DSMC Method Research Articles

Investigation on the Opposing Jet in the Hypersonic Rarefied Flow over a Vehicle Based on the DSMC Method

In this paper, an opposing jet is applied to the space shuttle arc leading edge and the lifting body cone leading edge in the hypersonic condition of the rarefied flow field. The DSMC numerical algorithm is used to simulate and analyze the underlying working physics of the opposing jet. The results provide a reference for designing hypersonic vehicles in near space that reduce drag and protect against heat.

Prediction of mole fraction distribution of various gases using dsmcFoam solver for the simulation of a stepped molecular pump under different operating conditions

In this paper, a stepped molecular pump is proposed, which greatly reduces the negative effect of the rotor opening on the clearance of the Holweck pumps due to the placement of the top cap inside the rotor of a gas centrifuge. The modified Sickafus relations were then extracted for the proposed stepped molecular pump and the compression ratio values for it were validated by DSMC method and experimental results. Due to the unknown molar fraction of gas components inside the space of the molecular pump, for different gases, the total space between the rotor and the casing with part of the space inside the rotor was simulated using a dsmcFoam solver. The results showed that by reducing the rotor velocity by 40%, the molar fraction of the heaviest gas (UF6) at the space above the molecular pump increases to about 20%. Also, at a certain velocity, by reducing the gas molecular weight from UF6 to Xe, the molar fraction of gas increases by 55%. Then, based on the molar fraction of the gas components predicted, it was observed that the use of a stepped molecular pump can increase the logarithm value of the compression ratio by up to 8%.

Investigation into the thermal effect of the LIPS-200 ion thruster plume

The distribution of the thermal effects of the ion thruster plume are essential for estimating the influence of the thruster plume, improving the layout of the spacecraft, and for the thermal shielding of critical sensitive components. In order to obtain the heat flow distribution in the plume of the LIPS-200 xenon ion thruster, an experimental study of the thermal effects of the plume has been conducted in this work, with a total heat flow sensor and a radiant heat flow sensor over an axial distance of 0.5–0.9 m and a thruster angle of 0°–60°. Combined with a Faraday probe and a retarding potential analyzer, the thermal accommodation coefficient of the sensor surface in the plume is available. The results of the experiment show that the xenon ion thruster plume heat flow is mainly concentrated within a range of 15°. The total and radial heat flow of the plume downstream of the thruster gradually decreases along the axial and radial directions, with the corresponding values of 11.78 kW m−2 and 0.3 kW m−2 for the axial 0.5 m position, respectively. At the same position, the radiation heat flow accounts for a very small part of the total heat flow, approximately 3%–5%. The thermal accommodation factor is 0.72–0.99 over the measured region. Furthermore, the PIC and DSMC methods based on the Maxwell thermal accommodation coefficient model (EX-PWS) show a maximum error of 28.6% between simulation and experiment for LIPS-200 ion thruster plume heat flow, which, on the one hand, provides an experimental basis for studying the interaction between the ion thruster and the spacecraft, and on the other hand provides optimization of the ion thruster plume simulation model.

Numerical estimations of lunar regolith trajectories and damage potential due to rocket plumes

This study presents a numerical investigation of rocket plumes carrying regolith particles in the context of the lunar environment (gravity and vacuum conditions). We investigated two lander masses with a single rocket hovering at 5 different low altitudes perpendicular to a flat surface. For the regolith, we considered 9 particle sizes, with diameters from 1μm to 1 cm. The initial condition of all particles was a null velocity at 0.3m above the ground. The particles started at 19 different radial positions from the centerline of the rocket jet, 1m to 10 m. We used a DSMC method to solve the rocket plume cases, considering the combustion product molecules from the propellant N2O4+Aerozine 50. Steady-state plume flow solutions are one-way coupled with discrete particles, considering drag and weight forces. The results showed that particle angle is nearly constant for small (dp<100μm) particles varying with initial radial position and lander altitude. Particle velocity is related to particle diameter as a power-law function and a Gaussian function of the initial particle position. Lander altitude and mass modulate the magnitude of particle velocity. Using the numerical solution data, we derived a numerical correlation for particle velocity that provides insight to avoid regolith abrasive blasting into the lunar lander, surrounding structures, and orbital satellites.

Investigation of the effect of bellows on the separation power in a gas centrifuge using DSMC method

At the beginning of the operation of a centrifuge machine, in order to prevent the increase of the friction power of the machine as well as purifying the gas inside the rotor, for optimal separation of the desired gas components by reducing the percentage of light gas, the space inside the machine will be in vacuum condition. The gas inside the machine is a dilute gas due to the initial vacuum and high-speed rotation of the rotor. The DSMC method was chosen to simulation the dilute gas inside the rotor. The rotors that are longer than the first critical length, require a component called bellows on the rotor to avoid resonant speeds. In this paper, showed that bellows with right triangle geometry have the best performance on the separation power of a centrifuge machine and also bellows have a significant effect on the other parameters of a machine.

DSMC simulations of neutral gas flow in the DTT particle exhaust system

Divertor Tokamak Test Facility (DTT) is a new European superconducting tokamak, currently under final design, addressed to investigate alternative power exhaust solutions for DEMO. Although the divertor system is not finalized yet, the machine and port geometry set limitations on the divertor pumping system operational space. A numerical study of neutral gas dynamics in the divertor region is performed based on the DSMC method by applying the DIVGAS code. The study includes both single-null (SN) and double-null (DN) divertor configurations. For both configurations, the SolEdge2D–EIRENE plasma simulations have been performed for a deuterium plasma with neon seeding and the extracted information about the neutral particles on the predefined interfaces is imposed as incoming boundary conditions for DIVGAS simulations. In the SN case, two plasma puffing scenarios and three candidate pumping port arrangements have been considered. The divertor dome influence on the pumped fluxes can reach 50%. An increase of the capture coefficient six times leads to a decrease in the pressure at the pumping openings by a factor of about 4.5–7. The influence of the size of the lower vertical opening has been studied showing that the enlarged vertical port may establish as the main pumping opening. In the DN case, when the pumping is performed from both lower and upper divertor the overall pumped fluxes at the upper divertor are always higher than the corresponding ones for the lower divertor by a factor of 2–2.5, mainly due to the difference in the pumping areas. In both SN and DN cases, the neutrals outflux toward the X-point dominates the particle transport in the private flux region. The operational space provided by this first assessment is relatively stable against modified classical divertor geometries and allows a more thorough assessment of the pumping technology of the DTT fusion device in the future.

Novel direct simulation Monte Carlo method for spherocylinders

Traditional discrete element models of granular flows for non-spherical particles can be limited by costly contact detection. The aim of the current work is develop the foundation towards a more computationally efficient method to solve flows with non-spherical particles. This study investigates extending the direct simulation Monte Carlo, or DSMC, method to the rotational relaxation of spherocylinders. While rotational energies have been accounted for in gases within DSMC, similar models for non-spherical particles are unavailable. We propose a modified DSMC method that samples from post-collisional energies and scattering distributions derived from deterministic discrete element models. We demonstrate how to integrate derived distributions into an adapted DSMC method for spherocylinders. To assess the fidelity of the model, we consider the case of the rotational relaxing dilute gas. While the study considers spherocylinders, the methodology itself may be generalized to more complex particle shapes.

Geometry effects on flow characteristics of micro-scale planar nozzles

A numerical investigation of geometry effects on the flow characteristics associated with converging-diverging 2D planar micronozzles is reported. The classical N–S with linear slip model, DSMC method, and a hybrid N–S/DSMC based on the continuum breakdown concept are employed for the simulations. The various methods adopted are validated with available experimental data. The study addresses the issue of heterogeneous findings on optimized half divergence angle recommended by previous studies. The analysis is conducted for various throat dimensions (2–200 µm thoat height), divergence angles (5∘–30∘), and divergence length. The performance and flow characteristics are compared at two distinct operating conditions, i.e. when the flow is mostly subsonic and supersonic in the divergent section. Results show an optimum divergence angle and length, maximizing the performance for a specific operating condition and nozzle size. Literature data suggest various divergence angles for optimum performance. This is due to the differences in operating conditions and the size of the micronozzles used. The current study shows that differences in flow behavior are mainly due to the pressure difference across the nozzle. When the micronozzle is operating under low-pressure differences, the flow is primarily subsonic in the divergent section. However, it accelerates due to the effect created by the growing thick boundary layer. The flow at higher pressure differences is characterized by clear flow separation and the occupation of the separated flow to a considerable portion of the divergent section. The separated phenomenon becomes less pronounced as the pressure difference and nozzle size decreases. As the nozzle size decreases to the nanoscale, Re is very low, and the subsonic layer fully occupies the divergent nozzle section even at very high-pressure differences. The results show that the performance is significantly influenced by the wall thermal conditions. The study highlights the differences in flow behaviour between micro and nano-scale nozzles at various operating conditions. Based on numerical data obtained in this present work, a new correlation is proposed to predict thrust per unit width for micronozzles.

Investigation of capillary size on the separation factor of gaseous separation membrane with DSMC method

Due to significant development of membrane applications in separation science, studying on membranes and geometrical effects is of great importance. The geometry and quantity of pores directly affect the separation factor. In an isotopic gaseous separation system, by increasing the product withdrawal rate from the system, the amount of separation will decrease. Generally, as the rate of withdrawal from the system increases, the amount of separation factor will decrease. In this research, using the DSMC method (Direct Simulating Monte Carlo Method), the gaseous separation system and flow through membrane is followed by focusing on effects of pore diameter. In this work, a mixture contains 32SF6 (light component) and 34SF6 (heavy component) is selected for separation. The results indicate when the capillary diameter increases, the product concentration is reduced, which means that the separation factor is reduced. It is shown for capillaries with diameters of greater than the nominal value, the separation will be stopped. As the diameter of the membrane capillaries increases, the withdrawal rate of the gas flow from the system will increase. Therefore, increasing the diameter of the membrane capillaries will increase the withdrawal rate of the system and reduce the separation factor. Also, diffusion velocities are evaluated.

Adjoint DSMC for nonlinear Boltzmann equation constrained optimization

Applications for kinetic equations such as optimal design and inverse problems often involve finding unknown parameters through gradient-based optimization algorithms. Based on the adjoint-state method, we derive two different frameworks for approximating the gradient of an objective functional constrained by the nonlinear Boltzmann equation. While the forward problem can be solved by the DSMC method, it is difficult to efficiently solve the high-dimensional continuous adjoint equation obtained by the “optimize-then-discretize” approach. This challenge motivates us to propose an adjoint DSMC method following the “discretize-then-optimize” approach for Boltzmann-constrained optimization. We also analyze the properties of the two frameworks and their connections. Several numerical examples are presented to demonstrate their accuracy and efficiency.

Numerical Simulation of Chemical Reactions on Rarefied Plasma Plume by DSMC Method

Chemical reactions in a rarefied plasma plume greatly influence the spatiotemporal distribution and transport characteristics of the flow field. In this article, such chemical reactions are studied using a direct simulation Monte Carlo method. Five particles, including molecular hydrogen H 2, atomic hydrogen H , atomic metal X , H 2+ ions, and H + ions, are injected from the sidewall of a cylinder. The chemical reaction network includes H 2 dissociation/recombination in the bulk and on the solid boundaries, and ion recombination on the wall. First, H 2 dissociation and H recombination are studied—the rate of H 2 dissociation is faster than the rate of H recombination. Second, chemical reactions involving H 2+, H +, and H , on the wall, are studied based on the foregoing study—the number densities of H 2+ and H + are significantly reduced after the chemical reactions on the wall, otherwise the number densities of H 2 and H are increased. This variation greatly influences the spatiotemporal distribution of the flow field.

Investigation of the continuum-rarefied flow and isotope separation using a hybrid CFD-DSMC simulation for [formula omitted] in a gas centrifuge

UF6 gas flow in the total regions of a rotor with the radius of 0.1 m and the length of 1 m in axisymmetric and steady states was simulated using a new hybrid CFD-DSMC method in the OpenFOAM framework. Implicit coupled density-based scheme was performed for CFD method, and Variable Hard Sphere (VHS) and diffuse model were employed in DSMC method. Also, as an initial estimation, the local Knudsen number was applied to determine the interface location between the continuum-rarefied regions (r = 0.0855 m). Then it was modified (r = 0.084 m) to reduce the computational cost. The comparison results of pure CFD and CFD-DSMC methods illustrated that there were large differences between the flow properties in the rarefied regions. Finally, the results showed that the separation factor of 6.5% and the separation power of 9.5% were different.

Comparison of different approaches to simulation of heterogeneous reactions by dsmc method

The present work is devoted to simulation of hydrogen dissociation on the surface of a heated wire in a resting gas by the direct simulation Monte Carlo (DSMC) method. Two approaches to simulating heterogeneous reactions are investigated: with and without regard to the velocities of particles impinging on the surface. A numerical study was performed based on a two-step hydrogen dissociation-recombination model.

Molecular dynamics simulations on the scattering of heavy gases on the composite surfaces

Cercignani-Lampis-Lord (CLL) is a boundary condition used in the DSMC method, due to the use of tangential and normal momentum accommodation coefficients (TMAC and NMAC) extractable by Molecular Dynamics (MD) simulations or experimental platforms, the accuracy of this boundary condition is by up to 15% relative to diffuse model (Mehta et al., 2014) [1]. These coefficients in slip, transitional, and free molecular flow regimes takes a value other than the unit. Since the temperature and velocity of the molecules after their scattering from the surface in the CLL model, drag coefficient, slip velocity, shear stress, and jumping temperature is completely dependent on the values of these coefficients, it is very important to determine these coefficients for different gases and surfaces. In this paper, first the DGEBA-TETA/carbon composite was simulated with MD method using an efficient algorithm and then using this method shown that in the interaction of heavy gases such as uranium, tellurium and sulfur hexafluoride with a composite surface, TMAC and NMAC were strongly dependent on Knudsen number and temperature of gases, velocity and temperature of composite, and the dependency of the TMAC was less than the NMAC for different conditions of gas characteristics. In these cases, tellurium hexafluoride had the greatest impact.

Effect of Obstacle’s Length-to-Height Ratio on Aerodynamic Quantities of Rarefied Hypersonic Flow

The DSMC method was used to calculate and analyse the flow field structure and the surface aerodynamic quantities when the hypersonic rarefied gas flow passing obstacle at a height of 70km. The changes of surface aerodynamic quantities such as skin friction coefficient, heat transfer coefficient, and pressure coefficient when the length-to-height ratio of the rectangular obstacle is 1/1, 1/2, 1/3, and 1/4 are analysed. The results show that under the above aspect ratio of the obstacle, a recirculation region is formed at each corner of the obstacle. A bow shock will be formed on the windward side of the obstacle, and with the increase of the obstacle’s height, the bow shock will be superimposed on the separated shock wave in front. A strong expansion wave will be formed on the backside of the obstacle, which affects the downstream flow field structure and aerodynamic quantities. When the obstacle’s height increases, the maximum value of the aerodynamic quantities on each surface of the obstacle will increase significantly. It is calculated that the quantities such as heat transfer coefficient and pressure coefficient reach the maximum at the convex point of the windward surface.

Investigation on the simulation approach for Martian rarefied aeolian activities based on discrete element method

Due to the tiny size of dust particles and the low atmospheric pressure, the Martian aeolian activity between Martian dust particles and Martian airflow should be considered as a rarefied two-phase flow. In this paper, a simulation approach for the rarefied characteristic of Martian dust storm has been studied based on discrete element method (DEM). First, the simulation approach based on the DSMC method was studied, and a series of DSMC simulation of Martian rarefied airflow were carried out in dsmcFoam. Second, the DEM simulation approach was used for the simulation of Martian rarefied airflow, and the simulation accuracy was proved by comparing with the DSMC simulation results. Finally, a series of simulation of Martian aeolian activity have been carried out in the DEM simulation software EDEM. This paper provides a new approach for the investigation on the two-phase flow of Martian aeolian activities.

Effect of pore throat structure on micro-scale seepage characteristics of tight gas reservoirs

At present, the effects of pore throat structure on micro-scale seepage characteristics of tight gas reservoirs are less researched, and traditional numerical simulation methods are faced with a great number of challenges in the study of micro-scale flow. In this paper, the flow pattern of tight gas was studied based on the actual temperature and pressure of tight gas reservoir and the characteristic size of reservoir pore throat, and the rationality of tight gas flow was simulated by means of lattice Boltzmann method. Then, considering the influences of micro-scale effect, slippage effect and other factors, a tight gas flow model was established on the basis of LBGK-D2Q9 model, and its calculation results were compared with the analytical solutions and the numerical solutions listed in the literature. Finally, the influential laws of pore throat structure on the micro-scale seepage characteristics of tight gas were discussed. And the following research results were obtained. First, when the pressure is in the range of 3–70 MPa and the temperature is in the range of 293.15–373.15 K, the Knudsen number (Kn) is less than 0.1 and the gas flow is in the pattern of slippage flow and weak continuous flow. And in this case, it is reasonable to adopt the LBGK-D2Q9 model to simulate tight gas flow. Second, the effect of the characteristic size of the flow channel on the Kn is much greater than that of the pressure change. When the pore–throat ratio is constant, the Kn increases slowly along the throat. And its increasing trend gets more obvious with the increase of pore–throat ratio. Third, the presence of the throat makes the non-linear distribution characteristics of the pressure in the pore throat significant, and the pressure drop mainly lies in the throat. And the higher the pore–throat ratio is, the larger the pressure drop range in the throat is. Fourth, the non-linear distribution of pressure decreases the gas flow speed significantly, thus reducing the mass flow rate in the flow channel. In conclusion, the simulation result of the model established in this paper is highly coincident with the analytical solutions and the numerical solutions calculated by DSMC and IP methods in the literature, which verifies that this proposed model is reliable. The research results reveal the importance of “connecting fracture and expanding throat” in the practical development engineering of tight gas reservoirs.

DSMC modeling of rarefied ionization reactions and applications to hypervelocity spacecraft reentry flows

The DSMC modeling is developed to simulate three-dimensional (3D) rarefied ionization flows and numerically forecast the communication blackout around spacecraft during hypervelocity reentry. A new weighting factor scheme for rare species is introduced, whose key point is to modify the corresponding chemical reaction coefficients involving electrons, meanwhile reproduce the rare species in resultants and preserve/delete common species in reactants according to the weighting factors. The resulting DSMC method is highly efficient in simulating weakly inhomogeneous flows including the Couette shear flow and controlling statistical fluctuation with high resolution. The accurate reliability of the present DSMC modeling is also validated by the comparison with a series of experimental measurements of the Shenzhou reentry capsule tested in a low-density wind tunnel from the HAI of CARDC. The obtained electron number density distribution for the RAM-C II vehicle agrees well with the flight experiment data, while the electron density contours for the Stardust hypervelocity reentry match the reference data completely. In addition, the present 3D DSMC algorithm can capture distribution of the electron, N+ and O+ number densities better than the axis-symmetric DSMC model. The introduction of rare species weighting factor scheme can significantly improve the smoothness of the number density contours of rare species, especially for that of electron in weak ionization case, while it has negligible effect on the macroscopic flow parameters. The ionization characteristics of the Chinese lunar capsule reentry process are numerically analyzed and forecasted in the rarefied transitional flow regime at the flying altitudes between 80 and 97 km, and the simulations predict communication blackout altitudes which are in good agreement with the actual reentry flight data. For the spacecraft reentry with hypervelocity larger than the second cosmic speed, it is forecasted and verified by the present DSMC modeling that ionization reactions will cover the windward capsule surface, leading to reentry communication blackout, and the communication interruption must be considered in the communication design during reentry in rarefied flow regimes.

Рост плотности и расхода тяжелого компонента при истечении разреженной газовой смеси в вакуум

Gas dynamics of a rarefied mixture flowing from a chamber into vacuum is studied for the case of disparate-mass components. The modeling was fulfilled by the DSMC method. An increase of the heavier component density is observed in the vicinity of the chamber’s outlet. A significant impact of the lighter component on the jet dynamics consists in an increase of the heavier component flux and direction of heavier particles to the axis.

Modeling and simulating of feed flow in a gas centrifuge using the Monte Carlo method to calculate the maximum separation power.

Most of the gas enters into a small portion of the rotating cylinder by increasing the rotational speed in a rotating cylinder. Navier-Stokes equations were used to evaluate gas behavior in this area. In this paper, the mass source calculated by the DSMC method at the boundary of the two regions has been used in the Onsager-Pancake equation and finite difference method was used to solve this equation. One of the assumed flow functions taking into account the effects of the scoop and thermal driving is the Olander's flow function. By combining the flow function that resulted from the Onsager-Pancake equation and the Olander's flow function, a new flow function is suggested, that in addition to applying the effect of thermal and mechanical driving, the feed driving added to it with the DSMC method. The results obtained using this new flow function in the modified diffusion equation by Onsager-Cohen, showing the resulted optimal separation power from that in comparison to the Olander's function occurs in a state where thermal driving is insignificant and scoop driving has increased. The effects of scoop drive have increased by increasing the feed value with the new flow function. Furthermore, the diffusion equations have been solved for 235UF6 and 238UF6 using the new flow function and it has been calculated the separation parameters.