Direct Simulation Monte Carlo Simulations Research Articles

Robust cut-cell algorithms for DSMC implementations employing multi-level Cartesian grids

Robust cut-cell algorithms are detailed for general multi-level Cartesian grid direct simulation Monte Carlo (DSMC) implementations. Different approaches for each component of the cut-cell algorithms are elaborated and compared, based on time efficiency, robustness, and ease of implementation. Special situations that arise in sorting the surface triangles, calculating the cut-cell volume, and identifying multiple cut-volumes contained in a single Cartesian cell, are handled by the algorithms, and their effects on the overall simulation results are analyzed using test cases. Three-dimensional DSMC simulations are conducted for a Mach number 20.2 N2 gas flowing over a Planetary Probe geometry showing good agreement with experimental heat flux measurements. Rarefied flow over a geometry resembling the MIR Space Station is also conducted, to demonstrate the ability of the proposed cut-cell algorithms to handle complex geometries. The time required to cut the surface meshes from the background Cartesian grids and to calculate the volume of the resulting cut-cells is found to be comparable to the time cost for one DSMC simulation time step for cases considered.

Modeling and measurements of water–vapor flow and icing at low pressures with application to pharmaceutical freeze-drying

A modeling and computational framework for analysis of rarefied water vapor flow and icing in application to pharmaceutical freeze-drying is developed. The direct simulation Monte Carlo (DSMC) technique is applied to model the relevant gaseous transport processes in a low-pressure environment encountered in freeze-drying. The developing ice front on a supercooled surface is simulated based on the water vapor mass flux computed from DSMC. Verification of icing simulations has been done by comparison with the analytical solution for a free-molecular flow over a circular cylinder. To validate the vapor flow and icing simulations, measurements of ice accretion in a laboratory-scale freeze-dryer are conducted with the use of time-lapse photography. The simulations corresponding to the measured time-average water sublimation rate agree well with the observed patterns and rates of ice accretion. The developed computational framework has been applied to investigate factors underlying the observed non-uniformity of ice growth. It has been shown that two key factors impact the uniformity of ice accretion: (i) the direction of the vapor flow at the inlet to the condenser which is governed by the geometry of a duct connecting the product chamber to the condenser; and (ii) the pressure of non-condensable gases in the condenser reservoir. The DSMC simulations demonstrate that by tailoring the condensing surfaces topology to the flowfield structure of the water vapor jet expanding into a low-pressure reservoir, it is possible to significantly increase the total rate of vapor removal and improve the overall efficiency of the freeze-drying process.

DSMC simulation of the gas flow through a bend and a short microchannel

The present work is related to the study of the gas flows through micro-channels with 90° bend, and short straight channels. The direct simulation Monte Carlo (DSMC) method has been used to study the flow. The DSMC simulations of the gas flow through micro-channels of real dimensions, which are used in the laboratory or in industry, are computationally very expensive, requiring large amounts of the computer resources and time. This fact places a limit on the applicability of the DSMC method while considering the real channel dimensions. It is a good practice to approximate the three dimensional micro-channel into two dimensions, and to study the flow characteristics, when the channel width is essentially large in comparison with their heights. However, the simulation of gas flows in more complicated channels with rectangular cross-section having comparable height and width unavoidably requires a 3D consideration. In the present paper, the 3D flow through a bend and short straight channels are presented, and the flow characteristics studied using the DSMC method. The complete 3D simulations were carried out for the case the height H at 19.83e-6m considering to the same as the one used in the laboratory (without taking similarity of the flow into consideration for the reduction of the actual dimensions of the channel). However, the other dimensions (length and width) were chosen different from the real channel due to the computational requirements. Two types of pressure boundary treatment have been implemented in three dimensions using the DSMC method

A parametric study of Io’s thermophysical surface properties and subsequent numerical atmospheric simulations based on the best fit parameters

Io’s sublimation atmosphere is inextricably linked to the SO2 surface frost temperature distribution which is poorly constrained by observations. We constrain Io’s surface thermal distribution by a parametric study of its thermophysical properties in an attempt to better model the morphology of Io’s sublimation atmosphere. Io’s surface thermal distribution is represented by three thermal units: sulfur dioxide (SO2) frosts/ices, non-frosts (probably sulfur allotropes and/or pyroclastic dusts), and hot spots. The hot spots included in our thermal model are static high temperature surfaces with areas and temperatures based on Keck infrared observations. Elsewhere, over frosts and non-frosts, our thermal model solves the one-dimensional heat conduction equation in depth into Io’s surface and includes the effects of eclipse by Jupiter, radiation from Jupiter, and latent heat of sublimation and condensation. The best fit parameters for the SO2 frost and non-frost units are found by using a least-squares method and fitting to observations of the Hubble Space Telescope’s Space Telescope Imaging Spectrograph (HST STIS) mid- to near-UV reflectance spectra and Galileo PPR brightness temperature. The thermophysical parameters are the frost Bond albedo, αF, and thermal inertia, ΓF, as well as the non-frost surface Bond albedo, αNF, and thermal inertia, ΓNF. The best fit parameters are found to be αF≈0.55±0.02 and ΓF≈200±50Jm−2K−1s−1/2 for the SO2 frost surface and αNF≈0.49±0.02 and ΓNF≈20±10Jm−2K−1s−1/2 for the non-frost surface.These surface thermophysical parameters are then used as boundary conditions in global atmospheric simulations of Io’s sublimation-driven atmosphere using the direct simulation Monte Carlo (DSMC) method. These simulations are unsteady, three-dimensional, parallelized across 360 processors, and include the following physical effects: inhomogeneous surface frosts, plasma heating, and a temperature-dependent residence time on the non-frost surface. The DSMC simulations show that the sub-jovian hemisphere is significantly affected by the daily solar eclipse. The simulated SO2 surface frost temperature is found to drop only ∼5K during eclipse due to the high thermal inertia of SO2 surface frosts but the SO2 gas column density falls by a factor of 20 compared to the pre-eclipse column due to the exponential dependence of the SO2 vapor pressure on the SO2 surface frost temperature. Supersonic winds exist prior to eclipse but become subsonic during eclipse because the collapse of the atmosphere significantly decreases the day-to-night pressure gradient that drives the winds. Prior to eclipse, the supersonic winds condense on and near the cold nightside and form a highly non-equilibrium oblique shock near the dawn terminator. In eclipse, no shock exists since the gas is subsonic and the shock only reestablishes itself an hour or more after egress from eclipse. Furthermore, the excess gas that condenses on the non-frost surface during eclipse leads to an enhancement of the atmosphere near dawn. The dawn atmospheric enhancement drives winds that oppose those that are driven away from the peak pressure region above the warmest area of the SO2 frost surface. These opposing winds meet and are collisional enough to form stagnation point flow.The simulations are compared to Lyman-α observations in an attempt to explain the asymmetry between the dayside atmospheres of the anti-jovian and sub-jovian hemispheres. Lyman-α observations indicate that the anti-jovian hemisphere has higher column densities than the sub-jovian hemisphere and also has a larger latitudinal extent. A composite “average dayside atmosphere” is formed from a collisionless simulation of Io’s atmosphere throughout an entire orbit. This composite “average dayside” atmosphere without the effect of global winds indicates that the sub-jovian hemisphere has lower average column densities than the anti-jovian hemisphere (with the strongest effect at the sub-jovian point) due primarily to the diurnally averaged effect of eclipse. This is in qualitative agreement with the sub-jovian/anti-jovian asymmetry in the Lyman-α observations which were alternatively explained by the bias of volcanic centers on the anti-jovian hemisphere. Lastly, the column densities in the simulated average dayside atmosphere agree with those inferred from Lyman-α observations despite the thermophysical parameters being constrained by mid- to near UV observations which show much higher instantaneous SO2 gas column densities. This may resolve the apparent discrepancy between the lower “average dayside” column densities observed in the Lyman-α and the higher instantaneous column densities observed in the mid- to near UV.

Asymptotic modelling of flows in microchannel by using Navier–Stokes or Burnett equations and comparison with DSMC simulations

The modelling of isothermal gas flows driven by pressure drops, in coplanar microchannels is investigated. The goal is to construct an asymptotic model deduced from Navier–Stokes or Burnett equations for this type of flow, assuming slip boundary conditions along the walls. The dimensionless balance equations are written, taking into account a geometrical parameter introduced in this study. The application of the Principle of Least Degeneracy produces models with small Mach numbers and small or moderate Knudsen numbers and allows the development of asymptotic models. The first and second approximations associated with the Navier–Stokes or Burnett equations are presented and discussed. Navier–Stokes and Burnett second approximations reduce the mass flow rates.Additionally, first asymptotic solutions as against Direct Simulation Monte Carlo (DSMC) simulations show overall satisfactory agreements.

Numerical modeling of an ITER type Cryopump

The present article is focused on the computational investigation of a 2D axisymmetric complex geometry of a model cryopump by the Direct Simulation Monte Carlo (DSMC) method. Since the flow close to the cryopanels can be assumed free molecular due to low pressures, the capture coefficient of the cryopanels can be estimated by applying the Test Particle Monte Carlo method. Then, this information can be used as input data to the corresponding DSMC simulations. The macroscopic parameters of practical interest as the bulk velocity, the pressure and the temperature in the whole flow field have been calculated as functions of the incoming gas throughput and of the pump inlet valve position. The importance of these calculations is based on the fact that it can provide information for quantities which are not accessible for measurement during pump operation and that it can be used for prediction of the pump behavior. This paper describes a post-operational investigation of a built pump and is thought as a proof-of-principle test to include this approach in the design process of a future pump development. Finally, the presented code could be further developed and benchmarked towards the control of the final pump as installed in ITER.

Direct simulation Monte Carlo modeling of metal vapor flows in application to thin film deposition

Thin films of metal for electronics, nano/microelectromechanical systems and optical coatings are often prepared by various vacuum deposition techniques. Modeling such metal vapor flows using methods such as the direct simulation Monte Carlo (DSMC) can aid in the design and analysis of deposition systems and accelerate development of films with desired properties. The determination of suitable variable hard sphere (VHS) molecular model parameters for DSMC simulations using measured growth rate distribution is demonstrated with aluminum vapor as an example. Axisymmetric DSMC simulations using a VHS model corresponding to a reference diameter of 0.8 nm and a viscosity-temperature exponent of 1 are shown to agree well with available experimental data. The model is then used in two-dimensional DSMC simulations to study the interaction of plumes from multiple sources. An expression for substrate mass flux assuming no interaction between sources agrees well with DSMC simulations for a mass flow rate of 0.1 g/min corresponding to a Knudsen number (Kn) of about 0.1. The non-additive interaction of plumes at a higher flow rate of 1 g/min corresponding to a Kn of about 0.01 results in a higher mass flux non-uniformity in the DSMC simulations which is not captured by the simplified analytical expression.

A variable hard sphere-based phenomenological inelastic collision model for rarefied gas flow simulations by the direct simulation Monte Carlo method

A modified phenomenological model is constructed for the simulation of rarefied flows of polyatomic non-polar gas molecules by the direct simulation Monte Carlo (DSMC) method. This variable hard sphere-based model employs a constant rotational collision number, but all its collisions are inelastic in nature and at the same time the correct macroscopic relaxation rate is maintained. In equilibrium conditions, there is equi-partition of energy between the rotational and translational modes and it satisfies the principle of reciprocity or detailed balancing. The present model is applicable for moderate temperatures at which the molecules are in their vibrational ground state. For verification, the model is applied to the DSMC simulations of the translational and rotational energy distributions in nitrogen gas at equilibrium and the results are compared with their corresponding Maxwellian distributions. Next, the Couette flow, the temperature jump and the Rayleigh flow are simulated; the viscosity and thermal conductivity coefficients of nitrogen are numerically estimated and compared with experimentally measured values. The model is further applied to the simulation of the rotational relaxation of nitrogen through low- and high-Mach-number normal shock waves in a novel way. In all cases, the results are found to be in good agreement with theoretically expected and experimentally observed values. It is concluded that the inelastic collision of polyatomic molecules can be predicted well by employing the constructed variable hard sphere (VHS)-based collision model.

Direct simulation Monte Carlo-based expressions for the gas mass flow rate and pressure profile in a microscale tube

The direct simulation Monte Carlo (DSMC) method of Bird is used to develop simple closed-form expressions for the mass flow rate and the pressure profile for the steady isothermal flow of an ideal gas through a microscale tube connecting two infinite reservoirs at different pressures but at the temperature of the tube wall. Gas molecules reflect from the tube wall according to the Maxwell model (a linear combination of specular and diffuse reflections at the wall temperature) with a unity or sub-unity value of the accommodation coefficient (the probability that molecules reflect diffusely from the wall). The DSMC-based expressions have four parameters. Two parameters are specified so that the mass flow rate reduces to the known expression in the free-molecular regime. One parameter was previously determined by comparison to DSMC simulations in the slip regime. The remaining parameter is determined by comparison to DSMC simulations for pressures spanning the transition regime with several values of the accommodation coefficient. The expressions for the mass flow rate and the pressure profile agree well with the DSMC simulations (rms and maximum differences of 2% and 5% for all cases examined), with other more complicated expressions and with recent experiments involving microscale tubes and channels for all flow regimes.

An object-oriented serial implementation of a DSMC simulation package

This paper reports a scalar implementation of a multi-dimensional direct simulation Monte Carlo (DSMC) package named “Generalized Rarefied gAs Simulation Package” (GRASP). This implementation adopts a concept of simulation engine and it utilizes many Object-Oriented Programming features and software engineering design patterns. As a result, this implementation successfully resolves the problem of program functionality and interface conflictions for multi-dimensional DSMC implementations. The package has an open architecture which benefits further development and code maintenance. To reduce engineering time for three-dimensional simulations, one effective implementation is to adopt a hybrid grid scheme with a flexible data structure, which can automatically treat cubic cells adjacent to object surfaces. This package can utilize traditional structured, unstructured or hybrid grids to model multi-dimensional complex geometries and simulate rarefied non-equilibrium gas flows. Benchmark test cases indicate that this implementation has satisfactory accuracy for complex rarefied gas flow simulations.

The generalized Onsager model for the secondary flow in a high-speed rotating cylinder

AbstractThe generalizations of the Onsager model for the radial boundary layer and the Carrier–Maslen model for the end-cap axial boundary layer in a high-speed rotating cylinder are formulated for studying the secondary gas flow due to wall heating and due to insertion of mass, momentum and energy into the cylinder. The generalizations have wider applicability than the original Onsager and Carrier–Maslen models, because they are not restricted to the limit$\mathscr{A}\gg 1$, though they are restricted to the limit$\mathit{Re}\gg 1$and a high-aspect-ratio cylinder whose length/diameter ratio is large. Here, the stratification parameter$\mathscr{A}= \sqrt{m{\Omega }^{2} {R}^{2} / (2{k}_{B} T)} $. This parameter$\mathscr{A}$is the ratio of the peripheral speed,$\Omega R$, to the most probable molecular speed,$ \sqrt{2{k}_{B} T/ m} $, the Reynolds number$\mathit{Re}= {\rho }_{w} \Omega {R}^{2} / \ensuremath{\mu} $, where$m$is the molecular mass,$\Omega $and$R$are the rotational speed and radius of the cylinder,${k}_{B} $is the Boltzmann constant,$T$is the gas temperature,${\rho }_{w} $is the gas density at wall, and$\ensuremath{\mu} $is the gas viscosity. In the case of wall forcing, analytical solutions are obtained for the sixth-order generalized Onsager equations for the master potential, and for the fourth-order generalized Carrier–Maslen equation for the velocity potential. For the case of mass/momentum/energy insertion into the flow, the separation-of-variables procedure is used, and the appropriate homogeneous boundary conditions are specified so that the linear operators in the axial and radial directions are self-adjoint. The discrete eigenvalues and eigenfunctions of the linear operators (sixth-order and second-order in the radial and axial directions for the Onsager equation, and fourth-order and second-order in the axial and radial directions for the Carrier–Maslen equation) are determined. These solutions are compared with direct simulation Monte Carlo (DSMC) simulations. The comparison reveals that the boundary conditions in the simulations and analysis have to be matched with care. The commonly used ‘diffuse reflection’ boundary conditions at solid walls in DSMC simulations result in a non-zero slip velocity as well as a ‘temperature slip’ (gas temperature at the wall is different from wall temperature). These have to be incorporated in the analysis in order to make quantitative predictions. In the case of mass/momentum/energy sources within the flow, it is necessary to ensure that the homogeneous boundary conditions are accurately satisfied in the simulations. When these precautions are taken, there is excellent agreement between analysis and simulations, to within 10 %, even when the stratification parameter is as low as 0.707, the Reynolds number is as low as 100 and the aspect ratio (length/diameter) of the cylinder is as low as 2, and the secondary flow velocity is as high as 0.2 times the maximum base flow velocity. The predictions of the generalized models are also significantly better than those of the original Onsager and Carrier–Maslen models, which are restricted to thin boundary layers in the limit of high stratification parameter.

Graphics processing unit based direct simulation Monte Carlo

The direct simulation Monte Carlo (DSMC) is a computational method for fluid mechanics simulation in the regime of rarefied gas flow. It is a numerical solution of the Boltzmann equation based on an individual particle basis. Accurate simulations typically require particle numbers in the range of hundreds of thousands to millions. Such large simulations require an inordinate amount of time for processing using serial computing on central processing units (CPUs). In this paper we investigate data-parallel techniques on graphics processing units (GPUs) to execute very large scale DSMC simulations. We have designed and implemented Bird’s method on a three-dimensional simulation domain that includes complex geometry interactions. We also have tested and verified the statistical and theoretical accuracy of our implementation. Our results show substantial performance improvements (nearly two orders of magnitude) over Bird’s serial implementation without loss of accuracy.

Collision of viscoelastic spheres: Compact expressions for the coefficient of normal restitution

The coefficient of restitution of colliding viscoelastic spheres is known analytically as a complete series expansion in terms of the impact velocity where all (infinitely many) coefficients are known. While being analytically exact, this result is not suitable for applications in efficient event-driven molecular dynamics (eMD) or direct simulation Monte Carlo (DSMC) methods. Based on the analytic result, here we derive expressions for the coefficient of restitution that allow for application in efficient eMD and DSMC simulations of granular systems.

Proper cell dimension and number of particles per cell for DSMC

The Direct Simulation Monte Carlo (DSMC) method models fluid flows using simulation particles which represent a large number of real molecules in a probabilistic simulation to solve the Boltzmann equation. Different opinions still exist on some basic understandings of the controlling factors of DSMC method, such as the proper grid dimension and the proper number of particles in a cell. In this contribution, DSMC simulation of Poiseuille flow was carried out to evaluate the dependence of simulation results on cell dimension and number of particles per cell. In the simulation process a self-adaptive block-structured grid system was employed to guarantee that the number of particles per cell is constant. The simulation covers both 2D and 3D, slip flow regime and transition flow regime, and for each regime, covers both high pressure and low pressure cases. Our simulation results indicate that the number of particles per cell and scaling factor have little influence on simulation result for both slip flow and transition flow when the number of particles per cell is greater than 5, but the dimension of cell influences the accuracy of results significantly. The error caused by cell dimension decreases with the decrease of cell dimension. It is concluded that in the DSMC method it is necessary to ensure that the cell is less than 1/2 of molecular mean free path.

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.