Direct Simulation Monte Carlo Simulations Research Articles

A hybrid Gaussian mixture/DSMC approach to study the Fourier thermal problem

In rarefied gas dynamics scattering kernels deserve special attention since they contain all the essential information about the effects of physical and chemical properties of the gas–solid surface interface on the gas scattering process. However, to study the impact of the gas–surface interactions on the large-scale behavior of fluid flows, these scattering kernels need to be integrated in larger-scale models like Direct Simulation Monte Carlo (DSMC). In this work, the Gaussian mixture (GM) model, an unsupervised machine learning approach, is utilized to establish a scattering kernel for monoatomic (Ar) and diatomic (H2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {H}_{2}$$\\end{document}) gases directly from Molecular Dynamics (MD) simulations data. The GM scattering kernel is coupled to a pure DSMC solver to study isothermal and non-isothermal rarefied gas flows in a system with two parallel walls. To fully examine the coupling mechanism between the GM scattering kernel and the DSMC approach, a one-to-one correspondence between MD and DSMC particles is considered here. Benchmarked by MD results, the performance of the GM-DSMC is assessed against the Cercignani–Lampis–Lord (CLL) kernel incorporated into DSMC simulation (CLL-DSMC). The comparison of various physical and stochastic parameters shows the better performance of the GM-DSMC approach. Especially for the diatomic system, the GM-DSMC outperforms the CLL-DSMC approach. The fundamental superiority of the GM-DSMC approach confirms its potential as a multi-scale simulation approach for accurately measuring flow field properties in systems with highly nonequilibrium conditions.

Multi-Scale Simulations of Gas-Phase Particles Generated in Plasma Enhanced Atomic Layer Deposition Processes

Recently, Plasma Enhanced Atomic Layer Deposition (PEALD) has been investigated as an advanced semiconductor deposition method to expand the number and variety of materials other than those available in thermal ALD. The high reactivity of the plasma species at the deposition surface during PEALD has the advantage of increasing the degree of freedom of processing conditions and enabling a wider range of material properties. PEALD consists of four steps in the order of feed, 1st purge, reaction, and 2nd purge. In this reaction step, the secondary gas-phase reaction is important because the properties of the thin film vary greatly depending on the particles that arrive on the growing surface. Therefore, the particle distribution in the gas phase before arrival on the surface should be accurately predicted to estimate the film quality. Generally, the DSMC (Direct Simulation Monte Carlo) method is a commonly used method for analyzing particle distribution in the gas phase. The DSMC method requires reaction and scattering models that simulate the behavior between molecules. Variable Hard Sphere and Variable Soft Sphere are often used as the model in DSMC. These models are about molecular transport, such as molecular diffusion, and cannot deal with molecular reactions. The total collision energy model is determined for molecular reactions, but it may not accurately describe molecular reactions in non-equilibrium flow. The purpose of the study is to develop a new reaction-scattering model in non-equilibrium flow in the DSMC method for determining the particle distribution in the gas phase in the PEALD processes. Here, we focus on ammonia plasma used in the reaction step of boron nitride nanomaterial films, which are used in various applications, such as semiconductors and fine ceramics with two-dimensional and three-dimensional structures. This study focused on neutral and ionic molecules, NH3 and NH4 +, which can be the main collisional species in secondary gas-phase reactions.A molecular dynamics simulation with a reactive force field (ReaxFF) was performed. The left figure shows the simulation system of NH3 and NH4 + collisions. The periodic boundary conditions were applied to the simulation box for all directions in the size of 100 Å × 100 Å × 100 Å. Randomly oriented NH3 and NH4 + were placed in a line at an initial distance of 15 Å. NH4 + was given an electric charge of –0.22892 on N and 0.30723 on H. The initial translational energy of NH4 + was set at 5-60 eV, and the difference in the vertical coordinate at 0.1-5.0 Å. The collisions were sampled 2000 times.The right figure shows the calculated collision cross section, which determines whether a collision occurs or not. The collision coefficient bcoll represents the difference in the maximum vertical coordinate at which the absolute value of the scattering angle is greater than 1 degree. The collision cross section decreases as the translational energy increases because the negligible attraction-force act on NH3 and NH4 + at a long distance. When the translational energy exceeds 40 eV, the collisional cross-section no longer decreases and becomes asymptotic. The reason can be considered as follows. As the cross-section approaches 40 Å2, the collision cross section asymptotically approaches 40 Å2, regardless of the translational energy, because the attractive and repulsive forces are balanced. We compared our results with a reference model in grey color. In the reference model, Etr, 0 represents the minimum translational energy, σT,0 is the collision cross section at the minimum, Etr is the translational energy, and ω is a fitting parameter. Here, ω was set at –3.1. The reference model shows a good agreement with our results. However, the collision cross section is asymptotic above 40 eV, which may affect the results when the DSMC simulations are performed. We will apply the reaction scattering model to the DSMC method and analyze the gas-phase reaction of PEALD, including a comparison of the results of existing models. Figure 1

Micro-nozzle flow and thrust prediction with high-density ratio using DSMC selection limiter

Introduction:A Direct Simulation Monte Carlo (DSMC) solver with a modified collisional routine is used to investigate an argon gas flow through a millimeter-scaled thruster nozzle with high-density ratios.Method:The limiter scheme, denoted as the constant selection limiter (CSL), limits the possible number of selected collisional pairs to a constant value in accordance with the present simulation particles in the cell.Results:Results of the CSL scheme are compared with the experimental and numerical results of a compressible Navier–Stokes solver and discussed in comparison with baseline DSMC simulations. The influence of collision limitation by the CSL is discussed on the stagnation pressure of the thruster and on thrust and specific impulse prediction. The application of the limiter scheme makes the prediction of stagnation pressure challenging in some cases.Discussion:In contrast, thrust and specific impulse are predicted well, and their study remains valid. Investigated mass flow rates are 0.178 mg/s ≤m.≤ 71.360 mg/s, and flow Knudsen numbers below Kn = 0.01 and over Kn = 10 are present. Near atmospheric conditions are reached inside the thruster, generating pressure ratios up to 3,741 along the nozzle. The computational performance of the scheme is also discussed, and speed-up factors up to 0.51 are achieved.

Finding the bulk viscosity of air from Rayleigh-Brillouin light scattering spectra.

Spectral line shape models can successfully reproduce experimental Rayleigh-Brillouin spectra, but they need knowledge about the bulk viscosity ηb. Light scattering involves GHz frequencies, but since ηb is only documented at low frequencies, ηb is usually left as a free parameter, which is determined by a fit of the model to an experimental spectrum. The question is whether models work so well because of this freedom. Moreover, for light scattering in air, spectral models view "air" as an effective molecule. We critically evaluate the use of ηb as a fit parameter by comparing ηb obtained from fits of the Tenti S6 model to the result of Direct Simulation Monte Carlo (DSMC) for a mixture of Nitrogen and Oxygen. These simulations are used to compute light scattering spectra, which are then compared to experiments. The DSMC simulation parameters are cross-checked with a molecular dynamics simulation based on intermolecular potentials. At large values of the uniformity parameter y, y ≈ 4, where the Brillouin contribution to spectra is large, fitted ηb are 20% larger than the ones from DSMC, while the quality of the simulated spectra is comparable to that of the Tenti S6 line shape model. At smaller y, the difference between fitted and simulated ηb can be as large as 100%. We hypothesize the breakdown of the bulk viscosity concept to be the cause of this fallacy.

Numerical Study of Gas Flow in Super Nanoporous Materials Using the Direct Simulation Monte-Carlo Method.

The direct simulation Monte Carlo (DSMC) method, which is a probabilistic particle-based gas kinetic simulation approach, is employed in the present work to describe the physics of rarefied gas flow in super nanoporous materials (also known as mesoporous). The simulations are performed for different material porosities (0.5≤ϕ≤0.9), Knudsen numbers (0.05≤Kn≤1.0), and thermal boundary conditions (constant wall temperature and constant wall heat flux) at an inlet-to-outlet pressure ratio of 2. The present computational model captures the structure of heat and fluid flow in porous materials with various pore morphologies under rarefied gas flow regime and is applied to evaluate hydraulic tortuosity, permeability, and skin friction factor of gas (argon) flow in super nanoporous materials. The skin friction factors and permeabilities obtained from the present DSMC simulations are compared with the theoretical and numerical models available in the literature. The results show that the ratio of apparent to intrinsic permeability, hydraulic tortuosity, and skin friction factor increase with decreasing the material porosity. The hydraulic tortuosity and skin friction factor decrease with increasing the Knudsen number, leading to an increase in the apparent permeability. The results also show that the skin friction factor and apparent permeability increase with increasing the wall heat flux at a specific Knudsen number.

Development of a novel DC micro-discharge code on dsmcFoam+ for plasma effect in DSMC flow profile simulations and its application to a micro-plasma system

Recent advances in the miniaturisation of plasma-based microelectromechanical systems have permitted their application in the space sector, such as flow control of flying vehicles and the potential usage in high precision attitude and orbit control systems for CubeSats. To determine its contribution in pressure, velocity, and temperature profiles for thrust analysis on micro-fluidic channels in space/vacuum environments, a novel DC micro-discharge code has been developed in the dsmcFoam+ solver in order to simulate the ionic effects on the gas flow during the breakdown voltage in microgaps.The rarefied gas flow was solved using the direct simulation Monte Carlo (DSMC) method, with the Fowler–Nordheim equation to calculate the ionic current density during the vacuum field emissions effect for the micro-plasma simulation.The incorporation of the Fowler–Nordheim model avoids the addition of an exponential increase in computational power requirements for a DSMC simulation. Instead of introducing new electrons and ions as equivalent particles into the system, the existing DSMC gas particles in the cells are accelerated. Through this, a computationally lightweight alternative for micro-scale plasma simulations utilising the dsmcFoam+ solver is achieved, which can be tailored to the thrust requirements of a particular mission.

Fast vacuum plume prediction using a convolutional neural networks-based direct simulation Monte Carlo method

The vacuum plume, which can incur impingement forces, heat fluxes, and contaminations on the spacecraft, has been a vital issue in space missions such as lunar landings. The direct simulation Monte Carlo (DSMC) method is generally used to simulate the vacuum plume. However, DSMC is a particle simulation, and thus, it is very time-consuming, making it impossible to achieve real-time analysis during lunar landings. Motivated by this tricky issue, we explore the feasibility of deep learning to predict the vacuum plume using convolutional neural networks (CNN). In the study, a CNN-based DSMC method (CNN-DSMC) is proposed. The dataset is obtained by the DSMC simulation. The inputs of CNN-DSMC are the shape information and the boundary conditions, which are transformed into the signed distance function (SDF) and identifier matrix (IM), respectively. In particular, a shock-based partitioned method is developed to construct IM to suit the complex flow field with the shock wave. Finally, a vacuum plume velocity field is predicted using the proposed CNN-DSMC, and the prediction of CNN-DSMC is well consistent with DSMC results. Most importantly, compared with the traditional DSMC, the speedup of CNN-DSMC can be up to 4 orders of magnitude, suggesting that CNN-DSMC is a promising method for real-time analysis during lunar landings.

Unravelling CO oxidation reaction kinetics on single Pd nanoparticles in nanoconfinement using a nanofluidic reactor and DSMC simulations

Steady state catalytic oxidation of CO in nanofluidic channels decorated with Pd nano particles was studied using the Direct Simulation Monte Carlo (DSMC) method. Diffusion, collision, adsorption, desorption and reaction processes are simulated simultaneously. The influence of various adsorption (sticking coefficient, saturation coverage), desorption (activation energy, pre-exponential factor) and reaction (activation barrier) parameters on the final CO2 turnover are determined. These effects are considered to tune DSMC surface reaction model with respect to the experimental results. With DSMC, it was possible to get insights on reactivity of the individual Pd particles and the resulting varying reaction conditions along the channel due to local conversion effects. From the local coverages, the limit of CO:O2 inlet ratio to get maximum CO2 turnover without poisoning the catalyst with CO were determined. The approach paves the way to accurately represent micro- and nanoscale flows at the same system size as that of experiments.

Low-Speed DSMC Simulations of Hotwire Anemometers at High-Altitude Conditions

Numerical simulations of hotwire anemometers in low-speed, high-altitude conditions have been carried out using the direct simulation Monte Carlo (DSMC) method. Hotwire instruments are commonly used for in-situ turbulence measurements because of their ability to obtain high spatial and temporal resolution data. Fast time responses are achieved by the wires having small diameters (1–5 μm). Hotwire instruments are currently being used to make in-situ measurements of high-altitude turbulence (20–40 km). At these altitudes, hotwires experience Knudsen number values that lie in the transition-regime between slip-flow and free-molecular flow. This article expands the current knowledge of hotwire anemometers by investigating their behavior in the transition-regime. Challenges involved with simulating hotwires at high Knudsen number and low Reynolds number conditions are discussed. The ability of the DSMC method to simulate hotwires from the free-molecular to slip-flow regimes is demonstrated. Dependence of heat transfer on surface accommodation coefficient is explored and discussed. Simulation results of Nusselt number dependence on Reynolds number show good agreement with experimental data. Magnitude discrepancies are attributed to differences between simulation and experimental conditions, while discrepancies in trend are attributed to finite simulation domain size.

Binary gas mixtures separation using microscale radiometric pumps

In this paper, we suggest the application of micro-scale radiometric pumps for helium‑xenon binary mixture separation. For this purpose, we consider three geometries of radiometric pumps consisting of channels with their bottom or top surfaces periodically patterned with different structures including a simple vane or double isosceles triangular ratchets. In these geometries, the channel surfaces and structures are considered as diffuse reflectors. The temperature is kept constant on the horizontal walls of the channel; thus, radiometric flow is created by subjecting the adjacent sides of the vane/ratchet to constant but unequal temperatures. Numerical simulation is performed using the direct simulation Monte Carlo (DSMC) method. The DSMC simulations are performed at a Knudsen number for mixture based on the vane/ratchet height of around 0.2. The present study has two important aspects. The first is the amount of lateral and vertical separation that can be achieved by using newly designed Knudsen pumps is described. The second is to study the behavior of the flow field in binary gas mixtures. The features of each design in gas separation will be discussed.

DSMC simulation of two-step dissociation-recombination of hydrogen on tantalum surface

The presented work is devoted to the development of new approaches to simulating heterogeneous reactions of hydrogen dissociation and recombination during its interaction with the solid surface within the framework of the direct simulation Monte Carlo (DSMC) method. The DSMC algorithm including a two-step model of hydrogen dissociation is developed. A new technique for simulating heterogeneous reactions within the framework of the DSMC method is proposed, in which the reaction rate constant depends on the gas and surface temperature. The algorithm is verified on the example of a heated infinite tantalum wire placed in a hydrogen atmosphere. The influence of different approaches to simulating heterogeneous reactions on the flux of atomic hydrogen is studied. The results are compared with the results of simulation within the framework of the continuum approach. The developed approaches expand the possibilities of the DSMC method for the study of gas flows taking into account the influence of heterogeneous reactions.

Kinetic simulations of laser-induced plume expansion from a copper target into a vacuum or argon background gas based on ab initio calculation of Cu–Cu, Ar–Ar, and Ar–Cu interactions

The kinetic simulations of plume expansion induced by pulsed laser heating of a copper target in a vacuum or low-pressure argon background gas are performed based on the direct simulation Monte Carlo (DSMC) method and ab initio quantum mechanical calculation of interactions between copper and argon atoms. The potential energy curves (PECs) for Cu–Cu, Ar–Ar, and Ar–Cu interactions are obtained in density functional theory (DFT) calculations with the van der Waals (vdW) correction. The computed Cu–Cu PEC is strikingly different from the Lennard-Jones (LJ) potentials with semi-empirical parameters, which were previously suggested for kinetic simulations of the copper vapor flows. It is found that the Lorentz–Berthelot rule cannot reliably predict the parameters of the LJ potential for cross-species Ar–Cu interaction. The DFT-vdW PECs are fitted by the Morse long-range (MLR) potentials. The MLR potentials are used to compute the outcomes of binary collisions in the DSMC method based on the solution of the classical scattering problem and to parameterize the variable hard sphere (VHS) collision model. The results of the DSMC simulations based on DFT-vdW PECs are compared with the results obtained based on various parameterizations of the VHS model. It is shown that the previously developed parameterizations of the VHS model can either over- or underestimate the plume temperature and density compared to the results obtained based on the DFT-vdW PECs. The simulations also reveal the strong effect of the cross-species collision model parameters on the flow structure in the mixing layer, which is dominated by molecular diffusion.

DSMC simulation of rarefied gas flow over a 2D backward-facing step in the transitional flow regime: Effect of Mach number and wall temperature

Rarefied gas flow over a backward-facing step (BFS) is often encountered in separating flows prevalent in aerodynamic flows, engine flows, condensers, space vehicles, heat transfer systems, and microflows. Direct Simulation Monte Carlo (DSMC) is a powerful tool to investigate such flows. The purpose of this research is to assess the impact of Mach number and wall temperature on the flow and surface properties in the transitional flow regime. The Mach numbers considered are 5, 10, 25, 30, and the ratio of the temperature of the wall to that of freestream considered are 1, 2, 4, 8. The Reynolds number for the cases studied is 8.6, 17.2, 43, and 51.7, respectively. Typically the flow properties near the wall are found to increase with both Mach number and wall temperature owing to compressibility and viscous dissipation effects. The variation in flow properties is more sensitive to Mach number than the wall temperature. The surface properties are found to decrease with Mach number and increase with wall temperature. Moreover, in the wake of the step, the vortex’s recirculation length is reasonably independent of both free stream Mach number and wall temperature, whereas it decreases with Knudsen number.

Highly dilute gas flows over an ellipse

This paper presents recent investigation results on free molecular flows over a diffusely or specularly reflective ellipse, by using the gaskinetic theory. A virtual density distribution along the diffusely reflective surface is introduced to aid the investigations. Many local surface properties are obtained, including the surface slip velocity and coefficients for pressure, friction, and heat flux. Global coefficients for aerodynamic forces and moments and mass center–force center distances are also obtained by integrating the local surface distributions. In the end, analytical expressions for the flowfields around a diffusely or specularly reflective ellipse are also obtained. Special non-dimensional parameters, such as temperature and speed ratios, are explicitly embedded in these expressions. Particle simulations with the direct simulation Monte Carlo (DSMC) method are performed to validate the above results. Those expressions need computers for evaluations; however, the cost is very minor when compared with DSMC simulations. The approaches are heuristic to investigate other external collisionless flows, and the load coefficients can be considered as baseline references at the high Knudsen number limit. By using these collisionless flow results, it is feasible to further study less rarefied gas flows over an ellipse, for example, with an asymptotic method. Swift parameter studies based on these solutions can be performed to study their effect.

Analysis of gas flow over a cylinder at all Knudsen numbers based on non-newtonian constitutive models

This paper is focused on the gas properties over a cylinder from continuum to rarefied regimes based on the non-Newtonian constitutive model. This new constitutive model is first derived from Eu’s nonequilibrium ensemble method, which is intended for accurate description of nonequilibrium flows. Some assumptions and simplifications are made during the establishing progress of the new constitutive model by both Eu and Myong. To verify its accuracy, temperature contours and skin frictions around the cylinder are simulated by this new model. The inflow Mach number is equal to 10 and the Knudsen number ranges from 0.002 to 0.05. All simulation results are compared with Navier–Stokes (NS) and the direct simulation Monte Carlo (DSMC) methods in detail. The comparisons of friction around the surface show that the non-Newtonian constitutive models are better than the linear constitutive relations of NS equations for the prediction of nonequilibrium flow and much more close to DSMC simulation results.

Contribution of viscosity to the circulation deposition in the Richtmyer–Meshkov instability

This study focuses on the process of the circulation deposition in the Richtmyer–Meshkov instability (RMI). The growth rate of circulation and its sources are theoretically and numerically studied to reveal the physical mechanism of the viscosity in the circulation deposition process. We derive a predicting model of the circulation rate for RMI. More importantly, all the contributing sources are separately predicted. Particularly, the viscous source, which previously lacked theoretical or numerical investigations, is efficiently predicted. The RMI problems in a large range of initial conditions are simulated with the direct simulation Monte Carlo (DSMC) method to verify our predicting model and further reveal the circulation deposition mechanism. The DSMC simulations provide reliable quantification of the circulation deposition (especially viscous contribution) for RMI due to its molecular nature. Our model predicts the circulation rate, baroclinic and viscous sources accurately for all the cases in comparison with the simulations. A new physical insight into the mechanism of viscosity in RMI is provided. Unlike the previous understandings that nearly all circulation deposition in RMI comes from the baroclinic source, this study reveals the hidden positive contribution of the viscous source, especially for high Mach number conditions (up to 11 % of total circulation rate). For RMI, the large viscosity gradient inside the shock waves plays a crucial role in the circulation deposition even under high Reynolds number conditions. Our study also provides exciting opportunities to further understand the viscous contribution to the vorticity dynamics in the reshocked RMI and shock wave–turbulence interactions.

Three-dimensional DSMC simulation of thermal Knudsen force in micro gas actuator for mass analysis of gas mixture

High precision detection and measurement of the components of a gas mixture are highly significant in chemical industries. In the textile industry, CO2 is widely used to dye the textile material without water called Supercritical Fluid Dyeing Technology. In this study, a computational technique is applied to investigate the ability of an innovative MEMS gas actuator (MIKRA) for the sensation of the specific component in the gas mixture. This work also investigated various mixtures of gases and various relative concentrations of CO2 to N2. In this actuator, the temperature dissimilarity of two arms at rarefied conditions produces a Knudsen force. Due to the micro size of this sensor, this actuator is highly significant for the inaccessible detection domain. This work tries to reveal the main mechanism for this sensor to increase the precision of the detection. The flow patterns of a mixture gas within this micro gas sensor are examined by Direct Simulation Monte Carlo (DSMC) method since the domain of this micro gas is non-equilibrium. According to the obtained results, a three-dimensional model presents more reliable results and the effect of a gap for the three-dimensional model demonstrates the impact of this parameter on the effective Knudsen force.

Coarse-grain cross sections for rovibrational excitation and dissociation of the [formula omitted] system

We present a method to generate analytical coarse-grain cross sections for internal energy excitation and dissociation of nitrogen and apply it to the NASA Ames N2-Nab initio database. State-resolved cross sections from this database are reduced using the Uniform RoVibrational-Collisional bin model. With a 10-bin system as example we compare two sets of coarse-grain cross sections: one obtained by analytical inversion and another by direct binning. With analytical inversion we manage to compress the entire set of state-resolved data into a small set of parameters, sufficient to reconstruct the main features of the full database. This has the potential of massively reducing the computational cost in large-scale direct simulation Monte Carlo (DSMC) calculations, both concerning memory requirements and execution time. Combining this coarse-grain model with the N2-Nab initio database will enable much higher-fidelity DSMC simulation of nonequilibrium dissociation in shock-heated flows than is currently possible with conventional models.

Interaction of rigid body motion and rarefied gas dynamics based on the BGK model

In this paper we present simulations of moving rigid bodies immersed in a rarefied gas. The rarefied gas is simulated by solving the Bhatnager-Gross-Krook (BGK) model for the Boltzmann equation. The Newton-Euler equations are solved to simulate the rigid body motion. The force and the torque on the rigid body is computed from the surrounded gas. An explicit Euler scheme is used for the time integration of the Newton-Euler equations. The BGK model is solved by the semi-Lagrangian method suggested by Russo &amp; Filbet ^{[<span class="xref"><a href="#b22" ref-type="bibr">22</a></span>]}. Due to the motion of the rigid body, the computational domain for the rarefied gas (and the interface between the rigid body and the gas domain) changes with respect to time. To allow a simpler handling of the interface motion we have used a meshfree method for the interpolation procedure in the semi-Lagrangian scheme. We have considered a one way, as well as a two-way coupling of rigid body and gas flow. We use diffuse reflection boundary conditions on the rigid body and also on the boundary of the computational domain. In one space dimension the numerical results are compared with analytical as well as with Direct Simulation Monte Carlo (DSMC) solutions of the Boltzmann equation. In the two-dimensional case results are compared with DSMC simulations for the Boltzmann equation and with results obtained by other researchers. Several test problems and applications illustrate the versatility of the approach.

Systematic direct simulation Monte Carlo approach to characterize the effects of surface roughness on accommodation coefficients

The effects of surface roughness on accommodation coefficients are studied using the direct simulation Monte-Carlo (DSMC) approach. DSMC simulations are carried out by varying the roughness parameters. An empirical relationship between surface roughness and accommodation coefficients is established.