Abstract: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 e… Show more
“…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.…”
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.
“…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.…”
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.
“…2021; Yan et al. 2022). Figure 2.( a ) Measurements of the radii of the crest () and the trough () of a dual-mode interface from experimental schlieren images.…”
Section: Experimental and Numerical Methodsmentioning
confidence: 99%
“…Yan et al. (2022) investigated the cylindrically convergent RM instability with and without chemical reactions using the direct numerical simulation method to explore the influence of chemical reactions on the statistical characteristics of transition and turbulent mixing.…”
Section: Introductionmentioning
confidence: 99%
“…Li et al (2021) investigated the convergent RM instability in cylindrical and spherical geometries using the implicit large-eddy simulation method, highlighting the differences in the statistical characteristics of turbulent mixing between the cylindrically and spherically convergent RM instability. Yan et al (2022) investigated the cylindrically convergent RM instability with and without chemical reactions using the direct numerical simulation method to explore the influence of chemical reactions on the statistical characteristics of transition and turbulent mixing.…”
Shock-tube experiments are performed on the convergent Richtmyer–Meshkov (RM) instability of a multimode interface. The temporal growth of each Fourier mode perturbation is measured. The hydrodynamic instabilities, including the RM instability and the additional Rayleigh–Taylor (RT) effect, imposed by the convergent shock wave on the dual-mode interface, are investigated. The mode-coupling effect on the convergent RM instability coupled with the RT effect is quantified. It is evident that the amplitude growths of all first-order modes and second-order harmonics and their couplings depend on the variance of the interface radius, and are influenced by the mode-coupling from the very beginning. It is confirmed that the mode-coupling mechanism is closely related to the initial spectrum, including azimuthal wavenumbers, relative phases and initial amplitudes of the constituent modes. Different from the conclusion in previous studies on the convergent single-mode RM instability that the additional RT effect always suppresses the perturbation growth, the mode-coupling might result in the additional RT effect promoting the instability of the constituent Fourier mode. By considering the geometry convergence, the mode-coupling effect and other physical mechanisms, second-order nonlinear solutions are established to predict the RM instability and the additional RT effect in the cylindrical geometry, reasonably quantifying the amplitude growths of each mode, harmonic and coupling. The nonlinear solutions are further validated by simulations considering various initial spectra. Last, the temporal evolutions of the mixed mass and normalized mixed mass of a shocked multimode interface are calculated numerically to quantify the mixing of two fluids in the cylindrical geometry.
“…RMI has also been extensively studied [34][35][36][37] in theory [38][39][40][41][42] , numerical simulations [43][44][45][46][47][48][49][50][51][52][53][54][55][56] , and experiments [57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72] for general conditions. The physical comprehension of RMI is becoming clearer, however, as for general fluid cases, there are also significant nonequilibrium kinetic effects and this part is missing for the majority of existing studies.…”
Nonequilibrium kinetic effects are widespread in fluid systems and might have a significant impact on the inertial confinement fusion ignition process, and the entropy production rate is a key factor in accessing the compression process. But relevant research is little due to the lack of convenient physical model. In this work, we study the Richtmyer-Meshkov instability (RMI) and the reshock process by a two-fluid discrete Boltzmann method (DBM). The work starts from interpreting the experiment by Collins and Jacobs [J. Fluid Mech. 464, 113-136 (2002)]. Firstly, the DBM result for the perturbation amplitude evolution is in good agreement with that of experiment. It is found that shock wave causes substances near the substance interface to deviate more significantly from their thermodynamic equilibrium state. Greatly different from the case of normal shocking on unperturbed plane interface between two uniform media, which is well described by the Rankine-Hugoniot relations and where all Thermodynamic Non-Equilibrium (TNE) quantities quickly recover to zero behind the shock front, in the RMI case, the TNE quantities show complex but inspiring kinetic effects in the shocking process and behind the shock front. The kinetic effects are detected by two sets of TNE quantities. The first set are |∆ * 2 |, ∆ * 3,1 , ∆ * 3 , and ∆ * 4,2 . They correspond to the intensities of the Non-Organized Momentum Flux(NOMF), Non-Organized Energy Flux(NOEF), flux of NOMF and flux of NOEF. All the four TNE measures abruptly increase in the shocking process. ∆ * 3,1 and ∆ * 3 have the same dimension and show similar behaviors. They continue to increase in a much lower rate behind the shock front. |∆ * 2 | and ∆ * 4,2 have different dimensions, but show similar behaviors. They quickly decrease to be very small behind the shock front. The second set of TNE quantities are ṠNOMF , ṠNOEF and Ṡsum . They are entropy production rates due to NOMF, NOEF and their summation. It is found that the mixing zone is the primary contribution region to the ṠNOEF , while the flow field region excluding mixing zone is the primary contribution region to the ṠNOMF . Each substance behaves differently in terms of entropy production rate, and the light fluid has a higher entropy production rate than the heavy fluid.
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