Rarefied Region Research Articles

2.5D Magnetohydrodynamic Simulation of the Formation and Evolution of Plasmoids in Coronal Current Sheets

In the present paper, using MPI-AMRVAC, we perform a 2.5D numerical magnetohydrodynamic simulation of the dynamics and associated thermodynamical evolution of an initially force-free Harris current sheet subjected to an external velocity perturbation under the condition of uniform resistivity. The amplitude of the magnetic field is taken to be 10 G, typical of the solar corona. We impose a Gaussian velocity pulse across this current sheet that mimics the interaction of fast magnetoacoustic waves with a current sheet in the corona. This leads to a variety of dynamics and plasma processes in the current sheet, which is initially quasi-static. The initial pulse interacts with the current sheet and splits into a pair of counterpropagating wavefronts, which form a rarefied region that leads to an inflow and a thinning of the current sheet. The thinning results in Petschek-type magnetic reconnection followed by a tearing instability and plasmoid formation. The reconnection outflows containing outward-moving plasmoids have accelerated motions with velocities ranging from 105 to 303 km s−1. The average temperature and density of the plasmoids are found to be 8 MK and twice the background density of the solar corona, respectively. These estimates of the velocity, temperature, and density of the plasmoids are similar to values reported from various solar coronal observations. Therefore, we infer that the external triggering of a quasi-static current sheet by a single-velocity pulse is capable of initiating magnetic reconnection and plasmoid formation in the absence of a localized enhancement of resistivity in the solar corona.

Complete third-order polynomial expansion-based gas kinetic flux solver for flows from continuum regime to rarefied regime

The Grad's 13 distribution function was derived through a third-order Hermite polynomial expansion in terms of peculiar velocity. Recently, it has been adopted to construct a gas kinetic flux solver called G13-GKFS for simulation of flows from the continuum regime to the rarefied regime. However, this Grad's distribution function only considers the contracted polynomials that strictly satisfy orthogonality. In other words, the third-order terms of CiC12, CiC22, and CiC32 share the same coefficients (γi). However, the results from the discrete velocity method reveal that those coefficients could be different, especially in the rarefied regime. This may affect the accuracy of numerical results in the rarefied region. In order to consider different coefficients of the third-order terms, we propose a complete third-order polynomial expansion to approximate the distribution function in this work. To show the capability of current distribution function, a new GKFS is developed for flows from the continuum regime to the rarefied regime. Some benchmark cases are solved to demonstrate that the new GKFS outperforms the G13-GKFS in the rarefied regime.

Soliton solutions of the equations of hydrodynamics in describing collisions and oscillations of atomic nuclei

The hydrodynamic approach was used to find an analytical solution of the hydrodynamic equations in the soliton approximation for layer collisions in the one- and two-dimensional cases. The compression stage, the decompression stage, and the expansion stage are considered within the framework of a single formula for layers with energies on the order of ten MeV per nucleon. Our generalization to the two-dimensional case leads to the idea of the formation of a rarefied bubble region at the stage of expansion. The approach can be used in other fields for calculations of the nonlinear dynamics of oscillations of complex systems.

A Numerical Study of an Ellipsoidal Nanoparticles under High Vacuum Using the DSMC Method

The semiconductor and display manufacturing process requires high precision. Therefore, inside the equipment, fine impurity particles affect the yield rate of production. However, since most manufacturing processes are performed under high-vacuum conditions, it is difficult to estimate particle flow with conventional analytical tools. In this study, high-vacuum flow was analyzed using the direct simulation Monte Carlo (DSMC) method, and various forces acting on fine particles in a high-vacuum flow field were calculated. To compute the computationally intensive DSMC method, GPU-based computer unified device architecture (CUDA) technology was used. The force acting on the particles in the high-vacuum rarefied gas region was verified using the results of previous studies, and the results were derived for the difficult-to-experiment region. An ellipsoid shape with an aspect ratio rather than a spherical shape was also analyzed. The change in drag force according to various aspect ratios was analyzed and compared with the results of the spherical shape under the same flow conditions.

Molecular Kinetic Simulations of Transient and Steady Wave Propagation into a Planet’s Exosphere

The vertical propagation of wave energy into a planet’s exosphere, a process that affects atmospheric evolution, is calculated here using 1D molecular kinetic simulations. Effects sensitive to molecular interactions are examined by comparing simulation results to solutions of linear fluid models for steady wave activity using parameters associated with Mars’ upper atmosphere. In addition to correctly describing the wave behavior in the exobase region, these simulations directly yield nonlinear effects such as atmospheric heating. They also readily include the transient behavior due to the onset and decay of waves propagating into the rarefied region of a planet’s atmosphere. This is a first step in understanding the effects of variable wave activity in the region where the atmosphere evolves from collisional to collisionless.

Data-driven constitutive relation reveals scaling law for hydrodynamic transport coefficients.

Finding extended hydrodynamics equationsvalid from the dense gas region to the rarefied gas region remains a great challenge. The key to success is to obtain accurate constitutive relations for stress and heat flux. Data-driven models offer a new phenomenological approach to learning constitutive relations from data. Such models enable complex constitutive relations that extend Newton's law of viscosity and Fourier's law of heat conduction by regression on higher derivatives. However, the choices of derivatives in these models are ad hoc without a clear physical explanation. We investigated data-driven models theoretically on a linear system. We argue that these models are equivalent to nonlinear length scale scaling laws of transport coefficients. The equivalence to scaling laws justified the physical plausibility and revealed the limitation of data-driven models. Our argument also points out that modeling the scaling law could avoid practical difficulties in data-driven models like derivative estimation and variable selection on noisy data. We further proposed a constitutive relation model based on scaling law and tested it on the calculation of Rayleigh scattering spectra. The result shows our data-driven model has a clear advantage over the Chapman-Enskog expansion and moment methods.

Investigation of feed flow effect using CFD-DSMC method in a gas centrifuge

In this study, the effect of rarefied region in the rotor of the centrifuge was investigated. In a rotor of the centrifuge, the feed inlet is positioned in the rarefied area. The continuum hypothesis is not valid in the rarefied area; therefore, it desires to be analyzed by probabilistic methods like Direct Simulation Monte Carlo (DSMC). In the present study, Computational Fluid Dynamic (CFD) method is used to simulate the continuum area, and the DSMC method is employed in the rarefied area. An implicit coupled density-based scheme was performed for CFD method, and Variable Hard Sphere (VHS) and diffuse model were employed in the DSMC method. Also, the local Knudsen number was defined to determine the interface location between the continuum-rarefied regions (r=0.086 m). The comparison results of pure CFD and CFD-DSMC methods illustrated large differences between the flow properties in the rarefied regions. The results showed that the value of separation power obtained from pure CFD and CFD-DSMC solution is 10.5% different.

A particle-based ellipsoidal statistical Bhatnagar–Gross–Krook solver with variable weights for the simulation of large density gradients in micro- and nano-nozzles

This paper demonstrates the efficiency of a modified particle based Ellipsoidal Statistical Bhatnagar–Gross–Krook (ESBGK) solver to simulate micro-nozzles. For this, the common particle ESBGK algorithm is adapted to handle variable particle weights including the creation of additional particles in regions with low statistical samples and merging of particles in dense regions. After the description of the methods and their implementation, the simulation results of a micro-nozzle geometry using the Direct Simulation Monte Carlo, the common particle ESBGK, and the proposed modified ESBGK method are compared concerning accuracy and efficiency. All three methods show good agreement; however, the modified ESBGK method has the highest efficiency, saving a factor of around 500 of computational time to produce a comparable statistical sample size in the rarefied expansion region.

Acetonitrile confined in carbon nanotubes, part I: Structure, dynamic and transport properties

In the first part of our study, here an all atom molecular dynamic study on the effect of confinement on structure, dynamic and transport properties of acetonitrile is presented. For this purpose, Single Walled Carbon Nanotubes (SWCNTs) were filled with the acetonitrile by employing isothermal-isobaric ensemble followed by canonical ensemble molecular dynamics simulations for investigating interactions between the acetonitrile and SWCNTs. Several interesting features of the acetonitrile were identified as the diameter of CNTs becomes smaller. First, two distinct regions were identified i.e., a core region along the longitudinal direction dominated by rarefaction effects and an interface shell with relatively high density of fluid. Volume of rarefied region decreases with larger values of tube diameters. Secondly, interfacial mobility in the vicinity fluid-CNT interface favors axial mean squared displacements of the acetonitrile molecules. Analyses also show that radial mobility of the molecules strongly depends on the size of the core region and diameter of the tube whereas the axial self-diffusion coefficient varies almost exponentially with the tube diameter. Thirdly, a preferred coordination between each pair of the C (methyl group carbon), C (nitrile group carbon) and N atoms, and an ordering in the vicinity of wall were observed contrary to those of larger tubes. Fourthly, we observed that the E2g mode frequencies of SWCNT dominates those of C1-C2-N bending and C1-C2 stretching modes. The frequencies of both SWCNTs and those of the fluid are the same in these modes. Lastly, the shear viscosity diminishes with the diameter of the tube.

Kinetic Methods for Solving Unsteady Problems with Jet Flows

The study of nonstationary rarefied gas flows is currently paid much attention. Such interest to these problems is caused by the creation of pulsed jets used for the deposition of thin films and special coatings on solid surfaces. However the problems of nonstationary rarefied gas flows have not been studied sufficiently fully because of their large computational complexity. In this paper the computational aspects of investigating the nonstationary flows of a reflected gas from a wall and flowing through a suddenly formed gap is considering. The objective of this study is to analyze the possible numerical kinetic approaches for solving such nonstationary problems and to identify the difficulties encountered in solving.When studying the gas flows in strong rarefaction regimes one should consider the Boltzmann kinetic equation, but its numerical implementation is rather laborious. In order to use more simple approaches based for example on approximation kinetic equations (Ellipsoidal-Statistical model, Shakhov model), it is important to estimate the difference of the solutions of the model equations and the Boltzmann equation. For this purpose two auxiliary problems are considered: reflection of the gas flow from the wall and outflow of the free jet into the rarefied background gas. Numerical solution of these problems shows a weak dependence of the solution on the type of the collision operator in the rarefied region, but a strong dependence on the velocity grid step . The detailed velocity grid is necessary to avoid non-monotonous behavior of macroparameters caused by the “ray effect”. To reduce numerical costs on detailed grid a hybrid method based on the synthesis of model equation and the Boltzmann equation is proposed. Such approach can be promising since it reduces the domain in which the Boltzmann collision integral should be used.The results presented in this paper were obtained using two different software packages Unified Flow Solver (UFS) [13] and Nesvetay 3D [14-15]. Note that UFS uses the discrete ordinate method for velocity space on a uniform grid and a hierarchical adaptive mesh refinement in physical space. The possibility of calculating both the Boltzmann equation and model equations is realized. The Nesvetay 3D complex was created to solve the Shakhov model equation, (S-model) and makes it possible to calculate on non-structured non uniform grids in velocity and physical spaces.Translated from Russian. Original text: Mathematics and Mathematical Modeling. 2018. no. 4. Pp. 27-44.

Numerical models for the dust in RCW 120

Context. The interstellar bubble RCW 120 seen around a type O runaway star is driven by the stellar wind and the ionising radiation emitted by the star. The boundary between the stellar wind and interstellar medium (ISM) is associated with the arc-shaped mid-infrared dust emission around the star within the HII region. Aims. We aim to investigate the arc-shaped bow shock in RCW 120 by means of numerical simulations, including the radiation, dust, HII region, and wind bubble. Methods. We performed 3D radiation-hydrodynamic simulations including dust using the GUACHO code. Our model includes a detailed treatment of dust grains in the ISM and takes into account the drag forces between dust and gas and the effect of radiation pressure on the gas and dust. The dust is treated as a pressureless gas component. The simulation uses typical properties of RCW 120. We analyse five simulations to deduce the effect of the ionising radiation and dust on both the emission intensity and the shape of the shock. Results. The interaction of the wind and the ionising radiation from a runaway star with the ISM forms an arc-shaped bow shock where the dust from the ISM accumulates in front of the moving star. Moreover, the dust forms a second small arc-shaped structure within the rarefied region at the back of the star inside the bubble. In order to obtain the decoupling between the gas and the dust, it is necessary to include the radiation-hydrodynamic equations together with the dust and the stellar motion. In this work all these elements are considered together, and we show that the decoupling between gas and dust obtained in the simulation is in agreement with the morphology of the infrared observations of RCW 120.

Impact of homogeneous and ionization unstable glow discharge plasma on a shock wave in air

The work is aimed at exploring the possibility of control of strong shock waves up to their completely destruction. The impact on shock waves by creating a region of gas-discharge plasma in propagation media is proposed. A diffuse or ionization unstable discharge with the ionization strata of different scale on the path of a shock wave propagation is organized. As a result, the shock wave propagates over the region of homogeneous highly non-equilibrium plasma or over the medium of layered structure with higher degree of ionization and electron temperature in the layers. Numerical simulation of the propagation of a shock wave over the region of energy impact was carried out on the basis of the systems of Euler and Navier-Stokes equations with the flow parameters obtained in the experiment. The homogeneous plasma region was simulated by a rarefied gas region with increased temperature and constant pressure. The area formed by the ionization unstable discharge was simulated by a thermally stratified gas area. The strong influence of the ionization of the propagation medium on the transformation of the shock wave with the formation of a new shock wave configuration is shown. Stratification of the medium leads to a distortion of this configuration up to complete destruction of it.

What can ISM and non-photospheric highly ionised lines in white dwarf spectra reveal about the β CMa tunnel?

AbstractWhite dwarfs are useful objects with which to study the local interstellar medium (ISM). High ionisation state absorption features that cannot be attributed to the photosphere or the ISM have been observed along the line-of-sight to a number of white dwarf stars. Suggested origins of these lines include ionisation from past supernovae, stellar winds, circumstellar disks, photoionisation from nearby hot stars or also from the white dwarf itself. In this study we consider the origin of these non-photospheric highly ionised lines in two stars towards a rarefied region of the galaxy known as the extended β CMa Tunnel. We present preliminary results from our analysis of the first of these two stars.

On the canonical isotherms for bulk fluid, surface adsorption and adsorption in pores: A common thread

Kinetic Monte Carlo simulated isotherms calculated in the canonical ensemble, at temperatures below the critical temperature, for bulk fluid, surface adsorption and adsorption in a confined space, show a van der Waals (vdW) loop with a vertical phase transition between the rarefied and dense spinodal points at the co-existence chemical potential, µco. Microscopic examination of the state points on this loop reveals features that are common to these systems. At state points with chemical potentials greater than μco the microscopic configurations show clusters, which coalesce to form two co-existing phases along the vertical section of the loop (the coexistence line). As more molecules are added, the dense region expands at the expense of the rarefied region, to the point where the rarefied region becomes spherical (cylindrical for 2D-systems) with a curvature greater than that of the coexisting phases. This results in a decrease of chemical potential from µco to the liquid spinodal point where the rarefied region disappears. With a further increase in loading, the chemical potential and the density increase. The existence of a vdW loop is the microscopic reason for the hysteresis observed in the grand canonical isotherm, where the adsorption and desorption boundaries of the hysteresis loop are first-order transitions, enclosing the vertical section of the vdW loop of the canonical isotherm. However, a first-order transition is rarely observed in experiments where transitions are usually steep, but not vertical. From our extensive simulations, we provide two possible reasons: (1) the finite extent of the system and (2) the existence of high energy sites that localize the clusters. In the first case, the desorption branch, and in the second case the adsorption branch, either comes close to, or collapses onto the coexistence line. When both occur, the hysteresis loop disappears and the isotherm is reversible, as often observed experimentally.

Waves in strong centrifugal field: dissipative gas

In the fast rotating gas (with the velocity typical for Iguassu gas centrifuge), three families of linear waves exist with different polarizations and law of dispersion. The energy of the waves is basically concentrated at the axis of rotation in the rarefied region. Therefore, these waves decay on the distance comparable with the wavelength. There is only one type of waves propagating strictly along the axis of rotation with the law of dispersion similar to ordinary acoustic waves. These waves are interested for the physics of gas centrifuges. The energy density of these waves concentrates at the wall of the rotor. These waves have weak damping due to the molecular viscosity and heat conductivity. The damping coefficient is determined for this type of waves by numerical calculations. Analytical approximations for the damping coefficient are defined as well. At the parameters typical for the Iguassu centrifuge, the damping is defined by interaction of the waves with the rotor wall.

Kinetic Methods for Solving Non-stationary Jet Flow Problems

The study of non-stationary rarefied gas flows is, currently, attracting a great deal of attention. Such an interest arises from creating the pulsed jets used for deposition of thin films and special coatings on the solid surfaces. However, the problems of non-stationary rarefied gas flows are still understudied because of their large computational complexity. The paper considers the computational aspects of investigating non-stationary movement of gas reflected from a wall and flowing through a suddenly formed gap. The study objective is to analyse the possible numerical kinetic approaches to solve such problems and identify the difficulties in their solving. When modeling the gas flows in strong rarefaction one should consider the Boltzmann kinetic equation, but its numerical implementation is rather time-consuming. In order to use more simple approaches based, for example, on approximation kinetic equations (Ellipsoidal-Statistical model, Shakhov model), it is important to estimate the difference between the solutions of the model equations and of the Boltzmann equation. For this purpose, two auxiliary problems are considered, namely reflection of the gas flow from the wall and outflow of the free jet into the rarefied background gas.A numerical solution of these problems shows a weak dependence of the solution on the type of the collision operator in the rarefied region, but at the same time a strong dependence of a behavior of the macro-parameters on the velocity grid step. The detailed velocity grid is necessary to avoid a non-monotonous behavior of the macro-parameters caused by so-called ray effect. To reduce computational costs of the detailed velocity grid solution, a hybrid method based on the synthesis of model equations and the Boltzmann equation is proposed. Such an approach can be promising since it reduces the domain in which the Boltzmann collision integral should be used.The article presents the results obtained using two different software packages, namely a Unified Flow Solver (UFS) [13] and a Nesvetay 3D software complex [14-15]. Note that the UFS uses the discrete ordinate method for velocity space on a uniform grid and a hierarchical adaptive mesh refinement in physical space. The possibility to calculate both the Boltzmann equation and the model equations is realized. The Nesvetay 3D software complex was created to solve the Shakhov model equation (S-model) for calculations based on non-structured non-uniform grids, both in velocity space and in physical one.

Assessment of the LD-DSMC hybrid method for hypersonic rarefied flow

Hypersonic aerothermodynamics for a probe entering a planetary atmosphere is an important issue in space exploration. The probe experiences various Knudsen number regimes, ranging from rarefied to continuum, due to density variation in the planet’s atmosphere. To simulate such multiscale flows, a novel hybrid particle scheme is employed in the present work. The hybrid particle scheme employs the direct simulation Monte Carlo (DSMC) method in rarefied flow regions and the low diffusion (LD) particle method in continuum flow regions. Numerical procedures in the low diffusion particle method are implemented within an existing DSMC algorithm. The hybrid scheme is assessed using two hypersonic, blunt body flow problems: Mach 10 nitrogen flow over a sphere, and Mach 40 carbon dioxide flow over the Mars Path Finder each with a global Knudsen number of 0.002. Standard DSMC and CFD results are compared with the LD-DSMC hybrid simulation results. The hybrid scheme results show good overall agreement with results from standard DSMC computation, while CFD is inaccurate especially in the wake where a highly rarefied region exists. The LD-DSMC hybrid solution is able to increase computational efficiency upto 50% in run time in comparison to DSMC. And sensitivity to numerical parameters of the LD-DSMC method is also studied.

Phase transitions during compression and decompression of clots from platelet-poor plasma, platelet-rich plasma and whole blood.

The objective of this paper is to measure and mathematically model the compression behavior of various human blood clots. We show by a combination of confocal and scanning electron microscopy that compression proceeds by the passage of a front through the sample that separates a densified region of the clot from a rarefied region, and that the compression/decompression response is reversible with hysteresis. These observations form the basis of a model for the compression response of clots based on the continuum theory of phase transitions. Our studies may reveal how clot rheology under large compression in vivo due to muscle contraction, platelet retraction and hydrodynamic flow varies under various pathophysiological conditions and could inform the design of fibrin based biomaterials.

DEM/FEM Simulations of Dynamic Response of Projectile Penetrating into Granular Medium

Dynamic elastic Finite Element Method (FEM) and Discrete element method (DEM) simulations are carried out to investigate dynamic penetration of a projectile into a target of granular medium. It was found that the highly densified region of granular medium was generated just ahead of the projectile and began to propagate spherically with much higher velocity than that of projectile which leaves relatively rarefied medium region. This propagation phenomenon was probably the result of a collision and momentum transfer between particles in target granular medium. The propagation velocity of the densified region decreased during penetration as depending not only on the packing ratio of target medium but also on the projectile velocity. The resistance force of projectile was also investigated in the case of penetration of projectiles with various body lengths. The resistance force increased rapidly and reached to the peak. The peak value was expressed in terms of momentum change of target particles. The resistance force decreased periodically after the peak value. The period clearly depended on the length of projectile. It is obvious that this was caused by the stress wave reverberations in the projectiles with various body lengths.

Global MHD simulations of Neptune's magnetosphere

AbstractA global magnetohydrodynamic (MHD) simulation has been performed in order to investigate the outer boundaries of Neptune's magnetosphere at the time of Voyager 2's flyby in 1989 and to better understand the dynamics of magnetospheres formed by highly inclined planetary dipoles. Using the MHD code Gorgon, we have implemented a precessing dipole to mimic Neptune's tilted magnetic field and rotation axes. By using the solar wind parameters measured by Voyager 2, the simulation is verified by finding good agreement with Voyager 2 magnetometer observations. Overall, there is a large‐scale reconfiguration of magnetic topology and plasma distribution. During the “pole‐on” magnetospheric configuration, there only exists one tail current sheet, contained between a rarefied lobe region which extends outward from the dayside cusp, and a lobe region attached to the nightside cusp. It is found that the tail current always closes to the magnetopause current system, rather than closing in on itself, as suggested by other models. The bow shock position and shape is found to be dependent on Neptune's daily rotation, with maximum standoff being during the pole‐on case. Reconnection is found on the magnetopause but is highly modulated by the interplanetary magnetic field (IMF) and time of day, turning “off” and “on” when the magnetic shear between the IMF and planetary fields is large enough. The simulation shows that the most likely location for reconnection to occur during Voyager 2's flyby was far from the spacecraft trajectory, which may explain the relative lack of associated signatures in the observations.