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The effects of an inlet inertial jet on the thermal blending of hot and cold heat transfer fluid (molten salt) for a single tank sensible thermal energy storage system are studied using numerical simulations. The simulations show the evolution of the initial stratified layer (thermocline) for a temperature difference of 300 K with a corresponding Atwood number (At) of 0.066. Three diffuser arrangements are investigated: a flat plate solid diffuser, a coaxial ring diffuser with a solid center, and a proposed hemispherical diffuser. The thermal stratifications are examined by a mathematical model named Ideal stratification index (ISI). It is observed that the buoyancy-driven mixing is minimum for the hemispherical diffuser, and the resulting thermocline is 6% better compared to alternative diffusers at 27 l/min. Additionally, the working of the proposed diffuser is demonstrated via experiments with a saline-freshwater combination. These results reveal that the single tank thermocline storage performance can be improved for higher charging/discharging rates using hemispherical diffusers.

The evolution of shear instability between elastic–plastic solid and ideal fluid which is concerned in oblique impact is studied by developing an approximate linear theoretical model. With the velocities expressed by the velocity potentials from the incompressible and irrotational continuity equations and the pressures obtained by integrating momentum equations with arbitrary densities, the motion equations of the interface amplitude are deduced by considering the continuity of normal velocities and the force equilibrium with the perfectly elastic–plastic properties of solid at interface. The completely analytical formulas of the growth rate and the amplitude evolution are achieved by solving the motion equations. Consistent results are performed by the model and 2D Lagrange simulations. The characteristics of the amplitude development and Atwood number effects on the growth are discussed. The growth of the amplitude is suppressed by elastic–plastic properties of solids in purely elastic stage or after elastic–plastic transition, and the amplitude oscillates if the interface is stable. The system varies from stable to unstable state as Atwood number decreasing. For large Atwood number, elastic–plastic properties play a dominant role on the interface evolution which may influence the formation of the wavy morphology of the interface while metallic plates are suffering obliquely impact.

International audience; The isothermal mixing of a heavy and a light liquid of different physical properties is numerically investigated by means of Large Eddy Simulations. The validation is based on experimental data held in a system reproducing various components of a pressurized water nuclear reactor, during a scenario of cold water injection at a low Atwood number of 0.05. The flow has two distinct stages: first a buoyancy-driven phase is characterized by a fluid front development in the cold leg and gives rise to Kelvin-Helmholtz whorls under the action of density changes. Then, the heavy liquid discharges into the downcomer filled with light liquid, which causes a turbulent mixing. These phenomena are analyzed through a single-phase approach where the density of the working fluid is either variable or modeled by the Boussinesq approximation. The influence of grid refinement is deeply examined, which shows that the mesh convergence is well achieved for the main flow quantities, unlike the low-magnitude spanwise components. Overall, the numerical solutions are found to reproduce the experimental measurements with a fair accuracy for both physical models used. These latter exhibit similar trends, due to the small density difference under consideration. The predictions in the downcomer appear to be more challenging owing to a strongest turbulence than in the cold leg, some flow features being not properly captured. However, the experimental data in the downcomer are found to be incomplete and somewhat dubious for a strict validation of the numerical simulations. Lastly, the flow distribution in the dowcomer is investigated, providing further insight on the mixing process.

The Richtmyer–Meshkov instability (RMI) arises at an impulsively accelerated interface between two materials of different density. Historically, this instability was studied in fluids. Recently, RMI studies have been extended to investigate material properties of solids. Material strength at high strain-rates in solids have been extracted from the amplitude and growth of the RMI spike in an untamped environment, specifically, the metal-vacuum interface. This technique has also been shown to elucidate material properties in a distended tamping media, metal-porous solid interface. Here, a bridge to understanding the nonlinear mechanical behavior of copper into a liquid tamping media is investigated experimentally and computationally. We show the RMI growth rate and resulting profile are dependent on initial shock strength, as well as the nondimensional perturbation, with an initial Atwood number of $$-0.78$$ . Data collected from a tamped liquid environment range in metal breakout pressures up to ten GPa. This information is used to calibrate and validate numeric model parameters. The oscillatory shock front in the liquid tamping media is used to approximate the viscosity from a transient 1-D analytic approximation. The viscosity is found to be in agreement with other experimental work, however is not determined to be the only dissipative force in the experiment. Hydrocode simulations of our experiments show reasonable alignment with current and previously published work.

The demand for renewable energy sources is limited by their inherent intermittent nature. The thermal energy storage technique overcomes this shortcoming by allowing storage of naturally occurring energy (e.g. solar) during “non-peak hours”. The article presents an experimental investigation of the sparsely studied ‘single medium thermocline’ (SMT) based single tank sensible thermal energy storage (TES). The work aims to reconsider its potential by minimizing the fluid dynamic perturbations during the charging cycle which disrupt the stability of the thermocline leading to undesirable energy losses. The article discusses the effect of Atwood number (density stratification) and mean temperature on TES effectiveness as well as providing the appropriate thermodynamic insights. Implementation of the experimental procedures and strategies discussed in this article demonstrates a stable thermocline which persists for more than 6 h (hours) with minimal energy degradation.

The Lattice Boltzmann Method (LBM) was implemented to simulate the two-dimensional (2-D) Rayleigh–Taylor instability (RTI) during the mixing of the immiscible fluids. Two important parameters of the density and the viscosity as represented respectively by the Atwood and the Reynolds numbers were considered. In the calculation the density of two immiscible fluids was calculated by using the equation of state (EOS). In the present simulations, both Atwood and Reynolds numbers were varied in order to investigate the time variations of the interfacial behavior during RTI, the position of bubbles and spikes, and the horizontal average density. The results indicate that the Atwood number has a higher effect than the Reynolds number in the mixing process during RTI. The bubbles and spikes positions go farther in the displacement with the increase of both Reynolds and Atwood numbers. Moreover, the increase of both Reynolds and Atwood numbers accelerate the mixing process during RTI.

The stability characteristics of an inviscid, incompressible and immiscible cylindrical interface are examined using linear temporal theory. The cylindrical interface is subjected to two instability mechanisms, namely Rayleigh–Taylor (R–T) and Kelvin–Helmholtz (K–H) instabilities. The combined action of R–T and K–H in the presence of surface tension is investigated for a hollow jet in an unbounded liquid medium and reported. The problem includes the motion in an axial direction (K–H mechanism) and the radial direction (R–T mechanism) to destabilize the interface. The instability behavior is described by a few operating parameters, namely, Bond number (Bo), Weber number (We) and Atwood number (A). Here, Bond number is attributed to R–T instability whereas Weber number is attributed to K–H instability. The temporal analysis reveals that the Bond number plays a significant role in determining the dominant growth rate, most unstable axial wavenumber and cut-off axial wavenumber. Furthermore, it is also shown through dimensionless energy budget arguments, even a small amount of energy in the radial motion causes the most unstable wavenumber associated with primary atomization to increase significantly.

Developments of two-dimensional single-mode light/heavy interfaces driven by convergent shock waves are numerically investigated, focusing on the effect of the Atwood number on the Rayleigh–Taylor stabilization, the compressibility and the nonlinearity. Five different test gases, including $$\hbox {CO}_2$$ , Kr, R22, R12 and $$\hbox {SF}_6$$ , are considered with air as the ambient gas. It is clarified for the first time that the unperturbed interface begins to decelerate when the shock focuses at the convergence center, and the acceleration during the deceleration phase is proportional to the Atwood number. During the first reshock, the interface moves outwards with a deceleration until it starts moving inwards. When the initial interface is weakly disturbed, a more obvious amplitude reduction is observed for the case with a larger Atwood number before the reshock, which means that the Rayleigh–Taylor stabilization is stronger. To assess the effect of the Atwood number on the compressibility and the nonlinearity, three models, including a linear incompressible model, a nonlinear incompressible model and a linear compressible model, are adopted to predict the amplitude growth before the reshock. The results show that the nonlinearity is weak, and is almost not influenced by the Atwood number before the reshock. The compressibility, however, greatly changes the amplitude growth. As the Atwood number increases, the compressibility plays a less significant role in the amplitude growth because a heavier gas is harder to be compressed. Although a gas with a larger specific heat ratio is also difficult to be compressed, the specific heat ratio plays a minor role to the compressibility relative to the Atwood number. During the reshock, the amplitude grows linearly until the nonlinearity in the cases with large Atwood numbers is strong enough to reduce the amplitude growth rate.

Deaeration is a process of eliminating aspirated air from liquid in hydraulic reservoirs to avoid cavitation in the downstream pump blades. The complex fluid dynamics associated with deaeration is investigated. The three-dimensional buoyancy driven chaotic behavior of gas-liquid interfacial two-phase flow is studied. Parametric study is executed to understand change in internal flow physics (bubble coalescence, disintegration, horizontal spread, bubble velocity etc.), strength of accelerating Rayleigh-Taylor instability, turbulent kinetic energy, amplitude of upward velocity near free surface, and rise in free surface level with the variation of parameters like incoming mixture flow rate, incoming volume fraction of air, liquid fill depth, and Atwood number. The computations show increment in cavitation, wavenumber and amplitude of upward velocity towards oscillating free surface with incoming flow rate (Re). Cavitation and free surface instability show incremental trend with volume fraction of incoming air forming a kink (cavitation reduces) due to bubble coalescence in a threshold range of volume fraction of incoming air. With the variation of Atwood number, initially cavitation reduces. But after a critical value (A*) of Atwood number, effect of bubble disintegration, and rise of cavitation become prominent, which is formulated with respect to incoming flow rate (Re). With liquid fill depth, cavitation shows a slight decrement with almost equal deaeration and constant wavelength of free surface oscillation at an increasing buoyancy driven upward velocity. Some glimpse of design solution to reduce the cavitation and enhance the deaeration is also studied and formulated to get better understanding.

Flow transitions and vortical developments during vortex-ring collisions with a sharp water–oil density interface are studied using planar laser-induced fluorescence and time-resolved particle-image velocimetry techniques. Circular vortex-rings at Reynolds numbers of Re = 1000 , 2000 and 4000 colliding with a density interface characterized by an Atwood number of approximately A= 0.045 were investigated. Results show that at Re = 1000 , collision with the density interface produces vortical structures and flow transitions that are relatively similar to those for a solid-boundary collision. However, the dynamics underlying the present vortical formations and behaviour are different from those associated with solid-boundary collisions, in that the former are driven by baroclinic vorticity generation. Flow behaviour at Re = 2000 shows more significant deformation of the density interface by the vortex-ring but overall behaviour remains comparable. Last but not least, at Re = 4000 , the largest Reynolds number investigated here, the vortex-ring penetrates the density interface almost completely. However, buoyancy effects eventually limit its penetration and reverse its translational direction, such that it crosses back into the oil layer again with its vortex core rotational senses reversed as well. At the same time, vortex-ring fluid is shed and a significant trailing-jet is left in the former’s wake. Nanyang Technological University The authors acknowledge support for the present study by the School of Mechanical & Aerospace Engineering and CN Yang Scholars" Programme at Nanyang Technological University, Singapore. Funding provided for the first author to present this work at the 15th Asian Symposium on Visualization under a School of Mechanical & Aerospace Engineering Enrichment Grant is also gratefully acknowledged.

A study has been made of the interaction between a plane shock wave in a gas or a gas suspension and regions of square and rhombiform cross sections differing from the environment in density. A high-stability monotonic scheme with small numerical dissipation was used for calculation. Comparisons with experiments on the refraction of the shock wave on the interface of a binary gas have confirmed the adequacy of the scheme. The influence of the density-ratio factor (Atwood number), the shape of inhomogeneities, and the particle size on the shock wave structure and the development of a Richtmyer–Meshkov instability has been shown.

In this paper, the Richtmyer–Meshkov instabilities in spherical and cylindrical converging geometries with a Mach number of approximately 1.5 are investigated by using the high resolution implicit large eddy simulation method, and the influence of the geometric effect on the turbulent mixing is investigated. The heavy fluid is sulphur hexafluoride (SF6), and the light fluid is nitrogen (N2). The shock wave converges from the heavy fluid into the light fluid. The Atwood number is 0.678. The total structured and uniform Cartesian grid node number in the main computational domain is 20483. In addition, to avoid the influence of boundary reflection, a sufficiently long sponge layer with 50 non-uniform coarse grids is added for each non-periodic boundary. Present numerical simulations have high and nonlinear initial perturbation levels, which rapidly lead to turbulent mixing in the mixing layers. Firstly, some physical-variable mean profiles, including mass fraction, Taylor Reynolds number, turbulent kinetic energy, enstrophy and helicity, are provided. Second, the mixing characteristics in the spherical and cylindrical turbulent mixing layers are investigated, such as molecular mixing fraction, efficiency Atwood number, turbulent mass-flux velocity and density self-correlation. Then, Reynolds stress and anisotropy are also investigated. Finally, the radial velocity, velocity divergence and enstrophy in the spherical and cylindrical turbulent mixing layers are studied using the method of conditional statistical analysis. Present numerical results show that the geometric effect has a great influence on the converging Richtmyer–Meshkov instability mixing layers.

The Richtmyer–Meshkov (RM) instability is numerically investigated on an unperturbed interface subjected to a diffracted convergent shock created by diffracting an initially cylindrical shock over a rigid cylinder. Four gas interfaces are considered with Atwood number ranging from $-0.18$ to 0.67. Results indicate that the diffracted convergent shock increases its strength gradually and reduces its amplitude quickly when it propagates towards the convergence centre. After the strike of the diffracted convergent shock, the initially unperturbed interface deforms with a bulge structure at the centre and two interface steps at both sides, which can be ascribed to the non-uniformity of the pressure distribution behind the diffracted convergent shock. With the decrease of Atwood number, the bulge structure becomes more pronounced. Quantitatively, the interface amplitude experiences a fast but short growing stage and then enters a linear stage. A good collapse of the dimensionless amplitude is found for all cases, which indicates a weak dependence of the growth rate on Atwood number in the deformed shock-induced RM instability. Then the impulsive theory is modified by eliminating the Atwood number and considering the geometry convergence, which well predicts the amplitude growth for the deformed shock-induced RM instability. Finally, the underlying mechanism is decoupled into three parts, and it is found that both the impulsive pressure perturbation and the geometry convergence promote the growth of interface perturbation while the continuous pressure perturbation inhibits the growth. As the Atwood number decreases, the impulsive perturbation plays an increasingly important role, which suggests that the impulsive perturbation dominates the deformed shock-induced RM instability at the linear stage.

The influences of the Schmidt number and fluid models of the Boussinesq approximation and variable density (low-Mach formulation) are investigated using large eddy simulation (LES) where fluid naturally advects between two tanks connected by a pipe. The geometry resembles a reactor-like vessel which comprises of a cold leg-downcomer region. The closed system consists of two miscible fluids with different densities and viscosities separated by a valve. Analysis with Reynolds-Averaged Navier–Stokes (RANS) is used for calculating Taylor length scales to establish minimum grid resolution for LES. Using particle image velocimetry (PIV) data, validation is conducted for four different magnitudes of Schmidt numbers. Evidence indicates that capturing the effects from the highest Schmidt number is essential for properly predicting fluctuations and instabilities in the flow. Although downcomer comparisons with PIV consist of larger errors, they are explained through additional sensitivity analyses involving initial conditions, geometry, and residual energy. Lastly, the influence of larger density differences is demonstrated using simulations with a higher Atwood number, temporally scaled using the fluid front velocity. Recommendations are made regarding future experiments and simulations for design of similar buoyant mixing problems.

This article is a maiden and naive attempt to formulate, analyse and investigate the Rayleigh–Taylor (RT) instability of two superimposed horizontal layers of nanofluids having different densities. Conservation equations are formulated and linearised by keeping in mind that density of the base fluids as well as nanoparticles is not constant. Linearised perturbed equations are sorted out by using the technique of normal modes and a dispersion relation incorporating the effects of surface tension, Atwood number and volume fraction of nanoparticles is obtained. Stable and unstable modes of RT instability are scrutinised using Routh–Hurtwitz criterion in the presence/absence of nanoparticles and presented graphically. Numerical calculations have been performed to explore the effect of surface tension, Atwood number and volume fraction of the nanoparticles. It is observed that in the presence/absence of nanoparticles, surface tension has a significant impact on stabilising the unstable mode of RT instability whereas Atwood number and volume fraction of nanoparticles hasten this instability. The graphical representations of these numerical investigations confirm the very explanation of RT instability under the effect of different parameters that have significant impact on the intensity of growth rate.

Magnetohydrodynamical evolution of the Richtmyer-Meshkov instability (RMI) is investigated by two-dimensional MHD simulations. The RMI is suppressed by a strong magnetic field, whereas the RMI amplifies an ambient magnetic field by many orders of magnitude if the seed field is weak. We have found that the suppression and amplification processes can be evaluated continuously along with the amplitude of the Alfv\'en number $R_A$, which is defined as the ratio of the linear growth velocity of the RMI to the Alfv\'en speed at the interface. When the Alfv\'en number is less than unity, the Lorentz force acting on the fluid mitigates the unstable motion of the RMI significantly, and the interface oscillates stably in this limit. If $R_A \gtrsim 1$, on the other hand, the surface modulation increases due to the growth of the RMI. The maximum strength of the magnetic field is enhanced up to by a factor of $R_A$. This critical feature is universal and independent of the initial Mach number of the incident shock, the Atwood number, corrugation amplitude, and even the direction of the initial magnetic field., Comment: 11 pages, 8 figures, 1 table, accepted for publication in ApJ

We investigate the dynamics of a dilute suspension of small, heavy particles superposed on a reservoir of still, pure fluid. The study is performed by means of numerical simulations of the Saffman model for a dilute particle suspension (Saffman, J. Fluid Mech., vol. 13, issue 1, 1962, pp. 120–128). In the presence of gravity forces, the interface between the two phases is unstable and evolves in a turbulent mixing layer which broadens in time. In the case of negligible particle inertia, the particle-laden phase behaves as a denser fluid, and the dynamics of the system recovers to that of the incompressible Rayleigh–Taylor set-up. Conversely, particles with large inertia affect the evolution of turbulent flow, delaying the development of turbulent mixing and breaking the up–down symmetry within the mixing layer. The inertial dynamics also leads to particle clustering, characterised by regions with higher particle density than the initial uniform density, and by the increase of the local Atwood number.