Detailed measurements of a statistically steady Rayleigh–Taylor mixing layer from small to high Atwood numbers

Abstract

The self-similar evolution to turbulence of a multi-mode miscible Rayleigh–Taylor (RT) mixing layer has been investigated for Atwood numbers 0.03–0.6, using an air–helium gas channel experiment. Two co-flowing gas streams, one containing air (on top) and the other a helium–air mixture (at the bottom), initially flowed parallel to each other at the same velocity separated by a thin splitter plate. The streams met at the end of the splitter plate, with the downstream formation of a buoyancy unstable interface, and thereafter buoyancy-driven mixing. This buoyancy-driven mixing layer experiment permitted long data collection times, short transients and was statistically steady. Several significant designs and operating characteristics of the gas channel experiment are described that enabled the facility to be successfully run for At ~ 0.6. We report, and discuss, statistically converged measurements using digital image analysis and hot-wire anemometry. In particular, two hot-wire techniques were developed for measuring the various turbulence and mixing statistics in this air–helium RT experiment. Data collected and discussed include: mean density profiles, growth rate parameters, various turbulence and mixing statistics, and spectra of velocity, density and mass flux over a wide range of Atwood numbers (0.03 ≤ At ≤ 0.6). In particular, the measured data at the small Atwood number (0.03–0.04) were used to evaluate several turbulence-model constants. Measurements of the root mean square (r.m.s.) velocity and density fluctuations at the mixing layer centreline for the large At case showed a strong similarity to lower At behaviours when properly normalized. A novel conditional averaging technique provided new statistics for RT mixing layers by separating the bubble (light fluid) and spike (heavy fluid) dynamics. The conditional sampling highlighted differences in the vertical turbulent mass flux, and vertical velocity fluctuations, for the bubbles and spikes, which were not otherwise observable. Larger values of the vertical turbulent mass flux and vertical velocity fluctuations were found in the downward-falling spikes, consistent with larger growth rates and momentum of spikes compared with the bubbles.

Incompressible Rayleigh–Taylor Turbulence

“…Evidences of energy cascade from large to small length scales with an associated K41 spectrum (for both velocity and density) have been provided by an air-helium gas channel experiment by Banerjee et al (2010) (see Figure 5). Their observation is consistent with previous measurements in the water channel by Ramaprabhu & Andrews (2004) and Mueschke et al (2006).…”

“…We cite in this respect the works by Kinetic energy and density/temperature variance spectra for di↵erent Rayleigh-Taylor turbulent flows. Upper left: turbulent kinetic energy spectrum E v 0 , density fluctuations spectrum E ⇢ 0 and correlation spectrum E ⇢ 0 v 0 from an air-helium gas experiment at Atwood number A = 0.03 (Banerjee et al 2010). Spectra are compensated with k 5/3 to show the range of Kolmogorov scaling.…”

Acceleration and turbulence in Rayleigh–Taylor mixing

“…Unfortunately, experiments and simulations to date do not provide unequivocal support for these expectations. This conclusion is evident from careful assessments that can be found in the literature [7,10]. One reason for this behaviour may be that the concepts of classical turbulence may not apply to an accelerating RT flow.…”

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

“…An experimental estimate of the DSC was computed by Banerjee, Gore & Andrews (2010a) in a related flow for comparison with a modified version of the Besnard et al (1992) mix model. This estimate was based upon the Rayleigh-Taylor experimental data at low Atwood number from Banerjee, Kraft & Andrews (2010b). Results for terms in the evolution equation of b are scarcer yet, owing to the specific nature of the problem and the relatively recent derivation and presentation of these particular equations.…”

“…For this mixing flow, it is appropriate to estimate the kinematic viscosity of the gaseous mixture, one expression for which is given by Youngs (1984) as ν mix = (µ 1 + µ 2 )/(ρ 1 + ρ 2 ). While accurate for low Atwood numbers (Banerjee et al 2010b), for larger density ratios it is appropriate to use a more detailed expression for the dynamic viscosity of a binary mixture, as given by Reid, Prausnitz & Sherwood (1977),…”