Three-fluid Model Research Articles

Galactic outflows in different geometries

In the gravitational potential well of a galaxy, the behavior of outflows has been studied in different geometries i.e. constant flux tube, divergent and extreme divergent environments. First of all, we describe the hydrodynamic model by which we approach the outflows system. This model treats all the waves as fluids and applies fluid mechanics to them(cosmic rays, thermal plasma & Alfvén wave). Whereas outflows mean the gas regime above and below the center of the galactic disk, and we have taken it as a system where interaction between cosmic rays and plasma occurs. After discussing the hydrodynamic three-fluid model, we define three geometrical structures which can be acquired by outflows and relate these structures with thermal plasma, cosmic and Alfvén waves pressures, thus seeking for its behavior. The solution of the system is categorically divided into three branches, supersonic, subsonic and unphysical solutions.The most interesting of all is the transonic solution, a solution that evolves from subsonic to supersonic. First of all, we discuss only thermal plasma outflows and explain their evolution in three cases of outflows environments, followed by the addition of cosmic waves and Alfvén waves. After discussing three fluid outflows in different structures, we compared the results of thermal outflows with three fluid outflows and see how the addition of waves in the system affects the dynamics of the system. At last, the findings of this paper are discussed.

Influence of electrons on granulation-generated solar chromosphere heating and plasma outflows

Context. It is known that the solar atmosphere exhibits a varying degree of ionization through its different layers. The ionization degree directly depends on plasma temperature, that is, the lower the temperature, the lower the ionization degree. As a result, the plasma in the lower atmospheric layers (the photosphere and the chromosphere) is only partially ionized, which motivates the use of a three-fluid model. Aims. We consider, for the first time, the influence of electrons on granulation-generated solar chromosphere heating and plasma outflows. We attempt to detect variations in the ion temperature and plasma up- and downflows. Methods. We performed 2.5D numerical simulations of the generation and evolution of granulation-generated waves, flows, and other granulation-associated phenomena with an adapted JOANNA code. This code solves the simplified three-fluid equations for ions (protons) and electrons and neutrals (hydrogen atoms) that are coupled by collision forces. Results. Electron-neutral and electron–ion collisions provide extra heat in the low chromosphere and enhance plasma outflows in this region. The effect of electrons is small compared to ion–neutral collisions, which have a significantly greater effect on the heating process and the production of outflows. Ion–neutral collisions involve higher energy exchanges, making them the dominant mechanism over collisions with electrons. Conclusions. Electrons do not play a major role in heating and producing outflows, primarily because their mass is much lower compared to that of neutrals and ions, resulting in lower energy transfer during collisions.

Understanding the Variability of Helium Abundance in the Solar Corona Using Three-fluid Modeling and Ultraviolet Observations

The variability of helium abundance in the solar corona and the solar wind is an important signature of solar activity, solar cycle, and solar wind sources, as well as coronal heating processes. Motivated by recently reported remote-sensing UV imaging observations by Helium Resonance Scattering in the Corona and Heliosphere payload sounding rocket of helium abundance in the inner corona on 2009 September 14 near solar minimum, we present the results of the first three-dimensional three-fluid (electrons, protons, and alpha particles) model of tilted coronal streamer belt and slow solar wind that illustrates the various processes leading to helium abundance differentiation and variability. We find good qualitative agreement between the three-fluid model and the coronal helium abundance variability deduced from UV observations of streamers, providing insight on the effects of the physical processes, such as heating, gravitational settling, and interspecies Coulomb friction in the outflowing solar wind that produce the observed features. The study impacts our understanding of the origins of the slow solar wind.

EFFECTS OF PIPE DIAMETER ON INTERFACIAL AND WALL FRICTION FACTORS OF SWIRLING ANNULAR FLOWS IN A VERTICAL PIPE

Interfacial and wall friction factors, <i>f<sub>i</sub></i> and <i>f<sub>w</sub></i>, of swirling annular flows in a vertical pipe of 20 mm in diameter D were measured for comparison with those in a vertical pipe of <i>D </i>= 30 mm. A three-fluid model was applied to evaluate the friction factors. Measurements were carried out in two sections, one near the swirler and the other far downstream the swirler. The swirl intensity of the flow was evaluated by the interfacial swirl number si defined by the ratio of the azimuthal to the axial components of interfacial wave velocity. The interfacial swirl numbers were smaller in the smaller pipe. The ratio of <i>f<sub>i</sub></i> in swirling annular flows to that in non-swirling annular flows decreased to unity with decreasing <i>s<sub>i</sub></i>* which is the arithmetic mean value of <i>s<sub>i</sub></i> for 0 ≤ <i>z</i>* (= <i>z/D</i>) ≤ 3.8, where <i>z</i> is the axial coordinate in the test section, and is higher in <i>D </i>= 20 mm than in <i>D </i>= 30 mm. The ratio of <i>f<sub>w</sub></i> in swirling annular flows to that in non-swirling annular flows decreased to less than unity with decreasing <i>s<sub>i</sub></i>* and is higher in <i>D </i>= mm than in <i>D </i>=30 mm.

Simulating collectivity in dense baryon matter with multiple fluids

A novel three-fluid dynamical model for simulations of heavy-ion collisions at RHIC Beam Energy Scan programme, called MUFFIN, has been developed. The novelty consists of modular inclusion of the Equation of State, use of hyperbolic coordinates that allow to simulate higher collision energies, and fluctuating initial conditions. The model reproduces rapidity and pt spectra of collisions from √SNN = 7.7 to 62.4 GeV. Ideal fluid is assumed, and the elliptic flow is over-predicted, particularly at lower collision energies.

Time-dependent axial fluid model of the Hall thruster discharge and its plume

One-dimensional axial models of a Hall thruster give a good qualitative picture of the main physical phenomena in the discharge with small computational effort. Time-dependent models, in particular, are widely used for the analysis of low-frequency axial oscillations (i.e. the breathing mode). The standard time-dependent three-fluid model found in the literature is here enhanced by extending the physical domain beyond the cathodic surface into the far plume, and improving the modeling of some physical phenomena. A suite of five models is presented in this work with an increasing complexity of added physics; the most complete version accounting for ion and neutral energy evolution equations along with the partial inclusion of electron inertia. The added physics has a non negligible impact on both the dynamics of the breathing mode and the time-averaged response of the plasma. In particular, it is found that the onset of the instability is sensitive to both the level of modeled physics and the operational parameters. In some cases, the strong breathing mode oscillations can result in a weak plasma attachment to the anode, leading to the collapse of the normal anode sheath and to the subsequent failure of the model.

Effects of liquid viscosity on interfacial and wall friction factors of swirling annular flows in a vertical pipe

Experiments of gas–liquid swirling annular flows in a vertical pipe of diameter D = 30 mm were carried out to obtain interfacial and wall friction factors, fi and fw, based on a three-fluid model. The liquid phase was two kinds of glycerol-water solutions with the kinematic viscosity νL of two or four times larger than that of water. Experimental data were obtained in two axial sections with short and long axial distances from the swirler, which corresponds to swirling and non-swirling annular flow regimes, respectively. Both the azimuthal and axial components of interfacial velocity decayed with increasing νL. The interfacial swirl number si, which is the ratio of the azimuthal component to the axial component of interfacial velocity, was not affected by νL for z*(=z/D) ≤ 3.8, where z is the axial coordinate in the test section. The mean interfacial swirl number si∗, which is the arithmetic mean of si in z* ≤ 3.8, was expressed in terms of dimensionless numbers based on the gas and liquid volumetric fluxes without νL. The interfacial friction factor decreased with increasing νL in swirling flows. The functional form of the Colebrook equation had a prospect of correlating fi in both swirling and non-swirling annular flows. The wall friction factor ratio of fw in the swirling annular flow regime to that in the non-swirling annular flow regime decreased as νL increased for si∗ > 0.33. The wall friction factor ratio was well correlated in terms of si∗ and νL.

Study on the characteristics of different species in the vacuum arc devices with deuteride cathode

To study the physical mechanism of the separation between heavy and light species in the vacuum arc devices with deuteride cathodes, a three-fluid model based on magnetohydrodynamic (MHD) theory is established. In the model, different kinds of species are considered to be different kinds of fluids, and their physical parameters are calculated separately. Moreover, the distribution of arc current is calculated by the generalized Ohm's law, and the ionization and recombination of species are taken into account. In the paper, the two cases where the cathode is Zr or ZrD0.67 are simulated, respectively. The results show that in the case of ZrD0.67 cathode, the separation of light and heavy species is remarkable. Because of D's lighter mass and lower mass-to-charge ratio, the distribution of it is more uniform. In addition, the differences between species also lead to large differences in other physical characteristics, such as ion velocity, ion temperature, and so on. Notably, the desorption and ionization of deuterium lead to a decrease in plasma temperature. The self-generated magnetic field of the arc has an inhibitory effect on the expansion of each species, and it is more obvious for ions with lower mass-to-charge ratio. The simulation results are consistent with the experimental results. The theoretical analysis can provide theoretical guidance for the improvement of vacuum arc devices with composite or gas-saturated cathodes.

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.

Comparison of the 3-Fluid Dynamic Model with Experimental Data

The article considers a way to compare large bulks of experimental data with theoretical calculations, in which the quality of theoretical models is clearly demonstrated graphically. The main idea of the method consists in grouping physical observables, represented by experiment and theoretical calculation, into samples, each of which characterizes a certain physical process. A further choice of a convenient criterion for comparing measurements and calculations, its calculation and averaging within each sample and then over all samples, makes it possible to choose the best theoretical model in the entire measurement area. Published theoretical data of the three-fluid dynamic model (3FD) applied to the experimental data from heavy-ion collisions at the energy range $\sqrt{s_{NN}}\,=\,2.7 - 63$ GeV are used as example of application of the developed methodology. When analyzing the results, the quantum nature of the fireball, created at heavy ion collisions, was taken into account. Thus, even at energy $\sqrt{s_{NN}}\,=\,63$ GeV of central collisions of heavy ions, there is a nonzero probability of fireball formation without ignition of the quark-gluon plasma (QGP). At the same time, QGP ignition at central collision energies above at least $\sqrt{s_{NN}}\,=\,12 GeV occurs through two competing processes, through a first-order phase transition and through a smooth crossover. That is, in nature, these two possibilities are realized, which occur with approximately the same probabilities.

Effects of swirl intensity on interfacial and wall friction factors of annular flows in a vertical pipe

Interfacial and wall friction factors, fi and fw, of air-water swirling annular flows in a vertical pipe of diameter D = 30 mm were measured in three sections of L* (=L/D) = 7.3, 13 and 31, where L is the distance from a swirler. The gas and liquid volumetric fluxes, JG and JL, were 12.5 ≤ JG ≤ 20.0 m/s and 0.071 ≤ JL ≤ 0.213 m/s, respectively. The interfacial swirl number, si, defined by Viθ/Viz, where Viθ and Viz are the azimuthal and axial components of interfacial velocity, was introduced as an indicator of swirl intensity. For z* (=z/D) ≤ 7, where z is the axial coordinate in the test section, the si increased with z* at low JG and JL, and slightly decreased with z* at high JG and JL. The si decreased for z* > 7 and reached zero at z* ≈ 30. The fw estimated using the three-fluid model was larger than that estimated using the two-fluid model since the droplet flow rate was not negligible even in swirling annular flows. The three-fluid model was therefore more appropriate for evaluation of fi and fw than the two-fluid model. The ratio fw∗ increased with s¯i for s¯i > 0.25, where fw∗ is the ratio of fw to that of non-swirling flows and s¯i is the averaged value of si in the section. The ratio fi∗ increased with s¯i for s¯i > 0.18, wherefi∗ is the ratio of fi to that of non-swirling flows. Correlations in terms of s¯i have prospect to evaluate the fi and fw in swirling annular flows.

Analysis of two-phase flow in non-inertial coordinate using combination of three-fluid model and drift flux model

After the Fukushima accident, to increase the safety of nuclear power plants, work began on Floating Nuclear Power Plants with the construction of the power plant floats above 100 m eliminate the risk of earthquakes and tsunamis. The study investigated integration of three-fluid model and Drift Flux model, to analyze different two-phase flow regimes in a vertical channel under ocean motions. By upgrading the model, an attempt has been made to include the additional forces caused by ocean movements in momentum equations so that it can be used in the thermal-hydraulic analysis of two-phase flow in non-inertial coordinate the simulation results with the presented method converge well with the simulation results of the RELAP5 mod 3.2 code and experimental results. Compared to static state, under rolling motion, void fraction and Critical Heat Flux (CHF) vary periodically with time. The amplitude oscillation of CHF changes with increasing maximum angle in rolling motion and also with increasing acceleration amplitude in heaving motion.

Global Λ polarization in heavy-ion collisions at energies 2.4–7.7 GeV: Effect of meson-field interaction

Based on the three-fluid model, the global $\mathrm{\ensuremath{\Lambda}}$ polarization in $\mathrm{Au}+\mathrm{Au}$ collisions at 2.4 $\ensuremath{\le}\sqrt{{s}_{NN}}\ensuremath{\le}$ 7.7 GeV is calculated, including its rapidity and centrality dependence. Contributions from the thermal vorticity and meson-field term (proposed by Csernai, Kapusta, and Welle) to the global polarization are considered. The results are compared with data from recent and ongoing STAR and HADES experiments. It is predicted that the polarization maximum is reached at $\sqrt{{s}_{NN}}\ensuremath{\approx}3$ GeV, if the measurements are performed with the same acceptance. The value of the polarization is very sensitive to interplay of the aforementioned contributions. In particular, the thermal vorticity results in quite strong increase of the polarization from the midrapidity to forward/backward rapidities, while the meson-field contribution considerably flattens the rapidity dependence. The polarization turns out to be very sensitive to details of the equation of state. While collision dynamics become less equilibrium with decreasing collision energy, the present approach to polarization is based on the assumption of thermal equilibrium. It is found that equilibrium is achieved at the freeze-out stage, but this equilibration takes longer at moderately relativistic energies.

Damping rate measurements and predictions for gravity waves in an air–oil–water system

Dissipation of standing gravity waves of frequencies within 1–2 Hz is investigated experimentally. The waves are generated in a rectangular tank filled with water, the surface of which is covered with an oil layer of mean thickness, d. Damping rates are measured as a function of d, and compared with results from established theoretical models—in particular, with those from a recently developed three-fluid dissipation model that considers waves in a system of semi-infinitely deep fluids that lie above and below an interfacial fluid layer of finite thickness. Based on a comparison of experimental data with predictions, the oil–water interfacial elasticity, E2, is empirically determined to be a linear function of d. The theoretical predictions include contributions from the three-fluid dissipation model, which accounts for energy losses due to shear layers at the interfaces, friction in the fluid bulk, and compression–expansion oscillations of the elastic interfaces; and from a boundary-layer dissipation model, which accounts for energy losses due to boundary layers at the tank's solid surfaces. The linear function, E2(d), is used to compute the three-fluid model damping rate. An effective viscosity of the oil–water system is used to compute the boundary-layer model damping rate. The theoretical predictions are, on average, within 5% of measurements for all the wave frequencies considered. The promise shown by the three-fluid model is highlighted, as are the assumptions involved in the analysis and comparisons.

Generalized model of interacting dark energy and dark matter: Phase portrait analysis for evolving universe

The main aim of this work is to give a suitable explanation of present accelerating universe through an acceptable interactive dynamical cosmological model. A three-fluid cosmological model is introduced in the background of Friedmann–Lemaître–Robertson-Walker asymptotically flat spacetime. This model consists of interactive dark matter and dark energy with baryonic matter, taken as perfect fluid, satisfying barotropic equation of state. We consider dust as the candidate of dark matter. A scalar field [Formula: see text] represents dark energy with potential [Formula: see text]. Einstein’s field equations are utilized to construct a three-dimensional interactive autonomous system by choosing suitable interaction between dark energy and dark matter. We take the interaction kernel as [Formula: see text], where [Formula: see text] indicates the density of dark energy, [Formula: see text] is the interacting constant and [Formula: see text] is Hubble parameter. In order to explain the stability of this system, we obtain some suitable critical points. We analyze stability of obtained critical points to show the different phases of universe and cosmological implications. Surprisingly, we find some stable critical points which represent late-time dark energy-dominated era when a model parameter [Formula: see text] is equal to [Formula: see text]. We introduce a two-dimensional interactive autonomous system and after phase portrait analysis of it, we get several stable points which represent dark energy-dominated era and late-time cosmic acceleration simultaneously. Here, we also demonstrate the variation in interaction at vicinity of phantom barrier [Formula: see text]. From our work, we can also predict the future phase evolution of the universe.

Density fluctuations associated with turbulence and waves

Aims.The aim of this work is to demonstrate that the probe-to-spacecraft potential measured by RPW on Solar Orbiter can be used to derive the plasma (electron) density measurement, which exhibits both a high temporal resolution and a high level of accuracy. To investigate the physical nature of the solar wind turbulence and waves, we analyze the density and magnetic field fluctuations around the proton cyclotron frequency observed by Solar Orbiter during the first perihelion encounter (∼0.5 AU away from the Sun).Methods.We used the plasma density based on measurements of the probe-to-spacecraft potential in combination with magnetic field measurements by MAG to study the fields and density fluctuations in the solar wind. In particular, we used the polarization of the wave magnetic field, the phase between the compressible magnetic field and density fluctuations, and the compressibility ratio (the ratio of the normalized density fluctuations to the normalized compressible fluctuations of B) to characterize the observed waves and turbulence.Results.We find that the density fluctuations are 180° out of phase (anticorrelated) with the compressible component of magnetic fluctuations for intervals of turbulence, whereas they are in phase for the circular-polarized waves. We analyze, in detail, two specific events with a simultaneous presence of left- and right-handed waves at different frequencies. We compare the observed wave properties to a prediction of the three-fluid (electrons, protons, and alphas) model. We find a limit on the observed wavenumbers, 10−6 < k < 7 × 10−6m−1, which corresponds to a wavelength of 7 × 106 > λ > 106m. We conclude that it is most likely that both the left- and right-handed waves correspond to the low-wavenumber part (close to the cut-off at ΩcHe + +) of the proton-band electromagnetic ion cyclotron (left-handed wave in the plasma frame confined to the frequency range ΩcHe + + < ω < Ωcp) waves propagating in the outwards and inwards directions, respectively. The fact that both wave polarizations are observed at the same time and the identified wave mode has a low group velocity suggests that the double-banded events occur in the source regions of the waves.

Numerical Simulation of a High-Speed Impact of Metal Plates Using a Three-Fluid Model

The process of wave formation at the contact boundary of colliding metal plates is a fundamental basis of explosive welding technology. In this case, the metals are in a pseudo-liquid state at the initial stages of the process, and from a mathematical point of view, a wave formation process can be described by compressible multiphase models. The work is devoted to the development of a three-fluid mathematical model based on the Baer–Nunziato system of equations and a corresponding numerical algorithm based on the HLL and HLLC methods, stiff pressure, and velocity relaxation procedures for simulation of the high-speed impact of metal plates in a one-dimensional statement. The problem of collision of a lead plate at a speed of 500 m/s with a resting steel plate was simulated using the developed model and algorithm. The problem statement corresponded to full-scale experiments, with lead, steel, and ambient air as three phases. The arrival times of shock waves at the free boundaries of the plates and rarefaction waves at the contact boundary of the plates, as well as the acceleration of the contact boundary after the passage of rarefaction waves through it, were estimated. For the case of a 3-mm-thick steel plate and a 2-mm-thick lead plate, the simulated time of the rarefaction wave arrival at the contact boundary constituted 1.05 μs, and it was in good agreement with the experimental value 1.1 μs. The developed numerical approach can be extended to the multidimensional case for modeling the instability of the contact boundary and wave formation in the oblique collision of plates in the Eulerian formalism.

Three-fluid model of the plasma–sheath region for a planar probe immersed in an active oxygen discharge. Validity of the Boltzmann relation

This paper studies the effect of the generation-loss processes in the plasma–sheath region close to a probe immersed in an oxygen discharge considering a three-fluid model for the charged species. A significant deviation from the Boltzmann relationship is obtained for the negative ion density when different values of the electron temperature, the negative ion temperature, the negative ion concentration, and the collision mean free path are considered.

Four-fluid axisymmetric plasma equilibrium model including relativistic electrons and computational method and results

A non-relativistic multi-fluid plasma axisymmetric equilibrium model [A. Ishida et al., “Three-fluid axisymmetric equilibrium model and application to spherical torus plasmas sustained by RF electron heating,” Plasma Fusion Res. 10, 1403084 (2015)] was developed recently to account for the presence of an energetic electron fluid in addition to thermal electron and ion fluids. The equilibrium formulation of a multi-fluid plasma with relativistic energetic electrons is developed and reported in this paper. Relativistic effects in a fluid model approximation can appear in two ways: due to a large macroscopic fluid velocity comparable to the speed of light and a large particle's microscopic random motion which becomes significant if the temperature becomes comparable to or larger than the electron rest mass energy. It is found that the axial component of relativistic generalized angular momentum can be used to describe relativistic axisymmetric equilibrium. The formulation is applied to a four-fluid plasma composed of a relativistic energetic electron fluid, a thermal electron fluid, and fluids of two thermal ion species (e.g., proton and boron ions). The four-fluid density expression which is consistent with the electrostatic potential is obtained and applied in the computation. An example equilibrium approximating a four-fluid plasma recently observed in a solenoid-free ECRH sustained spherical torus plasma [Y.-K. M. Peng et al., “Initial results of the EXL-50 experiment,” (to be published)] is calculated and presented. A second equilibrium that extends the energetic electron temperature of the first example to 679 keV is calculated revealing significant relativistic effects.

Enhancing filter cake removal by engineering parameter optimization for clean development of fossil hydrogen energy: A numerical simulation

Long-term zonal isolation is crucial for the development of fossil hydrogen energy, while efficient filter cake removal is the basis for successful zonal isolation. However, enhanced filter cake removal usually relies on adding chemicals into preflush fluid, which are potential pollutants to the environment. In this study, engineering parameter optimization is used to realize enhanced filter cake removal. Firstly, filter cake removal was identified as multiple-phase fluid flow, and a new three-fluid numerical model was established accordingly. The effects of five engineering parameters on the removal efficiency were simulated and the results showed that borehole enlargement and casing eccentricity reduced removal efficiency. The critical borehole deviation angle and casing rotation speed for optimal removal efficiency were 45° and 40 rpm, respectively, while the removal efficiency monotonously increased with flushing velocity. After all engineering parameters were optimized, the maximum removal efficiency was as high as 89.34%, which was comparable to that achieved by using potentially polluting chemicals. The borehole enlargement rate was identified as the most sensitive parameter, followed by casing eccentricity, flushing velocity, borehole deviation angle, and casing rotation speed subsequently. Two empirical models to predict removal efficiency were developed for convenient field application. Briefly, the complex removal behaviors of the filter cake are better understood for reducing the risks of failed zonal isolation and avoiding chemical overuse, which potentially contributes to the cleaner and more environment-friendly production of fossil hydrogen energy.