Multifluid Simulations Research Articles

Ion energization in Ganymede’s magnetosphere: Using multifluid simulations to interpret ion energy spectrograms

We investigate the ion population and energy distribution within Ganymede’s magnetosphere by examining Ganymede’s ionospheric outflow as a source of heavy (O+) and light (H+) ions and the Jovian magnetospheric plasma as an external source of heavy ions. We develop a method for examining the energy distributions of each ion species in a three‐dimensional multifluid simulation in a way directly comparable to the observations of the Plasma Experiment on the Galileo spacecraft. This is used to provide new insight to the existing controversy over the composition of Ganymede’s observed ionospheric outflow, and enables further examination of the energetic signatures of the ion population trapped within Ganymede’s magnetosphere. The model‐predicted ionospheric outflow is consistent with the in situ ion energy spectrograms observed by the Galileo Plasma Experiment at closest approach, and requires that both ionospheric H+ and O+ are present in the population of ions exiting Ganymede’s ionosphere over the polar cap. The outward flux of ionospheric ions was calculated to be ~1026 ions/cm2/s, which is in agreement with independently calculated sputtering rates of Ganymede’s icy surface. The modeled spectrograms define characteristic energy signatures and populations for various regions of Ganymede’s magnetosphere, which illustrate the major sources of ions trapped within the magnetosphere are Ganymede’s ionospheric O+ and H+. The fact that very little plasma was observed inside Ganymede’s magnetosphere during the G8 flyby is attributed to the region being shadowed from the sun for ~60 h, which may indicate the importance of photoionization for sustaining Ganymede’s ionospheric plasma source.

Prompt ionospheric/magnetospheric responses 29 October 2003 Halloween storm: Outflow and energization

3D multifluid simulations of the 29 October 2003 Halloween storm show the event to be a good example of conditions which lead to prompt penetration of solar wind electric field into the magnetosphere and prompt acceleration of heavy ionospheric ions. Causal relationships are established that tie solar wind conditions to ionospheric/magnetospheric responses, and the results are correlated with features in both IMAGE/HENA data and AMIE cross‐polar cap potential. The simulations are able to capture the AMIE potentials. Difference between model results and AMIE data can be attributed to the ability of the model to capture fast enhancements in the convective electric field that can be tied with the IMF variations. The total auroral currents show a smoother profile, with the magnetosphere acting like an inductor. A period of southward IMF with simultaneous rapid By rotation leads to the largest currents and ionospheric outflows. These outflows produce an initial ionospheric mass loading of the magnetosphere and originate from the dayside cusp/cleft region. During this period the energization of O+ lags that of H+, consistent with that seen in the HENA data. Once the ionospheric outflows mass load the magnetosphere, prompt acceleration of O+ is seen simultaneous with H+ acceleration. This prompt response is due to the acceleration of O+ ions that have previously flowed into the magnetosphere. The enhanced convective electric field, also leads to enhanced ionospheric outflows that resupply ionospheric ions into the magnetosphere. During this period of resupply, the nightside auroral zone becomes an important contributor to the outflows.

Turbulent transport and its effect on the dead zone in protoplanetary discs

Protostellar accretion discs have cool, dense midplanes where externally originating ionisation sources such as X-rays or cosmic rays are unable to penetrate. This suggests that for a wide range of radii, MHD turbulence can only be sustained in the surface layers where the ionisation fraction is sufficiently high. A dead zone is expected to exist near the midplane, such that active accretion only occurs near the upper and lower disc surfaces. Recent work, however, suggests that under suitable conditions the dead zone may be enlivened by turbulent transport of ions from the surface layers into the dense interior. In this paper we present a suite of simulations that examine where, and under which conditions, a dead zone can be enlivened by turbulent mixing. We use three-dimensional, multifluid shearing box MHD simulations, which include vertical stratification, ionisation chemistry, ohmic resistivity, and ionisation due to X-rays from the central protostar. We compare the results of the MHD simulations with a simple reaction-diffusion model. The simulations show that in the absence of gas-phase heavy metals, such as magnesium, turbulent mixing has essentially no effect on the dead zone. The addition of a relatively low abundance of magnesium, however, increases the recombination time and allows turbulent mixing of ions to enliven the dead zone completely beyond a distance of 5 AU from the central star, for our particular disc model. During the late stages of protoplanetary disc evolution, when small grains have been depleted and the disc surface density has decreased below its high initial value, the structure of the dead zone may be significantly altered by the action of turbulent transport.

Shock-bubble interactions: Features of divergent shock-refraction geometry observed in experiments and simulations

The interaction of a planar shock wave with a spherical bubble in divergent shock-refraction geometry is studied here using shock tube experiments and numerical simulations. The particular case of a helium bubble in ambient air or nitrogen (A≈−0.8) is considered, for 1.4<M<3.0. Experimental planar laser diagnostics and three-dimensional multifluid Eulerian simulations clearly resolve features arising as a consequence of divergent shock refraction, including the formation of a long-lived primary vortex ring, as well as counter-rotating secondary and tertiary upstream vortex rings that appear at late times for M⩾2. Remarkable correspondence between experimental and numerical results is observed, which improves with increasing M, and three-dimensional effects are found to be relatively insignificant. Shocked-bubble velocities, length scales, and circulations extracted from simulations and experiments are used successfully to evaluate the usefulness of various analytical models, and characteristic dimensionless time scales are developed that collapse temporal trends in these quantities. Those linked directly to baroclinicity tend to follow time scales based on shock wave speeds, while those linked to interface deformation and vortex- or shear-induced motion tend to follow a time scale based on the postshock flow speed, though no single time scale is found to be universally successful.

Three‐dimensional multifluid simulation of the plasma interaction at Titan

Using a three‐dimensional multifluid simulation, we demonstrate the importance of ion gyroradius and heavy ion effects when characterizing Titan's plasma interaction with the Kronian magnetosphere. Ion gyroradius and heavy ion effects drastically change the mass loading and magnetic field draping at Titan. We find that the large ion gyroradius of picked up ionospheric species results in an extension of the ionosphere and therefore the mass loading and magnetic pileup region on the anti‐Saturn side of Titan. Also, the additional thermal pressure provided by heavy ion cyclotron motion near Titan causes boundary layer currents to form at higher altitudes. The Saturn‐facing side of Titan's ionosphere experiences both magnetic shielding from the incident plasma at lower altitudes and additional heating due to the acceleration of heavy ions in the ionosphere. Finally, we find that well‐confined heavy ion beams form on the anti‐Saturn side of Titan's magnetosphere and extend more than three Titan radii from Titan's main ion tail. The location of this ion beam is dependent on the Kronian field orientation, and we find that during the TA, TB, and T3 encounters, the bulk of the ion beam was located below Titan's equatorial plane. We also find that for a single set of incident conditions, good agreement with Cassini magnetometer data from the TA, TB, and T3 encounters is obtained with the ion loss rate similar to that measured by Cassini during the TA encounter.

Saturation‐Dependent Hydraulic Conductivity Anisotropy for Multifluid Systems in Porous Media

The hydraulic conductivity of unsaturated anisotropic soils has recently been described with a tensorial connectivity–tortuosity (TCT) concept. We extend this concept to unsaturated porous media with two or three immiscible fluids. Mathematical expressions to describe the conductivity of each fluid in anisotropic porous media under unsaturated condition are derived in the form of symmetric second order tensors. The theory is applicable to the generalized hydraulic conductivity model and compatible types of saturation–pressure formulation. The extended model shows that the anisotropic coefficient of any one of the fluids is independent of the saturation of other fluids. Synthetic Miller‐similar soils generated to be anisotropic were defined by allowing the saturated hydraulic conductivity to have different correlation ranges for different directions of flow. The extended TCT concept was tested using synthetic soils with four levels of heterogeneity and four levels of anisotropy. Numerical experiments of infiltration of two liquid phases, water and the nonaqueous phase liquid (NAPL) carbon tetrachloride, were performed to test the extended model. The results show that, similar to water in a two‐fluid (air–water) system, NAPL retention curves in a three‐fluid (air–NAPL–water) system were independent of flow direction but dependent on soil heterogeneity, whereas the connectivity–tortuosity coefficients are functions of both soil heterogeneity and anisotropy. The extended TCT model accurately describes unsaturated hydraulic functions of anisotropic soils and can be combined into commonly used relative permeability functions for use in multifluid flow and transport numerical simulations.

Simulations of Kelvin–Helmholtz modes in the dusty plasma environment of noctilucent clouds

AbstractWe present results of quantitative multi-fluid simulations of the nonlinear dynamics of Kelvin–Helmholtz modes in the partially ionized dusty plasma of noctilucent clouds. Noctilucent clouds are a typical example of dusty plasmas in the Earth's mesosphere/lower thermosphere. A specific feature observed in noctilucent clouds is wavy, turbulent structure. Possible explanations for these structures, which are discussed in the literature, are based on hydrodynamical models. The dusty plasma aspect has been widely neglected, so far. In this paper we examine the nonlinear dynamics of Kelvin–Helmholtz modes in noctilucent clouds from the viewpoint of dusty plasma dynamics. The corresponding results are in good qualitative and quantitative agreement with observations.

Segregation in polydisperse fluidized beds: Validation of a multi-fluid model

In many industrial-scale fluidized-bed reactors, particle mixing and segregation play an important role in determining reactor performance. Detailed information about the particle size distribution (PSD) throughout the bed at different operating conditions is crucial for design and scale up of practical systems. In this work, a multi-fluid model based on the Euler–Euler approach and the direct quadrature method of moments (DQMOM) is used to describe particle segregation, and the model predictions are validated with available experimental and simulation data. For binary mixtures, multi-fluid simulations are compared with digital image analysis experiments for beds of glass beads. By properly defining the solid–solid drag force, the multi-fluid model can reproduce the segregation rate found experimentally for different flow conditions with binary mixtures. Segregation phenomena in gas–solid fluidized beds with a continuous PSD are also investigated. Here, the multi-fluid simulations are compared with discrete particle simulations (DPS). Using the moments of the PSD from DPS, the weights and abscissas used in DQMOM are initialized in the multi-fluid model. The segregation rate and the local moments of the PSD predicted by the multi-fluid model are compared to the DPS results. The dependence of the results on the number of DQMOM nodes is also investigated.

Computational heat transfer and two-phase flow topology in miniature tubes

Detailed computational multi-fluid dynamics simulations have been performed to study the effect of two-phase flow regime on heat transfer in small diameter pipes. Overall the heat removal rate in two-phase flow is higher than in single phase. Subtle differences in thermal removal rates are revealed when the flow-regime transitions from bubbly to slug and slug-train configurations. It is found that the wall thermal layer is affected by two separate mechanisms: an early-stage compression due to gas-jet fragmentation into slugs or bubbles, and a background inclusion-induced flow superimposed on the equivalent single-phase fully developed flow far downstream. The first mechanism resembles a confinement or blockage effect, and is shown to directly influence radial temperature gradients. The downstream mechanism is a cell-based developed flow (rather than fully developed), and is shown here to increase the wall shear in the vicinity of the cell, leading to higher heat transfer rates. The mean Nusselt number distribution shows that the bubbly, slug and slug-train patterns transport as much as three to four times more heat from the tube wall to the bulk flow than pure water flow. A mechanistic heat transfer model is proposed, based on frequency and length scale of inclusions.

High‐resolution multifluid simulations of the plasma environment near the Martian magnetic anomalies

Three‐dimensional high‐resolution (∼40 km), multifluid simulations of the solar wind interaction at Mars during the southern hemisphere summer solstice indicate that the region around the magnetic anomalies can be complex and highly structured. The anomalous magnetic field leads to the formation of multiple cusps and a void region where the ionosphere is eroded. Most importantly, the anomalous magnetic field changes the nature of the magnetic pileup layer (MPL) when compared to over unmagnetized regions. While the altitude of the MPL is approximately the same in both the northern and southern hemispheres for this orientation, plasma in the MPL near the magnetic anomalies is cooler, with less solar wind and more of ionospheric origin. The solar wind density is reduced by a factor of 3 in the southern MPL, in comparison to the northern MPL, while the ionospheric density is 10–600 times more dense in the southern MPL, depending on altitude, location, and species.

Polar wind outflow model: Saturn results

The Saturnian system's configuration and dynamics are to a large extent controlled by the planet's rapid rotation and the plasma in the magnetosphere. Therefore characterizing the relative importance of the various plasma sources is crucial to understanding Saturn's magnetosphere. Most research in this area focuses on the addition of mass from the icy satellites, the rings, and Titan, while comparatively little attention has been paid to the ionospheric source. We investigate the ionospheric source at high latitude using multifluid numerical simulations of Saturn's polar wind and find that the magnitude of the particle source rate out of the polar cap is between 2.1 × 1026 and 7.5 × 1027 s−1. Our multifluid simulations are carried out using the Polar Wind Outflow Model (PWOM). This new model is capable of calculating the polar wind at Earth and Saturn by solving the gyrotropic transport equations. The polar wind at Saturn is modeled from below the peak ionospheric density to an altitude of one Saturn radius, yielding fluxes for H3+, H+, and electrons. Because the neutral temperature is ill constrained, we calculate source rates for various Saturnian atmospheric profiles corresponding to neutral temperatures of 420, 600, 800, 1000, 1500 K. We compare the results with those calculated from other models and measurements where appropriate.

901 鉛直管内気泡乱流の数値予測(GS-5 乱流(1))

901 鉛直管内気泡乱流の数値予測(GS-5 乱流(1))

Three‐dimensional multifluid simulations of ionospheric loss at Mars from nominal solar wind conditions to magnetic cloud events

Three‐dimensional multifluid simulations of the solar wind interaction with a magnetized Mars are used to determine both the effect of the crustal magnetic field on ionospheric loss rate and the ionospheric loss rate as a function of solar wind conditions. Ionospheric losses on the order of 1025 O2+ ions per second are found for quiet solar wind conditions. This is of the same order as that estimated from Phobos 2 measurements. Varying the orientation of Mars' magnetic anomalies relative to the incident solar wind direction leads to only minor variation in the ionospheric loss rates of O2+ for each set of solar wind conditions studied. Solar wind parameters were varied from nominal solar wind conditions to conditions with high‐speed flows, high densities, and large IMF magnitudes. Outflow rates on the order of 1026 O2+ ions per second were seen for storm‐like conditions. The simulations indicate that ionospheric outflow rates increase by a larger percentage for high solar wind number density when compared to high solar wind speed or strong IMF conditions alone. This is due to the higher solar wind density and temperature of the precipitating ions. The results also indicate a significant influence of pickup on ionospheric loss.

Simulations of Kelvin-Helmholtz modes in partially ionized dusty plasmas comparing different charge numbers, charge polarities, and masses of the dust

Results of multifluid simulations of Kelvin-Helmholtz modes in partially ionized, dusty plasmas are presented assuming different masses and charges of the dust. The results show a stabilizing effect for more massive dust grains and indicate a destabilizing effect for higher charge numbers. No significant dependence on the charge polarity of the dust was found.

A Hybrid Method for Predicting Dispersed Gas-Liquid and Liquid-Liquid Multi-Phase Flows

A hybrid CMFD (computational multi-fluid dynamics) method is proposed for the prediction of gas-liquid and/or liquid-liquid dispersed two-phase flows including large-scale interface, poly-dispersed bubbles and drops. The method is the hybrid integration of an interface tracking method (ITM), three kinds of particle tracking methods (PTM) and an averaging method based on a multi-fluid model (MFM). The integration enables us to cover a wide range of d*=d/Δx, where d is the particle diameter and Δx the grid size, and to perform various kinds of multiphase CFD such as standard interface tracking, particle tracking and multi-fluid simulations, and hybrid simulations by making an arbitrary combination of ITM, PTM and MFM. The field equations and numerical solution procedure of the proposed method are described in detail. To demonstrate its potential, a poly-dispersed air-water bubbly flow in a vertical square duct and an air-water bubble plume in an open vessel are computed using the combination of ITM, PTM and MFM.

A simple algebraic interface capturing scheme using hyperbolic tangent function

AbstractThis paper presents a simple and practical scheme for capturing moving interfaces or free boundaries in multi‐fluid simulations. The scheme, which is called THINC (tangent of hyperbola for interface capturing), makes use of the hyperbolic tangent function to compute the numerical flux for the fluid fraction function, and gives a conservative, oscillation‐less and smearing‐less solution to the fluid fraction function even for the extremely distorted interfaces of arbitrary complexity. The numerical results from the THINC scheme possess adequate quality for practical applications, which make the extra geometric reconstruction, such as those in most of the volume of fluid (VOF) methods unnecessary. Thus the scheme is quite simple. The numerical tests show that the THINC scheme has competitive accuracy compared to most exiting methods. Copyright © 2005 John Wiley & Sons, Ltd.

2601 CIP/MM有限体積法とTHINGスキームによる多層流シミュレーション(OS-26A CIP 法および多相流解析技術の最近の進展,OS-26 CIP 法および多相流解析技術の最近の進展)

2601 CIP/MM有限体積法とTHINGスキームによる多層流シミュレーション(OS-26A CIP 法および多相流解析技術の最近の進展,OS-26 CIP 法および多相流解析技術の最近の進展)

Comparison of multifluid and discrete particle modelling in numerical predictions of gas particle flow in circulating fluidised beds

From the perspective of wanting to evaluate the modelling of the particulate phase in multifluid computational fluid dynamics simulations, numerical predictions from a multifluid model is compared with predictions from a discrete particle model. Simulations with both one and three representative particle diameters for the particulate phase are performed. The predicted results are compared with experimental findings obtained with Laser Doppler Anemometry. The numerical predictions from the discrete particle code are found to be in better agreement with the experimental findings, but the multifluid code is by far the most efficient. To evaluate the modelling of collisions in the multifluid model, discrete particle simulations which only take into account of energy loss caused by head-on collisions are compared with discrete particle simulations, which take nonfrontal collisions into account.

Generation of Magnetic Fields in Dusty Protoplanetary Disks

The remanent magnetization of meteorite material in the solar system indicates that magnetic fields of some Gauss were present in the early protoplanetary disk. It is shown that such relatively strong magnetic fields can be generated in dusty protoplanetary disks by relative shear motions of the charged dust and the neutral gas components. The ultimate energy source is the gravitational field of the stellar object that results in a sheared accretion flow. Self-consistent multi-fluid simulations show that for plasma parameters typical for protoplanetary disks shear flows with collisional momentum transfer between the different components of the dusty plasma result in a very efficient generation of magnetic fields with strengths of about 0.1–1 Gauss on spatial scales of two astronomical units in about two years. Such strong magnetic fields should influence the coupling of the stellar dipole field and the disk, the accretion flow, stellar winds and jets and the formation of protoplanetary objects.

Circulation of ionospheric and solar wind particle populations during extended southward interplanetary magnetic field

Single particles trajectories using time‐dependent electric and magnetic fields from multifluid simulations are used to examine the energy and mass transport due to entry of solar wind particles and from ionospheric outflows incorporating both light and heavy ions. It is shown the particles move with the convection cells derived from the multifluid simulations, and that strong particle acceleration occurs at both the dayside and nightside tips of the flow reversal regions. However, different particle populations have limited access to various parts of the convection pattern, and this leads to substantial dawn‐dusk asymmetries in the particle populations within the magnetosphere. For the strong southward interplanetary magnetic field (IMF) conditions for the event studied, fast solar wind particles are able to enter from the dawnside and contribute to the asymmetric ring current. The rest of the fast particles flow down the mantle and do not enter the near‐Earth magnetosphere. The remaining slow component is convected into the magnetosphere over a few tens of minutes to form cold populations in the mantle and LLBL. Solar wind He++ and O6+ are shown to penetrate deeper than the solar wind protons. Light ionospheric ions from the cusp and dawnside auroral oval have similar access problems and flow primarily down the tail and make little contribution to the plasma content to the near‐Earth plasma sheet. Nightside auroral protons are shown to form a cold component in the plasma sheet boundary layer. When they are eventually convected in to the near‐Earth plasma sheet they are accelerated preferentially to the duskside and experience further energy gains as they are convected sunward. These energetic protons contribute to the asymmetric ring current, with leakage from the magnetosphere occurring as they approach the dayside reconnection region. Heavy ionospheric ions enter the convection pattern differently from their light ions counterparts. O+ ions from the cusp can enter the near‐Earth plasma sheet to provide some mass loading, but the biggest contributor is the dawnside auroral oval. The dawn‐dusk electric field accelerates these ions toward the dusk side, but on sufficient low L shells that these ions can dominate the symmetric ring current composition. The O+ ions that originate from the midnight and dusk sectors go to forming hot populations in the dusk LLBL.