FIG 1 - uploaded by Dov Shvarts
Content may be subject to copyright.
Source publication
The nonlinear growth of the multimode Rayleigh-Taylor (RT), Richtmyer-Meshkov (RM), and Kelvin-Helmholtz (KH) instabilities is treated by a similar statistical mechanics merger model, using bubbles as the elementary particle in the RM and RT instabilities and eddies in the KH instability. Two particle interaction is demonstrated and merger rates ar...
Context in source publication
Context 1
... results for these instabilities are presented in the following sections. An example of the agreement of the rising bubble locations and heights between the model and the simulation is shown on Figure 1 for the RT A \ 1 case (for more detail see Oron et al. 1998). Similar results are achieved for the low Atwood case RM instability ( Rikanati et al. 1998). ...
Citations
... During the implosion acceleration phase, KHI also interacts with RTI, where a lighter material overlays the dense metal shell. 20 These instabilities disrupt capsule symmetry, impede ignition hotspot formation, reduce laser energy deposition, limit implosion velocity, and potentially rupture the fuel shell, ultimately leading to ICF ignition failure. 5,21 Moreover, recent studies demonstrated that the kinetic effects, marked by significant discrete effects and nonequilibrium effects, have a substantial impact on the success of ignition in ICF. ...
This study investigates the complex kinetics of thermodynamic nonequilibrium effects (TNEs) and their relative importance during the development of the Kelvin–Helmholtz instability (KHI) using high-order discrete Boltzmann models (DBMs). First, the capabilities and differences among various discrete velocity sets in capturing TNEs and distribution functions are assessed. This analysis proposes practical guidelines for constructing discrete velocity stencils to enhance phase-space discretization and improve the robustness of high-order DBM simulation. At different stages of KHI and under varying initial conditions, multiscale TNEs, such as viscous stresses of different orders, emerge with distinct dominant roles. Specifically, three scenarios are identified: (i) regimes dominated by first-order TNEs, (ii) alternation between first- and second-order TNEs, and (iii) states where second-order TNEs govern the system's behavior. To quantitatively capture these transitions, criteria for TNE dominance at different orders in KHI evolution are established based on the relative thermodynamic nonequilibrium intensity ( RTNE). In scenarios dominated by second-order TNEs, differences between first-order and second-order models are compared in terms of macroscopic quantities, nonequilibrium effects, and kinetic moments, revealing the physical limitations of low-order models in capturing TNEs. Furthermore, the effectiveness, extensibility, and limitations of a representative high-order model are examined under second-order TNE-dominated conditions. To encapsulate these findings, a nonequilibrium phase diagram that visually maps the multiscale characteristics of KHI is constructed. This diagram not only provides intuitive insights into the dynamic interplay of different nonequilibrium effects but also serves as a kinetic roadmap for selecting suitable models under diverse nonequilibrium conditions.
... KHI also couples with RMI, which emerges at the multilayered target capsule interface due to ablation shockwaves and rarefaction waves induced during implosion. During the implosion acceleration phase, KHI also interacts with RTI, where a lighter material overlays the dense metal shell 20 . These instabilities disrupt capsule symmetry, impede ignition hotspot formation, reduce laser energy deposition, limit implosion velocity, and potentially rupture the fuel shell, ultimately leading to ICF ignition failure 5,21 . ...
This study investigates the complex dynamics of thermodynamic nonequilibrium effects (TNEs) and their relative importance during the development of the Kelvin-Helmholtz instability (KHI) using high-order discrete Boltzmann models (DBMs). First, the capabilities and differences among various discrete velocity sets in capturing TNEs and distribution functions are assessed. Based on this analysis, practical guidelines for constructing discrete velocity stencils are proposed to enhance phase-space discretization and improve the robustness of high-order DBMs. At different stages of KHI and under varying initial conditions, multiscale TNEs, such as viscous stresses of different orders, emerge with distinct dominant roles. Specifically, three scenarios are identified: (i) regimes dominated by first-order TNEs, (ii) alternation between first- and second-order TNEs, and (iii) states where second-order TNEs govern the system's behavior. To quantitatively capture these transitions, criteria for TNE dominance at different orders in KHI evolution are established based on the relative thermodynamic nonequilibrium intensity. In scenarios dominated by second-order TNEs, differences between first-order and second-order models are compared in terms of macroscopic quantities, nonequilibrium effects, and moment relations, revealing the physical limitations of low-order models in capturing TNEs. Furthermore, the effectiveness, extensibility, and limitations of a representative high-order model are examined under second-order TNE-dominated conditions. To encapsulate these findings, a nonequilibrium phase diagram that visually maps the multiscale characteristics of KHI is constructed. This diagram not only provides intuitive insights into the dynamic interplay of different nonequilibrium effects but also serves as a kinetic roadmap for selecting suitable models under diverse nonequilibrium conditions.
... Images of the instability evolution that use MR and water (A t ¼ 0.46) and MR and air (A t ¼ 1) is shown in Fig. 8(g) and 8(f). Measurements of the late time RT spike reveal poor agreement with analytical models [89,90]. ...
The focus of experiments and the sophistication of diagnostics employed in Rayleigh Taylor Instability (RTI) induced mixing studies have evolved considerably over the past seven decades. The first theoretical analysis by Taylor and experimental results by Lewis on RTI in 1950 examined two-dimensional, single-mode RTI using conventional photographic techniques. Over the next 70 years, several experimental designs have been used to creating an RTI unstable interface between two materials of different densities. These early experiments though innovative, were arduous to diagnose and provided little information on the internal, turbulent structure and initial conditions of the RT mixing layer. Coupled with the availability of high-fidelity diagnostics, the experiments designed and developed in the last three decades allow detailed measurements of various turbulence statistics that have allowed broadly to validate and verify late-time non-linear models and mix-models for buoyancy-driven flows. Besides, they have provided valuable insights to solve several long-standing disagreements in the field. This review serves as an opportunity to discuss the understanding of the RTI problem and highlight valuable insights gained into the RTI driven mixing process through experiments. For the current review, the focus is on low to high Atwood number (> 0.1) experiments.
... Now it is clear that, when the initial perturbations involve only random short-wavelength perturbations, α b would take a universal value of α b ≈ 0.025 through the bubble merger mechanism. 29,[31][32][33][34][35][36][37] In contrast, if the long-wavelength perturbations are included, α b would strongly depend on the initial perturbations through the bubble competition mechanism. 7,13,23,29,30,[38][39][40] In history, "merger" and "competition" had been used to describe the same process since 1960s, but Dimonte et al. distinguished them in 2004 to quantify the long-wavelength perturbations. ...
A flow of semi-bounded Rayleigh–Taylor instability (SB-RTI) is constructed and simulated to understand the bubble dynamics of the multi-mode Rayleigh–Taylor mixing (MM-RTM). SB-RTI is similar to the well-known single-mode Rayleigh–Taylor instability (SM-RTI), and it acts as a bridge from SM-RTI to MM-RTM. This idea is inspired by Meshkov’s recent experimental observation on the structure of the mixing zone of MM-RTM [E. E. Meshkov, J. Exp. Theor. Phys. 126, 126–131 (2018)]. We suppose that the bubble mixing zone consists of two parts, namely, the turbulent mixing zone at the center and the laminar-like mixing zone nearby the edge. For the latter, the bubble fronts are situated in an environment similar to that of SM-RTI bubbles in the potential flow stage, but with a much looser environment between neighboring bubbles. Therefore, a semi-bounded initial perturbation is designed to produce a bubble environment similar to that in MM-RTM. A non-dimensional potential speed of FrpSB≈0.63 is obtained in SB-RTI, which is larger than that of FrpSM=0.56 in SM-RTI. Combining this knowledge and the widely reported quadratic growth coefficient of αb ≈ 0.025 in the short-wavelength MM-RTM, we derive β ≡ D(t)/hb(t) ≈ (1 + A)/4. This relation is consistent with the MM-RTM simulations from Dimonte et al. [Phys. Fluids 16, 1668–1693 (2004)]. The current three-dimensional and previous two-dimensional results [Zhou et al., Phys. Rev. E 97, 033108 (2018)] support a united mechanism of bubble dynamics in short-wavelength MM-RTM.
... Youngs 1984; Cook, Cabot & Miller 2004; Dimonte et al. 2004; Cabot & Cook 2006) and modelling (e.g. Zufiria 1988; Ofer et al. 1996; Rikanati et al. 2000) interest over the past 25 years, yet many uncertainties remain. It is reasonable to infer that the rate of instability growth is controlled by the distribution of energy in the system, particularly the balance between energy needed to sustain the instability and energy used in other ways. ...
We seek to understand the distribution of irreversible energy conversions (mixing efficiency) between quiescent initial and final states in a miscible Rayleigh–Taylor driven system. The configuration we examine is a Rayleigh–Taylor unstable interface sitting between stably stratified layers with linear density profiles above and below. Our experiments in brine solution measure vertical profiles of density before and after the unstable interface is allowed to relax to a stable state. Our analysis suggests that less than half the initially available energy is irreversibly released as heat due to viscous dissipation, while more than half irreversibly changes the probability density function of the density field by scalar diffusion and therefore remains as potential energy, but in a less useful form. While similar distributions are observed in Rayleigh–Taylor driven mixing flows between homogeneous layers, our new configuration admits energetically consistent end-state density profiles that span all possible mixing efficiencies, ranging from all available energy being expended as dissipation, to none. We present experiments that show that the fluid relaxes to a state with a significantly lower mixing efficiency than the value for ideal mixing in this configuration, and deduce that this mixing efficiency more accurately characterizes Rayleigh–Taylor driven mixing than previous measurements. We argue that the physical mechanisms intrinsic to Rayleigh–Taylor instability are optimal conditions for mixing, and speculate that we have observed an upper bound to fluid mixing in general.
... So-called 'bubble competition' and 'bubble merger' models (e.g. Zufiria (1988); Ofer et al. (1996); Rikanati et al. (2000)) assume the development of each mode can be described independently by a buoyancy-drag model, and a 1. Overview 1.2 chosen interaction mechanism couples the modes together and provides a mechanism for the dominant scale to change. Some models use a 'takeover' analogy whereby smaller bubbles are engulfed, others demand that the bubble structures maintain geometrical self-similarity throughout their growth and in some way 'merge'. ...
Rayleigh-Taylor instability has been an area of active research in fluid dynamics for
the last twenty years, but relatively little attention has been paid to the dynamics
of problems where Rayleigh-Taylor instability plays a role, but is only one component of a more complex system. Here, Rayleigh-Taylor instability between miscible fluids is examined in situations where it is confined by various means: by geometric
restriction, by penetration into a stable linear stratification, and by impingement
on a stable density interface. Water-based experiments are modelled using a variety
of techniques, ranging from simple hand calculation of energy exchange to full
three-dimensional numerical simulation. Since there are well known difficulties in
modelling unconfined Rayleigh-Taylor instability, the confined test cases have been sequenced to begin with dynamically simple benchmark systems on which existing
modelling approaches perform well, then they progress to more complex systems and
explore the limitations of the various models. Some work on the phenomenology of
turbulent mixing is also presented, including a new experimental technique that allows mixed fluid to be visualised directly, and an analysis of energy transport and mixing efficiency in variable density flows dominated by mixing.
... So-called 'bubble competition' and 'bubble merger' models (e.g. Zufiria (1988); Ofer et al. (1996); Rikanati et al. (2000)) assume the development of each mode can be described independently by a buoyancy-drag model, and a 1. Overview 1.2 chosen interaction mechanism couples the modes together and provides a mechanism for the dominant scale to change. Some models use a 'takeover' analogy whereby smaller bubbles are engulfed, others demand that the bubble structures maintain geometrical self-similarity throughout their growth and in some way 'merge'. ...
Rayleigh-Taylor instability has been an area of active research in fluid dynamics for
the last twenty years, but relatively little attention has been paid to the dynamics
of problems where Rayleigh-Taylor instability plays a role, but is only one component of a more complex system. Here, Rayleigh-Taylor instability between miscible fluids is examined in situations where it is confined by various means: by geometric
restriction, by penetration into a stable linear stratification, and by impingement
on a stable density interface. Water-based experiments are modelled using a variety
of techniques, ranging from simple hand calculation of energy exchange to full
three-dimensional numerical simulation. Since there are well known difficulties in
modelling unconfined Rayleigh-Taylor instability, the confined test cases have been sequenced to begin with dynamically simple benchmark systems on which existing
modelling approaches perform well, then they progress to more complex systems and
explore the limitations of the various models. Some work on the phenomenology of
turbulent mixing is also presented, including a new experimental technique that allows mixed fluid to be visualised directly, and an analysis of energy transport and mixing efficiency in variable density flows dominated by mixing.
... The extent of penetration of one ‡uid into another is de…ned as the distance between the centerplane of the mixing layer and the bubble and spike fronts, h b and h s , respec- (Youngs 1984), dimensional analysis (Anuchina et al. 1978;Cook & Dimotakis 2001), self-similar analysis (Ristorcelli & Clark 2004), bubble merger or competition models (Shvarts et al. 1995;Rikanati et al. 2000;Dimonte et al. 2005), experiments (Andrews & Spalding 1990;Linden et al. 1994;Snider & Andrews 1996;Dimonte & Schneider 2000;Banerjee & Andrews 2006), and numerical simulations (Youngs 1994;Ramaprabhu et al. 2005;Cabot & Cook 2006) showed that the late-time penetration of the bubbles and spikes (for cases where dissipative, di¤usive and surface tension e¤ects can be neglected) scale as ...
Experiments and simulations were performed to examine the complex processes that occur in Rayleigh-Taylor driven mixing. A water channel facility was used to examine a buoyancy-driven Rayleigh-Taylor mixing layer. Measurements of fluctuating density statistics and the molecular mixing parameter were made for Pr = 7 (hot/cold water) and Sc ~ 10^3 (salt/fresh water) cases. For the hot/cold water case, a high-resolution thermocouple was used to measure instantaneous temperature values that were related to the density field via an equation of state. For the Sc ~ 10^3 case, the degree of molecular mixing was measured by monitoring a diffusion-limited chemical reaction between the two fluid streams. The degree of molecular mixing was quantified by developing a new mathematical relationship between the amount of chemical product formed and the density variance. Comparisons between the Sc = 7 and Sc ~ 10^3 cases are used to elucidate the dependence of \theta the Schmidt number.
To further examine the turbulent mixing processes, a direct numerical simulation (DNS) model of the Sc = 7 water channel experiment was constructed to provide statistics that could not be experimentally measured. To determine the key physical mechanisms that influence the growth of turbulent Rayleigh-Taylor mixing layers, the budgets of the exact mean mass fraction, turbulent kinetic energy, turbulent kinetic energy dissipation rate, mass fraction variance, and mass fraction variance dissipation rate equations were examined. The budgets of the unclosed turbulent transport equations were used to quantitatively assess the relative magnitudes of different production, dissipation, transport, and mixing processes.
Finally, three-equation and four-equation turbulent mixing models were developed and calibrated to predict the degree of molecular mixing within a Rayleigh-Taylor mixing layer. The DNS data sets were used to assess the validity of and calibrate the turbulent viscosity, gradient-diffusion, and scale-similarity closures a priori. The modeled transport equations were implemented in a one-dimensional numerical simulation code and were shown to accurately reproduce the experimental and DNS results a posteriori. The calibrated model parameters from the Sc = 7 case were used as the starting point for determining the appropriate model constants for the mass fraction variance transport equation for the Sc ~ 10^3 case.
In this paper, we study turbulent mixing between two miscible fluids that is induced gravitationally by Rayleigh–Taylor instability in a tightly confined domain. In our experimental configurations, one lateral dimension is between two and three orders of magnitude smaller than the other. Our motivation is to examine the relationship between domain width and certain key flow statistics, as the geometric restriction changes in relative significance. We match our experiments with carefully-resolved numerical simulations and in order to impose appropriate initial conditions, we extend Taylor’s linear model of instability growth to characterise the influence of geometry on early modal development and use measured experimental data to inform our initialisation. We find that our experiments exhibit initial conditions with a k−1 spectral scaling of interfacial perturbation of volume fraction with a high degree of repeatability, where k denotes wavenumber. We discovered that our form of geometric restriction couples favourably with the spectral composition of our initial condition. We observe no early-stage transient relaxation towards self–similarity, because the instability already begins in that stable self–similar equilibrium, and this important special case has not previously been noticed despite decades of related research. We present our statistical observations from both experiment and numerical simulation as a validation resource for the community; such simulations are inexpensive to compute yet capture many dynamically significant properties.
