Direct Simulation Monte Carlo Code Research Articles

Gas physisorption impact on prolate dust in free-molecule flows: A static study

Gas–solid coupling systems operating at low pressure or the micro/nanoscale generally exist in nature and industrial manufacture. Although the gas-scattering model has been widely used to study this problem on the dust surface, the consideration of gas physisorption was often neglected in previous applications of gas–surface scattering models. Therefore, this study aims to investigate the distribution of gas physisorption on the dust surface and assess its impact on the static force experienced by nonspherical dust in free-molecule flows. In this study, the prolate dust spinning around its minor axis is considered and the in-house direct simulation Monte Carlo code is used. Results show that gas physisorption on prolate dust is influenced by changes in gas number densities, Mach number, and dust shape. Furthermore, the gas physisorption enhances the gas–dust coupling for dust with a smooth surface at low gas pressure, attributed to the increasing ratio of Maxwell diffuse scattering of gas molecules on the gas-adsorbed part of the surface. Hence, gas physisorption was suggested as a potential factor for gas–dust coupling at low gas pressure.

Numerical simulation of lateral jet interaction with rarefied hypersonic flow over a two-dimensional blunt body

Reaction Control System (RCS) is a direct force control system that successfully adjusts a craft's attitude or orbit using the reaction force created by jet flow. RCS is frequently employed in the management of near-space vehicles due to its properties of fast response time and effective control efficiency. When the near-space vehicle is navigating at high altitude in a low density atmosphere, the Navier–Stokes equation is no longer applicable. The numerical approach utilized in this study is known as the Conserved Discrete Unified Gas Kinetic Scheme, and the governing equation is the Boltzmann equation, which is not constrained by the continuum hypothesis. In velocity space, an unstructured mesh is utilized, which minimizes the amount of discrete velocity points and considerably increases computation efficiency. The numerical results are in good agreement with the direct simulation Monte Carlo code DS2V when modeling large Knudsen number lateral jet flow. The interaction flow field between hypersonic free stream and lateral jet is then simulated at altitudes of 60–90 km using argon as the working gas and a two-dimensional blunt cone with lateral jet as the study object. Under a fixed jet pressure ratio, preliminary research was conducted on the variation of the lateral jet interference flow field characteristics with the freestream Knudsen number and angle of attack. The differences in surface pressure and heat flux caused by jet opening and shutting are compared. Under rarefied atmospheric conditions, the variation of the force/moment amplification coefficient is given. The numerical results show that when the angle of attack is 0°, the separation area in front of the nozzle and a pair of opposite vortices, which are common in the jet interference flow field, gradually disappear with increasing altitude, but the separation vortex reappears when the angle of attack of the freestream is increased. The high-pressure region generated upstream of the nozzle is the primary cause of the extra force/moment. The density of the main flow decreases as altitude increases, various shock wave patterns of the interference flow field gradually dissipate and the force/moment amplification factor changes considerably. The rarefied gas effect has a significant effect on the lateral jet interference flow.

Development and Validation of an in-House Direct Simulation Monte Carlo Code for Supersonic Rarefied Gas Microflows

An in-house Direct Simulation Monte Carlo (DSMC) code has been developed using an object-oriented interface for the purpose of eventually modelling gas and plasma microflows in micromechanical systems, by coupling it with an existing Particle-In-Cell (PIC) solver. The code is validated with canonical flow problems such as the micro-Couette and micro-Poiseuille flows. Since the emphasis is on supersonic and highly compressible flows, we perform validation studies of our algorithm for high velocity and Mach number cases, as compared to known analytical or semi-analytical profiles via asymptotic Bhatnagar-Gross-Krook (BGK) and Chapman-Enskog theory. Reasonably good agreement is found for all the test cases, which indicates the reliability of the present algorithm for modelling supersonic rarefied gas flows. Our results have implications for future validation studies of DSMC codes, where concrete quantitative theoretical and experimental comparisons across different flow configurations are required.

Effect of formation of argon clusters on a supersonic outflow into a rarefied medium

A model of the argon condensation process has been developed for the direct simulation Monte Carlo (DSMC) method. The model includes the following processes: formation of dimers, merging of clusters, sticking of monomers to clusters, evaporation of monomers from clusters, and inelastic collisions between particles. The proposed model is implemented in the DSMC code SMILE++. The model is then verified and validated. Calculations of jet flows exhausting into a rarefied medium are performed on the basis of the proposed model.

Aerodynamic Analysis of an Entry Capsule at Titan in Transition Regime

The interest of the scientific community in Titan, Saturn’s largest moon, is still strong. In fact, after the successful Cassini–Huygens mission, which landed the Huygens capsule on Titan, other missions are planned in the coming years. The aims of this work are to provide the extent of global aerodynamic force, to provide thermal and aerodynamic loads on a capsule entering Titan atmosphere, and to evaluate the effects of chemistry on 1) flowfield parameters, 2) surface catalyticity, 3) temperature and pressure distributions on a heat shield, and 4) global aerodynamic force. To develop this study, the authors used the Huygens capsule and related entry trajectory. The study was carried out in the altitude interval of 295–470 km by means of the direct simulation Monte Carlo codes: DS2V for the solution of two-dimensional/axisymmetric flowfields, and DS3V for the solution of three-dimensional flowfields. The Titan atmosphere is a mixture of nitrogen, methane, and argon. The chemical model is made of 221 reactions, making gas around the capsule a mixture of 18 species. Chemistry strongly influences local aerodynamic quantities, both in the flowfield and on the capsule surface; whereas the chemical effects on the global aerodynamic force are negligible. Our computations also verified the lack of ionization.

Exponential Bhatnagar-Gross-Krook integrator for multiscale particle-based kinetic simulations.

Despite the development of an extensive toolbox of multiscale rarefied flow simulators, such simulations remain challenging due to the significant disparity of collisional and macroscopic spatiotemporal scales. Our study offers a novel and consistent numerical scheme for a coupled treatment of particles advection and collision governed by the BGK evolution, honoring positivity of the velocity distribution. Our method shares its framework, in spirit, with the unified gas kinetic class of multiscale schemes. Yet it provides attractive features for particle-based stochastic simulations, readily implementable to existing direct simulation Monte Carlo codes. Two main innovations are integrated in the presented BGK particle method. The first ingredient is a high-order time integration that can be interpreted probabilistically, independent of the time step size. The next one is identifying modified particle distributions that remain invariant under the advection-relaxation evolution. We demonstrate accuracy and performance of the devised scheme for prototypic gas flows over a wide range of rarefaction parameters. Due to the resulting robustness and flexibility of the devised exponential BGK integrator, the scheme paves the way towards more affordable simulations of large-scale and multiscale rarefied gas phenomena.

Influence of Air Pressure on Surface Flashover

The surface flashover is one of the most important factors that limit the performance of electric devices. In this article, the processes of surface flashover under different pressures are observed by a high-speed camera, and the differences between the plasma evolution processes are presented. Moreover, the simulation model of surface flashover under atmospheric conditions is established by a particle-in-cell code with direct simulation Monte Carlo (PIC-DSMC) code. Compared to the results of vacuum surface flashover, the reasons that caused the differences of the plasma evolution on surface flashover between vacuum condition and atmospheric condition are discussed. It is found that the competition between gas discharge and surface flashover would become more notable with the increase of air pressure. The results would be helpful to further understand the mechanism of the surface flashover.

Aerothermochemical analysis of the Orion capsule in rarefied transitional flow regime during Mars entry

It is well known that NASA developed the Orion project, besides for a rescue shuttle for the International Space Station, also for the transportation of instruments and astronauts to Moon, Mars and beyond. The forthcoming use of Orion for Mars landing stimulated Zuppardi to compute global aerodynamic coefficients in rarefied, transitional flow along a high altitude entry path. A Direct Simulation Monte Carlo (DSMC) code computed the coefficients at the altitudes of 80, 90 and 100 km, in the range of angles of attack 0–180 deg. The aim of the present paper, that can be considered as the logic follow on of the previous paper by Zuppardi, is to evaluate, in high altitude entry path, the influence of: 1) chemical reactions on the flow field and on some local quantities (temperature, pressure and heat flux) along the Orion surface, 2) typology of entry trajectory (direct and orbit) on both local quantities and drag coefficient, 3) heat flux associated to the surface recombination reactions. Computations were carried out in axisymmetric flow and in the altitudes interval 60–100 km by means of a home made code for the computation of the entry trajectories and of the powerful and advanced two-dimentional/axisymmetric DSMC code (DS2V) for the solution of the flow field around Orion.

Aerodynamic Comparison of Two Concept Capsules in Earth Reentry

Aerodynamics of two capsules of different conception both equipped with aerodynamic control surfaces has been compared at high-altitude Earth reentry path. The capsules are comparable in size but completely different in shape and, hence, in the aerodynamic behavior. The capsules are: 1) a circular cylinder provided with four flapped fins (finned cylinder), 2) a capsule, here tagged as Reentry Space Vehicle (RSV), very similar in shape and dimensions to the Intermediate eXperimental Vehicle. The study was carried out computationally in hypersonic, rarefied flow in terms of aerodynamic global coefficients (lift, drag, moments, etc.) computed by a three-dimensional direct simulation Monte Carlo code at the altitudes of 100 and 120 km, in the interval of angles of attack 0–50 deg and with flap angles of 0 and 20 deg. Computations verified that while RSV exerts a stronger aerodynamic force for the reduction of the capsule reentry velocity, the finned cylinder is better in terms of the attitude control capability. In fact, equilibrium of the finned cylinder is stable at zero angle of attack at the two altitudes, whereas the angle of attack of stable equilibrium of RSV changes with altitude. Hence, RSV needs to be provided with an active attitude control system.

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.

Initiation and Growth of the Secondary Electron Avalanche along High-Gradient Insulators in Vacuum

High-gradient insulators (HGIs) are materials created by alternating layers of insulating and conducting materials, which can result in a higher holdoff voltage than a monolithic insulator of the same length. We model the HGIs periodic electric field and use both a particle-in-cell direct simulation Monte Carlo code and a test particle approach to parameterize the growth of the secondary electron emission avalanches (SEEAs). To determine the effect of various HGI design parameters on secondary electron trajectories and SEEA growth, the following factors are investigated: layer width, edge layer materials, secondary electron yield, cell coupling, and surface defects as an electron source. We propose an alternative mechanism for initiating surface flashover, which considers surface defects on the downstream side of insulating layers, which differs from the current theory of cell coupling between adjacent insulating layers. Our results indicate surface conditioning is necessary because surface defects are a significant electron source in many cases. Our results reinforce the theory that thin layer widths are better at minimizing the growth of a surface avalanche, even though they will be more susceptible to cell coupling. If an HGI will not be conditioned prior to use, then thin layers are essential because of the significant avalanche growth capable along thicker layers. Finally, a metal layer adjacent to the cathode and an insulating layer adjacent the anode seems the optimal configuration to minimize the probability of flashover.

Determining Aerothermodynamic Effects on Very-Low-Earth-Orbit Satellites Using Direct Simulation Monte Carlo Method

Very low Earth orbits (VLEOs) have an altitude of 100–450 km and have become a popular topic in space technology owing to their high application potential. However, spacecraft experience stronger aerothermodynamic effects at VLEOs. In this study, we used a parallel direct simulation Monte Carlo (DSMC) code called PDSC++ and compared it with a traditional DSMC code. The results are in good agreement with the benchmarks. We also simulated the aerothermodynamic factors of a CubeSat, including the operating attitude, orbit altitude, size configuration, and solar panel deployment. The simulations indicate that CubeSats experience minimum drag at an angle of attack of 45°. The orbit altitude strongly affects the particle flow around and stress on a CubeSat. Moreover, a large CubeSat with solar panels experiences high drag and stress. These results can be used as a guide for further research on the service length and other configurational factors of CubeSats.

On an Axisymmetric Direct Simulation Monte Carlo Method

This study proposes an application of the variable time step (VTS) method to solve the non-conservation of fluxes encountered in the conventional direct simulation Monte Carlo (DSMC) method in axisymmetric simulations. A legacy parallel DSMC code with an unstructured cell using C++language (PDSC++) was employed by adjusting the reference scale of the original VTS to fulfill the requirements of axisymmetric simulation. Three test cases were simulated to verify the proposed axisymmetric DSMC method. First, the hypersonic flow past a cylinder was simulated using different wall boundary conditions. Second, the hypersonic flow past a 1.6-m sphere was simulated considering complicated air chemistry. Third, the flow field of the hypersonic flow past a double-cone blunt body was simulated and compared with the experimental data. The results showed that the newly proposed axisymmetric DSMC method can meet the simulation accuracy without an inconvenience through particle cloning and destruction.

Challenges and opportunities in verification and validation of low temperature plasma simulations and experiments

This paper describes the verification and validation (V&V) framework developed for the stochastic Particle-in-Cell, Direct Simulation Monte Carlo code Aleph. An ideal framework for V&V from the viewpoint of the authors is described where a physics problem is defined, and relevant physics models and parameters to the defined problem are assessed and captured in a Phenomena Identification and Ranking Table (PIRT). Numerous V&V examples guided by the PIRT for a simple gas discharge are shown to demonstrate the V&V process applied to a real-world simulation tool with the overall goal to demonstrably increase the confidence in the results for the simulation tool and its predictive capability. Although many examples are provided here to demonstrate elements of the framework, the primary goal of this work is to introduce this framework and not to provide a fully complete implementation, which would be a much longer document. Comparisons and contrasts are made to more usual approaches to V&V, and techniques new to the low-temperature plasma community are introduced. Specific challenges relating to the sufficiency of available data (e.g., cross sections), the limits of ad hoc validation approaches, the additional difficulty of utilizing a stochastic simulation tool, and the extreme cost of formal validation are discussed.

Computer analysis of rarefied aerodynamics around a winged space-plane for Mars entry

The forthcoming use of Orion for Mars landing stimulated Zuppardi to compute global aerodynamic coefficients in rarefied flow along an entry path. Zuppardi and Mongelluzzo also studied Aerodynamics of a blunt cylinder, provided with flapped fins, as a possible alternative to Orion for Mars Entry, Descent and Landing. Computer tests were carried out, in the altitude interval 60-100 km, by three codes: i) home made code computing the entry trajectory, ii) Direct Simulation Monte Carlo code (DS2V), solving 2D/axisymmetric flow field and computing local quantities, iii) Direct Simulation Monte Carlo code (DS3V) solving 3D flow field and computing global aerodynamic coefficients. The comparison of the aerodynamic behaviour of the two capsules in axisymmetric flow field verified that heat flux and wall temperature for the finned-cylinder are higher than those of Orion. The DS3V results verified that Orion is better than the finned-cylinder to produce an aerodynamic force for slowing down the capsule. On the contrary, the results indicated that the finned-cylinder is better in terms of attitude control capability. The purpose of the present paper is to compare Aerodynamics of: Orion, finned-cylinder, a hypothetical, winged space-plane in high altitude Mars entry path. Computations were carried out by means of the two above mentioned DSMC codes, along both orbit and direct entry trajectories. While the global aerodynamic coefficients of the space-plane are comparable with those of the finned cylinder, the aerodynamic and thermal stresses (or pressure, temperature and heat flux) at the nose stagnation point are higher for the space-plane. Therefore, the finned-cylinder seems to be a valid alternative to Orion.

Developments on two lithium vapor-box linear test-stand experiments

Abstract The lithium vapor-box divertor is a possible fusion power exhaust solution. It uses condensation pumping to create a gradient of vapor density in a divertor slot; this should allow a stable detachment front without active feedback. As initial explorations of the concept, two test stands which take the form of three connected cylindrical stainless steel boxes are being developed: one without plasma at PPPL, to test models of lithium evaporation and flow; and one for the linear plasma device Magnum-PSI (at DIFFER in Eindhoven, The Netherlands) to test the ability of a lithium vapor cloud to induce volumetric detachment and redistribute the plasma power. The first experiment uses boxes with diameters of 6 cm, joined by apertures with diameters of 2.2 cm. Up to 1 g of Li is placed in one box, which is heated to up to 600 ° C . The Li evaporates, then flows to and condenses in the two other, cooler boxes over several minutes. The quantity of Li transported is assessed by weighing the boxes before and after the heating cycle, and is compared to the quantity predicted to flow for the box at its measured temperature using a Direct Simulation Monte Carlo code, SPARTA. With good experimental conditions, the two values agree to within 15%. The experiment on Magnum-PSI is in the conceptual design stage. The design is assessed by simulations using the code B2.5-Eunomia. They show that when the H + plasma beam, with n e = 4 × 10 20 m −3 , T e = 1.5 eV , and r = 1 cm , is passed through a 16 cm long, 12 Pa, 625 ° C Li vapor cloud, the plasma heat flux and pressure on the target are significantly reduced compared to the case without Li. With the Li present, the plasma is cooled by excitation of Li neutrals followed by radiation until it volumetrically recombines, lowering the heat flux from 3.7 MW m−2 to 0.13 MW m−2, and the pressure is reduced by 93%, largely by collisions of H + with Li 0 .

Aerodynamics of Orion in Rarefied Flow Along a Mars Entry Path

It is well known that the Orion capsule was born as a rescue shuttle for the International Space Station. NASA developed the Orion project for the transportation of instruments and astronauts to moon, Mars, and beyond. Orion is similar in shape but larger than the Apollo command module; Orion will be able to host up to six astronauts, but Apollo command module could host only three astronauts. The aerodynamics of Orion during reentry to Earth in all rarefied regimes (that is, from free molecule regime to continuum) was already studied. The forthcoming use of Orion for Mars landing stimulated the author to evaluate global aerodynamic coefficients in rarefied flow along an entry path. The study considered problems both in axisymmetric and in three-dimensional flows by means of two direct simulation Monte Carlo codes. Global aerodynamic coefficients were computed at the altitudes of 80, 90, and 100 km. Special attention was paid to longitudinal stability.

Deterministic and stochastic modeling of rarefied gas flows in fusion particle exhaust systems

In the present work, a deterministic approach is applied for the first time ever to simulate the rarefied gas flow in the particle exhaust system of a nuclear fusion device. As an example of such a system, the pumping area of the DEMO (DEMOnstration Fusion Power Plant) fusion reactor is considered, which is characterized by high geometrical complexity and strong gradients of macroscopic quantities. The Knudsen number in this system may vary from free molecular up to the slip regime and the flow behavior must be described by the Boltzmann equation. In the present work, the Boltzmann equation is approximated by the well-known Bhatnagar–Gross–Krook and Shakhov kinetic models supplemented with the deterministic discrete velocity method. In addition, in order to assess the capabilities of the deterministic modeling, the problem has also been studied by solving the Boltzmann equation with the stochastic direct simulation Monte Carlo (DSMC) method. Extended comparisons between the deterministic and stochastic methods in terms of all macroscopic quantities of practical interest, namely, pressure, number density, temperature, and pumping fluxes, are performed and remarks about the effectiveness of the implemented deterministic approach have been drawn. Results are obtained by assuming He and D2 gas flows, various values of the capture coefficient at the pumping opening, and two different scenarios of the inlet gas temperature. In all examined cases, the deterministic results are in very good agreement with the DSMC ones, with the maximum relative deviation being less than 4%. The nonlinear deterministic code is significantly faster than the stochastic DSMC code for acceptable noise levels. The pumping fluxes and the pressure values in the vicinity of the pumping opening, both quantities useful for pumping system evaluation, have been calculated in terms of the capture coefficient. The present work may support decision making on the suitability of the pumping technology of DEMO and the design of the pumping system.

Rendezvous algorithms for large-scale modeling and simulation

Rendezvous algorithms encode a communication pattern that is useful when processors sending data do not know who the receiving processors should be, or vice versa. The idea is to define an intermediate decomposition where datums from different sending processors can ”rendezvous” to perform a computation, in a manner that both the senders and eventual receivers of the results can identify the appropriate rendezvous processor.Originally designed for interpolating between overlaid grids with independent parallel decompositions (Plimpton et al., 2004), we have recently found rendezvous algorithms useful for a variety of operations in particle- or grid-based simulation codes when running large problems on large numbers of processors. In particular, we show they can perform well when a load-balanced intermediate decomposition is randomized and not spatial, requiring all-to-all communication to move data between processors. In this case rendezvous algorithms leverage the large bisection communication bandwidths which parallel machines provide.We describe how rendezvous algorithms work in a scientific computing context and give specific examples for molecular dynamics and Direct Simulation Monte Carlo codes which result in dramatic performance improvements versus simpler algorithms which do not scale as well. We explain how a generic rendezvous algorithm can be implemented, and also point out similarities with the MapReduce paradigm popularized by Google and Hadoop.

Study on Breakdown Phenomenon of Electrode Induced by High-Energy Protons Bombarding

Ion bombardment of electrodes in an electric vacuum device can induce high-voltage breakdown. In order to explain this phenomenon, we, for the first time, analyzed a typical model of protons impacting the electrode with the help of a particle-in-cell (PIC)-direct simulation Monte Carlo (DSMC) code. In this model, we considered both the secondary electron yield and the gas desorption from the electrode. The temporal and spatial distribution evolution of electrons, ions, and neutrals under different electrode conditions is presented. The critical value of local gas density to induce breakdown is 1025 m−3. According to the discussion of the formation of the electrons avalanche, the electron ionizing gas is the key component for affecting the formation of a breakdown, and the production of plasma sheath near the electrode greatly contributes to the electrons avalanche.