Direct Simulation Monte Carlo Research Articles

Multiscale mechanics of yttria film formation during plasma spray coating

In this study, we proposed a multiscale analysis method that integrates the direct simulation Monte Carlo (DSMC) method and all-atom molecular dynamics (MD) simulation to comprehend the process of unsteady plasma spray coating of yttria nanoparticles (YNPs) on an alumina substrate. The correlation between the increase in the powder feed rate and growth mechanism of the film microstructure was obtained by solving the collisions of the sprayed YNPs and corresponding spatial trajectories. The results showed that higher powder feed rates form a wider spray cone angle, and a reduction in spray distance increased the probability of powder impinging normal to the substrate. This also explained the changes in the interfacial adhesion and hardness of the films with the powder feed rate and spray distance observed in the experiments. In particular, vertically incident YNPs not only constituted the densest bulk layer, but also contributed to strong adhesion by increasing the probability of generating Y-O-Al binding structures at the interface. The findings were the first to examine the complexity of chemo-mechanical behavior between spatial particle trajectories and facing material, thus throwing light on an important factor in the quality of sprayed ceramic coatings.

Numerical investigation of gas separation via thermally induced flows in ratchet-like patterned microchannels

Gas separation can be achieved via thermally induced flows inside a microchannel. To obtain the optimum parameters for the best gas-separation efficiency, the direct simulation Monte Carlo (DSMC) method is used to numerically simulate a ratchet-like patterned microchannel with triangular hot plates. The analysis is based on the molar fraction of binary gas mixtures (He–Xe) in a steady state. The influence of temperature, Knudsen number, surface accommodation coefficient, and geometric parameters of the microchannel on its gas separation efficiency are studied using the controlled variable method. Results show that the separated heavier gas species (Xe) is mainly accumulated in wide or narrow microchannel at the last stage of the microchannel. The gas-accumulating position can be controlled by changing the microchannel width, microchannel length, and ratchet angle. The lighter gas moves from the cold to the hot side and concentrates in the hot region, while the heavier gas concentrates in the cold region. The gas separation efficiency improves as the temperature difference increases and the surface accommodation coefficient of the inclined surface decreases. The surface accommodation coefficient directly affects the transition between the thermal edge flow and radiometric flow near the upper tip of the triangle in the microchannel. The gas separation efficiency with a radiometric flow at the upper tip of the triangle is better than that with a thermal edge flow. In addition, the study gives the optimum parameter values for the best gas separation efficiency. These results can be applied to the realization and design of gas separators in various industry fields.

Stochastic Analysis of Predator-Prey Models under Combined Gaussian and Poisson White Noise via Stochastic Averaging Method.

In the present paper, the statistical responses of two-special prey–predator type ecosystem models excited by combined Gaussian and Poisson white noise are investigated by generalizing the stochastic averaging method. First, we unify the deterministic models for the two cases where preys are abundant and the predator population is large, respectively. Then, under some natural assumptions of small perturbations and system parameters, the stochastic models are introduced. The stochastic averaging method is generalized to compute the statistical responses described by stationary probability density functions (PDFs) and moments for population densities in the ecosystems using a perturbation technique. Based on these statistical responses, the effects of ecosystem parameters and the noise parameters on the stationary PDFs and moments are discussed. Additionally, we also calculate the Gaussian approximate solution to illustrate the effectiveness of the perturbation results. The results show that the larger the mean arrival rate, the smaller the difference between the perturbation solution and Gaussian approximation solution. In addition, direct Monte Carlo simulation is performed to validate the above results.

Analytical prediction of low-frequency fluctuations inside a one-dimensional shock

Linear instability of high-speed boundary layers is routinely examined assuming quiescent edge conditions, without reference to the internal structure of shocks or to instabilities potentially generated in them. Our recent work has shown that the kinetically modeled internal nonequilibrium zone of straight shocks away from solid boundaries exhibits low-frequency molecular fluctuations. The presence of the dominant low frequencies observed using the direct simulation Monte Carlo (DSMC) method has been explained as a consequence of the well-known bimodal probability density function (PDF) of the energy of particles inside a shock. Here, PDFs of particle energies are derived in the upstream and downstream equilibrium regions, as well as inside shocks, and it is shown for the first time that they have the form of the noncentral Chi-squared (NCCS) distributions. A linear correlation is proposed to relate the change in the shape of the analytical PDFs at a specified upstream number density and temperature as a function of Mach number, within the range \(3 \le M \le 10\), with the DSMC-derived average characteristic low-frequency of shocks, as computed in our earlier work. At a given Mach number \(M=7.2\) and upstream number density \(n_1=10^{22}\,\hbox {m}^{-3}\), it is shown that the variation in DSMC-derived low frequencies is correlated with the change in most-probable-speed inside shocks at the location of maximum bulk velocity gradient for upstream translational temperature in the range \(\sim 90 \le T_{tr,1}/(K) \le 1420\). Using the proposed linear functions, average low frequencies are estimated within the examined ranges of Mach number and input temperature and a semi-empirical relationship is derived to predict low-frequency oscillations in shocks. Our model can be used to provide realistic physics-based boundary conditions in receptivity and linear stability analysis studies of laminar-turbulent transition in high-speed flows.

Lagrangian particle tracking with new weighted fraction Monte Carlo method for studying the soot particle size distributions in premixed flames

PurposeThe purpose of this paper is to study the soot formation and evolution by using this newly developed Lagrangian particle tracking with weighted fraction Monte Carlo (LPT-WFMC) method.Design/methodology/approachThe weighted soot particles are used in this MC framework and is tracked using Lagrangian approach. A detailed soot model based on the LPT-WFMC method is used to study the soot formation and evolution in ethylene laminar premixed flames.FindingsThe LPT-WFMC method is validated by both experimental and numerical results of the direct simulation Monte Carlo (DSMC) and Multi-Monte Carlo (MMC) methods. Compared with DSMC and MMC methods, the stochastic error analysis shows this new LPT-WFMC method could further extend the particle size distributions (PSDs) and improve the accuracy for predicting soot PSDs at larger particle size regime.Originality/valueCompared with conventional weighted particle schemes, the weight distributions in LPT-WFMC method are adjustable by adopting different fraction functions. As a result, the number of numerical soot particles in each size interval could be also adjustable. The stochastic error of PSDs in larger particle size regime can also be minimized by increasing the number of numerical soot particles at larger size interval.

Time-dependent homogeneous states of binary granular suspensions

The time evolution of a homogeneous bidisperse granular suspension is studied in the context of the Enskog kinetic equation. The influence of the surrounding viscous gas on the solid particles is modeled via a deterministic viscous drag force plus a stochastic Langevin-like term. It is found first that, regardless of the initial conditions, the system reaches (after a transient period lasting a few collisions per particle) a universal unsteady hydrodynamic regime where the distribution function of each species not only depends on the dimensionless velocity (as in the homogeneous cooling state) but also on the instantaneous temperature scaled with respect to the background temperature. To confirm this result, theoretical predictions for the time-dependent partial temperatures are compared against direct simulation Monte Carlo (DSMC) results; the comparison shows an excellent agreement confirming the applicability of hydrodynamics in granular suspensions. Also, in the transient regime, the so-called Mpemba-like effect (namely, when an initially hotter sample cools sooner than the colder one) is analyzed for inelastic collisions. The theoretical analysis of the Mpemba effect is performed for initial states close to and far away from the asymptotic steady state. In both cases, good agreement is found again between theory and DSMC results. As a complement to the previous studies, we determine in this paper the dependence of the steady values of the dynamic properties of the suspension on the parameter space of the system. More specifically, we focus our attention on the temperature ratio T1/T2 and the fourth degree cumulants c1 and c2 (measuring the departure of the velocity distributions f1 and f2 from their Maxwellian forms). While our approximate theoretical expression for T1/T2 agrees very well with computer simulations, some discrepancies are found for the cumulants. Finally, a linear stability analysis of the steady state solution is also carried out showing that the steady state is always linearly stable.

Geotechnical reliability-based design using generalized subset simulation with a design response vector

This study proposes an efficient full probabilistic design method using an advanced Monte Carlo simulation (MCS) algorithm, so-called generalized Subset Simulation (GSS), for which a concept of design response vector is proposed. The proposed design response vector contains responses of all possible designs and is used to, simultaneously, explore failure domains of different designs. With the design response vector, the proposed approach determines feasible design domains of different geotechnical limit states by a single GSS run. The GSS run can be terminated as the target reliability level (or other user-defined reliability levels) is reached to avoid completely exploring the whole design space. This provides significant computational savings, particularly as the design space is relatively large and the target reliability level is relatively high. The proposed approach is illustrated using a drilled shaft design example. Results show that it provides an efficient and robust vehicle to determine the feasible design domains for full probabilistic design compared with direct MCS and original Subset Simulation-based approaches. Moreover, based on failure samples generated by GSS, the design point is, approximately, determined and can be used to back-calculate case-dependent resistance (or deformation) factors, which links MCS-based full probabilistic design to semi-probabilistic design.

Direct-simulation Monte Carlo modeling of reactor-scale gas-dynamic phenomena in a multiwafer atomic-layer deposition batch reactor

Atomic layer deposition (ALD) using multiwafer batch reactors has now emerged as the manufacturing process of choice for modern microelectronics at a massive scale. Stringent process requirements of thin film deposition uniformity within wafer (WiW) and wafer–wafer (WTW) in the batch, film conformity along submicrometer wafer features, thin film quality, and the utilization of expensive precursors in the reactor dictate ALD reactor design and process parameter optimization. This paper discusses a particle-based direct-simulation Monte Carlo (DSMC) of the full reactor scale simulation that overcomes the low Knudsen number limitation of typical continuum computational fluid dynamics approaches used for modeling low-pressure ALD reactors. A representative industrial multiwafer batch reactor used for the deposition of Si-based thin films with N2 and Si2Cl6 (hexachlorodisilane) as process feed gases with pressures in the range 43–130 Pa and a uniform reactor temperature of 600 °C is simulated. The model provides detailed insights into the flow physics associated with the transport of the precursor species from the inlets, through wafer feed nozzles, into the interwafer regions, and finally through the outlet. The reactor operating conditions are shown to be in the slip/transitional flow regime for much of the reactor volume and especially the feed gas nozzle and interwafer regions (where the Knudsen number approaches ∼0.2), justifying the need for a high-Knudsen number DSMC approach as in this work. For the simulated conditions, the nonuniformity of precursor species immediately above the wafer surface is predicted to be within <1% for a given wafer and <2% across the entire multiwafer stack. Results indicate that higher pressure degrades WiW and WTW uniformity. A reactor flow efficiency is defined and found to be ∼99%, irrespective of the chamber pressure.

Design and numerical investigation on the intake of atmosphere-breathing electric propulsion

Atmosphere-Breathing Electric Propulsion (ABEP) is a promising propulsion concept for Very Low Earth Orbit (VLEO). Spacecraft (S/C) operating at lower altitudes has higher coverage and resolution. However, the rarefied gas causes drag on the S/Cs, so the propulsion is needed to overcome the drag. The ABEP system captures the rarefied ambient gas as the propellant, and collecting the gas efficiently by intake is significant for the ABEP application. Given the flow regime of ambient gas is free molecular flow, the Direct Simulation Monte Carlo (DSMC) method is used for numerical investigation in this paper. The intake schemes of three geometric configurations under three reflection models are proposed and simulated. The operating characteristics of different schemes are analyzed and the performance parameters are obtained. Based on the analysis results, an optimized intake scheme is proposed, achieving the compression ratio of 183.8 and capture efficiency of 74%.

Study of the linear mercury diffusion pump with the fixed mass-flow-rate model by direct simulation Monte Carlo method

The linear mercury diffusion pump is proposed as the primary pump for sustaining the continuous working of KALPUREX (Karlsruhe liquid metal based pumping process for fusion reactor exhaust gases), which is considered as the exhaust pumping solution for reducing the tritium inventory in future fusion reactor with the fuel cycle based on the Direct Internal Recycling (DIR) concept. In this work, a preliminary simulation study of the linear mercury diffusion pump (LDP) is performed based on the Direct Simulation Monte Carlo (DSMC) method. While the dsmcFoam solver in the OpenFOAM platform is used, the inlet model named by fixed mass-flow-rate (FixedMFR) model is developed to control the mass flow rate into the pump, in accord with the condition of the experiment in 1950s. The simulated pumping speeds are in reasonable agreement with the experimental results when the pressure is in the range of 1 × 10−2 ~ 2 × 10−2 Pa, which implies that the DSMC model can be used for simulating the performance of the LDP. It should be noted that in the preliminary DSMC model, the mesh size is too large. Due to the large mesh size, the expansion of the mercury vapor steam is overestimated and the pumping speed is underestimated. Further work is required to find a proper way to generate the computational mesh for predicting the pumping performance of the LDP accurately and effectively.

Flow and thermal field investigation of rarefied gas in a trapezoidal micro/nano-cavity using DSMC

The impetus of the this study is to investigate flow and thermal field in rarefied gas flows inside a trapezoidal micro/nano-cavity using the direct simulation Monte Carlo (DSMC) technique. The investigation covers the hydrodynamic properties and thermal behavior of the flow. The selected Knudsen numbers for this study are arranged in the slip and transition regimes. The results show the center of the vortex location moves by variation in the Knudsen numbers. Also, as the Knudsen number increases, the non-dimensional shear stress increases, but the distribution deviates from a symmetrical profile. The cold to hot transfer, which is in contrast with the conventional Fourier law, is observed. We show that the heat transfer is affected by the second derivative of the velocity. By increasing the Knudsen number, the transferred heat through the walls decreases, but the contraction/expansion effects on the temperature in the corner of the cavity become higher.

Neumann enriched polynomial chaos approach for stochastic finite element problems

An enrichment scheme based upon the Neumann expansion method is proposed to augment the deterministic coefficient vectors associated with the polynomial chaos expansion method. The proposed approach relies upon a split of the random variables into two statistically independent sets. The principal variability of the system is captured by propagating a limited number of random variables through a low-ordered polynomial chaos expansion method. The remaining random variables are propagated by a Neumann expansion method. In turn, the random variables associated with the Neumann expansion method are utilised to enrich the polynomial chaos approach. The effect of this enrichment is explicitly captured in a new augmented definition of the coefficients of the polynomial chaos expansion. This approach allows one to consider a larger number of random variables within the scope of spectral stochastic finite element analysis in a computationally efficient manner. Closed-form expressions for the first two response moments are provided. The proposed enrichment method is used to analyse two numerical examples: the bending of a cantilever beam and the flow through porous media. Both systems contain distributed stochastic properties. The results are compared with those obtained using direct Monte Carlo simulations and using the classical polynomial chaos expansion approach.

On the Development of a Module for the Modification of Computational Meshes by the dsmcInitialise Utility

The research, the results of which are presented in this article, is devoted to the development of a software module with a graphical user interface that provides a modification of the computational mesh based on the dsmcInitialise utility, which is used at the preprocessing stage of numerical modeling of continuum mechanics problems using the OpenFOAM software environment. The paper describes the existing graphical shells for working with OpenFOAM with an indication of their shortcomings, formulates the relevance of the work, and defines the goals and objectives of the study. The article presents the features of the direct Monte Carlo simulation method, a description of the dsmcInitialise utility integrated into OpenFOAM and designed for such modeling, as well as a description of the corresponding dictionary file with parameters. The article includes diagrams of the structure and logic of the application, describes the technology stack used. The results of the application of the program on the example of one of the training problem of OpenFOAM are presented. The final conclusions are formulated, as well as the provisions that determine the scientific novelty of the research, and its intended practical value is determined. A link to the repository with the source code of the presented software module is provided.

Derivation of a Closed Form Expression for Estimating the Reduced Flow Rate for Pressure Driven Rarefied Gas Flow Through Circular Nano/Micro Pores

In this paper, a new model to predict the gas flow rate through short tubes under rarefied condition based on the sigmoidal bahaviour of gas reduced flow rate (W) versus the rarefaction parameter (d) under rarefied condition was developed. The data produced by Varoutis et al. via Direct Simulation Monte Carlo (DSMC) method were utilised to obtain the model coefficients as functions of tube length to radius (w) and pressure ratio (Pr). Then, the model was tested against the published experimental data.There was a high degree of agreement between the model predictions and the experimental data. Moreover, the new model was capable to predict the reduced flow rate of rarefied systems, not only at free molecular region and hydrodynamic region, but also at transition region, hence covering all the Knudsen number domain within the utilised data. Therefore, the proposed model was capable to make predictions as well as meet all the criteria of the rarefied gas flow within the following conditions: 0<Pr<0.9, 0.01<d<1000 and 0.0<w<20. Thus, the proposed model provides a useful tool to make a valid prediction of the rarefied gas flow behavior in a wide range of gas transport regime.

Coupling kinetic and continuum using data-driven maximum entropy distribution

An important class of multi-scale flow scenarios deals with an interplay between kinetic and continuum phenomena. While hybrid solvers provide a natural way to cope with these settings, two issues restrict their performance. Foremost, the inverse problem implied by estimating distributions has to be addressed, to provide boundary conditions for the kinetic solver. The next issue comes from defining a robust yet accurate switching criterion between the two solvers. This study introduces a data-driven kinetic-continuum coupling, where the Maximum-Entropy-Distribution (MED) is employed to parametrize distributions arising from continuum field variables. Two regression methodologies of Gaussian-Processes (GPs) and Artificial-Neural-Networks (ANNs) are utilized to predict MEDs efficiently. Hence the MED estimates are employed to carry out the coupling, besides providing a switching criterion. To achieve the latter, a continuum breakdown parameter is defined by means of the Fisher information distance computed from the MED estimates. We test the performance of our devised MED estimators by recovering bi-modal densities. Next, MED estimates are integrated into a hybrid kinetic-continuum solution algorithm. Here Direct Simulation Monte-Carlo (DSMC) and Smoothed-Particle Hydrodynamics (SPH) are chosen as kinetic and continuum solvers, respectively. The problem of monatomic gas inside Sod's shock tube is investigated, where DSMC-SPH coupling is realized by applying the devised MED estimates. Very good agreements with respect to benchmark solutions along with a promising speed-up are observed in our reported test cases.

An efficient algorithm of the unified stochastic particle Bhatnagar-Gross-Krook method for the simulation of multi-scale gas flows

The unified stochastic particle method based on the Bhatnagar-Gross-Krook model (USP-BGK) has been proposed recently to overcome the low accuracy and efficiency of the traditional stochastic particle methods, such as the direct simulation Monte Carlo (DSMC) method, for the simulation of multi-scale gas flows. However, running with extra virtual particles and space interpolation, the previous USP-BGK method cannot be directly transplanted into the existing DSMC codes. In this work, the implementation of USP-BGK is simplified using new temporal evolution and spatial reconstruction schemes. As a result, the present algorithm of the USP-BGK method is similar to the DSMC method and can be implemented efficiently based on any existing DSMC codes just by modifying the collision module.

A metamodeling-based robust optimisation approach for structures subjected to random underground blast excitation

The blast hazards are associated with extreme randomness. Thus, structures under blast should be properly designed for such highly uncertain phenomena. However, codal stipulations and existing literature do not consider important uncertainty-related design issues, such as record-to-record variation of blast load, high uncertainty levels associated with blast parameters, and robustness of structural behaviour under extreme blast events. In the present study, a computationally efficient robust optimisation (RO) approach is proposed for blast-excited structures by addressing these issues. In doing so, a new CDF-based constraint formulation is developed in the dual response surface-based metamodeling framework to avoid the use of direct Monte Carlo simulation (MCS) during RO iterations. Thereby, the proposed approach becomes computationally much efficient than the conventional direct MCS-based RO. Since the proposed approach resorts to matching the CDF of the actual response, instead of the conventional RO formulations based on the first two statistical moments only, the approach is more realistic. The present approach adopts the moving least-squares method instead of the usual least-squares method to retain accuracy in response approximation. The blast load time-history is generated by a stochastic field model with proper validation through real blast data. Three example problems have been investigated to establish the effectiveness of the proposed RO procedure. The RO results depict that the present method yields economic design solutions, which are also insensitive to high uncertainty levels associated with the extreme blast load. The COV of performance function is substantially low even when input parameter uncertainty is high.

Velocity-Slip and Temperature-Jump Effects in Near-Continuum Hypersonic Flows

Velocity-slip and temperature-jump effects on sharp leading-edge geometries are studied for three canonical hypersonic flows: the hollow-cylinder-flare, the double-cone, and the double-wedge. Simulation results are compared between the direct simulation Monte Carlo (DSMC) method that naturally captures slip effects and computational fluid dynamics (CFD) using an appropriate slip model. Only the leading-edge portions of these flow configurations are studied. The simulations are verified to be converged in terms of grid and particle resolution. Overall, excellent agreement is found between DSMC and CFD predictions of the leading-edge boundary layer, the magnitude of velocity-slip and temperature-jump, and surface heat flux for all cases considered, with the exception of the double-cone case due to the relatively high Knudsen number of the flow. The largest discrepancies were found for the double-cone (transitional flow conditions), and near-exact agreement was found for the double-wedge (continuum flow conditions). It was determined that slip effects cannot account for the discrepancy between CFD predictions and experimentally measured heat flux for the hollow-cylinder flare. Furthermore, it was determined that the previously recommended threshold for the continuum breakdown parameter might be overly conservative in the near-wall region if appropriate slip models are used in CFD.

Optimization of a conical cascade using invasive weed optimization (IWO) algorithm for multi-component systems: Investigation of the effect of feed flow on the separation factor of centrifuge machines in the cascade by DSMC method

One of the desirable properties that can be mentioned in the design of a cascade is to maximize the amount of separation work for the minimum number of machines so that the input feed does not exceed its maximum amount. For this purpose, the dilute gas area and part of the continuums area inside gas centrifuge are considered as the computational area for calculating the mass source. The mass source is calculated by direct simulation Monte-Carlo (DSMC) method. Based on the separation parameters obtained from the proposed flow function, the optimum cascade design was performed using the invasive weed optimization (IWO) algorithm. The results show that by considering the exact effect of feed by DSMC method in the Onsager equation, with increasing the separation parameters in a centrifuge machine, for a certain amount of separation in the product and waste streams in an optimal cascade, fewer centrifuge machines were obtained.

Particle Simulation of Linear Diffusion Pumps for DEMO Torus Exhaust Pumping

It is currently foreseen to implement Mercury-driven Linear Diffusion Pumps (LDP) in the primary pumping system of the European demonstration fusion power plant (DEMO). Here, a simulation model using the Direct Simulation Monte Carlo (DSMC) method is presented and verified. By a series of simulations the sensitivity of a LDP is analyzed with respect to inlet pressure, compression ratio, gas species dependence, backstreaming and condensation as well as the impact of geometric parameters to explore the operational limits of a LDP. The simulation results confirm that DSMC is a useful tool for the simulation and optimization of LDPs in conditions relevant for fusion reactor exhaust pumping.