Multi-fluid Model Research Articles

Comprehensive Comparison of Two Global Multi‐Species MHD Models of Mars

AbstractUnderstanding the interaction between Mars and the solar wind is crucial for comprehending the atmospheric evolution and climate change on Mars. To gain a comprehensive understanding of the Martian plasma environment, global numerical simulations are essential in addition to spacecraft observations. However, there are still discrepancies among different simulation models. This study investigates how these discrepancies stem from the considered physical processes and numerical implementations. We compare two global multispecies MHD models: the “Sun model” based on the BATS‐R‐US code and the “Sakata model” based on a newly developed multifluid model MAESTRO. By employing the same typical upstream conditions and the same neutral atmosphere for current Mars, along with similar numerical implementations such as inner boundary conditions, we obtain simulation results that exhibit unprecedented agreement between the two models. The dayside results are nearly identical, especially along the subsolar line, indicating the robustness of MHD models to predict dayside interaction under given upstream conditions and ionosphere assumptions. The escape rates of planetary ions are also in good agreement. However, discrepancies remain in the terminator and nightside regions. Detailed numerical implementations, including inner boundary conditions, magnetic field divergence control methods, and radial resolutions, are shown to influence certain aspects of the results greatly, such as magnetotail configuration and ion diffusion.

Speed of Sound Measurements of R-1130(E) and an Azeotropic Blend of R-1336mzz(Z)/1130(E)

Sound speed data measured using a dual-path pulse-echo instrument are reported for pure trans-1,2-dichloroethene (R-1130(E)) and an azeotropic blend of cis-1,1,1,4,4,4-hexafluorobutene (R-1336mzz(Z)) and R-1130(E) with a composition of 74.8 mass % R-1336mzz(Z) with the balance being R-1130(E). The azeotropic blend of R-1336mzz(Z)/1130(E) is classified as R-514A in ANSI/ASHRAE standard 34. Liquid phase speed of sound data are reported from just above the saturation pressure of pure R-1130(E) or the bubble point pressure of R-514A to a maximum pressure of 26.7 MPa. The relative combined expanded uncertainty in the speed of sound varies from 0.032 % to 0.148 % with the greatest deviations occurring at the lowest sound speeds. At present, no reference Helmholtz-energy-explicit equation of state (EOS) is available for R-1130(E). Therefore, the reported data for pure R-1130(E) are compared to an extended corresponding states (ECS) model. Deviations between the pure R-1130(E) sound speed data and the ECS model were found to be consistently negative ranging between − 4.1 % and − 3.5 %. The R-514A data are compared to a multifluid model inclusive of the established reference Helmholtz-energy-explicit EOS for R-1336mzz(Z) and ECS model for R-1130(E) with estimated binary interaction parameters. Deviations between the experimental speed of sound data and the multifluid model were also found to be consistently negative. However, deviations from the multifluid model were found to be as great as − 17.1 %. The large deviations from the ECS model and multifluid model underscore the need for a robust Helmholtz-energy-explicit EOS for R-1130(E).

Exploring the dynamics of the heavy magnetized dusty plasma in laboratory experiments and solar wind interaction with lunar terminator: Theoretical predictions into the role of polarization force

This study is motivated by the lack of research that connects the dynamics of space dusty plasma (DP) with the existing experimental findings and the role of the magnetic field in the case of massive DP. For that purpose, we presented a theoretical interpretation of the dynamics of strongly (experimental) and weakly (space) magnetized DP, including the influence of the polarization force (PF). We used the multifluid model to describe the dynamics of dust particles while the hot plasma of electrons and ions is described by the Boltzmann distribution. We derived the dispersion relation to investigate the behavior of the compressive dust-acoustic waves (DAWs). To get a full picture of the mechanism of dust particles, we used the reductive perturbation technique to obtain the periodic solution for the Zakharov–Kuznetsov equation (ZK), which is coincidental with the observed wave profiles. In the case of the experimental application, we observed that the non-propagating instability starts at a small value of the polarization parameter (R), which is 0.02. Therefore, for values of R less than 0.02, the linear analysis revealed that increasing the value of the polarization parameter is not significant in distinguishing the growth rates. Moreover, we noted that both R and the applied magnetic field enhance the strength of the wave electric field. Interestingly, calculating the value of the electric field required to levitate the dust particles that are subject to a high magnetic field agrees with our theoretical findings. The current model has also been applied to DP observed in the lunar terminator. Our results reveal no role for the PF in the lunar terminator. The analysis conducted using the New Hampshire Dispersion Relation Solver (NHDS) confirms the dominance of electrostatic modes in response to the solar wind interaction with the lunar terminator. Moreover, at certain values of plasma parameters such as the temperature of solar wind electrons and ions and the density of dust particles and solar wind electrons, there is a cutoff in the fluid dispersion curve corresponding to certain values of the normalized wavenumber. Such electrostatic profiles could contribute to the observed glow in the horizontal direction of the lunar terminator.

The Asymmetrical Distribution of a Dominant Motional Electric Field within the Martian Magnetosheath

Attributed to the lack of an Earth-like global intrinsic dipole magnetic field on Mars, the induced electromagnetic field environment plays a crucial role in the evolution of its atmosphere. The dominant motional electric field (EM) induced by the bulk motion of the magnetic field within the Martian magnetosheath serves to accelerate ions toward escape velocity, thereby forming a plume escape channel. However, the distribution morphology of EM itself has received limited attention in previous research. In this study, by taking advantage of the multi-fluid Hall-MHD model cooperating with the Martian crustal field model, we focus on elucidating the physical mechanisms underlying the asymmetrical distribution of EM and examining the influence of the crustal field on this asymmetry. The results obtained from the simulation conducted in the absence of the crustal field indicate that the EM is more intense within the −ZMSE magnetosheath, where EM is directed toward Mars, primarily due to its corresponding higher velocity and a stronger magnetic field at lower solar zenith angles. The Martian crustal field has the ability to enhance the local EM around the inner boundary of the magnetosheath by amplifying both the magnetic field and its associated velocity. Accordingly, these findings provide valuable insights into the asymmetric nature of EM within the Martian magnetosheath under typical quiet-time solar wind conditions.

Fission and fusion of heavy nuclei induced by the passage of a radiation-mediated shock in BNS mergers

ABSTRACT We compute the structure of a Newtonian, multi-ion radiation-mediated shock (RMS) for different compositions anticipated in various stellar explosions. We use a multifluid RMS model that incorporates electrostatic coupling between the different plasma constituents as well as Coulomb friction in a self-consistent manner, and approximates the effect of pair creation and the presence of free neutrons in the shock upstream on the shock structure. We find that under certain conditions a significant velocity separation is developed between different ions in the shock downstream and demonstrate that in fast enough shocks ion–ion collisions may trigger fusion and fission events at a relatively high rate. Our analysis ignores anomalous coupling through plasma microturbulence, which might reduce the velocity spread downstream below the activation energy for nuclear reactions. A rough estimate of the scale separation in RMS suggests that for shocks propagating in binary neutron star (BNS) merger ejecta, the anomalous coupling length may exceed the radiation length, allowing a considerable composition change behind the shock via inelastic collisions of $\alpha$ particles with heavy elements at shock velocities $\beta _\mathrm{ u}\gtrsim 0.25$. A sufficient abundance of free neutrons in the shock upstream, as expected during the first second after the merger, is also expected to alter the ejecta composition through neutron capture downstream. The resultant change in the composition profile may affect the properties of the early kilonova emission. The generation of microturbulence due to velocity separation can also give rise to particle acceleration that might alter the breakout signal in supernovae and other systems.

Modeling the plasma composition of 67P/C-G at different heliocentric distances

The Rosetta spacecraft accompanied the comet 67P/C-G for nearly 2 years, collecting valuable data on the neutral and ion composition of the coma. The Rosetta Plasma Consortium (RPC) provided continuous measurements of the in situ plasma density while ROSINA-COPS monitored the neutral composition. In this work, we aim to estimate the composition of the cometary ionosphere at different heliocentric distances of the comet. Läuter et al. (2020) derived the temporal evolution of the volatile sublimation rates for 50 separated time intervals on the orbit of 67P/C-G using the COPS and DFMS data. We use these sublimation rates as inputs in a multifluid chemical-hydrodynamical model for 36 of the time intervals for heliocentric distances <3 au. We compare the total ion densities obtained from our models with the local plasma density measured by the RPC instruments. We find that at the location of the spacecraft, our modeled ion densities match with the in situ measured plasma density within factors of 1−3 for many of the time intervals. We obtain the cometocentric distance variation of the ions H2O+ and H3O+ and the ion groups created respectively by the ionization and protonation of neutral species. We see that H3O+ is dominant at the spacecraft location for nearly all the time intervals while ions created due to protonation are dominant at low cometocentric distances for the intervals near perihelion. We also discuss our ion densities in the context of their detection by DFMS.

The Effect of the Interplanetary Magnetic Field Clock Angle and the Latitude Location of the Intense Crustal Magnetic Field on the Ion Escape at Mars: An MHD Simulation Study

AbstractIn this paper, using a three‐dimensional multifluid MHD model, we studied the effects of the interplanetary magnetic field (IMF) clock angle and the latitude position of the intense crustal magnetic field (ICMF) on the escape of ions O+, , and at Mars. The main results are as follows: (a) The IMF clock angle affects the ion escape at Mars. When the ICMF is on the dayside, the ion escape rate reaches a maximum at the IMF clock angles close to 60°–90° and a minimum at the IMF clock angles close to 120°–150°, because the ICMF can change the topology of the magnetic field and affect the interaction between the solar wind and Mars. The difference between the maximum and minimum ion escape rates due to the IMF clock angle can reach over 50%. (b) Compared with the −ESW hemisphere, the escape flux of and in the +ESW hemisphere is more significant. However, O+ generally has a larger escape flux in the −ESW hemisphere. The different results in the ±ESW hemispheres might be due to the larger distribution of the hot oxygen corona, which changes the flow pattern of O+. (c) The latitude location of the ICMF can also affect the ion escape. When the ICMF is on the dayside, as the subsolar point varies from 25°S to 25°N, that is, the intense crustal magnetic field position keeps shifting southward, the ion escape rate shows a gradual increase.

Shocks in the warm neutral medium

Context. Atomic and molecular line emissions from shocks may provide valuable information on the injection of mechanical energy into the interstellar medium (ISM), the generation of turbulence, and the processes of phase transition between the warm neutral medium (WNM) and the cold neutral medium (CNM). Aims. In this series of papers, we investigate the properties of shocks propagating in the WNM. Our objective is to identify the tracers of these shocks, use them to interpret ancillary observations of the local diffuse matter, and provide predictions for future observations. Methods. Shocks propagating in the WNM are studied using the Paris-Durham shock code, a multi-fluid model built to follow the thermodynamical and chemical structures of shock waves at steady-state in a plane-parallel geometry. The code, designed to take into account the impact of an external radiation field, is updated to treat self-irradiated shocks at intermediate (30 &lt; VS &lt; 100 km s−1) and high velocity (VS ⩾ 100 km s−1), which emit ultraviolet (UV), extreme-ultraviolet (EUV), and X-ray photons. The couplings between the photons generated by the shock, the radiative precursor, and the shock structure are computed self-consistently using an exact radiative-transfer algorithm for line emission. The resulting code is explored over a wide range of parameters (0.1 ⩽ nH ⩽ 2 cm−3, 10 ⩽ VS ⩽ 500 km s−1, and 0.1 ⩽ B ⩽ 10 μG), which covers the typical conditions of the WNM in the solar neighborhood. Results. The explored physical conditions lead to the existence of a diversity of stationary magnetohydrodynamic solutions, including J-type, CJ-type, and C-type shocks. These shocks are found to naturally induce phase transition between the WNM and the CNM, provided that the postshock thermal pressure is higher than the maximum pressure of the WNM and that the maximum density allowed by magnetic compression is greater than the minimum density of the CNM. The input flux of mechanical energy is primarily reprocessed into line emissions from the X-ray to the submillimeter domain. Intermediate- and high-velocity shocks are found to generate a UV radiation field that scales as VS3 for VS &lt; 100 km s−1 and as VS2 at higher velocities, and an X-ray radiation field that scales as VS3 for VS ⩾ 100 km s−1. Both radiation fields may extend over large distances in the preshock depending on the density of the surrounding medium and the hardness of the X-ray field, which is solely driven by the shock velocity. Conclusions. This first paper presents the thermochemical trajectories of shocks in the WNM and their associated spectra. It corresponds to a new milestone in the development of the Paris-Durham shock code and a stepping stone for the analysis of observations that will be carried out in forthcoming works.

Efficient Approximation with Space Filling Quadtrees: Application to Phase Equilibria in Binary Mixtures.

A relatively succinct set of property calculations can be used to construct efficient (in memory and speed) numerical approximations of that function in a rectangular domain. Through the use of adaptive subdivision with quadtrees and bi-Chebyshev expansions in each leaf, the function can be practically represented to the order of the noise in the function to be approximated. A further benefit is that evaluation of the approximation is noniterative and thus cannot fail to converge (a relatively common problem in thermophysical property libraries, especially for mixtures). Evaluation of the approximation function requires only a few bisection steps to identify the leaf of interest such that evaluation of the approximation data structure takes less than a microsecond. The technique is demonstrated by application to the vapor-liquid-equilibria evaluated with two different models (COSMO-SAC activity coefficient model and multifluid model). For the more expensive COSMO-SAC case, the approximation function is more than 2000 times faster to evaluate, and deviations in pressure are less than a part in 108 which is practically equal to the iteration convergence criterion.

Numerical Solutions of Van Der Pol-Mathieu Type Nonlinear Ordinary Differential Equation in Complex Plasma

The description dust plasma behavior via a multi-fluid model, Where it represents that Boltzmann distributed electrons and ions, the dust momentum and Poisson's equations, in addition to the continuity equation that has a source term for the dust grains. The Runge-Kutta technique of fourth order was then used to numerically solve the equation. The solution shows a variety of behaviors under wide range of parameters changes. In particular, the solution of the equation shows a chaotic behavior at α= 1.0. In this study, the chaotic behavior in the plasma complex is graphically studied and discussed for some certain parameters. The aim of this study can be helped the researchers to investigate several nonlinear oscillations in different plasma and fluid mechanics models.

Eulerian-Eulerian-VOF multifluid modelling of liquid–gas reacting flow for hydrogen generation in an alkaline water electrolyser

Alkaline water electrolysis is a promising technology for hydrogen production. However, its efficiency drops considerably at high current densities due to the mass transfer limitation and the increase in electrical resistivity arising from the complexity of the liquid–gas reacting flow behaviour within the electrolyser cell. In this work, a computational fluid dynamics (CFD) model is developed to describe the liquid–gas reactive flow behaviour. The model integrates the Eulerian-Eulerian two-fluid model and the multifluid Volume of Fluid (VOF) model, allowing the mathematical model to capture the electrochemical reaction effect on hydrogen gas formation and bulk flow bubble behaviour. The model is validated against prior experimental results. The simulation results suggest that, at higher current densities, the electrical performances and the mass transfer rates are highly influenced by the formation of gas bubbles, which may block the active sites for the electrochemical reaction to occur. Quantitatively, at 4000 A/m2, the mass transfer rate is reduced by 50% at regions above the cathode compared to electrode region, while electrical conductivity near the flow channel wall, drops by 17% compared to the bulk liquid electrical conductivity. The predicted electrical conductivity is comparable to the Bruggemann correlation with an average relative error of less than 2%, confirming the model’s validity in predicting the reacting flow behaviour and performance of the electrolyser. The numerical model offers a cost-effective tool for insightful understanding and refining the design and operation of hydrogen generation systems.

CFD study of the residence time distribution of shaft-injected hydrogen in a blast furnace

Hydrogen, as a carbon-free reducing agent, can be adopted in the blast furnace (BF) ironmaking process to replace carbon-bearing materials towards green steelmaking partially. Theoretically, hydrogen can be introduced into the BF via shaft injection, and its residence time distribution (RTD) has not been studied or reported in detail in open literature. In this study, a multi-fluid BF model is developed further to investigate the RTD of hydrogen when injected into the BF through shaft inlets. It is observed that the RTD of shaft-injected hydrogen exhibits some features of piston-type flow but varies at different monitoring points. For the case studied, increasing the hydrogen injection rate decreases the average residence time of hydrogen from 12.2 s to 10.1 s. Similarly, increasing the hydrogen injection temperature slightly reduces the average residence time from 10.4 s to 9.5 s. These results indicate that the hydrogen flow rate has a relatively more significant effect on the RTD than the injection temperature. Moreover, it is found the utilisation efficiency of shaft-injected hydrogen is influenced by both the limited residence time and conditions on the trajectories followed by the fluid particles. The model presented in this study provides an alternative and cost-effective method to enhance our understanding of the hydrogen RTD inside an ironmaking BF.

Simulating the Escaping Atmosphere of GJ 436 b with Two-fluid Magnetohydrodynamic Models

Observations of transmission spectra reveal that hot Jupiters and Neptunes are likely to possess escaping atmospheres driven by stellar radiation. Numerous models predict that magnetic fields may exert significant influences on the atmospheres of hot planets. Generally, the escaping atmospheres are not entirely ionized, and magnetic fields only directly affect the escape of ionized components within them. Considering the chemical reactions between ionized components and neutral atoms, as well as collision processes, magnetic fields indirectly impact the escape of neutral atoms, thereby influencing the detection signals of planetary atmospheres in transmission spectra. In order to simulate this process, we developed a magnetohydrodynamic multi-fluid model based on MHD code PLUTO. As an initial exploration, we investigated the impact of magnetic fields on the decoupling of H+ and H in the escaping atmosphere of the hot Neptune GJ436b. Due to the strong resonant interactions between H and H+, the coupling between them is tight even if the magnetic field is strong. Of course, alternatively, our work also suggests that merging H and H+ into a single flow can be a reasonable assumption in MHD simulations of escaping atmospheres. However, our simulation results indicate that under the influence of magnetic fields, there are noticeable regional differences in the decoupling of H+ and H. With the increase of magnetic field strength, the degree of decoupling also increases. For heavier particles such as O, the decoupling between O and H+ is more pronounced. Our findings provide important insights for future studies on the decoupling processes of heavy atoms in the escaping atmospheres of hot Jupiters and hot Neptunes under the influence of magnetic fields.

Impact of rotor–stator axial spacing on the gas–liquid–solid flow characteristics of a multiphase rotodynamic pump based on the Euler multi-fluid model

Multiphase rotodynamic pumps are used by the oil and gas industry to transport mixed media in pipelines. The characteristics of gas–liquid–solid flow in such pumps are significantly affected by the rotor–stator axial spacing so that further investigation is required. Based on the Euler multi-fluid model, the Computational Fluid Dynamics simulations were conducted in this study on the gas–liquid–solid multiphase rotodynamic pump at the rotor–stator axial spacings of 8, 10, 12, 14, and 16 mm, respectively. Changes in the pump's characteristics of external, multiphase flow, and pressure fluctuation were systematically analyzed by using ANSYS-CFX. The results showed that, an overall decreasing trend for the efficiency and head of the multiphase rotodynamic pump were demonstrated with increases in the rotor–stator axial spacing from 8 to 16 mm, which can be categorized into plummets I, moderation, and plummets II. As the rotor–stator axial spacing increased, the pressurization decreased from the inlet to outlet of guide vane while the aggregation of gas and solid increased. Additionally, vorticity increased and vortex structure was found to be more significant. As a result, the overall performance of the multiphase rotodynamic pump deteriorated. The pressure fluctuation in the multiphase rotodynamic pump was determined by the rotor–stator interaction and multiphase flow under gas–liquid–solid flow conditions, resulting in a non-positive correlation between the pressure fluctuation and the pump's external and internal flow characteristics. The location of maximum pressure fluctuation in the multiphase rotodynamic pump was changed from the impeller outlet to the guide vane inlet with increases in rotor–stator axial spacing.

Envelope solitary waves in two-negative ions with stationary dust grains

Using a multi-fluid model, we look at how modulated electrostatic dust-ion-acoustic wave packets move nonlinearly through a plasma made up of a three-ion fluid with Maxwellian electrons and stationary dust grains. A nonlinear Schrödinger (NLS) equation describes the electric potential envelope wave packet. The analysis reveals the existence of different types of localized modes, namely bright, dark, and grey solitons. We numerically analyse the coefficients of the NLS equation to identify stable or unstable regions for wave packet propagation. It is found that higher relative density ratios increase the group velocity of the wave packets. Stable pulses can become unstable when plasma parameters exceed certain relative density ratio values. Stable pulses can exist within a crucial window of the relative dust density ratio. Controlling the dust grain density ratio outside the zone can cause unstable wave packets or bright envelope solitons to propagate.

A multifluid model with chemically reacting components — Construction of weak solutions

We investigate the existence of weak solutions to a multi-component system, consisting of compressible chemically reacting components, coupled with the compressible Stokes equation for the velocity. Specifically, we consider the case of irreversible chemical reactions and assume a nonlinear relation between the pressure and the particular densities. These assumptions cause the additional difficulties in the mathematical analysis, due to the possible presence of vacuum.It is shown that there exists a global weak solution, satisfying the L∞ bounds for all the components. We obtain strong compactness of the sequence of densities in Lp spaces, under the assumption that all components are strictly positive. The applied method captures the properties of models of high generality, which admit an arbitrary number of components. Furthermore, the framework that we develop can handle models that contain both diffusing and non-diffusing elements.

One-dimensional, multi-fluid model of the plasma-wall transition. II. Negative ions

The plasma-wall transition is investigated by a one-dimensional steady-state multifluid model, which was presented in detail in Part I [T. Gyergyek et al., AIP Adv. 14, 045201 (2024)]. In this work, the plasma-wall transition is analyzed for the case where the plasma consists of singly charged positive ions, electrons, and singly charged negative ions. When the temperature and initial density of the negative ions are varied, a transition between two types of solutions of the model is observed. We call them the low and high solution, with respect to the absolute value of the potential drop. When the density and temperature of the negative ions are above a critical value, the low solution is observed. As the mass of the positive ions increases, these critical values also increase, but only until the ion mass is below about 1000 electron masses. With larger ion masses, the critical density of the negative ions and the temperature no longer change. In the low solution, the potential drop in front of the sheath is determined by the negative ions and is smaller in absolute terms than in the case of the high solution, where the potential drop in front of the sheath is determined by the electrons. If the problem is analyzed on the pre-sheath scale, the transition between the low and high solution is very sharp. However, when the neutrality condition is replaced by the Poisson equation, this transition becomes blurred and the solutions of the model equations exhibit oscillations. The role of the smallness parameter is highlighted. It is shown how the initial electric field is determined. Deviation of the negative ion density profile from the Boltzmann relation is discussed.

Hydrodynamic simulation-informed compartment modelling of an annular centrifugal contactor

Abstract The geometrical and hydraulic parameters have a great impact on the mass transfer characteristics of annular centrifugal contactors. The objective of this study is to evaluate the mass transfer performance of a single annular centrifugal contactor by applying the computational fluid dynamics informed compartment modelling approach. In the study, a steady state compartment model of an annular centrifugal contactor is developed in gProms general purpose process modeller by using the hydrodynamic parameters obtained from computational fluid dynamics simulations performed in OpenFOAM with the GEneralised Multifluid Modelling Approach (GEMMA). The mass transfer rate predicted by the developed compartment model is compared with data obtained from uranium extraction with Tributyl Phosphate experiments performed with a laboratory-scale annular centrifugal contactor. Uranium concentrations in the organic and aqueous outlets and the mass transfer rate evaluated by the developed compartmented contactor model are in good agreement with the experimental data. The results reveal that the use of a hydrodynamic-informed compartment modelling approach raises the possibility of designing full-scale annular centrifugal contactors without the need for detailed computational fluid dynamics simulations and the prediction of mass transfer performance of the whole system from laboratory scale experiments.

A unified two-scale gas–liquid multi-fluid model with capillarity and interface regularization through a mass transfer between scales

In this contribution, we derive a gas–liquid two-scale multi-fluid model with capillarity effects to enable a novel interface regularization approach for multi-fluid models. As this unified modelling is capable of switching from the interface representation of a separated to a disperse regime it lays a new way of modelling regime transitions as it occurs in atomization processes. Above a preset length threshold at large scale, a multi-fluid diffuse interface model resolves the dynamics of the interface while, at small-scale, a set of geometric variables is used to characterize the interface geometry. These variables result from a reduced-order modelling of the small-scale kinetic equation that describes a collection of liquid inclusions. The flow model can be viewed as a two-phase two-scale mixture, and the equations of motion are obtained thanks to the Hamilton’s Stationary Action Principle, which requires to specify the kinetic and potential energies at play. We particularly focus on modelling the effects of capillarity on the mixture’s energy by including dependencies on additional variables accounting for the interface’s geometry at both scales. The regularization of the large-scale interface is then introduced as a local and dissipative process. The local curvature is limited via a relaxation towards a modified Laplace equilibrium such that an inter-scale mass transfer is triggered when the mean curvature is too high. We propose an original numerical method and assess the properties and potential of the modelling strategy on the relevant test-case of a two-dimensional liquid column in a compressible gas flow.

Modeling of tungsten impurity transport and distribution in EAST based on multi-fluid and kinetic Monte Carlo simulations

In recent years, the materials of plasma facing components, such as divertor target plates, domes, and outer walls of tokamaks, such as ASDEX Upgrade, WEST, JET, EAST, and ITER, have been changed from carbon to tungsten because of its lower erosion and tritium retention rates. Impurities are produced by interactions between the plasma and the first wall. This study provides an investigation to simulate the transport and distribution of tungsten impurities in the edge plasma on EAST. The 2D multi-fluid edge plasma transport code SOLPS-ITER and 2D kinetic Monte Carlo impurity transport code DIVIMP were used in the simulations. The multi-fluid model in SOLPS-ITER and the kinetic Monte Carlo model in DIVIMP were employed to treat tungsten impurity ions. The 2D density contour distributions in the computational region and the 1D density radial profiles at the inner and outer midplanes of tungsten impurity particles with ionization states (W0–W+74) and the total tungsten particles with all charge states were obtained. With the heating power 1.5 MW and the line-averaged plasma density 2 × 1019 m−3, the results from SOLPS-ITER and DIVIMP show that the maximum density of tungsten ion with single ionization state is about 1014 m−3 and the total density of tungsten impurities with all charge states is about 1015 m−3 at the core boundary. To the best of our knowledge, the simulation results from SOLPS-ITER and DIVIMP are compared for the first time to benchmark SOLPS-ITER with the multi-fluid mode and DIVIMP with the kinetic model for tungsten impurity transport. The density distributions of tungsten impurities with different ionization states from SOLPS-ITER and DIVIMP are highly similar, and good agreement can be found under similar conditions involved in the calculation. From the comparison benchmark between SOLPS-ITER and DIVIMP for tungsten impurity transport, it can be concluded that the impurity transport approximation used by DIVIMP is good.