On the Kolmogorov inertial subrange developing from Richtmyer-Meshkov instability

Tritschler, Volker; Hickel, Stefan; Hu, Xiangyu; Adams, Nikolaus A.

doi:10.1063/1.4813608

Cited by 26 publications

(15 citation statements)

References 37 publications

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“…In a recent experimental investigation of a shock accelerated shear-layer Weber et al (2012) showed a k −5/3 inertial range followed by an exponential decay in the dissipation range of the scalar spectrum. This result was numerically reproduced by Tritschler et al (2013a).…”

Section: Spectral Quantitiesmentioning

confidence: 54%

“…The initial data of the post-shock state of the light gas as well as the pre-shock state of the light and heavy gas are given in table 1. Tritschler et al (2013a) introduced a generic initial perturbation of the material interface that resembles a stochastic random perturbation being, however, deterministic and thus exactly reproducible for different simulation runs. This multimode perturbation is given by the following function η(y, z) = a 1 sin (k 0 y) sin (k 0 z) + a 2 13 n=1 15 m=3 a n,m sin (k n y + φ n ) sin (k m z + χ m ) (3.2) with the constant amplitudes a 1 = −0.0025 m and a 2 = 0.00025 m and wavenumbers k 0 = 10π/L yz , k n = 2πn/L yz and k m = 2πm/L yz .…”

Section: Initial Conditionsmentioning

confidence: 99%

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On the Richtmyer–Meshkov instability evolving from a deterministic multimode planar interface

et al. 2014

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We investigate the shock-induced turbulent mixing between a light and a heavy gas, where a Richtmyer-Meshkov instability (RMI) is initiated by a shock wave with Mach number Ma = 1.5. The prescribed initial conditions define a deterministic multimode interface perturbation between the gases, which can be imposed exactly for different simulation codes and resolutions to allow for quantitative comparison. Wellresolved large-eddy simulations are performed using two different and independently developed numerical methods with the objective of assessing turbulence structures, prediction uncertainties and convergence behaviour. The two numerical methods differ fundamentally with respect to the employed subgrid-scale regularisation, each representing state-of-the-art approaches to RMI. Unlike previous studies, the focus of the present investigation is to quantify the uncertainties introduced by the numerical method, as there is strong evidence that subgrid-scale regularisation and truncation errors may have a significant effect on the linear and nonlinear stages of the RMI evolution. Fourier diagnostics reveal that the larger energy-containing scales converge rapidly with increasing mesh resolution and thus are in excellent agreement for the two numerical methods. Spectra of gradient-dependent quantities, such as enstrophy and scalar dissipation rate, show stronger dependences on the small-scale flow field structures as a consequence of truncation error effects, which for one numerical method are dominantly dissipative and for the other dominantly dispersive. Additionally, the study reveals details of various stages of RMI, as the flow transitions from large-scale nonlinear entrainment to fully developed turbulent mixing. The growth rates of the mixing zone widths as obtained by the two numerical methods are ∼t 7/12 before re-shock and ∼(t − t 0 ) 2/7 long after re-shock. The decay rate of turbulence kinetic energy is consistently ∼(t − t 0 ) −10/7 at late times, where the molecular mixing fraction approaches an asymptotic limit Θ ≈ 0.85. The anisotropy measure a xyz approaches an asymptotic limit of ≈0.04, implying that no full recovery of isotropy within the mixing zone is obtained, even after re-shock. Spectra of density, turbulence kinetic energy, scalar dissipation rate and enstrophy are presented and show excellent agreement for the resolved scales. The probability density function of the heavy-gas mass fraction and vorticity reveal that the light-heavy gas composition within the mixing zone is accurately predicted, whereas it is more difficult to capture the long-term behaviour of the vorticity.

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Section: Spectral Quantitiesmentioning

confidence: 54%

Section: Initial Conditionsmentioning

confidence: 99%

On the Richtmyer–Meshkov instability evolving from a deterministic multimode planar interface

et al. 2014

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“…The estimate was obtained from fitting model spectra to the experimental spectra, which resulted in an estimate of 125 μm η 214 μm. Tritschler et al [17] found for the same shock Mach number a similar range for the Kolmogorov length scale 75 μm η 224 μm. Consistent with these estimates Lombardini et al [9] found η ≈ 620 μm for RMI driven by a Ma = 1.05 shock wave and η ≈ 72 μm for Ma = 5 long after the shock-interface interaction.…”

Section: Introductionmentioning

confidence: 62%

“…Temporal integration is performed by a third-order total variation diminishing Runge-Kutta scheme [27]. The present numerical model has been tested and validated for shock induced turbulent multispecies mixing problems at finite Reynolds numbers [17,28,29]. Moreover, it has been demonstrated that it is a state-of-the-art approach to turbulent mixing processes evolving from RMI [15].…”

Section: Methodsmentioning

confidence: 99%

Evolution of length scales and statistics of Richtmyer-Meshkov instability from direct numerical simulations

et al. 2014

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In this study we present direct numerical simulation results of the Richtmyer-Meshkov instability (RMI) initiated by Ma=1.05,Ma=1.2, and Ma=1.5 shock waves interacting with a perturbed planar interface between air and SF(6). At the lowest shock Mach number the fluids slowly mix due to viscous diffusion, whereas at the highest shock Mach number the mixing zone becomes turbulent. When a minimum critical Taylor microscale Reynolds number is exceeded, an inertial range spectrum emerges, providing further evidence of transition to turbulence. The scales of turbulent motion, i.e., the Kolmogorov length scale, the Taylor microscale, and the integral length, scale are presented. The separation of these scales is found to increase as the Reynolds number is increased. Turbulence statistics, i.e., the probability density functions of the velocity and its longitudinal and transverse derivatives, show a self-similar decay and thus that turbulence evolving from RMI is not fundamentally different from isotropic turbulence, though nominally being only isotropic and homogeneous in the transverse directions.

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“…Previous published direct numerical simulations of RMI include a study by Olson and Greenough [18], as well as the studies of Tritschler et al [19,20].…”

Section: Introductionmentioning

confidence: 99%

Direct numerical simulation of the multimode narrowband Richtmyer–Meshkov instability

Groom

Thornber

2019

Computers & Fluids

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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.

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On the Kolmogorov inertial subrange developing from Richtmyer-Meshkov instability

Cited by 26 publications

References 37 publications

On the Richtmyer–Meshkov instability evolving from a deterministic multimode planar interface

On the Richtmyer–Meshkov instability evolving from a deterministic multimode planar interface

Evolution of length scales and statistics of Richtmyer-Meshkov instability from direct numerical simulations

Direct numerical simulation of the multimode narrowband Richtmyer–Meshkov instability

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