Direct Simulation Monte Carlo Technique Research Articles

Plasma plume simulation of an atomic oxygen-fed ion thruster in very-low-earth-orbit

The plasma plume flow of an atomic oxygen-fed (AO-fed) ion thruster is numerically investigated as a simplification of the atmosphere-breathing electric propulsion (ABEP). A predictive analysis is conducted focusing on the ion backflow phenomenon and plume-background interaction in very-low-earth-orbit (VLEO). The computational framework employs two sequentially integrated numerical methods: a zero-dimensional (0-D) analytical model for the radio-frequency ion thruster and a hybrid method of the particle-in-cell (PIC) and direct simulation Monte Carlo (DSMC) techniques. The 0-D analytic model is employed for the prediction of exhaust conditions, while the hybrid PIC-DSMC method adopts these predictions to conduct the plasma plume simulations. A generalized collision cross-section model is introduced to enable consistent kinetic simulations for both AO and xenon propellants in VLEO atmosphere. The plasma plume simulations are conducted in an axisymmetric domain, including a cylindrical satellite body to consider wake flow. The exhaust ions exhibit diffusive transport transverse to the ion beam direction, implying the ion backflow. The backflowing ion current density can be increased in AO-fed thrusters, which require a high propellant flow rate to achieve a practical thrust. The AO-fed ion thruster shows a more active interaction between its plasma plume and the VLEO atmosphere compared to conventional xenon-based thrusters. The intensified plume-background interaction modifies the backflowing ion current density and the kinetic energy of individual ions, factors related to the spacecraft’s surface contamination.

Planar phonon anisotropy, and a way to detect local equilibrium temperature in graphene

The effect of inclusion of the planar phonon anisotropy on thermo-electrical behavior of graphene is analyzed. Charge transport is simulated by means of Direct Simulation Monte Carlo technique coupled with numerical solution of the phonon Boltzmann equations based on deterministic methods.The definition of the crystal lattice local equilibrium temperature is investigated as well and the results furnish possible alternative approaches to identify it starting from measurements of electric current density, with relevant experimental advantages, which could help to overcome the present difficulties regarding thermal investigation of graphene.Positive implications are expected for many applications, as the field of electronic devices, which needs a coherent tool for simulation of charge and hot phonon transport; the correct definition of the local equilibrium temperature is in turn fundamental for the study, design and prototyping of cooling mechanisms for graphene-based devices.

Rocket‐Released Neutral Clouds in the Ionosphere: Formation, Evolution, and Detection

AbstractReleasing diffuse artificial clouds into the space environment using a rocket or spacecraft can modify the natural plasma state. This uses space itself as a laboratory for studying plasma phenomena that cannot be reproduced on the ground. The Space Measurement of A Rocket‐released Turbulence (SMART) mission will inject a beam of barium neutral vapor into the ionosphere and perpendicular to the Earth's magnetic field. Barium atoms will be photoionized, forming an ion ring distribution that is unstable to lower hybrid waves. Large amplitude lower hybrid waves nonlinearly scatter to whistler and magnetosonic waves that can propagate out to the magnetosphere. This paper details the theory, modeling, and simulation we used to design this release experiment to optimize the energy in the plasma waves under a variety of constraints. A product of this analysis is quantitative predictions for some in situ and remote measurements. Hydrocode simulations of barium vapourization and acceleration via shaped charge provide the initial state of the neutral beam. We optimize the apogee, orientation, and position of the payload and instruments. Cloud dynamics are simulated with a direct simulation Monte Carlo technique, which includes photoionization with metastable barium states, collisions with the neutral background atmosphere, optical line emission, gravity, and electromagnetic forces. We predict the plasma density measured by the instrument payload and the remotely measured optical intensity. We also examine how the plasma wave growth differs at the measurement location compared to the bulk of the barium cloud.

Investigation of rarefied flow over an open cavity using direct simulation Monte Carlo

AbstractThe present study employs the direct simulation Monte Carlo (DSMC) technique to analyse the flow over a cavity, a commonly observed anomaly on a re-entry vehicle’s surface. The flow characteristics are examined for different Mach numbers ( ${\rm{Ma}}$ ) and Knudsen number ( ${\rm{Kn}}$ ). The Mach numbers varied from 5 to 25, while the Knudsen numbers varied from 0.05 to 21.10. The influence of the ${\rm{Ma}}$ and ${\rm{Kn}}$ on flow characteristics has been elucidated graphically in various sections. The flow properties showed significant variation with ${\rm{Ma}}$ and ${\rm{Kn}}$ and showed an increasing trend due to compressibility and viscous heating effects. The surface characteristics were observed to diminish as ${\rm{Ma}}$ increases, while they showed complex trends for various ${\rm{Kn}}$ . In all flow regimes, there was an appearance of flow recirculation. When chemical reactions were taken into consideration and compared with non-reacting flows, flow temperature was primarily influenced (which decreased due to energy absorption) compared to other properties. The results obtained are a complex interplay of the viscous heating, compression and rarefaction effects.

Microscale Modeling of Particle Impact on Thermal Protection System Materials During High-Speed Entry

Micron-sized particles suspended in planetary atmospheres can damage thermal protection systems (TPS) during entry of space capsules into planetary bodies. TPS materials are complex heterogeneous carbon composites, where the microstructure of the composite can play a pivotal role in the propagation of damage caused by the impact. Here, we present the application of a novel computational technique called the lattice particle method to understand the initiation and growth of craters formed on TPS materials upon impact by particles. The simulations are initially compared against experiments that used borosilicate as the impacting particle and fused silica as the target surface. The simulations reproduce the damage profiles, diameters, and depths of the craters being formed on the target silica surface. A parametric study is then performed by varying the fracture strength of the target surface and the impacting particle. It is found that the profiles of the damaged region on the silica surface primarily depend on the fracture strength of the silica surface, and not the impacting particle. The simulations are extended to model the damage of porous carbon composites that are used as TPS materials. Microstructures of carbon composites are generated using an in-house code that has been shown to reproduce features of the real material in past studies. While the crater depth on the fused silica surface was within 38% irrespective of the fracture strength of the particle, the damaged depth changes by at least an order of magnitude when a carbon composite surface is used and the fracture strength of the impacting particle is varied. Finally, the influence of damage on the effective permeability is computed using the direct simulation Monte Carlo technique. The maximum increase in the permeability force for the damaged microstructures is found to be 22%, which is within the statistical variability of the material properties observed for the TPS material that is under investigation.

Effective Permeability of Carbon Composites Under Reentry Conditions

Effective permeability of a porous carbon composite used as thermal protection system on space capsules is computed using the direct simulation Monte Carlo technique. The microstructure of the carbon composite is synthetically generated using an in-house code. Permeabilities obtained using synthetic microstructures of the precursor (carbon fibers) are compared with two independent experimental dataset, and good agreement is observed. It is conclusively shown that the difference in permeability values between the two experimental datasets arose from the variations in the sample density. An approach to digitally infuse resin into the precursor is proposed. Comparison of the permeability for the full composite (carbon fibers with resin) with experimental data resulted in errors within 7.5%, indicating that representative microstructures generated digitally can be used to compute and predict effective permeability of porous carbon composites. Simulations of Ar and air permeating through the full composite are performed, and an intrinsic material permeability () of and a Klinkenberg constant () of that is only dependent on the temperature and the molecular weight of the gaseous species are obtained. It is shown that this new generalized relation could be used for other gases such as CO and .

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.

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.

Simulation of Multiple-Component Charged Aerosol Evolution

The study of the nuclear source term requires the computation of aerosol dynamics. Solutions to the aerosol general dynamic equation (GDE) are difficult to obtain by analytical or numerical methods when more realistic problems are considered. The direct simulation Monte Carlo (DSMC) technique is capable of simulating aerosol evolution reducing simplifications in the implementation of the aerosol GDE. In this work we present a DSMC program for the simulation of multicomponent polydisperse aerosol evolution, with the successful integration of the following processes: deposition, electrostatic dispersion, coagulation (considering charge effects), and condensation, assuming a spatially homogeneous medium and spherical particles. Two problems with different particle compositions were simulated to obtain information about the interactions through the different processes and the interacting particles as well as particle number and mass distributions with discrimination of charge levels. This information allowed us to explore the synergistic nature of these processes. It was found that the problem with denser particles had an overall stronger activity in coagulation and initially a stronger activity in deposition compared to the problem with less dense particles.

Monte Carlo simulation for aerodynamic coefficients of satellites in Low-Earth Orbit

Fast and accurate prediction for aerodynamic coefficients of satellites in LEO (Low-Earth Orbit) is a fundamental prerequisite for the determination and control of orbit. Based on the test particle Monte Carlo (TPMC) method for the calculation of molecular flux rate through a pipe in vacuum technology, combined with the free-molecular theory, the TPMC method for the fast and accurate prediction of aerodynamic coefficients of satellites in LEO has been developed, with its main steps and important procedures presented. The method is validated by comparing the aerodynamic coefficients of a satellite with two solar panels with results from the DSMC (direct simulation Monte Carlo) technique and the panel integral method based on free-molecular flow theory. The case also indicates that the TPMC method is applicable to complex configurations in engineering. Results also shows that the TPMC method is capable of dealing with multiple reflections that the panel integral method cannot consider, resulting in an accurate aerodynamic coefficient. In addition, the CPU time and physical memory needed by the TPMC method is less than that of the DSMC technique by an order of 3–4 and 1 to 2, respectively, without compromising the solution accuracy, indicating that the TPMC is an ideal method for fast and accurate prediction for aerodynamic coefficients of satellites in lower LEO.

Comparison of numerical predictions of the supersonic expansion inside micronozzles of micro–resistojets

The present work provides a numerical investigation of the supersonic flow inside a planar micronozzle configuration under different gas rarefaction conditions. Two different propellants have been considered, namely water vapor and nitrogen, which relate to their use in VLMs (the former) and cold gas microthrusters (the latter), respectively. Furthermore, two different numerical approaches have been used due to the different gas rarefaction regime, i.e. the typical continuum Navier–Stokes with partial slip assumption at walls and the particle–based Direct Simulation Monte Carlo (DSMC) technique. As a result, under high–pressure operating conditions, both water and nitrogen flows supersonically expanded into the micronozzle without chocking in combination with a linear growth of the boundary layer on walls. However, when low–pressure operating condition are imposed and a molecular regime is established inside the micronozzle, a very rapid expansion occurred close to the nozzle exit in combination with a strong chocking of the flow and a micronozzle quality reduction of about 40%. Furthermore, water exhibited specific higher specific impulse than nitrogen above 60%.

Evolution of Aerosols Coupled to Environments: Verification of Direct Simulation Monte Carlo (DSMC)

Applications of aerosol dynamics include modeling cloud formation and pollution in atmospheric sciences, inhalation and radiation doses in health physics, and particle transport and contamination in nuclear safety. To improve the fidelity of computed aerosol evolution to realistic process models and phenomena, efforts have been directed at the use of the Direct Simulation Monte Carlo (DSMC) technique. This paper first verifies the results obtained from the DSMC technique against a known analytical solution of a specialized case in which the evolution of a purely growing aerosol is coupled to its environment. Next, it applies the DSMC technique to the evolution of aerosol particles undergoing condensation, coagulation, and deposition as coupled to the environment.

Study of rarefied gas flows in backward facing micro-step using Direct Simulation Monte Carlo

A backward facing micro-step is a building block for many microfluidic devices. Due to micron sized characteristic dimensions, the gas flow in such a geometry is rarefied in nature. Such rarefied gas flows are widely solved using the Direct Simulation Monte Carlo (DSMC) technique. Flow separation, circulation and re-attachment are some of the basic characteristics of step flows. The objective of this study is to analyze the effect of rarefaction on the flow properties and the separation of the flow. The range of selected Knudsen number (Kn) covers the slip and transition regime from a value of 0.0311–13.25. The pressure ratios employed are 3 and 5. It is observed that the slip velocity continuously increases while the centre-line velocity first decreases, then remains constant and finally increases with increase in Kn. At the step, separation of the flow is seen for Kn < 0.1325 while no such separation is observed in the range of Kn from 0.198 to 13.25. The corresponding Re for these ranges are 6.43 to 0.67 and 0.392 to 0.012 respectively. The re-attachment length decreases with increase in Kn whereas it increases with increase in Re. A stronger pressure force and a weaker diffusion effect leads to flow separation in the slip regime whereas stronger diffusion and weaker pressure force lead to an absence of flow separation in the transition regime. Finally, this work presents for the first time the existence of the Knudsen minimum for such a backward step geometry.

TiOx deposited by magnetron sputtering: a joint modelling and experimental study

This paper presents a 3D multiscale simulation approach to model magnetron reactive sputter deposition of TiOx⩽2 at various O2 inlets and its validation against experimental results. The simulation first involves the transport of sputtered material in a vacuum chamber by means of a three-dimensional direct simulation Monte Carlo (DSMC) technique. Second, the film growth at different positions on a 3D substrate is simulated using a kinetic Monte Carlo (kMC) method. When simulating the transport of species in the chamber, wall chemistry reactions are taken into account in order to get the proper content of the reactive species in the volume. Angular and energy distributions of particles are extracted from DSMC and used for film growth modelling by kMC.Along with the simulation, experimental deposition of TiOx coatings on silicon samples placed at different positions on a curved sample holder was performed. The experimental results are in agreement with the simulated ones. For a given coater, the plasma phase hysteresis behaviour, film composition and film morphology are predicted. The used methodology can be applied to any coater and any films. This paves the way to the elaboration of a virtual coater allowing a user to predict composition and morphology of films deposited in silico.

Benchmark problems in aerosol evolution: Comparison of some exact and DSMC results

Aerosols are generated in many normal or accident situations associated with the nuclear enterprise. For a good understanding and modeling of the nuclear source term, for example, good experimental data and computational programs relating to aerosol evolution are needed. In the past several years there has been an effort to explore use of the Direct Simulation Monte Carlo (DSMC) approach for such estimations to improve fidelity of computations to the actual physics and chemistry of the accidents. An integral part of these efforts has been verification and validation of the DSMC technique against other available results wherever possible. This paper explores verification of DSMC against one existing and two new benchmark problems covering condensation, coagulation, deposition and two-component aerosols. The simulations compare well with the exact results, providing further confidence in the use of DSMC.

Application of Multicore Processing and Volume Parallelization in EBPVD Process Simulated Using DSMC

The present work is focused towards exploring the parallelization opportunities to extend the capability of available computational resources for analyzing larger control volumes and complex geometries for an Electron Beam Physical Vapour Deposition (EBPVD) process using Direct Simulation Monte Carlo technique. The work first establishes the efficacy of the model by comparing the simulated results with published experimental results for copper deposition in a vacuum chamber. The model is then extended to incorporate additional geometries and tracks the results of the copper deposition in an extension of the cubic chamber. The copper deposition in the extended geometry is simulated in two ways: initially by considering the entire volume as a single control volume and secondly by creating a virtual partition to divide the entire volume under consideration into two sub-control volumes which are simulated independently. The results obtained show that this independent treatment of the control volume gives comparable results thereby implying that large control volumes can be simulated by dividing them into smaller and more manageable sub-volumes, and simulating these sub-volumes independently. The paper further reports about employing object oriented programming techniques and multicore processing to support development and execution of the program.

Analytic Free-Molecular Aerodynamics for Rapid Propagation of Resident Space Objects

Aerodynamic forces and moments are significant perturbations on low-Earth-orbiting objects, second in magnitude to the nonspherical gravity field. Traditionally, the aerodynamic perturbations are calculated using a direct simulation Monte Carlo method. Under certain assumptions, these forces and moments can be described analytically via free-molecular flow theory. Using symbolic manipulation techniques, exact expressions for the free-molecular aerodynamics of analytic shapes can be derived. In this investigation, analytic expressions for the aerodynamic force and moment coefficients of primitive and composite parametric surfaces are derived, then validated against industry-standard direct simulation Monte Carlo techniques. A framework for the rapid and accurate calculation of free-molecular aerodynamics of composite geometries based on superposition is described. This framework is applied to axisymmetric composite geometries. Results within 6% of direct simulation Monte Carlo calculations are obtained in 0.05% of the time. The analytic aerodynamics models enable rapid trajectory and uncertainty propagation for low-Earth-orbiting objects. A case study on aerodynamic perturbations of a low-Earth-orbit nanosatellite is included to demonstrate application of these analytic models. The case study shows that these derived analytical free-molecular aerodynamics produce results that are applicable to inclusion in rapid trajectory propagation tools for orbit prediction and conceptual mission design.

Novel Hybrid Hard Sphere Model for Direct Simulation Monte Carlo Computations

This paper concerns the development of a novel hybrid hard sphere molecular model in direct simulation Monte Carlo technique. Usually, the variable hard sphere model is applied to simulate molecular collisions. However, this model is not accurate enough when temperatures are quite low or extremely high. The generalized hard sphere model can give the viscosity behavior of gases more accurately over a wide temperature range, but it is seldom used in practical engineering applications due to its poor computational efficiency. In this paper, a hybrid hard sphere model is presented to improve the computational efficiency of the original generalized hard sphere model. The modification is based upon the variable hard sphere and generalized hard sphere models and agrees quite well with the experimental observations. To investigate the accuracy and capability of the newly proposed model, two test cases involving thermal equilibrium and nonequilibrium are simulated. The results are compared with those of existing models and experimental data. The results show that the computational efficiency of the new model is much higher than the original generalized hard sphere model especially at low temperatures.

Continuum and Kinetic Simulations of Heat Transfer Trough Rarefied Gas in Annular and Planar Geometries in the Slip Regime

Steady-state heat transfer through a rarefied gas confined between parallel plates or coaxial cylinders, whose surfaces are maintained at different temperatures, is investigated using the nonlinear Shakhov (S) model kinetic equation and Direct Simulation Monte Carlo (DSMC) technique in the slip regime. The profiles of heat flux and temperature are reported for different values of gas rarefaction parameter δ, ratios of hotter to cooler surface temperatures T, and inner to outer radii ratio R. The results of S-model kinetic equation and DSMC technique are compared to the numerical and analytical solutions of the Fourier equation subjected to the Lin and Willis temperature-jump boundary condition. The analytical expressions are derived for temperature and heat flux for both geometries with hotter and colder surfaces having different values of the thermal accommodation coefficient. The results of the comparison between the kinetic and continuum approaches showed that the Lin and Willis temperature-jump model accurately predicts heat flux and temperature profiles for small temperature ratio T=1.1 and large radius ratios R≥0.5; however, for large temperature ratio, a pronounced disagreement is observed.

Parallel Fokker–Planck-DSMC algorithm for rarefied gas flow simulation in complex domains at all Knudsen numbers

A major challenge for the conventional Direct Simulation Monte Carlo (DSMC) technique lies in the fact that its computational cost becomes prohibitive in the near continuum regime, where the Knudsen number (Kn)—characterizing the degree of rarefaction—becomes small. In contrast, the Fokker–Planck (FP) based particle Monte Carlo scheme allows for computationally efficient simulations of rarefied gas flows in the low and intermediate Kn regime. The Fokker–Planck collision operator—instead of performing binary collisions employed by the DSMC method—integrates continuous stochastic processes for the phase space evolution in time. This allows for time step and grid cell sizes larger than the respective collisional scales required by DSMC. Dynamically switching between the FP and the DSMC collision operators in each computational cell is the basis of the combined FP-DSMC method, which has been proven successful in simulating flows covering the whole Kn range. Until recently, this algorithm had only been applied to two-dimensional test cases. In this contribution, we present the first general purpose implementation of the combined FP-DSMC method. Utilizing both shared- and distributed-memory parallelization, this implementation provides the capability for simulations involving many particles and complex geometries by exploiting state of the art computer cluster technologies.