Simultaneous direct measurements of concentration and velocity in the Richtmyer–Meshkov instability

Abstract

The Richtmyer–Meshkov instability (RMI) is experimentally investigated in a vertical shock tube using a broadband initial condition imposed on an interface between a helium–acetone mixture and argon (Atwood number $A\approx 0.7$). In the present work, a shear layer is introduced at the interface to serve as a statistically repeatable, broadband initial condition to the RMI, and the density interface is accelerated by either an $M=1.6$ or $M=2.2$ planar shock wave. The development of the ensuing mixing layer is investigated using simultaneous planar laser-induced fluorescence (PLIF) and particle image velocimetry (PIV). PLIF images are processed to reveal the light-gas mole fraction, while PIV particle image pairs yield corresponding two-component planar velocity results. Field structure and distribution are explored through probability density functions (PDFs), and a decomposition is performed on concentration and velocity results to obtain a mean flow field and define fluctuations. Simultaneous concentration and velocity field measurements allow – for the first time in this regime – experimentally determined turbulence quantities such as Reynolds stresses, turbulent mass-flux velocities and turbulent kinetic energy to be obtained. We show that by the latest times the mixing layer has passed the turbulent threshold, and there is evidence of turbulent mixing occurring sooner for the higher Mach number case. Interface measurements show nonlinear growth with a power-law fit to the thickness data, and that integral measurements of mixing layer thickness are proportional to threshold measurements. Spectral analysis demonstrates the emergence of an inertial range with a slope ${\sim}k^{-5/3}$ when considering both density and velocity effects in planar turbulent kinetic energy (TKE) measurements.