Direct Simulation Monte Carlo Algorithm Research Articles

Experimental investigation and numerical simulation of intense plume impingement effects from a 10 N bipropellant thruster

The intense interaction between thruster plumes and spacecraft surfaces presents substantial challenges for the advancement of space technologies. The impingement effects from a 10 N bipropellant thruster plume on a vertical instrumented plate were experimentally and numerically investigated in this study. Impingement pressure and heat flux were measured using micro differential pressure transducers and Gardon gauges, respectively, while the spatial distribution of the plume was captured using the high-speed camera. The phenomena and the distribution characteristics of plume impingement have been summarized, thereby providing a comprehensive validation dataset for subsequent predictions. Numerical simulations are conducted utilizing the coupled hybrid Computational Fluid Dynamics and Direct Simulation Monte Carlo (CFD-DSMC) algorithm. The dependence of the simulation outcomes on grid resolution was critically assessed, and the accuracy of the results was validated by comparison with experimental data. An integrated methodology, combining experimental and numerical approaches, was developed to calculate the maximum heat flux under realistic grid configurations. This method has proven to be effective and supports the accurate and efficient evaluation of intense plume impingement effects for engineering applications.

Translational and rotational non-Gaussianities in homogeneous freely evolving granular gases.

The importance of roughness in the modeling of granular gases has been increasingly considered in recent years. In this paper, a freely evolving homogeneous granular gas of inelastic and rough hard disks or spheres is studied under the assumptions of the Boltzmann kinetic equation. The homogeneous cooling state is studied from a theoretical point of view using a Sonine approximation, in contrast to a previous Maxwellian approach. A general theoretical description is done in terms of d_{t} translational and d_{r} rotational degrees of freedom, which accounts for the cases of spheres (d_{t}=d_{r}=3) and disks (d_{t}=2,d_{r}=1) within a unified framework. The non-Gaussianities of the velocity distribution function of this state are determined by means of the first nontrivial cumulants and by the derivation of non-Maxwellian high-velocity tails. The results are validated by computer simulations using direct simulation Monte Carlo and event-driven molecular dynamics algorithms.

Adjoint DSMC for nonlinear spatially-homogeneous Boltzmann equation with a general collision model

We derive an adjoint method for the Direct Simulation Monte Carlo (DSMC) method for the spatially homogeneous Boltzmann equation with a general collision law. This generalizes our previous results in Caflisch et al. (2021) [9], which was restricted to the case of Maxwell molecules, for which the collision rate is constant. The main difficulty in generalizing the previous results is that a rejection sampling step is required in the DSMC algorithm in order to handle the variable collision rate. We find a new term corresponding to the so-called score function in the adjoint equation and a new adjoint Jacobian matrix capturing the dependence of the collision parameter on the velocities. The new formula works for a much more general class of collision models.

Topology optimization for rarefied gas flow problems using density method and adjoint IP-DSMC

In this paper, a topology optimization method based on direct simulation Monte Carlo (DSMC) is presented for rarefied gas flows. Distribution of fluid and solid in the design domain is characterized by a pseudo density. The traditional DSMC algorithm is extended to include the pseudo density by interpreting solid as an imaginary gas with fixed temperature and zero macroscopic velocity. Treating the pseudo density as the design variable, design sensitivity is obtained through the Lagrangian multiplier method and the adjoint state method. A discrete version of the adjoint equations is used, so that the adjoint variables can be evaluated using the information stored during the forward DSMC process. The information preservation (IP) method for subsonic flow is also considered in order to reduce random noise and simplify the discrete adjoint equations. The extended DSMC algorithm is verified by numerical examples, and optimized design for bent pipe is also included.

Ground experiment verification and on-orbit prediction of the two-stage cooling at pK level in the Chinese space station

In order to infer the expected temperature of the two-stage cooling experiment onboard the Chinese space station (CSS) through ground experiments, we apply the direct simulation Monte Carlo algorithm to construct a simulation model suitable for both the standard gravity and the microgravity conditions. The simulations are verified by the ground experimental results, from which we can deduce that the on-orbit experiments can reach the order of as low as 100 pK. This algorithm calculates the corresponding relationship between the temperature in the ground experiments and that in the microgravity conditions, keeping the other experimental parameters unchanged, which provides an important basis of design for the on-orbit atomic cooling experiment onboard the CSS which is due to be launched at the end of 2022.

A novel transient-adaptive subcell algorithm with a hybrid application of different collision techniques in direct simulation Monte Carlo (DSMC)

A novel hybrid transient adaptive subcell (TAS) direct simulation Monte Carlo (DSMC) algorithm is proposed to simulate rarefied gas flows in a wide range of Knudsen numbers. It is derived and analyzed by using a time and spatial discrete operator approach based on the non-homogeneous, local N-particle kinetic equation, first proposed by Stefanov. The novel algorithm is considered together with the standard and hybrid collision algorithms built on uniform grids. The standard collision algorithm uses only one single scheme—the NoTime Counter (NTC), or the Generalized or Simplified Bernoulli trials (GBT, SBT). The hybrid algorithm employs NTC, GBT, or SBT depending on the instantaneous number of particles in the considered cell. The novel hybrid TAS algorithm benefits from both the hybrid collision approach and the transient adaptive subcell grid covering each collision cell to achieve a uniform accuracy of order O(Δt, Δr) independently of the number of particles in the cells. To this aim, a local time step is defined as coherent with the TAS grid covering the corresponding collision cell. The novel hybrid TAS algorithm is tested on two-dimensional benchmark problems: supersonic rarefied gas flow past of a flat plate under an angle of incidence and pressure-driven gas flow in a microchannel. The results obtained by the hybrid TAS algorithm are compared to those obtained by the standard algorithms and the available Bird's DS2V code using nearest neighbor collision and open-source OpenFOAM code. The comparison shows an excellent accuracy of the suggested algorithm in predicting the flow field.

A variable time step self-consistent mean field DSMC model for three-dimensional environments.

A self-consistent mean field direct simulation Monte Carlo (SCMFD) algorithm was recently proposed for simulating collision environments for a range of one-dimensional model systems. This work extends the one-dimensional SCMFD approach to three dimensions and introduces a variable time step (3D-vt-SCMFD), enabling the modeling of a considerably wider range of different collision environments. We demonstrate the performance of the augmented method by modeling a varied set of test systems: ideal gas mixtures, Poiseuille flow of argon, and expansion of gas into high vacuum. For the gas mixtures, the 3D-vt-SCMFD method reproduces the properties (mean free path, mean free time, collision frequency, and temperature) in excellent agreement with theoretical predictions. From the Poiseuille flow simulations, we extract flow profiles that agree with the solution to the Navier-Stokes equations in the high-density limit and resemble free molecular flow at low densities, as expected. The measured viscosity from 3D-vt-SCMF is ∼15% lower than the theoretical prediction from Chapman-Enskog theory. The expansion of gas into vacuum is examined in the effusive regime and at the hydrodynamic limit. In both cases, 3D-vt-SCMDF simulations produce gas beam density, velocity, and temperature profiles in excellent agreement with analytical models. In summary, our tests show that 3D-vt-SCMFD is robust and computationally efficient, while also illustrating the diversity of systems the SCMFD model can be successfully applied to.

Pauli principle and the Monte Carlo method for charge transport in graphene

The attempt to include the Pauli principle in the Monte Carlo method by acting also on the free flight step and not only at the end of each collision is investigated. The charge transport in suspended monolayer graphene is considered as test case. The results are compared with those obtained in the standard Ensemble Monte Carlo technique and in the new Direct Simulation Monte Carlo algorithm which is able to correctly handle with Pauli's principle. The physical aspects of the investigated approach are analyzed as well.

Pitot probe response for pulsed supersonic gas flow characterization in beam profile monitor.

For beam profile measurement of high-intensity proton beams in the low-energy high-intensity proton accelerator at Bhabha Atomic Research Centre, a recent noninvasive technique based on gas sheets will be explored. The gas sheet for this instrument needs to be characterized for calibration and fine tuning of the sheet properties to provide better profile measurements. Pulsed sheet generators for similar applications have been characterized using movable vacuum chambers with a small slit and a gauge mounted inside. Pitot probes are more compact instruments and have been used to measure gas jet profiles in molecular beam applications where the jet was not pulsed. The performance of Pitot probes in the measurement of pulsed supersonic gas flow in vacuum was, therefore, investigated in this work. A test system was developed to generate a pulsed supersonic gas jet in vacuum, and a Pitot probe was inserted into the flow at various axial locations with respect to the nozzle. Measurements taken along the nozzle axis using this probe, as well as the axial Mach number and impact pressure computed using computational fluid dynamics and direct simulation Monte Carlo algorithms, were compared with fitting formulas. Schlieren images of the jet with and without the Pitot tube were also taken under different vacuum conditions.

Understanding the role of energetic particles during the growth of TiO2 thin films by reactive magnetron sputtering through multi-scale Monte Carlo simulations and experimental deposition

In this paper, a previously established 3D multi-scale simulation chain of plasma deposition process, based on a combination of a direct simulation Monte Carlo (gas phase) algorithm and a kinetic Monte Carlo (kMC) (film growth) code, is improved by the addition of a particle-in-cell Monte Carlo collision algorithm in order to take into account and clarify the role of charged particles. The kinetic Monte Carlo code is also extended with a binary collision approximation algorithm to handle charged particles. This modelling strategy is successfully applied to the growth of TiO2 thin films by means of reactive magnetron sputtering. In order to highlight the effects of negative oxygen ions, two substrate locations are selected: one in the median plane of the targets and another one off the median plane. The model efficiently predicts the densities and fluxes of both charged and neutral particles towards the substrate. Typical results such as particle densities, the discharge current density and ion flux onto the target, and the various substrate locations are calculated. The angular distribution and energy distribution of all involved particles are sampled at these very same substrate locations and the nanoscale modelling (NASCAM) code, implementing the kMC approach, uses these results to explain the morphology of the experimentally deposited coatings. The changes throughout the transition from metallic deposition to stoichiometric TiO2 of the columnar structure of the deposited films is explained by the suppression of the atom diffusion on the growing film due to Ti oxidation. Moreover, the high-energy negative atomic oxygen ions originating from the targets are identified as the origin of the abnormally low inclination of the columnar structure experimentally observed for the oxide mode coatings. Measurements of the normalized energy flux (energy per deposited atom) are experimentally investigated to support and highlight the important role of energetic particles during film growth.

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.

Numerical analysis of nonlinear thermal stress flow between concentric elliptical cylinders

The present study numerically investigates nonlinear thermal stress in a rarefied gas flow between two coaxial elliptic cylinders with a hot outer wall. Monatomic argon is considered, and isothermal boundary conditions are implemented on the walls. Three different numerical methods are used to solve this problem, i.e., first, the direct simulation Monte Carlo (DSMC) method is used and validated against the numerical solution of the Boltzmann equation available in the literature. The results of the DSMC algorithm are compared with the results of the discrete unified gas kinetic scheme and the continuum set of equations of slow non-isothermal flows, which includes nonlinear thermal stress terms compared to the Navier–Stokes equations. For the first time, the flow is examined in a wide range of Knudsen numbers in the slip regime from the Knudsen number (Kn) of Kn = 0.005 to Kn = 0.1. At a minimal Knudsen number, there is just one vortex due to the nonlinear thermal stress flow; however, as Kn increases, the velocity peak near the inner cylinder is replaced with another vortex, which is created due to the second-order thermal creep effects on the inner wall of the cylinder. We show that as Kn increases, the inner vortex increases in size, while the outer vortex shrinks. The mechanisms of the formation of both vortices are described in detail. Other flow characteristics, including walls’ velocity slip, shear stress, and vorticity, are discussed.

Adaptive simulations enable computational design of electron beam processing of nanomaterials with supersonic micro-jet precursor

Focused Electron Beam Induced Processing (FEBIP) is a powerful tool for the “direct-write” of nanomaterials with the possibility of atomistic control on suspended 2D material substrates. FEBIP capabilities have been significantly expanded by using a localized jet-based delivery of precursors, and especially when a thermally energized supersonic micro-jet enhances the delivery of mass flux along with controlling the far-from-equilibrium thermodynamic state of adsorbed adatoms. The possibilities of growing nanomaterials with “dialed-in” composition with ultra-high growth rates and aspect ratios up to 100:1 have been demonstrated using the supersonic micro-jet-FEBIP. Bringing this scientific discovery to the level of maturity required for practical applications in additive nanomanufacturing requires simulation tools that are capable of capturing the complex flow physics of micro-jet-substrate interactions that bridge a wide range of flow regimes from the high-density gas micro-jet expanding into the vacuum environment of FEBIP. To address this significant computational challenge, a new approach has been developed and described in this work for a multiscale adaptive DSMC (Direct Simulation Monte Carlo) algorithm to predict the micro-jet gas dynamics in an FEBIP environment, spanning the full range of flow regimes from low Knudsen (Kn) number O(0.01) continuum flow to high Kn of O(10) for the molecular flow within a unified computational framework. The fundamental principles of the adaptive DSMC algorithm are described, its viability as a DSMC technique is demonstrated, and computational improvements for the benchmark cases are discussed in the context of advancing 3D nanofabrication with FEBIP. Ultimately, combining the first principle simulations via adaptive DSMC with the complementary experimental data will enable the creation of the powerful CAD tools for in silico design and optimal operation of micro-jet-FEBIP.

A kinetic Fokker–Planck approach for modeling variable hard-sphere gas mixtures

Kinetic Fokker–Planck (FP) methods for modeling rarefied gas flows have received increasing attention over the last few years. However, formulating such models for realistic multi-species gases is still an open subject of research. Therefore, in this letter, we develop a kinetic FP model for describing gas mixtures with particles interacting according to the variable hard-sphere interaction potential. In accordance with the kinetic FP framework, a stochastic solution algorithm is employed in order to solve the model on a particle level. Different test cases are carried out, and the performance of the proposed method is compared with the direct simulation Monte Carlo algorithm.

Parallelization of a stochastic Euler-Lagrange model applied to large scale dense bubbly flows

A parallel and scalable stochastic Direct Simulation Monte Carlo (DSMC) method applied to large-scale dense bubbly flows is reported in this paper. The DSMC method is applied to speed up the bubble-bubble collision handling relative to the Discrete Bubble Model proposed by Darmana et al. (2006) [1]. The DSMC algorithm has been modified and extended to account for bubble-bubble interactions arising due to uncorrelated and correlated bubble velocities. The algorithm is fully coupled with an in-house CFD code and parallelized using the MPI framework. The model is verified and validated on multiple cores with different test cases, ranging from impinging particle streams to laboratory-scale bubble columns. The parallel performance is shown using two different large scale systems: with an uniform and a non-uniform distribution of bubbles. The hydrodynamics of a pilot-scale bubble column is analyzed and the effect of the column scale is reported via the comparison of bubble columns at three different scales.

Investigating the Simulation Rate of an Axially Symmetric Rarefied Gas Flow Using v-DSMC

This article reports a comparative study of the convergence rate of an axially symmetric binary gas flow inside a rotating cylinder using an improved direct simulation Monte Carlo algorithm for rarefied gases (v-DSMC) and the conventional DSMC. Subsequently, a comparison between the convergence behavior of the v-DSMC and analytical data is carried out to scrutinize the validity of the v-DSMC algorithm. This method makes use of a modified collision model of variable hard sphere (VHS) termed Maxwell-VHS, which considers an equal contingency of collision but an arbitrary viscosity variation with temperature, for all adjacent gas particles. The results of the numerical simulation declare the convergence rate of the v-DSMC is noticeably faster than those performed by the conventional DSMC; however, a slight computational error occurs at the same simulation time due to higher accuracy of collision sampling in the conventional DSMC. Moreover, the results show a good agreement between the convergence behaviors of the v-DSMC in comparison with the analytical data.

Direct Simulation Monte Carlo investigation of fluid characteristics and gas transport in porous microchannels

The impetus of the current research is to use the direct simulation Monte Carlo (DSMC) algorithm to investigate fluid behaviour and gas transport in porous microchannels. Here, we demonstrate DSMC’s capability to simulate porous media up to 40% porosity. In this study, the porous geometry is generated by a random distribution of circular obstacles through the microchannel with no interpenetration between the obstacles. The influence of the morphology along with rarefaction and gas type on the apparent permeability is investigated. Moreover, the effects of porosity, solid particle’s diameter and specific surface area are considered. Our results demonstrate that although decreasing porosity intensifies tortuosity in the flow field, the tortuosity reduces at higher Knudsen numbers due to slip flow at solid boundaries. In addition, our study on two different gas species showed that the gas type affects slippage and apparent gas permeability. Finally, comparing different apparent permeability models showed that Beskok and Karniadakis model is valid only up to the early transition regime and at higher Knudsen numbers, the current data matches those models that take Knudsen diffusion into account as well.

A novel spatio-temporally adaptive parallel three-dimensional DSMC solver for unsteady rarefied micro/nano gas flows

An efficient parallel multi-scale direct simulation Monte Carlo algorithm to simulate three-dimensional rarefied gas flows over complex geometries is presented. The proposed algorithm employs a novel spatio-temporal adaptivity scheme. Based on the gradients of flow macro-properties, the spatio-temporal adaptivity scheme computes the cell size distribution and assigns the appropriate number of time sub-steps for each cell. The temporal adaptivity scheme provides local time step adaptation through different temporal levels employed in different cells. Spatial representation is based on a hierarchical octree Cartesian grid with low memory storage requirement. The hierarchical octree grid endows the method with straightforward and efficient data management suitable for particle ray tracing and dynamic grid refinement and coarsening. Solid objects, represented by triangulated surfaces, are incorporated using a cut-cell algorithm. A new parallelization scheme suitable for simulating strongly unsteady, non-equilibrium flows is proposed. The parallelization scheme, implemented for multi-core Central Processing Units (CPUs), significantly reduces the computational cost of modeling these flows. Performance of the method is assessed by comparing with benchmarked test cases for various rarefied gas flows.

Modified Collision Energy, a New Chemical Model in the DSMC Algorithm

A new chemical model in the direct simulation Monte Carlo (DSMC) algorithm, entitled modified collision energy (MCE), has been developed for simulation of reactive rarefied flows without some limitations of the conventional macroscopic models. Determination of correct values of the experimental parameters for computing the Arrhenius reaction rate is a serious challenge in some macroscopic chemical reaction models such as total collision energy (TCE) and general collision energy (GCE). A slight variation of these constant parameters in the Arrhenius relation could lead to significant change in the results. On the other hand, these experimental parameters have been extracted empirically only for limit number of gases and so they cannot be used for simulation of chemical reactions in various types of gases. Since some of these constants have been determined experimentally by several studies, they have been reported by different values in different references. The proposed MCE model in the present study is a reliable method to properly determine values of these parameters for all types of gases with the intrinsic properties of the particles and without need of any experimental data. Extraction of the constant parameters has been carried out using the analytical method or numerical quantum kinetics (QK) or modified quantum kinetics (MQK) models. The proposed MCE method has been evaluated in four test cases, including assessment of the reaction rate in equilibrium and nonequilibrium conditions, studying of the rarefied flow along the stagnation line, and investigation of the hypersonic gas flow over the axial symmetry blunt nose. The results show that the proposed method has desirable accuracy without use of any experimental parameters. The MCE method can also be used to calibrate the macroscopic reactive models such as the TCE and GCE.

Assessment of the LD-DSMC hybrid method for hypersonic rarefied flow

Hypersonic aerothermodynamics for a probe entering a planetary atmosphere is an important issue in space exploration. The probe experiences various Knudsen number regimes, ranging from rarefied to continuum, due to density variation in the planet’s atmosphere. To simulate such multiscale flows, a novel hybrid particle scheme is employed in the present work. The hybrid particle scheme employs the direct simulation Monte Carlo (DSMC) method in rarefied flow regions and the low diffusion (LD) particle method in continuum flow regions. Numerical procedures in the low diffusion particle method are implemented within an existing DSMC algorithm. The hybrid scheme is assessed using two hypersonic, blunt body flow problems: Mach 10 nitrogen flow over a sphere, and Mach 40 carbon dioxide flow over the Mars Path Finder each with a global Knudsen number of 0.002. Standard DSMC and CFD results are compared with the LD-DSMC hybrid simulation results. The hybrid scheme results show good overall agreement with results from standard DSMC computation, while CFD is inaccurate especially in the wake where a highly rarefied region exists. The LD-DSMC hybrid solution is able to increase computational efficiency upto 50% in run time in comparison to DSMC. And sensitivity to numerical parameters of the LD-DSMC method is also studied.