Statistical characteristics of turbulent mixing in spherical and cylindrical converging Richtmyer–Meshkov instabilities

Li, Xinliang; Fu, Yaowei; Yu, Changping; Li, Li

doi:10.1017/jfm.2021.818

Cited by 10 publications

(12 citation statements)

References 67 publications

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“…In addition, we employ the standard third-order Runge-Kutta method as the time-marching scheme. The software Opencfd-Comb has been widely validated in our previous work, including supersonic jet flows (Fu et al 2019a,b) and RMI (Fu, Yu & Li 2020;Li et al 2021).…”

Section: Numerical Settingsmentioning

confidence: 99%

Effect of chemical reaction on mixing transition and turbulent statistics of cylindrical Richtmyer–Meshkov instability

Yan

Wang

et al. 2022

J. Fluid Mech.

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Direct numerical simulations of a three-dimensional cylindrical Richtmyer–Meshkov instability with and without chemical reactions are carried out to explore the chemical reaction effects on the statistical characteristics of transition and turbulent mixing. We adopt 9-species and 19-reaction models of non-premixed hydrogen and oxygen separated by a multimode perturbed cylindrical interface. A new definition of mixing width suitable for a chemical reaction is introduced, and we investigate the spatio-temporal evolution of typical flow parameters within the mixing regions. After reshock with a fuller mixing of fuels and oxygen, the chemical reaction becomes sufficiently apparent at affecting the evolution of the flow fields. Because of the generation of a combustion wave within the combustion regions and propagation, the growth of the mixing width with a chemical reaction is accelerated, especially around the outer radius with large temperature gradient profiles. However, the viscous dissipation rate in the early stage of the chemical reaction is greater because of heat release, which results in weakened turbulent mixing within the mixing regions. We confirm that small-scale structures begin to develop after reshock and then decay over time. During the developing process, helicity also begins to develop, in addition to kinetic energy, viscous dissipation rate, enstrophy, etc. In the present numerical simulations with cylindrical geometry, the fluctuating flow fields evolve from quasi-two-dimensional perturbations, and the generations of helicity can capture this transition process. The weakened fluctuations during shock compression can be explained as the inverse energy cascade, and the chemical reaction can promote this inverse energy cascade process.

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Section: Numerical Settingsmentioning

confidence: 99%

Effect of chemical reaction on mixing transition and turbulent statistics of cylindrical Richtmyer–Meshkov instability

Yan

Wang

et al. 2022

J. Fluid Mech.

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“…In terms of the flow cross-section area, RM instability can be categorized into two types: area-invariant RM instability and area-varied RM instability. The former usually refers to planar shock-induced RM instability, which has been extensively studied by experimentalists (Biamino et al 2015;Reese et al 2018;Liang et al 2021;Sewell et al 2021), theorists (Richtmyer 1960;Zhang & Sohn 1997;Dimonte & Ramaprabhu 2010;Zhang & Guo 2016) and numerical experts (Schilling & Latini 2010;Lombardini, Pullin & Meiron 2014;Wonga & Lelea 2017;Li et al 2022). It is widely accepted that pressure disturbance (caused by pressure waves behind the refracted shock) and baroclinic vorticity (caused by the misalignment of pressure and density gradients) are the major mechanisms for the growth of area-invariant RM instability (Brouillette 2002;Ranjan, Oakley & Bonazza 2011;Zhou 2017).…”

Section: Introductionmentioning

confidence: 99%

“…2021), theorists (Richtmyer 1960; Zhang & Sohn 1997; Dimonte & Ramaprabhu 2010; Zhang & Guo 2016) and numerical experts (Schilling & Latini 2010; Lombardini, Pullin & Meiron 2014; Wonga & Lelea 2017; Li et al. 2022). It is widely accepted that pressure disturbance (caused by pressure waves behind the refracted shock) and baroclinic vorticity (caused by the misalignment of pressure and density gradients) are the major mechanisms for the growth of area-invariant RM instability (Brouillette 2002; Ranjan, Oakley & Bonazza 2011; Zhou 2017).…”

Section: Introductionmentioning

confidence: 99%

Divergent Richtmyer–Meshkov instability on a heavy gas layer

Zhang

Ding

et al. 2023

J. Fluid Mech.

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Experiments on divergent Richtmyer–Meshkov (RM) instability at a heavy gas layer are performed in a specially designed shock tube. A novel soap-film technique is extended to generate gas layers with controllable thicknesses and shapes. An unperturbed gas layer is first examined and its two interfaces are found to move uniformly at the early stage and be decelerated later. A general one-dimensional theory applicable to an arbitrary-thickness layer is established, which gives a good prediction of the layer motion in divergent geometry. Then, six kinds of perturbed SF $_6$ layers with various thicknesses and shapes surrounded by air are examined. At the early stage, the amplitude growths of the inner interface for various-thickness layers collapse quite well and also can be predicted by the Bell model for cylindrical RM instability at a single interface, which indicates a negligible interface coupling effect. Later, a rarefaction wave accelerates the inner interface, causing a dramatic rise in the growth rate. It is found that a thicker gas layer will result in a larger extent that the rarefaction wave can promote the instability growth. A modified Bell model accounting for both Rayleigh–Taylor (RT) instability and interface stretching caused by a rarefaction wave is established, which well reproduces the quick instability growth. At late stages, reverberating waves inside the layer are negligibly weak such that the inner interface growth is dominated by RM instability and RT stability. The major factors driving the outer interface development are a compression wave and interface coupling. A new interface coupling phenomenon existing uniquely in divergent geometry caused by the gradual thinning of the gas layer is observed and also modelled.

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“…An important issue of these classical hydrodynamic instabilities is how these finger structures on an unstable interface grow in time and space. There have been sets of experimental (Jacobs & Catton 1988;Luo, Wang & Si 2013;Liu et al 2018;Luo et al 2018;Liang et al 2019;Lherm et al 2022) and numerical (Ristorcelli & Clark 2004;Ramaprabhu, Dimonte & Andrews 2005;Li et al 2021;Yan et al 2022) data available for their growth rate and shape evolution since Taylor's pioneering work in 1950, and yet there is still a lack of a unified and accurate theory to characterize them.…”

Section: Introductionmentioning

confidence: 99%

A unified theoretical model for spatiotemporal development of Rayleigh–Taylor and Richtmyer–Meshkov fingers

2022

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An initially perturbed interface between two fluids of different densities is usually unstable when driven by an acceleration or a shock wave; it is known as a Rayleigh–Taylor instability or a Richtmyer–Meshkov instability. One of the most significant issues in these instabilities is the spatiotemporal development of fingers generated at the interface, which plays an important role in both scientific research (e.g. supernova explosion) and engineering applications (e.g. inertial confinement fusion). Accurate theoretical solution of these interfacial fingers remains as an unsolved and challenging problem since Taylor's seminal work more than seven decades ago. This paper reports a unified theory established for such phenomena by combining the classical potential-flow theory and a dual-source model to address the long-standing difficulty highlighted by the initial-value sensitivity and strong nonlinearity. It is the first time for a theory to accurately predict the long-time developments in both growth rate and shape curvature of interfacial fingers at all density ratios in two and three dimensions. Moreover, the new theory clearly reveals the nonlinear coupling mechanism for interfacial evolution, and especially explains the origin of overshot in the growth rate curve.

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Statistical characteristics of turbulent mixing in spherical and cylindrical converging Richtmyer–Meshkov instabilities

Cited by 10 publications

References 67 publications

Effect of chemical reaction on mixing transition and turbulent statistics of cylindrical Richtmyer–Meshkov instability

Effect of chemical reaction on mixing transition and turbulent statistics of cylindrical Richtmyer–Meshkov instability

Divergent Richtmyer–Meshkov instability on a heavy gas layer

A unified theoretical model for spatiotemporal development of Rayleigh–Taylor and Richtmyer–Meshkov fingers

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