One-fluid Model Research Articles

Capture of the Morphology Transfer Process in a High-Momentum Centrally Aerated Bubble Column with a Hybrid Multifield Two-Fluid Model

The role of pool scrubbing in attenuating radioactivity release after severe accidents has been explored extensively. It is known that scrubbing efficiency is largely determined by the hydrodynamic phenomenology in pools, which is still insufficiently understood. Aerosol gas forms large globules at the nozzle exit, which subsequently break up into a swarm of stable bubbles, where the change of bubble size can reach more than two orders depending on the injection rate. Furthermore, with the increase of flow rates, the injection regime changes from globule to jet characterized by a continuous gas structure. The flow field in the pool can be divided into two zones, injection and rise (swarm), according to the gas-liquid interface morphology. In different zones, scrubbing is governed by different mechanisms such as inertial impact, diffusion, and gravity, whereby bubble rise velocity is one major influential parameter. So far, numerical analysis of pool scrubbing is routinely based on system codes, which rely on empirical correlations for the determination of hydrodynamic parameters as well as scrubbing zones. More recently, owing to the increasing availability of computational resources, knowledge is improved through three-dimensional computational fluid dynamics simulations. Nevertheless, morphology and regime change still present a challenge for both two-fluid and interface-tracking models. Because of the limitation of closures, the conventional two-fluid model (TFM) is generally effective for bubble size smaller than cell size while interface-tracking (capturing) methods demand dozens of cells per bubble size. Combining the two kinds of approaches into one simulation is not straightforward. The present work aims to present a hybrid multifield TFM with extensions for capturing the transfer between different morphologies and for considering the effect of mesh resolution in momentum exchange. The developments are validated by simulating the complex hydrodynamic process in a pool-scrubbing column, which operates in the globule regime with an injection Weber number between 103 and 105. By comparison with experimental data, the results are shown to be promising, which provides a versatile framework for investigation of particle scrubbing in the future. The most attractive feature of the model is that compared to one-fluid interface-tracking models, it reliably predicts the bubble rise velocity. Furthermore, it is able to capture the lateral gas distribution without the need of applying a population balance model since most large bubbles are resolved.

Regularization errors introduced by the one-fluid formulation in the solution of two-phase elliptic problems

This manuscript discusses the structure of the errors in the solution of elliptic problems introduced by the regularization of the fluid properties discontinuity in a small region of finite size. By using a multiscale approach, the problem of the error calculation is splitted into an outer problem, where the regularization region is replaced by a sharp interface, and an inner local one dimensional problem that eventually imposes effective jump conditions across the interface for the outer problem. Except in some particular cases, the use of regularization techniques introduces first order errors in the solution imposing an error flux jump that is proportional to the tangential Laplacian of the averaged solution and an error jump that is proportional to the normal flux, both multiplied by a prefactor that depends on the averaging rule used. In general, the optimal averaging procedure is shown to depend on the structure of the problem at hand. The errors introduced by standard arithmetic and harmonic averages are obtained for various analytical and numerical examples which are used to discuss the nature of the errors introduced and the importance of first order errors in the solution. The influence of the ratio between the regularization thickness and the grid size is also investigated in numerical implementations of the one-fluid model.

A Compressible Formulation of the One-Fluid Model for Two-Phase Flows

In this paper, we introduce a compressible formulation for dealing with 2D/3D compressible interfacial flows. It integrates a monolithic solver to achieve robust velocity–pressure coupling, ensuring precision and stability across diverse fluid flow conditions, including incompressible and compressible single-phase and two-phase flows. Validation of the model is conducted through various test scenarios, including Sod’s shock tube problem, isothermal viscous two-phase flows without capillary effects, and the impact of drops on viscous liquid films. The results highlight the ability of the scheme to handle compressible flow situations with capillary effects, which are important in computational fluid dynamics (CFD).

Effects of alpha-ion stopping on ignition and ignition criteria in inertial confinement fusion experiments

With the advent of ignited plasmas at the National Ignition Facility (NIF), alpha physics has become a driving factor in theoretical understanding and experimental behavior. In this communication, we explore aspects of direct alpha-ion heating through comparison of the consequences from the one-fluid and two-fluid models in the hydrodynamic approach. We show that the case with all alpha energy deposited in electrons raises the ignition criteria by ∼4 keV or ∼0.2 g/cm2 in the hotspot relative to the case with all alpha energy deposited in ions. In the case of the recently ignited NIF implosion, 30% of the 3.5 MeV α energy is deposited into the DT fuel ions, for which there is negligible difference between the one-fluid and two-fluid ignition criteria. However, changes in the ion stopping fraction through profile effects and alternate stopping power models could lead to ignition curve shifts of ∼1 keV.

Obliquely propagating nonlinear magnetosonic waves in non-Maxwellian plasmas

In this paper, propagation characteristics of obliquely propagating nonlinear magnetosonic waves in hot nonthermal plasmas have been studied. The expressions of modified temperatures have been derived for non-Maxwellian Q-nonextensive and (r, q) distributions and then incorporated into the one-fluid magnetohydrodynamic model. By employing the reductive perturbation technique, we derived the linear dispersion relation (LDR) and nonlinear Kadomstev–Petvashvilli (KP) equation for slow and fast magnetosonic wave modes in two dimensions. We then investigated the LDR and nonlinear propagation of KP solitons for both the slow and fast mode magnetosonic waves and found that propagation characteristics are significantly altered by considering the effect of modified temperature. The results presented here would depict a realistic picture of the propagation of nonlinear magnetosonic waves in non-Maxwellian plasmas.

Investigation on the cavitation and atomization characteristics of multiphase fluids in underwater explosion near a free surface

The characteristics of cavitation and atomization induced by underwater explosion near a free surface have been investigated by the multiphase fluid model based on two-fluid phase transition. This numerical method can provide the phase transition between liquid and its vapor phases during shock wave and rarefaction wave propagation at any time in underwater explosion. The detailed density, pressure, vapor, and liquid phases of volume fraction contours in cavitation and atomization zones can be obtained. The phase transition model was first used to quantitatively research the phenomenon of vapor liquefaction after shock wave propagation in initial water containing different trace amounts of vapor. Then the contribution of phase transition to the formation of cavitation and atomization in underwater explosion was investigated through a shock tube test and two typical underwater explosion cases. It is found that the phase transition effect between the vapor and liquid phases contributes more than 60% to the formation of the cavitation zone. Two charges under two different water surface conditions have been investigated by comparison with the case of a single charge. We can conclude that it is very necessary to introduce the phase transition model into the simulation of underwater explosion, which can provide details of the flow field in the cavitation and atomization zones that cannot be obtained by the one-fluid cavitation model.

Next-generation multifluid hydrodynamic model for nuclear collisions at sNN from a few GeV to a hundred GeV

We have developed a next-generation hybrid event-by-event three-fluid hydrodynamic model, suitable for simulations of heavy-ion collisions in the energy range from few up to tens of GeV per colliding $NN$ pair. At such energies the interpenetration time of the nuclei is of the same order as the lifetime of the system, however, this model treats the initial phase hydrodynamically. Thanks to that it is more sensitive to the equation of state than one-fluid models with initial states being parametrized or generated by transport approach. Hence, our model is well designed for simulations at collision energies, at which matter in the vicinity of the quantum chromodynamics critical endpoint is expected. The construction of the model is explained and basic observables like hadron spectra in rapidity and transverse momentum, as well as elliptic flow are calculated.

Investigation of liquid water heterogeneities in large area proton exchange membrane fuel cells using a Darcy two-phase flow model in a multiphysics code

Proper management of the liquid water and heat produced in proton exchange membrane (PEM) fuel cells remains crucial to increase both its performance and durability. In this study, a two-phase flow and multicomponent model, called two-fluid model, is developed in the commercial COMSOL Multiphysics® software to investigate the liquid water heterogeneities in large area PEM fuel cells, considering the real flow fields in the bipolar plate. A macroscopic pseudo-3D multi-layers approach has been chosen and generalized Darcy's relation is used both in the membrane-electrode assembly (MEA) and in the channel. The model considers two-phase flow and gas convection and diffusion coupled with electrochemistry and water transport through the membrane. The numerical results are compared to one-fluid model results and liquid water measurements obtained by neutron imaging for several operating conditions. Finally, according to the good agreement between the two-fluid and experimentation results, the numerical water distribution is examined in each component of the cell, exhibiting very heterogeneous water thickness over the cell surface.

Toward a universal description of multiphase turbulence phenomena based on the vorticity transport equation

Understanding the evolution of turbulence in multiphase flows remains a challenge due to the complex inter-phase interactions at different scales. This paper attempts to enlighten the multiphase turbulence phenomenon from a new perspective by exploiting the classical concept of vorticity and its role in the evolution of the turbulent energy cascade. We start with the vorticity transport equations for two different multiphase flow formulations, which are one-fluid and two-fluid models. By extending the decaying homogeneous isotropic turbulence (HIT) problem to the multiphase flow context, we performed two highly resolved simulations of HIT in the presence of (i) a thin interface layer and (ii) homogeneously distributed solid particle. These two configurations allow for the investigation of interfacial turbulence and particulate turbulence, respectively. In addition to the analysis of the global flow characteristic in both cases, we evaluate the spectral contribution of each production/dissipation mechanism in the vorticity transport equation to the distribution of vortical energy (enstrophy) across the scales. We base our discussion on the role of the main inter-phase interaction mechanisms in vorticity transport (i.e., the surface tension for interfacial turbulence and drag force for particulate turbulence) and unveil a similar contribution from these mechanisms to the multiphase turbulence cascade. The results also explain the deviation of kinetic energy and enstrophy spectra of multiphase HIT problems from their single-phase similitudes, confirming the validity of this approach for establishing a universal description of multiphase turbulence.

Behavior of ions from medium-density plasma in electric field created by plate–grid–plate geometry

The behavior of the ions from a medium-density plasma in an electric field created by the plate–grid–plate geometry was simulated with a two-dimensional one-fluid model in which electrons are assumed to be in thermal equilibrium, and the accuracy of the model was verified by comparing with other research results. The results show that the wire mesh parameters of the grid, including the wire mesh diameter and the spacing between the two wires of the grid, have an important influence on the ion extraction time and the ion collection ratio of the cathode plate. The blocking rate of the grid obtained by the theoretical simulation is almost equal to the geometrical blocking rate, and it is minimally affected by the initial ion density. These results can provide guidance for the optimization of wire mesh parameters of the grid, especially for the ion extraction and collection from a pulsed plasma.

Low-frequency zonal flow eigen-structures in tokamak plasmas

The nonlocal eigenmode analysis of low-frequency zonal flows (ZFs) in toroidally rotating tokamak plasmas is performed in the framework of the reduced one-fluid ideal magnetohydrodynamic model. It is shown that for typical profiles of plasma parameters toroidal plasma rotation results in the global ZF formation on the periphery of plasma column. For some types of equilibria these ZFs are aperiodically unstable that leads to the excitation of the differential plasma rotation at the tokamak plasma edge.

A lattice Boltzmann formulation of the one-fluid model for multiphase flow

A multiphase lattice Boltzmann model is constructed to numerically solve the one-fluid flow equations for immiscible fluids. The method features one solver for the macroscopic pressure and momentum and another for a scalar field that captures and sharpens the interface. The surface tension is set a priori and independently of other parameters. The interface capillary tensor is embedded within the moments of the lattice Boltzmann equation so that its divergence is captured locally. The algorithm is simple and can compute flows with large density and viscosity ratios while maintaining distributed but narrow interfaces. The model is validated against analytical solutions and benchmark simulations.

On the relations between large-scale models of superfluid helium-4

Superfluid helium-4 is characterized by extremely small values of kinematic viscosity, and its thermal conductivity can be huge, orders of magnitude larger than that of water or air. Additionally, quantum vortices may exist within the fluid. Therefore, its behavior cannot be explained by using the classical tools of Newtonian fluid mechanics, and, over the years, a few alternative models have been proposed. In order to highlight similarities and differences between these models, we recast them within a unifying framework, the general equation for non-equilibrium reversible-irreversible coupling (GENERIC). We begin by comparing the original two-fluid model, developed by Tisza and Landau, with the Hall–Vinen–Bekarevich–Khalatnikov model, both prescribing two types of fluid motion and two fluid densities, at flow scales appreciably larger than the typical distance between quantum vortices. We find from the geometrical structure of the models that only one fluid density plays the role of state variable, which should be taken into account when choosing an adequate expression for the free energy. We also recast within the GENERIC framework the one-fluid model of superfluid helium-4, where the inviscid component of two-fluid models is replaced by a caloric quantity, such as entropy. We find that the corresponding geometrical structures are analogous, with the roles of density and entropy swapped. In short, our work demonstrates that the studied models are compatible with each other, at least when focusing on the reversible parts of the models.

Numerical simulation of underwater explosion cavitation characteristics based on phase transition model in compressible multicomponent fluids

Underwater explosion cavitation has an important influence on the shock wave, explosion bubble, and structural deformation. The one-fluid model is usually used in underwater explosion cavitation. It is assumed that the cavitation is induced suddenly when the pressure is lower than the saturated pressure. The biggest deficiency of the model is that it is difficult to consider the temperature change in the cavitation domain. It is known that cavitation is sensitive to the temperature. In this paper, we study UNDEX cavitation characteristics based on the two-fluid model proposed by Chiapolino et al. (2017), which holds that the cavitation phenomenon is the result of the phase transition between the gas and liquid phases. This model is composed of the 4-equation model with phase transition relaxation, which is solved by a simple fractional step. In this article, we briefly introduce the compressible multiphase fluids model and successfully extent it to the engineering research field of underwater explosion cavitation. Through the quantitative analysis of the vapor phase content, it is suggested that the initial mass fraction of vapor phase in water should be set to less than 10−7. Meanwhile, it can be observed that the bulk cavitation near the free surface can evolve into a vortex ring until it collapses. Numerical results show that the collapsed pressure cannot be ignored relative to the shock wave in the bulk and local cavitation. Numerical results of this paper display that the phase transition model shows a great prospect of engineering application in underwater explosion cavitation.

A generalized high-order momentum preserving (HOMP) method in the one-fluid model for incompressible two phase flows with high density ratio

Numerical methods for the simulation of two-phase flows based on the common one-fluid model suffer from important transfer of momentum between the two-phases when the density ratio becomes important, such as with common air and water. This problem has been addressed from various numerical frameworks. It principally arises from the hypothesis that the momentum equation can be simplified by subtracting the continuity equation to it. While this approach is correct in a continuous point of view, it however brings numerical errors at the discrete level, from both spatial and temporal points of view, errors that can highly deteriorate the fluids dynamic. Moreover, we have found this problem to be more and more present as the grid is refined. To correct this problem, we propose a High-Order Momentum Preserving (HOMP) method that is, additionally, independent on the interface representation (may it be level set, volume of fluid, etc.). Furthermore, HOMP can be easily implemented in an existing finite volume code. We show that this method permits to efficiently suppress dreadful momentum transfers at the interface on demonstrating examples. We also present how it enhances the quality of two-phase flows computation through the simulation of the dynamic of a breaking wave and the impact of a droplet in a liquid pool.

Study on the cavitation effects induced by the interaction between underwater blast and various boundaries

The load of cavitation collapse is one of the main input loads to the structure subjected to underwater explosion. The cavitation effects near different boundaries are of particular importance in understanding the load mechanisms and designing the protective structures. In present study, a numerical model that couples a Runge Kutta Discontinuous Galerkin method, a finite element method and an isentropic one-fluid cavitation model is developed to study the cavitation effects induced by underwater explosion near different boundaries. The boundaries of a rigid plate, a steel plate, a rubber coated plate and a foam coated plate are investigated in detail, after validating the coupled numerical model by a case of 1D cavitating flow in an open tube, an experiment of a water-backed plate subjected to water blast and an experiment of underwater explosion near a circular plate. The evolutions of the cavitation region, the pressure profile near the structure and the responses of the structure are comprehensively discussed. The results are beneficial for guiding the design of the protective structures.

Weakly compressible Navier-Stokes solver based on evolving pressure projection method for two-phase flow simulations

An evolving pressure projection method for numerical computations of the weakly compressible Navier-Stokes equations is proposed. Fully explicit time integration is achieved using an independent pressure evolution equation. To damp the acoustic wave in a weakly compressible fluid flow, we iteratively compute the pressure evolution equation coupled with a projection step. Due to the simplicity and locality of this iteration procedure, it does not increase the computational amount too much. The computation is performed on a staggered Cartesian grid. By introducing the phase field model for interface capturing, this solver can be directly applied to two-phase flow simulations using a one-fluid model. Exact mass conservation is ensured by a finite-volume formulation of the conservative phase field equation. Various benchmarking problems are simulated to validate accuracy. The stability of a violent two-phase flow with large density and viscosity ratio is demonstrated in a three-dimensional dam break simulation. Numerical results show that the proposed method for weakly compressible Navier-Stokes equations can prevent oscillations of pressure and velocity.

Implications of hydrodynamics on the design of pulsed sieve-plate extraction columns: A one-fluid multiphase CFD model using the volume of fluid method

Presented is a detailed assessment of dispersive mixing and turbulence characterisation of an industrially representative pulsed sieve-plate extraction column (PSEC) obtained using multiphase CFD modelling. The system consists of a 150 mm diameter column with two perforated plates dispersing a 30 vol% dodecane/tributyl phosphate mixture in 3 M nitric acid. Operational conditions were chosen to examine pseudo steady-state dispersion regime operation. Three-dimensional transient flow calculations were performed using large eddy simulation (LES), coupled with the volume of fluid method. This study finds that LES is effective at capturing the different scales of turbulence present within PSECs, and their operational influence. Explicit analysis of the hydrodynamics established that the sieve-plates drive dispersive mixing through their influence on the resulting turbulent flow and flow structures. Furthermore, the standard round-hole sieve-plate design is found to perform poorly at producing and distributing the types of flow and turbulence beneficial to droplet size reduction.

Macroscopic two-fluid effects in magnetorheological fluids.

We investigate macroscopic two-fluid effects in magnetorheological fluids generalizing a one-fluid model studied before. In the bulk of the paper we use a model in which the carrier fluid, with density ρ_{1}, moves with velocity v_{1}, while the magnetic component (density ρ_{2}) and, therefore, the magnetization and the magnetic-field-induced relaxing strain field move with velocity v_{2}. In the framework of macroscopic dynamics we find, in particular, reversible dynamic and dissipative cross-coupling terms between the magnetization and the velocity difference. Experiments to detect some of these cross-coupling terms are suggested. We also compare the results of the two-fluid model presented here with two-fluid models available for electrorheological fluids. In two appendices we discuss the simplifying assumptions made to arrive at the model used in this paper and we also outline how to detect potential deviations from this model.

Condensate formation and multiscale dynamics in two-dimensional active suspensions.

The collective effects of microswimmers in active suspensions result in active turbulence, a spatiotemporally chaotic dynamics at mesoscale, which is characterized by the presence of vortices and jets at scales much larger than the characteristic size of the individual active constituents. To describe this dynamics, Navier-Stokes-based one-fluid models driven by small-scale forces have been proposed. Here, we provide a justification of such models for the case of dense suspensions in two dimensions (2D). We subsequently carry out an in-depth numerical study of the properties of one-fluid models as a function of the active driving in view of possible transition scenarios from active turbulence to large-scale pattern, referred to as condensate, formation induced by the classical inverse energy cascade in Newtonian 2D turbulence. Using a one-fluid model it was recently shown [M. Linkmann et al., Phys. Rev. Lett 122, 214503 (2019)10.1103/PhysRevLett.122.214503] that two-dimensional active suspensions support two nonequilibrium steady states, one with a condensate and one without, which are separated by a subcritical transition. Here, we report further details on this transition such as hysteresis and discuss a low-dimensional model that describes the main features of the transition through nonlocal-in-scale coupling between the small-scale driving and the condensate.