Method Of Direct Statistical Simulation Research Articles

Numerical Investigation of Radiation in a Shock-Heated CO2 and N2 Mixture by the Direct Statistical Simulation Method

Numerical Investigation of Radiation in a Shock-Heated CO2 and N2 Mixture by the Direct Statistical Simulation Method

Numerical simulation of flows over vacuometers by means of the Monte-Carlo method of direct statistical simulation

An upper atmosphere probe is considered. For the atmosphere parameters, a reconstruction method using the density data by a vacuometer located behind a wire screen is constructed. In the context of the Monte-Carlo method of direct statistical simulation, we propose a simplified simulation algorithm for the interactions of a molecule with the wire screen treated as a semipermeable membrane. To obtain a relationship between the transmitter reading and the parameters of the undisturbed atmosphere, we numerically simulate the flow over the transmitter.

Simulation of the heat exchange between the supersonic flow and the stationary body in a gas centrifuge

We have made comparative calculations of the heat exchange in the subpersonic flow of gaseous UF6 around the stationary cylindrical body inside the rotating rotor of the gas centrifuge. It has been revealed that the integral heat flux from the gas to the body calculated with the use of the ANSYS-CFX program complex from the viewpoint of the continuum model is much smaller than the heat flow calculated by the Monte Carlo method of direct statistical simulation. Estimates show that under the conditions being considered the boundary layer on the surface of the body has no time to be formed and has a thickness of the order of the mean free path of the gas molecules and, therefore, the use of the methods of continuum mechanics in this region is incorrect. On the contrary, the method of direct statistical simulation permits taking into account the interaction of gas molecules directly with the surface of the streamline body and obtaining more correct results.

Interference between a centered rarefaction wave and an inclined shock wave

The gas flow in the zone of interaction between an oblique shock and a centered isentropic rarefaction wave is studied using the direct statistical simulation method for solving the Boltzmann equation. The data of calculations of the shock and rarefaction wave structures, flow fields, and streamlines are given for the free-stream Mach number M∞ = 6, 4 and 2. The formation of the interaction zone is simulated by a gas flow past a double-plane wedge in which the break of the generating line leads to formation of the centered isentropic rarefaction wave. The results of calculations of this flow in solving the Boltzmann equation are given in the Euler approximation.

10.1007/s11454-008-1005-6

Processes of formation of silicon clusters upon expansion of vapor from a sudden source into vacuum are considered. Vapor expansion and condensation are described using the method of direct statistical simulation. The clustering model includes the description of cluster growth and decomposition processes, as well as energy exchange accompanying these processes. Main regularities of the cluster formation and growth during expansion of vapor into vacuum are considered. The model and the results are of considerable interest for solving problems associated with evaporation of rapidly heated small particles.

10.1007/s11454-008-1006-5

Processes of formation of silicon clusters upon expansion of vapor from a sudden source into a surrounding inert gas are considered. Vapor expansion and condensation are described using the method of direct statistical simulation. The clustering model includes the description of cluster growth and decomposition, as well as energy exchange accompanying these processes. Main regularities of the cluster formation and growth during expansion of vapor into a gas are considered. The model and the results are of considerable interest for solving problems associated with evaporation of rapidly heated small particles.

Temperature force of interaction between spherical particles

The force of interaction between small particles in a gas induced by a temperature difference between the particle surface and the gas far away from the particle is considered. The particle dimensions correspond to the free-molecular, transitional, and continuum heat transfer regimes. A Monte-Carlo numerical method of direct statistical simulation of the solution of the nonlinear Boltzmann equation and the results of asymptotic solutions are used. The force of interaction between two hot or cold spherical particles is investigated. The dependence of the temperature force on the particle size, i.e. on the flow regime (Knudsen number), and the distance between the particles is examined. Approximations for these dependences are constructed.

The effect of the flow-to-wall temperature ratio on strong condensation of gas

The method of direct statistical simulation is used to investigate the effect of the flow-to-wall temperature ratio T on the strong subsonic condensation of monatomic gas. It is demonstrated that the dependence of relative pressure at the boundary of the Knudsen layer on relative temperature at a fixed value of the Mach number M has a minimum. In so doing, the marked supercooling of condensing gas (T < 1) causes an abrupt increase in relative pressure. At the same time, for a “moderately cold” wall (1.5 < T < 10), the dependence of relative pressure on relative temperature at a fixed value of M is very weak. It is demonstrated that, in the case of supersonic condensation, the dependence of minimal possible relative pressure on T at a fixed value of M likewise has a minimum. The calculation results agree well with the results of calculations by the method of moments using the suggested approximation of the molecule distribution function.

The promising gas-dynamic schemes of vacuum deposition from the supersonic gas mixture flows

Gas jet deposition (GJD) becomes promising method of thin film and nanoparticle deposition. This paper is focused on elaboration of new methods of GJD based on different gas dynamic schemes of flow formation and interaction with substrate. Using direct statistical simulation method, the analysis was performed for: a) interaction of the jet from the sonic nozzle with a substrate; b) fan flow in the result of interaction of two opposite jets; c) convergent flow from the ring nozzle, directional to the axis; d) interaction of the jet after convergent flow with the substrate; e) fan flow in the result of interaction of two opposite jets after convergent expansion.

Direct statistical simulation of cluster formation and growth upon expansion of vapor from a sudden spherical source. II. Expansion into gas

Processes of formation of silicon clusters upon expansion of vapor from a sudden source into a surrounding inert gas are considered. Vapor expansion and condensation are described using the method of direct statistical simulation. The clustering model includes the description of cluster growth and decomposition, as well as energy exchange accompanying these processes. Main regularities of the cluster formation and growth during expansion of vapor into a gas are considered. The model and the results are of considerable interest for solving problems associated with evaporation of rapidly heated small particles.

New Monte Carlo global weight method for the approximate solution of the nonlinear Boltzmann equation

We develop new weight modifications of the method of direct statistical simulation for the approximate solution of the nonlinear Boltzmann equation by using the ingenious procedure proposed by the authors, viz. the stratification of collision distribution in a many-particle system by the number of a pair of interacting particles. We check the appropriate weight algorithms for the model problem with the known solution. They allow us to estimate the variations of functionals under small changes of parameters.

Effect of the Intermolecular Potential on the Generalized Newton-Fourier Relations in the Problem of Gas Outflow into a Vacuum

Using the numerical method of direct statistical simulation (Monte-Carlo method), the effect of the intermolecular potential exponent on the dependence of the stress and the heat flux on the stress rate tensor components and the temperature gradient is analyzed for the nonequilibrium, spherically symmetric outflow of a monatomic gas into a vacuum. Analytical approximations of the constitutive relations are presented. The dependence of the macroscopic parameters on the distance from the source is found.

New Monte Carlo global weight method for the approximate solution of the nonlinear Boltzmann equation

We develop new weight modifications of the method of direct statistical simulation for the approximate solution of the nonlinear Boltzmann equation by using the ingenious procedure proposed by the authors, viz. the stratification of collision distribution in a many-particle system by the number of a pair of interacting particles. We check the appropriate weight algorithms for the model problem with the known solution. They allow us to estimate the variations of functionals under small changes of parameters.

Mass Transfer in the Near-Surface Layer of a Cometary Nucleus: A Gas-Kinetic Approach

A self-consistent model of the kinetically nonequilibrium near-surface layer of a cometary nucleus is developed on the basis of the gas-kinetic approach. The weight method of direct statistical simulation is used to model numerically the two-dimensional gas outflow from an ice sample subjected to radiative heating. The effective coefficient of water ice sublimation is estimated. Mass transfer in a porous ice and mineral (scattering) nonisothermal medium is investigated by the method of test particles, and the effective gas release is evaluated taking into account the proper rotation of the cometary nucleus for various model parameters. In these calculations, allowance is made for the kinetic character of the flow and volume sublimation and condensation of the volatile constituents of the material of the cometary nucleus.

Direct statistical simulation of gas mixture mass transfer in a porous layer with condensation of one of the components and absorption of another

Based on the method of direct statistical simulation, a physical–mathematical model has been developed for gas mixture mass transfer in a highly porous body under the conditions of condensation of one of the components and trapping of a non-condensable admixture. Distributions of gas velocities and densities in a porous layer and in the space above it are found, as well as distributions of flows of a condensable component and absorbable admixture along the depth of the porous layer. The efficiencies of the absorption of the admixture in a porous layer and on a plane surface are compared.

Kinetics of intense evaporative mass transfer through a porous layer

A kinetic problem of mass transfer in a model porous body in the process of intense evaporation (condensation) and vapour escape into a vacuum is considered. Two computational methods have been used: the mean free path method and the method of direct statistical simulation. With the aid of the first method the location of the condensation zone within a porous body is determined as a function of the evaporating surface-to-porous layer temperature difference and also of the condensation coefficient. The second method is employed in a one-dimensional case to obtain (without condensation) the density, velocity and temperature distributions for a gas in a porous layer and in a gas medium behind the porous body. It is shown that the agreement between the parameters obtained by both methods for the gas flow escaping the porous layer is quite satisfactory

Effect of magnetic fields on the anisotropy of the distribution function of thermonuclear particles in LTF

The spontaneous magnetic fields produced by compression of spherical laser targets are known to reach, through development of hydrodynamic instability, strengths on the order of several times ten MG and thereby influence substantially the kinetics of fast charged particles. The same can be said also of external magnetic fields, since the target compression causes the fields to increase at the instant of maximum compression by 100 to 500 times, owing to the freezing-in of the force lines. Thus, even at an initial field strength [approx]10[sup 2] kG, the fields can reach in the course of compression tens of MG and alter substantially the kinetics of the fast particles. The present paper is devoted to the development of a method of direct statistical simulation of the physics of distribution of fast charged particles -- products of thermonuclear reactions accompanying LTF (laser thermonuclear fusion) in magnetic fields of arbitrary configuration. The authors use this method to investigate the influence of the magnetic fields on the distribution function f(r, v) itself as well as the energy transfer from the fast thermonuclear particles to the background plasma of the target and also on the flux anisotropy in the energy spectra of the particles emittedmore » from the target. They propose for the diagnostics of the magnetic field in the target a method based on an analysis of the degree of anisotropy of the flows of the particles leaving the target. 13 refs., 15 figs.« less

Two methods for solving the problem of heat transfer in a rarefied gas

The problem of stationary one-dimensional heat flow between parallel flat surfaces in a rarefied gas is solved using two independent numerical methods: the finite difference method of direct solution of the Boltzmann equation and the method of direct statistical simulation. By comparing the results, the accuracy of the methods is established and the algorithms for solving the problem are verified. The features of the flow are investigated for a wide range of Knudsen numbers.