Direct numerical simulation of the multimode narrowband Richtmyer–Meshkov instability

Abstract

Early to intermediate time behaviour of the planar Richtmyer-Meshkov instability (RMI) is investigated through direct numerical simulation (DNS) of the evolution of a deterministic interfacial perturbation initiated by a Ma = 1.84 shock. The model problem is the well studied initial condition from the recent θ-group collaboration [Phys. Fluids. 29 (2017) 105107]. A grid convergence study demonstrates that the Kolmogorov microscales are resolved by the finest grid for the entire duration of the simulation, and that both integral and spectral quantities of interest are converged. Compar-isons are made with implicit large eddy simulation (ILES) results from the θ-group collaboration, generated using the same numerical algorithm. The total amount of turbulent kinetic energy (TKE) is shown to be decreased in the DNS compared to the ILES, particularly in the transverse directions, giving rise to a greater level of anisotropy in the flow (70% vs. 40% more TKE in the shock parallel direction at the latest time considered). This decrease in transfer of TKE to the transverse components is shown to be due to the viscous suppression of secondary instabilities. Overall the agreement in the * large scales between the DNS and ILES is very good and hence the mixing width and growth rate exponent θ are very similar. There are substantial differences in the small scale behaviour however, with a 38% difference observed in the minimum values obtained for the mixing fractions Θ and Ξ.Differences in the late time decay of TKE are also observed, with decay rates calculated to be τ −1.41 and τ −1.25 for the DNS and ILES respectively.

The influence of initial perturbation power spectra on the growth of a turbulent mixing layer induced by Richtmyer–Meshkov instability

“…Finally, it would be useful to extend the just-saturated mode theory presented here to include the effects of viscosity and diffusivity on the growth rates of each mode. This would require direct numerical simulations (DNS) to be performed in order to validate the modifications, which would follow a similar approach to recent DNS of the narrowband case [31].…”

Reynolds number dependence of turbulence induced by the Richtmyer–Meshkov instability using direct numerical simulations

“…For high Reynolds numbers W grows independently of viscous effects, and the growth rate is instead damped by turbulent dissipation. This is beginning to occur in the two highest Re 0 cases, where comparisons with the ILES data from Thornber et al (2017) show that W is tending towards the high Reynolds number limit (Groom & Thornber 2019). The Re 0 = 174 case is representative of an intermediate regime where damping due to viscous dissipation has reduced but the amount of turbulence in the flow is still relatively low, thus the damping on the growth of W is lowest.…”

“…The inviscid flux component is calculated using the Harten-Lax-van Leer-Contact (HLLC) Riemann solver (Toro, Spruce & Speares 1994), while the viscous and diffusive fluxes are calculated using second-order central differences. This numerical algorithm has been extensively demonstrated to be an effective approach for solving shock-induced turbulent mixing problems (see Thornber et al 2010;Thornber 2016;Walchli & Thornber 2017;Groom & Thornber 2019).…”

“…This challenge also applies to RMI experiments and is due to the dependence of the growth rate exponent θ on initial conditions (Thornber et al 2010). As was illustrated in Groom & Thornber (2019), if the layer width grows as ∼ t θ then the Reynolds number based on this width evolves as ∼ t 2θ−1 . For the class of initial conditions presented here, it is expected that θ ≤ 1/3 (Elbaz & Shvarts 2018) and hence the Reynolds number decreases with time.…”

Refined modelling of the single-mode cylindrical Richtmyer–Meshkov instability

“…The RM instability and induced turbulent mixing flow have attracted much attention in the past half century (Rupert 1992;Brouillette 2002;Ranjan, Oakley & Bonazza 2011;Zhou 2017a,b). Previous research has mainly focused on the planar geometry both experimentally (Dimonte, Frerking & Schneider 1995;Jones & Jacobs 1997;Sadot et al 1998;Jacobs & Krivets 2005;Jourdan & Houas 2005;Mariani et al 2008) and numerically (Thornber & Zhou 2012;Tritschler et al 2014;Groom & Thornber 2019), not only because of the clarity of the physical image in the planar geometry but because of the difficulties encountered in the experimental set-up and numerical treatment of the shock wave and initial interface in the converging case.…”