Direct Simulation Monte Carlo Method Research Articles

Monte Carlo Simulation of Inlet Flows in Atmosphere-Breathing Electric Propulsion

A comprehensive numerical study is performed to investigate gas flows inside the inlet of the atmosphere-breathing electric propulsion system using the direct simulation Monte Carlo method. The effects of inlet geometries and gas–surface interaction (GSI) accommodation coefficients on gas pressure and flow rate are analyzed in depth, and a comprehensive assessment of the compression and collection performances of inlets is conducted. Inlet geometries have noticeable effects on gas pressures inside inlets, and the gas pressures of the two concave inlets are the highest. Among the four inlets considered here, the rounded concave inlet performs the best in terms of compression and collection performances. Relative to the simple slope inlet, the rounded concave inlet achieves a rate of increase of over 120% in gas pressure and more than 110% in gas flow rate. GSI accommodation coefficients play a crucial role in both the pressure and mass flux inside the inlet, and the drop of the GSI accommodation coefficient from 1 to 0.2 brings about a considerable increase in the pressure and mass flux, achieving an increase of a factor of 8 and 5, respectively. Therefore, smoothing the inlet surface is an effective means of improving the compression and collection performances of inlets.

Numerical investigation of impinging plume under vacuum and realistic nozzle outlet condition

During a lunar module landing, the gas extended from the engine nozzle impinges on the lunar surface. A recirculation bubble could form beneath the surface shock wave, which alters the flow pattern close to the surface, thus affecting the surface soil transportation process. This study conducted numerical simulations to investigate the flow characteristics, formation mechanism, and effects of this recirculation bubble on surface soil erosion using direct simulation Monte Carlo method or solving the Navier–Stokes equations. It is found that during the descent, the recirculation zone under the surface shock wave first disappears and then reappears. The shock wave systems in the plume at different lander heights is analyzed, revealing that the formation of the recirculation bubble can be attributed to the total pressure loss due to gas crossing different wave structures. When the lander descends to a close proximity to the lunar surface, the recirculation bubble can even expand into the nozzle. Furthermore, this study investigated the effects of the recirculation bubble on lunar soil transportation by a gas–solid two-phase solver. It is shown that the recirculation bubble at low landing altitude will entrain the lunar dusts and result in a high ejection angle of the latter, thus aggravating the obstruction of surface observation for the safe landing.

On an Efficient Solution of the Boltzmann Equation Using the Modified Time Relaxed Monte Carlo (MTRMC) Scheme

The study proposes a new method called MTRMC to simulate flow in rarefied regimes, which are important in various industrial and engineering applications. This new method utilizes a modified collision function with smaller number of inter-molecular collisions, making it more computationally efficient than the widely used direct simulation Monte Carlo (DSMC) method. The MTRMC method is used to analyze the flow over a flat nano-plate at various free stream velocities, ranging from low to supersonic speeds. The results are compared with those from DSMC and time relaxed Monte Carlo (TRMC) schemes, and the findings show that the MTRMC method is in good agreement with the standard schemes, with a significant reduction in computational expense, up to 51% in some cases.

Multi-Scale Simulations of Gas-Phase Particles Generated in Plasma Enhanced Atomic Layer Deposition Processes

Recently, Plasma Enhanced Atomic Layer Deposition (PEALD) has been investigated as an advanced semiconductor deposition method to expand the number and variety of materials other than those available in thermal ALD. The high reactivity of the plasma species at the deposition surface during PEALD has the advantage of increasing the degree of freedom of processing conditions and enabling a wider range of material properties. PEALD consists of four steps in the order of feed, 1st purge, reaction, and 2nd purge. In this reaction step, the secondary gas-phase reaction is important because the properties of the thin film vary greatly depending on the particles that arrive on the growing surface. Therefore, the particle distribution in the gas phase before arrival on the surface should be accurately predicted to estimate the film quality. Generally, the DSMC (Direct Simulation Monte Carlo) method is a commonly used method for analyzing particle distribution in the gas phase. The DSMC method requires reaction and scattering models that simulate the behavior between molecules. Variable Hard Sphere and Variable Soft Sphere are often used as the model in DSMC. These models are about molecular transport, such as molecular diffusion, and cannot deal with molecular reactions. The total collision energy model is determined for molecular reactions, but it may not accurately describe molecular reactions in non-equilibrium flow. The purpose of the study is to develop a new reaction-scattering model in non-equilibrium flow in the DSMC method for determining the particle distribution in the gas phase in the PEALD processes. Here, we focus on ammonia plasma used in the reaction step of boron nitride nanomaterial films, which are used in various applications, such as semiconductors and fine ceramics with two-dimensional and three-dimensional structures. This study focused on neutral and ionic molecules, NH3 and NH4 +, which can be the main collisional species in secondary gas-phase reactions.A molecular dynamics simulation with a reactive force field (ReaxFF) was performed. The left figure shows the simulation system of NH3 and NH4 + collisions. The periodic boundary conditions were applied to the simulation box for all directions in the size of 100 Å × 100 Å × 100 Å. Randomly oriented NH3 and NH4 + were placed in a line at an initial distance of 15 Å. NH4 + was given an electric charge of –0.22892 on N and 0.30723 on H. The initial translational energy of NH4 + was set at 5-60 eV, and the difference in the vertical coordinate at 0.1-5.0 Å. The collisions were sampled 2000 times.The right figure shows the calculated collision cross section, which determines whether a collision occurs or not. The collision coefficient bcoll represents the difference in the maximum vertical coordinate at which the absolute value of the scattering angle is greater than 1 degree. The collision cross section decreases as the translational energy increases because the negligible attraction-force act on NH3 and NH4 + at a long distance. When the translational energy exceeds 40 eV, the collisional cross-section no longer decreases and becomes asymptotic. The reason can be considered as follows. As the cross-section approaches 40 Å2, the collision cross section asymptotically approaches 40 Å2, regardless of the translational energy, because the attractive and repulsive forces are balanced. We compared our results with a reference model in grey color. In the reference model, Etr, 0 represents the minimum translational energy, σT,0 is the collision cross section at the minimum, Etr is the translational energy, and ω is a fitting parameter. Here, ω was set at –3.1. The reference model shows a good agreement with our results. However, the collision cross section is asymptotic above 40 eV, which may affect the results when the DSMC simulations are performed. We will apply the reaction scattering model to the DSMC method and analyze the gas-phase reaction of PEALD, including a comparison of the results of existing models. Figure 1

Influences of geometry configurations on the performance of micro-nozzles

Micro-nozzles play a critical role in various applications, such as micro-/nano-satellites in aerospace and heat dissipation and cooling in microelectronic systems (MEMS). The flows inside micro-nozzles can experience both continuum and rarefied flow due to their small size. In this research, we explore the optimal geometry configuration of micro-nozzles to achieve comprehensive performance and size, as well as background pressure compensation. Using classical computational fluid dynamics (CFD) and direct simulation Monte Carlo methods (DSMC), we investigate the effects of the expansion ratio, cross-profile shape, and plug on the performance of micro-nozzles operating over a wide range of pressures (0.5−100kPa). The results reveal that micro-nozzle performance is influenced by the interplay between flow expansion and viscous loss induced by the subsonic layer next to the micro-nozzle wall. The findings show that micro-nozzle performance improves with increasing expansion ratio in slip and continuum flow regimes, but decreases in the transition flow regime. Additionally, the results indicate that the axisymmetric micro-nozzle (with a circular cross-profile) outperforms the linear micro-nozzle (with a rectangular cross-profile) in terms of both performance and size when subject to the same conditions, making it the recommended choice for practical applications. We also find that plugs designed at the throat decrease performance, but increase stability under diverse background pressures. This study provides valuable insights for the design of high-efficiency micro-nozzles in applications such as nanosats and MEMS heat dissipation units.

Data Parallelization Algorithms for the Direct Simulation Monte Carlo Method for Rarefied Gas Flows on the Basis of OpenMP Technology

A data parallelization algorithm for the direct simulation Monte Carlo method for rarefied gas flows is considered. The scaling of performance of the main algorithm procedures are analyzed. Satisfactory performance scaling of the parallel particle indexing procedure is shown, and an algorithm for speeding up the operation of this procedure is proposed. Using examples of solving problems of free flow and flow around a cone for a 28-core node with shared memory, an acceptable speedup of the entire algorithm was obtained. The efficiency of the data parallelization algorithm and the computational domain decomposition algorithm for free flow is compared. Using the developed parallel code, a study of the supersonic rarefied flow around a cone is carried out.

Aerodynamic optimization of NACA 0012 airfoils with attached Gurney flap in the rarefied gas flow

The aerodynamic optimization of a Gurney flap attached to the NACA 0012 airfoil in rarefied gas flow is studied in this study. In order to investigate the effects of Gurney flap geometry (height, mounting angle, and mounting location) and angle of attack on the aerodynamic characteristics of the airfoil in the rarefied gas flow, the flow fields around NACA 0012 airfoils with Gurney flap attached are simulated by using the direct simulation Monte Carlo method. Furthermore, the multi-objective aerodynamic optimization of the airfoil with Gurney flap is performed at the single design point, and the Pareto front is obtained. Based on the benchmark configuration (obtained from the Pareto front), aerodynamic optimization by controlling the mounting angle of the Gurney flap and the angle of attack is investigated over a wide range of Mach numbers (ranging from 2 to 4) and Knudsen numbers (ranging from 0.024 to 0.24) by constructing an artificial neural network model. The results show that through optimization, the lift-to-drag ratio of the airfoil is increased by up to 29.25% under the combination of different Mach numbers and Knudsen numbers, which significantly improves the aerodynamic characteristics.

Data Parallelization Algorithms for the Direct Simulation Monte Carlo Method for Rarefied Gas Flows on the Basis of OpenMP Technology

Data Parallelization Algorithms for the Direct Simulation Monte Carlo Method for Rarefied Gas Flows on the Basis of OpenMP Technology

Evolution of the Shape of a Gas Cloud during Pulsed Laser Evaporation into Vacuum: Direct Simulation Monte Carlo and the Solution of a Model Equation

The dynamics of gas expansion during nanosecond laser evaporation into vacuum is studied. The problem is considered in an axisymmetric formulation for a wide range of parameters: the number of evaporated monolayers and the size of the evaporation spot. To obtain a reliable numerical solution, two different kinetic approaches are used—the direct simulation Monte Carlo method and solution of the BGK model kinetic equation. The change in the shape of the cloud of evaporated substance during the expansion process is analyzed. The strong influence of the degree of rarefaction on the shape of the forming cloud is shown. When a large number of monolayers evaporate, good agreement with the continuum solution is observed.

3D numerical study of neutral gas dynamics in the DTT particle exhaust using the DSMC method

Recently the design of the divertor tokamak test (DTT) Facility divertor has been modified and consolidated. The new divertor design presents significant geometrical differences compared to the previous ITER-like one, including the presence of a more flattened dome shape. This paper presents a complete 3D numerical analysis of the neutral gas dynamics inside the DTT subdivertor area for the latest divertor design. The analysis has been performed based on the direct simulation Monte Carlo method by applying the DIVGAS simulator code. SOLEDGE2D-EIRENE plasma simulations have been performed for a deuterium plasma scenario at the maximum additional power in partially detached condition achieved by neon impurity seeding and the extracted information about the neutral particles has been imposed as incoming boundary conditions. The pumping efficiency of the DTT divertor is examined by considering various cases with respect to the pumping probability and the effect of the toroidal and poloidal leakages is quantified. The results show that a significant percentage of the incoming flux of neutrals returns back to the plasma site through the entry gaps (60% for deuterium and 40% for neon), and, consequentially, only a small percentage (∼2%–15%) of the incoming flux can be pumped out from the system. The toroidal leakages affect significantly the pumping performance of the divertor causing a significant decrease in the pumped flux (and also in the pressure at the pumping opening) about 37%–47% and 43%–56% for deuterium and neon respectively. It is discussed how many pumping ports are needed depending on the achievable pumping performance per port. The number can be reduced by closing the toroidal gaps. The analysis shows that enlarging the poloidal gaps by a factor of two causes a significant increase in the poloidal flux losses by a factor 1.7. It is also illustrated how the presence of the cooling pipes leads to conductance losses.

Numerical investigation on flow and aerothermal characteristics of rarefied hypersonic flows over slender cavities

Flow and aerothermal characteristics of rarefied hypersonic flows passing through slender cavities are investigated comprehensively using the direct simulation Monte Carlo (DSMC) method by various cases, such as the cavity with different depth-to-width ratios and different inclination angles, and the freestream at different altitudes and Mach numbers. The cavity depth-to-width ratio has a great influence on flow structures and gas density inside the cavity, but a slight effect on gas temperature inside the cavity and on heat flux over cavity surfaces. In comparison to the vertical cavity, the upstream-inclined cavity reduces the gas density and the high-temperature area inside the cavity, showing a decrease rate of gas density of about 53 % for φ = -45°, while the downstream-inclined cavity greatly raises the gas density and slightly expands the high-temperature area, reaching a growth rate of gas density of about 114 % for φ = 45°. As the freestream altitude increases from 50 to 80 km, the main vortex expands remarkably while the heat flux near the top of the aft wall decreases sharply, and a noteworthy finding is that the dimensionless temperature contours inside the cavity for the cases of H = 50, 60, and even 70 km seem to be unchanged. Compared with the case of Ma = 6, the maximum density inside the cavity is increased by about 5.5 times for the case of Ma = 30, and it is about 7.3 times for the maximum temperature inside the cavity. However, raising the freestream Mach number seems to not alter the streamline patterns inside the cavity. The three-dimensional effect reduces the maximum density inside the cavity by about 14.5 % to 17.4 % and results in a smaller main vortex compared with the two-dimensional (2D) cavity, and moreover, the slender cavity can weaken the three-dimensional effect due to its larger depth-to-width ratio and the relatively short cavity width. Besides, the vortex-transport theory is proposed, which can well explain the change of gas density inside the cavity for all cases considered in this work.

Effect of Fluoride Layer Growth on the Deposition Rate under Different Microchannel Structures.

In the plasma-enhanced chemical vapor deposition (PECVD) process, a showerhead is used to enhance fluid uniformity in the chamber. The uniformity of the flow field will be affected by changing the microchannel on the showerhead, which in turn directly affects the uniformity of deposition. The showerhead will be etched during the cleaning process due to the presence of HF, which will form a fluoride layer. This layer will cause a decrease in the diameter of the microchannels, resulting in changes in the deposition uniformity. The impact of diameter changes can be reduced by making modifications to the microchannel structure. By adopting a coupling of the Navier-Stokes and Direct Simulation Monte Carlo (NS-DSMC) methods, we obtained the velocity variation of two typical microchannels (equal-diameter type and expansion type) under the same diameter change. The results indicate that compared to the equal-diameter type, the expansion type exhibits a smaller change in velocity for the same change in diameter. For the surface reaction limited regime, a stable velocity leads to a consistent residence time, which is advantageous for maintaining the uniformity of the film thickness. Therefore, compared to the equal-diameter type microchannel, the expansion type can reduce the impact of changes in diameter.

Ab initio modelling of transport phenomena in multi-component mixtures of rarefied gases

The direct simulation Monte Carlo method based on ab initio potentials is applied to model transport phenomena in binary, ternary and quaternary mixtures of noble gases. To this end, the Couette and Fourier problems are solved over the whole range of the rarefaction parameter spanning the near free-molecular, transitional, and slip flow regimes. Moreover, analytical solutions are obtained in the limits of the free-molecular and continuous medium regimes of flow. As a result, the shear stress, heat flux through multi-component mixtures, distributions of velocity, temperature, and mole fractions of each species are calculated as a function of the gas rarefaction. An analysis of these data points out the properties which are strongly affected by the chemical composition. It is found that the largest deviations of characteristics of mixtures from those of a single gas are observed for the binary mixture of helium and krypton, while their deviations for the ternary and quaternary mixtures are smaller. A temperature variation in a mixture leads to non-uniform distributions of chemical composition due to the thermal diffusion phenomenon. Such redistributions are analyzed in both problems and their effect on the heat and momentum transfer is evaluated. The reported results can be used to evaluate the main factors determining transport phenomena in practical applications such as vacuum systems, microfluidics, gas separation technology, space research etc.

Pollutant inhibition in an extreme ultraviolet lithography machine by dynamic gas lock

Dynamic gas lock (DGL) is an effective method to inhibit carbon deposition on optical surface in extreme ultraviolet (EUV) lithography machines. However, due to the complexity of the internal flow in DGL, relevant theoretical analyses remain incomplete. In this work, a direct simulation Monte Carlo (DSMC) method based on OpenFOAM platform is employed to study the transport process of rarefied gas in DGL and a project optics box (POB). The dsmcFoam + solver is extended and its applicability to DGL problems is verified. The results show that the number density of hydrocarbon in the POB decreases exponentially with the increase of the flow rate of clean gas, whereas the DGL inhibition rate is insensitive to the change of the pressure in the wafer chamber. Reducing the cone angle of the DGL, lowering the inlet position of the clean gas and using the clean gas with higher molar mass are all helpful to improve the inhibition effect of the DGL on the hydrocarbon diffusion. Additionally, the height of the DGL is relevant: with increase of the height, the inhibition rate rises at the same distance from the wafer surface; the number density of hydrocarbons is larger at higher heights. This study is expected to provide guidance for design of DGL technology under different EUV lithography conditions.

Kinetic simulation of ion thruster plume neutralization in a vacuum chamber

The electrical environment of a ground vacuum testing chamber creates facility effects for gridded ion thrusters. For example, it is well known that the plume from the thruster generates current paths that are very different from what occurs in space, and the neutralization of this plume is also different. For reasons such as this, it is important to clarify how the experimental testing environment affects plasma flows, but understanding this effect solely through ground experiments is difficult. To that end, this study utilizes particle-in-cell and direct simulation Monte Carlo methods to simulate xenon beam ions and electrons emitted from a neutralizer. First, we compare simulations conducted within the chamber to those conducted in space, demonstrating that grounded chamber walls increase the electric potential and electron temperature. Next, we investigate the impact of the neutralizer’s position and the background pressure on the plume in the vacuum chamber. We find that as the neutralizer position moves closer to the location of maximum potential, more electrons are extracted, resulting in increased neutralization of the plume. We also observe that high background pressure generates slow charge-exchange ions, creating ion sheaths on the side walls that alter ion current paths. Finally, we discuss how the potential at the thruster and neutralizer exits affects the plume. The relative potential of the neutralizer to the vacuum chamber wall is observed to significantly influence the behavior of the electrons, thereby altering the degree of plume neutralization. These findings are shown to be consistent with experimental results in the literature and demonstrate the promise of high-performance simulation.

Unified gas-kinetic wave-particle methods VII: Diatomic gas with rotational and vibrational nonequilibrium

Hypersonic flow around a vehicle in near space flight is associated with multiscale non-equilibrium physics at a large variation of local Knudsen number from the leading edge highly compressible flow to the trailing edge particle free transport. To accurately capture the solution in all flow regimes from the continuum Navier–Stokes solution to the rarefied gas dynamics in a single computation requires genuinely multiscale method. The unified gas-kinetic wave-particle (UGKWP) method targets on the simulation of such a multiscale transport. Due to the wave-particle decomposition, the dynamics in the Navier–Stokes wave and kinetic particle transport has been unified systematically and efficiently under the unified gas-kinetic scheme (UGKS) framework. In this study, the UGKWP method with the non-equilibrium among translation, rotation and vibration modes, is developed based on a multiple temperature relaxation model. The real gas effect for high speed flow in different flow regimes has been properly captured. Numerical tests, including Sod tube, normal shock structure, hypersonic flow around two-dimensional cylinder and three-dimensional flow around a sphere and space vehicle, have been conducted to validate the UGKWP method. In comparison with the discrete velocity method (DVM)-based Boltzmann solver and particle-based direct simulation Monte Carlo (DSMC) method, the UGKWP method shows remarkable advantages in terms of computational efficiency, memory reduction, and automatic recovering of multiscale solution in the high speed flow simulations.

Transport phenomena in the near-field region of Stefen flow

Stefan flow is a transport phenomenon concerning the movement of one component of a multi-component mixture that is induced by the production or removal of the component at an interface. Fick’s law is often used to describe the transport phenomena in many physical and chemical processes. However, when the system scales down to the order of molecular mean free path, the influence of interface that is not considered in Fick’s law, cannot be neglected. To predict the transport phenomena in the near-field region, the Herz-Knudsen (HK) relation is often adopted, in which the near-field region controlled by the HK relation was assumed as a zero-thickness layer. Our theoretical analysis has shown that this assumption is less physically realistic. In this study, we derive the thickness of the near-field region through the analysis of the theoretical binary diffusion coefficient and corresponding mass flux. Based on the analysis, we propose a modified Fick’s law to describe the far-field and near-field regions separately. The validity of this modified Fick’s law and its difference from Fick’s law coupled with the HK relation are demonstrated by comparing the partial pressure distributions of binary mixtures, predicted by the two versions of Fick’s law and the Direct Simulation Monte Carlo (DSMC) method, due to the deposition of one component on a cold surface. The comparison results show that the modified Fick’s law outperforms the Fick’s law coupled with the HK relation in accuracy at high deposition coefficients for H2O/N2 mixture and in stability within the range of this study. Moreover, the situations when the modified Fick’s law is required are discussed. This study provides a more molecular-level insight into the transport phenomena in the near-field region of Stefen flow.

Three-dimensional simulation of gas flow for predicting the pressure and velocity profiles inside a gas centrifuge machine using the DSMC method

In this article, using the direct simulation Monte Carlo (DSMC) method, the gas flow inside the gas centrifuge was modeled simultaneously in the Knudsen and hydrodynamic zones. So that the three-dimensional (3D) simulation of gas centrifuge in the presence of all drivers inside the rotor, including feed, scoop, baffle, etc. was done. The results showed that, the feed is an important factor in creating and intensifying the axial flow formed in the rotor axis, and choke phenomenon occurs at the point of its entry into the rotor. It was further revealed that the amount of separation power obtained from the simulation (using the DSMC method) and the experimental has a difference of 4.3%, showing the agreement of the 3D simulations with reality.

Numerical Study of Hypersonic Near-Continuum Flow by Improved Slip Boundary Condition

Appropriate numerical models and boundary conditions are required to accurately model hypersonic flows involving local nonequilibrium effects, which can be induced by the wall effect and large gradients of flow properties in the flowfield. Considering the strong density gradient near the wall for hypersonic flows, an improved Gökçen slip model is proposed in this paper by introducing a scaled mean free path to the conventional Gökçen’s model. Hypersonic argon flows over a circular cylinder and a blunt plate in the near-continuum regime are simulated by the proposed slip model with the conventional Navier–Stokes–Fourier equations and an extended continuum model, which was recently developed to model the shear nonequilibrium effect in high-speed flows. The accuracy of the new boundary model is evaluated by comparing the results with the direct simulation Monte Carlo method. The effects of Knudsen number, Mach number, and wall temperature on the nonequilibrium degree and aerodynamic predictions are also investigated. The numerical results show that the improved model can well predict the surface friction and heat transfer coefficients, exhibiting much better performance than the existing continuum models.

Molecular Dynamics Analysis of the Scattering Phenomena of Oxygen Molecules on an Ionomer Surface in Catalyst Layer of Fuel Cell

The purpose of this study is to clarify the effect of surface diffusion, which is the behavior of gas molecules on ionomer thin films, on the transport properties of oxygen in fuel cell catalyst layers. To this end, the direct simulation Monte Carlo (DSMC) and molecular dynamics (MD) methods were used in our simulations. The results of the DSMC method showed that the overall transport is strongly affected by the behavior of surface diffusion. It was found that the diffuse reflection model for surface diffusion used in the DSMC method has room for improvement as the MD results show a different trend that oxygen molecules tend to reflect in the direction of travel.