Direct Simulation Monte Carlo Simulations Research Articles

Light-Powered Micromotor: Design, Fabrication, and Mathematical Modeling

This paper reports on the experimental and theoretical studies of a light-driven micromotor, which is a “light mill” that rotates by absorbing photon energy. This light mill has four curved blades to form an axially asymmetric geometry. Upon lateral irradiation, the shape of the light mill induces an asymmetric photon heating to the surrounding gas molecules, leading to a gas convection that forces the light mill to rotate. The light mill was applied to actuate a scanning mirror for a laser beam. Using a Direct Simulation Monte Carlo (DSMC) model, we investigated the working principle behind the operation of the light mill. The DSMC simulation yielded results consistent to our experimental data. The simulation results were used to explain the heat-induced light-mill rotation, in which the mean free path of the surrounding gas takes an important role.

Development of a molecular dynamics-based coalescence model for DSMC simulations of ammonia condensate flows

A coalescence model for homogeneous condensation of ammonia in supersonic expansions to vacuum has been developed using molecular dynamics trajectory calculations. The MD calculations show that the sticking probability increases as the ammonia cluster size increases or the cluster temperature decreases. In addition, the sensitivity of the sticking probability to cluster size decreases as the temperature decreases. Comparison of the Ashgriz-Poo semiempirical coalescence model with MD simulations show that for cluster sizes larger than 100 the former model may be used. To model homogeneous nucleation in an ammonia jet, direct simulation Monte Carlo (DSMC) simulations were performed for different stagnation pressure conditions using the MD simulation outcomes for smaller cluster-cluster collisions and the Ashgriz-Poo model for cluster sizes larger than 100. We found that, by including the combined coalescence model, the average cluster sizes and size distributions predicted by DSMC agree reasonably well with experiment.

An experimental assembly for precise measurement of thermal accommodation coefficients

An experimental apparatus has been developed to determine thermal accommodation coefficients for a variety of gas-surface combinations. Results are obtained primarily through measurement of the pressure dependence of the conductive heat flux between parallel plates separated by a gas-filled gap. Measured heat-flux data are used in a formula based on Direct Simulation Monte Carlo (DSMC) simulations to determine the coefficients. The assembly also features a complementary capability for measuring the variation in gas density between the plates using electron-beam fluorescence. Surface materials examined include 304 stainless steel, gold, aluminum, platinum, silicon, silicon nitride, and polysilicon. Effects of gas composition, surface roughness, and surface contamination have been investigated with this system; the behavior of gas mixtures has also been explored. Without special cleaning procedures, thermal accommodation coefficients for most materials and surface finishes were determined to be near 0.95, 0.85, and 0.45 for argon, nitrogen, and helium, respectively. Surface cleaning by in situ argon-plasma treatment reduced coefficient values by up to 0.10 for helium and by ∼0.05 for nitrogen and argon. Results for both single-species and gas-mixture experiments compare favorably to DSMC simulations.

J054022 多孔質体内のナノスケール気体流れに関する数値的研究([J05402]マイクロ・ナノスケールの熱流体現象(2))

In porous media with holes as small as a molecular mean free path, Knudsen number of gas flow in the narrow channel is in the order of unity. Therefore, the direct simulation Monte Carlo (DSMC) method is suitable to solve the transport phenomena in porous media. However, even if the inside structures of porous media are measured transparently by microscopy technique such as 3D transmission electron microscopy (3D TEM), geometries obtained will be discrete. Moreover, performing DSMC simulation for nanoscale gas flow in porous media is difficult because of its complicated structure. Therefore, we need to estimate and simplify the real shapes of complicated channels inside porous media. In this work, we propose two schemes for estimation and simplification of solid bodies in porous media. In the first scheme, we simplify them as aggregations of cubes. In the second scheme, we simplify them as aggregations of polyhedra. We put cubes or polyhedra based on the discrete information of solid bodies in porous media. We examine merits and demerits of these schemes by performing numerical simulations of example problems.

Direct simulation Monte Carlo modeling of e-beam metal deposition

Three-dimensional direct simulation Monte Carlo (DSMC) method is applied here to model the electron-beam physical vapor deposition of copper thin films. Various molecular models for copper-copper interactions have been considered and a suitable molecular model has been determined based on comparisons of dimensional mass fluxes obtained from simulations and previous experiments. The variable hard sphere model that is determined for atomic copper vapor can be used in DSMC simulations for design and analysis of vacuum deposition systems, allowing for accurate prediction of growth rates, uniformity, and microstructure.

Prediction of shock structure using the bimodal distribution function

A modification of Mott-Smith method for predicting the one-dimensional shock wave solution is presented. Mott-Smith distribution function is used to construct the system of moment equations to study the steady-state structure of shock wave in a gas of Maxwell molecules and in argon. The predicted shock solutions using the newly proposed formalism are compared to the experimental data, direct-simulation Monte Carlo (DSMC) solution, and the solutions predicted by other existing theories for Mach numbers M<11 . The density, temperature, heat flux profiles, and shock thickness calculated at different Mach numbers have been shown to have good agreement with the experimental and DSMC solutions. In addition, the predicted shock thickness is in good agreement with the DSMC simulation result at low Mach numbers.

T0501-3-3 多孔質体内を流れる気体の熱流動解析([T0501-3]マイクロ・ナノスケールの熱流体現象(3))

Gas flow with surface reaction in porous media appears in various regions of engineering. In porous media with holes as small as a molecular mean free path, i. e., Knudsen number Kn of gas flow in the narrow channel is in the order of unity. Therefore, the direct simulation Monte Carlo (DSMC) method is suitable to solve transport phenomena in porous media. We perform 2D DSMC simulations of such a flow. Porous media are modeled as an aggregation of randomly-placed spherical particles. The shape of narrow channel in porous media is complicated. To reduce complexity, we propose the simplification for porous structures, i. e., we simplify solid bodies in porous media as aggregations of cubes or as aggregations of polyhedra. We perform simulations with and without simplification. We compare results and investigate effects of the simplification.

Atomistic hybrid DSMC/NEMD method for nonequilibrium multiscale simulations

A multiscale hybrid method for coupling the direct simulation Monte Carlo (DSMC) method to the nonequilibrium molecular dynamics (NEMD) method is introduced. The method addresses Knudsen layer type gas flows within a few mean free paths of an interface or about an object with dimensions of the order of a few mean free paths. It employs the NEMD method to resolve nanoscale phenomena closest to the interface along with coupled DSMC simulation of the remainder of the Knudsen layer. The hybrid DSMC/NEMD method is a particle based algorithm without a buffer zone. It incorporates a new, modified generalized soft sphere (MGSS) molecular collision model to improve the poor computational efficiency of the traditional generalized soft sphere GSS model and to achieve DSMC compatibility with Lennard-Jones NEMD molecular interactions. An equilibrium gas, a Fourier thermal flow, and an oscillatory Couette flow, are simulated to validate the method. The method shows good agreement with Maxwell–Boltzmann theory for the equilibrium system, Chapman–Enskog theory for Fourier flow, and pure DSMC simulations for oscillatory Couette flow. Speedup in CPU time of the hybrid solver is benchmarked against a pure NEMD solver baseline for different system sizes and solver domain partitions. Finally, the hybrid method is applied to investigate interaction of argon gas with solid surface molecules in a parametric study of the influence of wetting effects and solid molecular mass on energy transfer and thermal accommodation coefficients. It is determined that wetting effect strength and solid molecular mass have a significant impact on the energy transfer between gas and solid phases and thermal accommodation coefficient.

Modeling of CO2Homogeneous and Heterogeneous Condensation Plumes

A pure CO2 homogeneous condensation flow is simulated with a new direct simulation Monte Carlo (DSMC)-based condensation model, and comparisons of the measured [Ramos, A.; Fernández, J. M.; Tejeda, G.; Montero, S. Phys. Rev. A 2005, 72, 3204] and simulated CO2 cluster size and number density distributions were found to agree well for low stagnation pressures. The same carbon dioxide homogeneous condensation model was then applied to the study of an expanding heterogeneous condensation flow of a 5% CO2 and 95% mixture [Williams, W. D.; Lewis, J. W. L. DTIC Paper No. AEDC-TR-80-16, 1980]. To simulate this case, a new kinetic-based model of N2 molecules condensing on CO2 nuclei was developed using molecular dynamics techniques and was implemented in the DSMC simulation of the expanding mixture. Pure nitrogen flow for the same expansion conditions was observed to not produce any clusters. It was found that incorporation of the heterogeneous condensation process of N2 molecules condensing on CO2 nuclei causes the average N2 cluster size to increase from 10 (the homogeneous condensation result) to about 2000. The simulated Rayleigh scattering intensity results were found to agree well with the experimental data.

Extension of a Multiscale Particle Scheme to Near-Equilibrium Viscous Flows

A recently proposed low diffusion (LD) equilibrium particle method based on the direct simulation Monte Carlo (DSMC) method is modified for use with near-equilibrium viscous flows. A finite volume discretization of the viscous terms in the compressible Navier-Stokes equations is used to incorporate diffusive transport effects into the LD particle method, and a velocity and temperature slip wall boundary condition is employed for improved accuracy in the slip flow Knudsen number regime. The modified method is compared with both DSMC and theory for a series of unsteady boundary layer problems, and excellent agreement is observed. The computational cost of the modified LD particle method is shown for a representative near-equilibrium case to be roughly four orders of magnitude lower than that of DSMC, due to reduced scatter as well as less stringent cell size and time step requirements in the LD method. Simulation procedures are outlined for a strongly coupled hybrid algorithm, where the LD particle method is used in continuum flowfield regions and DSMC is employed in nonequilibrium regions. The hybrid scheme is evaluated through a comparison with numerical and experimental data for a flow of N2 through a small convergent-divergent nozzle into a near vacuum, and hybrid simulation results are generally found to agree very well with other available data. I. Introduction AS flows involving a wide range of characteristic length scales appear in a number of different engineering applications, including those related to atmospheric flow around reentry or hypersonic vehicles, high-altitude rocket plumes, flows within and around micro-electro-mechanical systems, and any supersonic flow where internal shock structures are of interest. In these types of flows, a near-equilibrium gas velocity distribution may exist through much of the flowfield, as the equilibrating effect of intermolecular collisions dominates over other processes (such as inhomogeneous diffusive transport or gas-surface interaction) which tend to pull the velocity distribution away from equilibrium. However, some flowfield regions may have characteristic length scales comparable to or smaller than the local mean free path, so that the influence of collisions does not dominate and the velocity distribution diverges considerably from the equilibrium limit. While simulation of near-equilibrium flowfield regions may be efficiently performed using computational fluid dynamics (CFD) techniques based on the Navier-Stokes equations, nonequilibrium regions must be simulated using more expensive techniques based on the Boltzmann equation. The Boltzmann equation is the governing equation for dilute gas flows at arbitrary Knudsen numbers, and its derivation follows from assumptions of molecular chaos and binary intermolecular collisions with no approximations regarding the shape of the velocity distribution. The most mature and commonly used simulation method for the Boltzmann equation is the direct simulation Monte Carlo (DSMC) method, first introduced by Bird. 1 In a DSMC simulation, a large number of representative particles are tracked through a computational grid, and move and collide in a manner consistent with physical arguments underlying the Boltzmann equation. While this method may be applied to both nonequilibrium and continuum flowfield regions, cell size and time step limitations often make it prohibitively expensive for simulating continuum flows where global characteristic length scales are far larger than the mean free path. In practice, such multiscale flows are usually simulated using both DSMC and CFD methods, by applying CFD techniques in near-equilibrium regions where the Navier-Stokes equations are valid, and using DSMC elsewhere in the flow. In the simplest type of hybrid CFD-DSMC approach, a CFD simulation is performed on a domain which 1

Collisionless gas flows over a flat cryogenic pump plate

This article concerns collisionless gas flows over a flat cryogenic pump plate with a specific sticking probability. It presents exact density, velocity, temperature, and pressure solutions which are useful in determining the plate sticking probability. At any point off the plate, the local velocity distribution function (VDF) consists of several pieces of Maxwellian VDFs, one is characterized by free stream flow properties and the others by plate surface properties. Integrating the VDFs with different moments leads to these exact solutions, which are further validated by simulations with the direct simulation Monte Carlo (DSMC) method. We use these solutions to derive several useful expressions, based on special measured flow field properties at specific locations off the plate, to evaluate the pump sticking probability. Also, the exact solutions complement past studies of aerodynamic coefficients and heat transfer rate for collisionless gas flowing over a flat plate. They explicitly express the physical and geometrical factors. Evaluations of those solutions are much faster than DSMC simulations. This study can find other useful applications, e.g., cold gas spray for thin film depositions inside a vacuum chamber, and spacecraft plume impingement estimations.

Kinetic nucleation model for free expanding water condensation plume simulations

Recent direct simulation Monte Carlo (DSMC) simulations of homogeneous condensation in free expansion water plumes [Z. Li, J. Zhong, D. A. Levin, and B. Garrison, AIAA J. 47, 1241 (2009)] show that the nucleation rate is a key factor for accurately modeling condensation phenomenon. In this work, we use molecular dynamics (MD) simulations of a free expansion to explore the microscopic mechanisms of water dimer formation and develop collision models required by DSMC. Bimolecular and termolecular dimer cluster formation mechanisms are considered and the former is found to be the main mechanism in expanding flows to vacuum. MD simulations between two water molecules using the simple point charge intermolecular potential were performed to predict the bimolecular dimer formation probability and the probability was found to decrease with collision energy. The formation probabilities and postcollisional velocity and energy distributions were then integrated into DSMC simulations of a free expansion of an orifice condensation plume with different chamber stagnation temperatures and pressures. The dimer mole fraction was found to increase with distance from the orifice and become constant after a distance of about two orifice diameters. Similar to experiment, the terminal dimer mole fraction was found to decrease with chamber stagnation temperatures and increase linearly with chamber stagnation pressures which is consistent with a bimolecular nucleation mechanism.

Convergence behavior of a new DSMC algorithm

The convergence rate of a new direct simulation Monte Carlo (DSMC) method, termed “sophisticated DSMC”, is investigated for one-dimensional Fourier flow. An argon-like hard-sphere gas at 273.15 K and 266.644 Pa is confined between two parallel, fully accommodating walls 1 mm apart that have unequal temperatures. The simulations are performed using a one-dimensional implementation of the sophisticated DSMC algorithm. In harmony with previous work, the primary convergence metric studied is the ratio of the DSMC-calculated thermal conductivity to its corresponding infinite-approximation Chapman–Enskog theoretical value. As discretization errors are reduced, the sophisticated DSMC algorithm is shown to approach the theoretical values to high precision. The convergence behavior of sophisticated DSMC is compared to that of original DSMC. The convergence of the new algorithm in a three-dimensional implementation is also characterized. Implementations using transient adaptive sub-cells and virtual sub-cells are compared. The new algorithm is shown to significantly reduce the computational resources required for a DSMC simulation to achieve a particular level of accuracy, thus improving the efficiency of the method by a factor of 2.

An efficient direct simulation Monte Carlo method for low Mach number noncontinuum gas flows based on the Bhatnagar–Gross–Krook model

The direct simulation Monte Carlo (DSMC) method is the preferred approach for simulating rarefied gas flows in complex geometries. However, the standard DSMC method becomes inefficient in the limit M=U¯/⟨c⟩→0 when the thermal velocity fluctuations which scale with the speed of sound ⟨c⟩ are much larger than characteristic ensemble-averaged flow speed U¯. In this paper, we propose a modified DSMC algorithm which simulates the linearized Bhatnagar–Gross–Krook (BGK) approximation to the Boltzmann equation. The particles in this method are uniformly distributed in space and have a rest-state, equilibrium Maxwellian velocity distribution. The deviations from the equilibrium state are captured by weightings, indicating that each particle represents a noninteger expectation for finding gas molecules with the simulation particle’s velocity in the spatial cell where it is found. The BGK approximation makes the implementation of such a method simple and efficient because the BGK collision rule can be implemented by adjusting particle weightings without the need to create new particles during the simulation. The method can be incorporated into existing DSMC simulation programs with minimal changes. We apply the new algorithm to two test problems—pressure-driven flow through a nanochannel and flow around an isolated sphere. Results obtained with the new method are in excellent agreement with previous theories and simulations.

1-D DSMC simulation of Io's atmospheric collapse and reformation during and after eclipse

A one-dimensional Direct Simulation Monte Carlo (DSMC) model is used to examine the effects of a non-condensable species on Io's sulfur dioxide sublimation atmosphere during eclipse and just after egress. Since the vapor pressure of SO 2 is extremely sensitive to temperature, the frost-supported dayside sublimation atmosphere had generally been expected to collapse during eclipse as the surface temperature dropped. For a pure SO 2 atmosphere, however, it was found that during the first 10 min of eclipse, essentially no change in the atmospheric properties occurs at altitudes above ∼ 100 km due to the finite ballistic/acoustic time. Hence immediately after ingress the auroral emission morphology above 100 km should resemble that of the immediate pre-eclipse state. Furthermore, the collapse dynamics are found to be greatly altered by the presence of even a small amount of a non-condensable species which forms a diffusion layer near the surface that prevents rapid collapse. It is found that after 10 min essentially no collapse has occurred at altitudes above ∼ 20 km when a nominal mole fraction of non-condensable gas is present. Collapse near the surface occurs relatively quickly until a static diffusion layer many mean free paths thick of the non-condensable gas builds up which then retards further collapse of the SO 2 atmosphere. For example, for an initial surface temperature of 110 K and 35% non-condensable mole-fraction, the ratio of the SO 2 column density to the initial column density was found to be 0.73 after 10 min, 0.50 after 30 min, and 0.18 at the end of eclipse. However, real gas species (SO, O 2) may not be perfectly non-condensable at Io's surface temperatures. If the gas species was even weakly condensable (non-zero sticking/reaction coefficient) then the effect of the diffusion layer on the dynamics was dramatically reduced. In fact, if the sticking coefficient of the non-condensable exceeds ∼0.25, the collapse dynamics are effectively the same as if there were no non-condensable present. This sensitivity results because the loss of non-condensable to the surface reduces the effective diffusion layer size, and the formation of an effective diffusion layer requires that the layer be stationary; this does not occur if the surface is a sink. Upon egress, vertical stratification of the condensable and non-condensable species occurs, with the non-condensable species being lifted (or pushed) to higher altitudes by the sublimating SO 2 after the sublimating atmosphere becomes collisional. Stratification should affect the morphology and intensity of auroral glows shortly after egress.

Computation of head–disk interface gap micro flowfields using DSMC and continuum–atomistic hybrid methods

AbstractThis paper discusses computational modeling of micro flow in the head–disk interface (HDI) gap using the direct simulation Monte Carlo (DSMC) method. Modeling considerations are discussed in detail both for a stand‐alone DSMC computation and for the case of a hybrid continuum–atomistic simulation that couples the Navier–Stokes (NS) equation to a DSMC solver. The impact of the number of particles and number of cells on the accuracy of a DSMC simulation of the HDI gap is investigated both for two‐ and three‐dimensional configurations. An appropriate implicit boundary treatment method for modeling inflow and outflow boundaries is used in this work for a three‐dimensional DSMC micro flow simulation. As the flow outside the slider is in the continuum regime, a hybrid continuum–atomistic method based on the Schwarz alternating method is used to couple the DSMC model in the slider bearing region to the flow outside the slider modeled by NS equation. Schwarz coupling is done in two dimensions by taking overlap regions along two directions and the Chapman–Enskog distribution is employed for imposing the boundary condition from the continuum region to the DSMC region. Converged hybrid flow solutions are obtained in about five iterations and the hybrid DSMC–NS solutions show good agreement with the exact solutions in the entire domain considered. An investigation on the impact of the size of the overlap region on the convergence behavior of the Schwarz method indicates that the hybrid coupling by the Schwarz method is weakly dependent on the size of the overlap region. However, the use of a finite overlap region will facilitate the exchange of boundary conditions as the hybrid solution has been found to diverge in the absence of an overlap region for coupling the two models. Copyright © 2009 John Wiley &amp; Sons, Ltd.

A hybrid particle approach for continuum and rarefied flow simulation

A hybrid particle scheme is presented for the simulation of compressible gas flows involving both continuum regions and rarefied regions with strong translational nonequilibrium. The direct simulation Monte Carlo (DSMC) method is applied in rarefied regions, while remaining portions of the flowfield are simulated using a DSMC-based low diffusion particle method for inviscid flow simulation. The hybrid scheme is suitable for either steady state or unsteady flow problems, and can simulate gas mixtures comprising an arbitrary number of species. Numerical procedures are described for strongly coupled two-way information transfer between continuum and rarefied regions, and additional procedures are outlined for the determination of continuum breakdown. The hybrid scheme is evaluated through a comparison with DSMC simulation results for a Mach 6 flow of N 2 over a cylinder, and good overall agreement is observed. Large potential efficiency gains (over three orders of magnitude) are estimated for the hybrid algorithm relative to DSMC in a simple example involving a rarefied expansion flow through a small nozzle into a vacuum chamber.

Simulation of unsteady flows by the DSMC macroscopic chemistry method

In the Direct Simulation Monte-Carlo (DSMC) method, a combination of statistical and deterministic procedures applied to a finite number of ‘simulator’ particles are used to model rarefied gas-kinetic processes. In the macroscopic chemistry method (MCM) for DSMC, chemical reactions are decoupled from the specific particle pairs selected for collisions. Information from all of the particles within a cell, not just those selected for collisions, is used to determine a reaction rate coefficient for that cell. Unlike collision-based methods, MCM can be used with any viscosity or non-reacting collision models and any non-reacting energy exchange models. It can be used to implement any reaction rate formulations, whether these be from experimental or theoretical studies. MCM has been previously validated for steady flow DSMC simulations. Here we show how MCM can be used to model chemical kinetics in DSMC simulations of unsteady flow. Results are compared with a collision-based chemistry procedure for two binary reactions in a 1-D unsteady shock-expansion tube simulation. Close agreement is demonstrated between the two methods for instantaneous, ensemble-averaged profiles of temperature, density and species mole fractions, as well as for the accumulated number of net reactions per cell.

Numerical Modeling of Gas Expansion from Microtubes

The expansion of argon jets from cylindrical microtubes is investigated using a three-dimensional unstructured direct simulation Monte Carlo (DSMC) method. The simulation results for a microtube with an aspect ratio (tube length to diameter) of 1.5 are shown to compare well with theoretical formulations of free-jet expansion. The DSMC simulations are performed in computational domains that feature both an internal microtube region and external jet expansion region. Microtubes with orifice diameters ranging between 100 μm and 100 nm are used in the simulations in order to investigate the effects of Knudsen number, aspect ratio, Reynolds number, and microtube scale on jet structure. The jet shape is shown to narrow with increasing Knudsen number, increasing aspect ratio and decreasing Reynolds number. The reduction in relative number density along the flow axis is shown to decrease with increasing Knudsen number and Reynolds number.

Hybrid Particle-Continuum Simulations of Nonequilibrium Hypersonic Blunt-Body Flowfields

A modular particle-continuum (MPC) numerical method is presented which solves the Navier-Stokes (NS) equations in regions of near-equilibrium and uses the direct simulation Monte Carlo (DSMC) method where the flow is in non-equilibrium. The MPC method is designed specifically for steady-state, hypersonic, nonequilibrium flows and couples existing, state-of-the-art DSMC and NS solvers into a single modular code. The MPC method is tested for 2D flow of N2 at various Mach numbers over a cylinder where the global Knudsen number is 0.01. For these conditions, NS simulations significantly over-predict the local shear-stress, and also over-predict the peak heating rate by 5-10% when compared with full DSMC simulations. DSMC also predicts faster wake closure and 10-15% higher temperatures in the immediate wake region. The MPC code is able to accurately reproduce DSMC flow field results, local velocity distributions, and surface properties up to 2.8 times faster than full DSMC simulations. The computational time saved by the MPC method is directly proportional to the fraction of the flow field which is in near-equilibrium. It is found that particle simulation of the shock interior is not necessary for accurate prediction of surface properties, however particle simulation of the boundary layer and near-wake region is.