Evaluation of turbulent mixing transition in a shock-driven variable-density flow

Abstract

The effect of initial conditions on transition to turbulence is studied in a variable-density shock-driven flow. Richtmyer–Meshkov instability (RMI) evolution of fluid interfaces with two different imposed initial perturbations is observed before and after interaction with a second shock reflected from the end wall of a shock tube (reshock). The first perturbation is a predominantly single-mode long-wavelength interface which is formed by inclining the entire tube to 80$^{\circ }$ relative to the horizontal, yielding an amplitude-to-wavelength ratio, $\unicode[STIX]{x1D702}/\unicode[STIX]{x1D706}=0.088$, and thus can be considered as half the wavelength of a triangular wave. The second interface is multi-mode, and contains additional shorter-wavelength perturbations due to the imposition of shear and buoyancy on the inclined perturbation of the first case. In both cases, the interface consists of a nitrogen-acetone mixture as the light gas over carbon dioxide as the heavy gas (Atwood number, $A\sim 0.22$) and the shock Mach number is $M\approx 1.55$. The initial condition was characterized through Proper Orthogonal Decomposition and density energy spectra from a large set of initial condition images. The evolving density and velocity fields are measured simultaneously using planar laser-induced fluorescence (PLIF) and particle image velocimetry (PIV) techniques. Density, velocity, and density–velocity cross-statistics are calculated using ensemble averaging to investigate the effects of additional modes on the mixing and turbulence quantities. The density and velocity data show that a distinct memory of the initial conditions is maintained in the flow before interaction with reshock. After reshock, the influence of the long-wavelength inclined perturbation present in both initial conditions is still apparent, but the distinction between the two cases becomes less evident as smaller scales are present even in the single-mode case. Several methods are used to calculate the Reynolds number and turbulence length scales, which indicate a transition to a more turbulent state after reshock. Further evidence of transition to turbulence after reshock is observed in the velocity and density fluctuation spectra, where a scaling close to $k^{-5/3}$ is observed for almost one decade, and in the enstrophy fluctuation spectra, where a scaling close to $k^{1/3}$ is observed for a similar range. Also, based on normalized cross correlation spectra, local isotropy is reached at lower wave numbers in the multi-mode case compared with the single-mode case before reshock. By breakdown of large scales to small scales after reshock, rapid decay can be observed in cross-correlation spectra in both cases.

High-resolution Navier-Stokes simulations of Richtmyer-Meshkov instability with reshock

“…Characterizing the turbulent mixing requires high-resolution temporal and spatial measurements of both the density and velocity fields. The simultaneous planar laser-induced fluorescence (PLIF) and particle image velocimetry (PIV) measurements have been used to collect density and velocity data from shock-induced mixing problems in many previous studies [13][14][15][16][17]. However, the method is only limited to the measurements of the fields in a two-dimensional plane and data of other important quantities such as pressure and temperature are still out of reach.…”

Long-term effect of Rayleigh–Taylor stabilization on converging Richtmyer–Meshkov instability

“…The perturbations grow linearly until their amplitudes become comparable to their wavelengths. Eventually, the interface develops into a turbulent mixing layer (Mohaghar et al 2017;Zhou 2017). The RM instability has become increasingly significant in many areas of scientific research such as inertial confinement fusion (ICF) (Lindl et al 2014), supersonic combustion (Yang, Kubota & Zukoski 1993) and astrophysical problems (Arnett et al 1989), and several comprehensive reviews on the RM instability have been made (Zabusky 1999;Brouillette 2002;Ranjan, Oakley & Bonazza 2011;Luo et al 2014b).…”

Turbulent transition of a gaseous mixing zone induced by the Richtmyer-Meshkov instability

“…In addition to the above characterization of the mixing zone, the analysis of its turbulent transition was also conducted based on transition criteria as defined in the literature (see Dimotakis [22] and Mohaghar [18]). These transition criteria should reflect the existence of an inertial range in the turbulence spectrum, which must translate into a noticeable separation between the energetic and dissipative scales.…”

“…The first historically deployed strategy relies on an initial, solid or soft physical separation between the two gaseous species [2,7,[10][11][12][13][14][15]. A more recent experimental strategy aims at getting rid of any physical separation between the two gases by generating diffuse shear layers or curtains [8,[16][17][18][19].…”

“…The turbulent transition is then considered to be effective when Re h > 10 4 . Mohaghar et al[18] also suggest using the turbulent kinetic energy Reynolds number Re K = √ K h/ν mix with a similar threshold for the turbulent transition. One can also consider the Taylor Reynolds number Re λ T…”