discussions on quantitative concentration measurement with PLIF , combining PLIF with a simultaneous PIV measurement and the stability and characterization of the initial conditions , and a detailed discussion of the present flow field, including a range of velocity and density statistics with sampling errors for certain quantities (Balakumar et al 2012).…”

“…Recent advances in the successful implementation of simultaneous particle-image velocimetry (PIV)-planar laser-induced fluorescence (PLIF) diagnostics to RM flows allow the measurement of instantaneous velocity and density two-dimensional fields at the same time ). An earlier paper focused on fundamental velocity statistics and select density-velocity correlations relevant to mixing, including the streamwise mass flux (ρu 1 ) and components of the general Reynolds stress tensor, R ij = ρ * u i u j (Balakumar et al 2012). (Here the double prime denotes fluctuations from a density-weighted or Favre average.)…”

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

“…We mainly limit our attention to the convergence effects and the baroclinic mechanism of the cylindrically converging RM instability with large initial deformation of the gas interfaces. It should be mentioned that the turbulent mixing is very interesting and important in the study of RM instability (Dimotakis 2005;Tomkins et al 2008;Balakumar et al 2012;Lombardini, Pullin & Meiron 2014a,b) but is outside the scope of the present work. Under the current conditions, the characteristics of the cylindrical converging shock are described first, and rich phenomena of the polygonal interfaces accelerated by the cylindrical converging shock and the reflected shock from the focal point, during the early stage of the RM instability, are obtained for the first time.…”

On the interaction of a planar shock with a light polygonal interface

“…The shapes of the gas interface in previous studies mainly include the single-mode interface (Meshkov 1969;Brouillette 2002;Jacobs & Krivets 2005;Mariani et al 2008;Long et al 2009;Balakumar et al 2012;, the spherical or cylindrical bubble formed by a soap film (Haas & Sturtevant 1987;Hosseini & Takayama 2005;Layes, Jourdan & Houas 2009;Haehn et al 2011Haehn et al , 2012Zhai et al 2011;Si et al 2012), the membrane-less gas cylinder (Jacobs 1992(Jacobs , 1993Tomkins et al 2008;Zhai et al 2014;Zou et al 2010) or gas curtain Orlicz et al 2009;Balakumar et al 2012;Balasubramanian et al 2012;Tomkins et al 2013) formed by the jet technique and the inclined planar interface (Wang et al 2012;McFarland et al 2014). Besides these classical interface shapes, Mikaelian (2005) theoretically and numerically studied the RMI on an initial interface with a discontinuous change in its first derivative.…”