Direct Simulation Monte Carlo Method Research Articles

A Numerical Study on a Pincette-like Device using Thermally Induced Knudsen Forces

In this study, we demonstrate that thermally induced Knudsen forces in a rarefied gas can be exploited to achieve a tweezer-like mechanism to trap and grasp a micro-object without physical contact. Using the direct simulation Monte Carlo (DSMC) method, we showed that a heated thin plate, mounted perpendicularly on a flat substrate, can act as the tweezer-like mechanism. Specifically, it is found that the pressure differences induced by the thermal edge flows around the corners of the beam and the tip of the thin plate, generate a force that attracts the beam to the plate horizontally and vertically.

Numerical analysis of evaporation from nanopores using the direct simulation Monte Carlo method

Liquid evaporation from nanopores has been more recent with progress in nanotechnology. The relevant application ranges from solar-driven water harvesting using nanoporous membranes to thermal management of high-power electronics via coolant evaporation from nanoscale pores. In this work, the direct simulation Monte Carlo (DSMC) method was used to simulate evaporation from nanopores into the half-space, with an axisymmetric computational domain which conforms to the real nanopore geometry. According to the position of liquid–vapor interface, the evaporation regime was divided into: pinning and receding. In the pinning regime, the interface was pinned at the top of the nanopores. A range of Knudsen numbers and Mach numbers were compared, and the structure of the Knudsen layer was also identified in detail. The Knudsen layer thickness was less than 10λ at low Mach number and grew to nearly 40λ at Ma∞ = 0.785. We also examined the effects of porosity on evaporation mass flux. The effects of the receding length were researched in the receding regime. The downstream density decreased from 2.4 × 10−3 to 4.29 × 10−4 kg/m3 with the receding ratio from 1 to 20. Furthermore, the evaporation coefficient was established to determine its impact on gas flow. The present results highlighted the non-equilibrium and non-continuum features of nanoporous evaporation, providing insights into the rarefied gas dynamics within nanopores coupled to the liquid–vapor phase change.

Continuum to rarefied diffusive tortuosity factors in porous media from X-ray microtomography

The diffusive tortuosity factor of a porous media quantifies the material’s resistance to diffusion, an important component of modeling flows in porous structures at the macroscale. Advances in X-ray micro-computed tomography (μ-CT) imaging provide the geometry of the material at the microscale (microstructure) thus enabling direct numerical simulation (DNS) of transport at the microscale. The data from these DNS are then used to close material’s macroscale transport models, which rely on effective material properties. In this work, we present numerical methods suitable for large scale simulations of diffusive transport through complex microstructures for the full range of Knudsen regimes. These numerical methods include a finite-volume method for continuum conditions, a random walk method for all regimes from continuum to rarefied, and the direct simulation Monte Carlo method. We show that for particle methods, the surface representation significantly affects the accuracy of the simulation for high Knudsen numbers, but not for continuum conditions. We discuss the upscaling of pore-resolved simulations to single species and multi-species volume-averaged models. Finally, diffusive tortuosities of a fibrous material are computed by applying the discussed numerical methods to 3D images of the actual microstructure obtained from X-ray computed micro-tomography.

Numerical simulation of pulsed planar evaporation into background gas based on direct Monte Carlo simulation and solution of the BGK model kinetic equation

A numerical study of the planar gas expansion under pulsed evaporation into the background gas is carried out. The chosen conditions are typical for nanosecond laser deposition of thin films and nanostructure synthesis, with the saturated gas pressure at the surface of 5.4 MPa and the background pressure of 50 and 500 Pa. The problem is solved based on the direct simulation Monte Carlo method and direct numerical solution of the BGK model kinetic equation. A generally good agreement was obtained for all computed macroscopic quantities, with the exception of the higher density peak in the compressed layer and a wider shock front in the background gas for the BGK model.

Influence of flow control on aerodynamic properties of an open cavity in rarefied hypersonic flows

The discontinuity at the thermal protection system tiles covered on an aerospace vehicle is modeled as an open cavity to numerically investigate rarefied hypersonic flows over it under various flow control styles using the direct simulation Monte Carlo method. The influence of flow control on flow structures (e.g., shock wave and vortex) and aerothermal properties (e.g., temperature distribution and wall heat flux) is analyzed in detail. The flow structures and aerothermal properties of the cavity flowfield are both changed greatly by the square control block on the cavity opening line, such as a reduction of about 79.5% of the maximum of wall heat fluxes near the reattachment corner, while these changes are gradually weakened with the control block moving down. The control blocks with different shapes still have the ability to change flow structures and thus the heat flux coefficients over the cavity surfaces, but shape has little effect, and the square control block has the strongest wall heat flux compared with the circular, triangular, and wedged control blocks. For the supersonic jet with different directions, the leftward jet has the best performance in eliminating high temperature gas inside the cavity and over the downstream wall and reducing wall heat fluxes over cavity surfaces, followed by the downward jet. The main reason is that the leftward and downward jets can effectively prevent momentum and energy exchanges between freestream with cavity surfaces.

Mean-field kinetic theory analysis of vapor flow between evaporating and condensing interfaces in the presence of non-condensable gas molecules

To investigate the vapor kinetic boundary condition (which is the boundary condition for the Boltzmann equation) in the presence of a non-condensable (NC) gas at a non-equilibrium liquid interface, we performed numerical simulations of non-equilibrium vapor (condensable gas) and NC gas mixture flows. The Enskog–Vlasov direct simulation Monte Carlo method (EVDSMC method) was utilized for this two-surface problem to obtain the evaporation and condensation coefficients, which represent the vapor–molecule evaporation and condensation rates, respectively. These coefficients are incorporated in the kinetic boundary condition. The simulation results showed that the evaporation and condensation coefficients decrease with increasing numbers of NC-gas molecules at the liquid interface with the same tendency. To investigate the validity of these coefficients, we also utilized the obtained evaporation and condensation coefficients for Boltzmann equation analysis. Hence, we concluded that these coefficients simply depend on the NC-gas number density at the liquid interface if the liquid temperature is constant. Thus, they are independent of the non-equilibrium or equilibrium state, and therefore, the coefficient values obtained for the equilibrium state can be used in the analysis of a non-equilibrium state. This finding will aid future predictions of non-equilibrium vapor flows with NC gas.

An adaptable direct simulation Monte Carlo method for simulating acoustic agglomeration of solid particles

An adaptable direct simulation Monte Carlo (DSMC) method that settles the challenge of coexistence of agglomeration and rebound as a consequence of inter-particle collisions was developed to simulate acoustic agglomeration of solid particles. The method was validated against experimental data under a range of operational conditions. Based on this, the evolution of particle size distribution, agglomeration efficiency and agglomeration behavior with time was numerically investigated. The effect of restitution coefficient on the performance of acoustic agglomeration was also examined. The results show that the occurrence of acoustic agglomeration yields a significant decrease in the number concentration of small particles and a small increase in the number concentration of large particles. Moreover, a worse performance of acoustic agglomeration at a higher restitution coefficient is observed. This study demonstrated the power of the proposed method in simulating the acoustic agglomeration and provided a fundamental approach for investigating the dispersed gas-solid two-phase flows.

The effect of thermal conductivity on the outgassing and local gas dynamics from cometary nuclei

Aims.The aim of this work is to investigate the parameters influencing the generation of the inner comae of a comet with a spherical nucleus and to model the gas activity distribution around its nuclei. Here, we investigate the influence of thermal conductivity combined with sub-surface H2O and CO2-ice sources on insolation-driven sublimation and the resulting gas flow field. In the process, we adopted some of the rotational and surface properties of the target of the Rosetta mission, comet 67P/Churyumov-Gerasimenko (67P/CG).Methods.We used a simplified model of heat transport through the surface layer to establish sublimation rates from a H2O- and CO2-ice sub-surface into a vacuum. We then applied the 3D Direct Simulation Monte Carlo method to model the coma as a sublimation-driven flow. The free parameters of the model were used to test the range of effects arising from thermal inertia and the depth of the source on the gas outflow.Results.Thermal inertia and the depth of the sublimation front can have a strong effect on the emission distribution of the flow at the surface. In models with a thermal inertia up to 80 TIU (thermal inertia units: J m−2K−1s−1∕2), the H2O distribution can be rotated about the rotation axis by about 20° relative to models with no thermal lag. For CO2, the maximum activity can be shifted towards the sunset terminator with activity going far into the nightside for cases with low thermal diffusivity. The presence of a small amount of CO2can reduce the presence of H2O by at least an order of magnitude on the nightside by blocking H2O flow. In addition, CO2can also decrease the speed of the mixed flow in the same region up to 200 m s−1, compared to cases with no CO2activity.Conclusions.Even low values of the thermal inertia can substantially modify the gas flow field. Including CO2leads to strong variations in the local CO2/H2O density ratio between the dayside and nightside. CO2can dominate the gas composition above the nightside and can also act to modify the H2O flow field close to the terminator.

Improved theory for shock waves using the OBurnett equations

The main goal of the present study is to thoroughly test the recently derived OBurnett equations for the normal shock wave flow problem for a wide range of Mach number ($3 \leq Ma \leq 9$). A dilute gas system composed of hard-sphere molecules is considered and the numerical results of the OBurnett equations are validated against in-house results from the direct simulation Monte Carlo method. The primary focus is to study the orbital structures in the phase space (velocity–temperature plane) and the variation of hydrodynamic fields across the shock. From the orbital structures, we observe that the heteroclinic trajectory exists for the OBurnett equations for all the Mach numbers considered, unlike the conventional Burnett equations. The thermodynamic consistency of the equations is also established by showing positive entropy generation across the shock. Further, the equations give smooth shock structures at all Mach numbers and significantly improve upon the results of the Navier–Stokes equations. With no tweaking of the equations in any way, the present work makes two important contributions by putting forward an improved theory of shock waves and establishing the validity of the OBurnett equations for solving complex flow problems.

Gas pressure control of electric arc synthesis of composite Sn–SnO2–C nanomaterials

It was found that the variation of a buffer gas pressure in the reactor chamber can control the structure of the synthesized materials during electric arc sputtering of composite Sn–C electrodes. The gas dynamic model calculated by the direct simulation Monte Carlo method shows that the buffer gas pressure affects the local parameters of tin and carbon vapor condensation. As a result, Core-shell Sn–SnO2 nanoparticles packed in a carbon matrix with various structural properties have been synthesized. It has been found that an increase in the buffer gas pressure leads both to an increase in the average size of the synthesized nanoparticles and to the formation of a more disordered structure of carbon. In turn, the tin and carbon structure affects the electrochemical characteristics of the synthesized Sn–C composite as anode materials for lithium-ion batteries.

Analysis of the Effect of Surface Diffusion on Effective Diffusivity of Oxygen in Catalyst Layer By Direct Simulation Monte Carlo

Because in the catalyst layers (CLs) of polymer electrolyte fuel cells (PEFCs) platinum (Pt) is used as catalyst, we need to reduce the amount of Pt for cost reduction. In order to maintain the same output even when the amount of Pt is reduced, it is necessary to increase the current density per unit area of Pt surface. At high current density, mass transport is a major factor in voltage drop. Therefore, improving the oxygen transport properties in CLs will lead to cost reduction of PEFCs. Although the transport properties of oxygen in the porous structure of CLs have been studied, the effect of surface diffusion, which is the motion of an oxygen molecule on the ionomer thin film, on transport properties has not yet been clarified. The purpose of the present study is to analyze how the motion of an oxygen molecule on the ionomer thin film affects the oxygen transport properties in the CLs of PEFCs.We used the direct simulation Monte Carlo (DSMC) method. In this study, a computational system was constructed based on an actual catalyst layer sample. The three dimensional structure of the sample was obtained as sequential slice images using a focused ion beam-scanning electron microscope (FIB-SEM). In order to examine the effect of surface diffusion on the transport properties of oxygen molecules, the simulation was performed using a various conditions of the surface diffusion. The behavior of surface diffusion was determined by a surface diffusion coefficient (D s) and a time constant (τ).Figure 1 shows the results of the effective diffusion coefficient of oxygen in the CL. The red line shows the effective diffusion coefficient of oxygen in the calculation without considering the surface diffusion, which is 2.75×10-6 m2/s. The plot marks shows the each surface diffusion coefficient. As the surface diffusion coefficient increases, the effective diffusion coefficient of oxygen increases. When the surface diffusion coefficient is small, the increase in the time constant results in the decrease in the effective diffusion coefficient of oxygen. When surface diffusion coefficient is large, the increase in the time constant leads to the larger effective diffusion coefficient of oxygen. However, when the surface diffusion coefficient is large, as the time constant increases, the effective diffusion coefficient of oxygen has a peak value and then decreases. Although the surface diffusion coefficient becomes larger, the effective diffusion coefficient does not continue to increase. This trend occurs presumably due to the tortuosity of the three dimensional structure. When an oxygen molecule moves along the bended three dimensional structure, the distance of the motion of the oxygen molecule become larger than the straight-line distance between the start and end points. This is the reason why the effective diffusion coefficient does not continue to increase.Fig. 1: Effective diffusion coefficient of oxygen in the catalyst layer as a function of the time constant of the surface diffusion. The difference in plot marks shows the difference in the surface diffusion coefficient. The red line shows the effective diffusion coefficient of oxygen in the calculation without considering the surface diffusion. Figure 1

Investigation of rarefied flow over backward-facing step in different rarefaction regimes using direct simulation Monte Carlo

AbstractHypersonic aerothermodynamics for a re-entry vehicle approaching the earth’s atmosphere is critical in the exploration of space. These vehicles often encounter various flow regimes due to the density variations and have surface abnormalities. The backward-facing step (BFS) is one such simplified configuration for modeling anomalies around such space vehicles. The present work examines rarefied hypersonic flow over a BFS using the direct simulation Monte Carlo (DSMC) method. The purpose of this research is focused on exploring the various loads encountered by a re-entry vehicle passing through different altitudes covering different rarefaction regimes. The fluid considered was non-reacting air, with the free-stream Mach number as 25, and the Knudsen number considered ranged from 0.05-21.10. The influence of the Knudsen number on flow characteristics has been elucidated graphically in various streamwise directions. The normalised flow properties such as velocity, pressure, temperature and density showed an increasing trend with the Knudsen number due to compressibility and viscous heating effects. In all flow regimes, there was an appearance of flow recirculation. With rarefaction, the recirculation lengths decreased, whereas the boundary layer thickness showed an increase. The aerodynamic surface properties such as pressure coefficient, skin friction, and heat transfer coefficient, by and large, showed an increase with the Knudsen number. When the chemical reactions were accounted for and compared against the non-reacting flows, the velocity, pressure, and density field showed no marked variation; however, considerable variations were observed in the temperature field. Furthermore, the present study also depicts the compressibility factor contour, showing the flow regions that diverge from the ideal gas behaviour.

Design and Optimization of vacuum Intake for Atmosphere-Breathing electric propulsion (ABEP) system

Atmosphere-breathing electric propulsion system is a concept for space mission for ultra-low Earth orbit, which can collect the rarefied atmospheric particles as propellant to compensate the aerodynamic drag. In the best case, it can extend the lifetime of spacecraft without carrying any propellant. As the key component of Atmosphere-breathing electric propulsion system, intake device can capture the ambient particles and drive propellant to electric thruster. Considering the requirement of propellant mass flow and ionization efficiency, the performance of intake needs to be improved, including capture efficiency and compression ratio. The previous studies about intake device are summarized and analyzed firstly in this paper, and a new intake device is proposed that consists of tapered chamber, grid ducts and tube. Then, the inlet boundary conditions are set based on the NRLMSISE-00 atm model, such as particle species, natural temperature, number density and so on. Lastly, the intake performance is analyzed under different gas-surface interaction models through Direct Simulation Monte Carlo method. Simulation results show that the combination of parabola chamber, honeycomb grid ducts and a certain length of tube is benefit to intake device under the mixture reflection model of specular and diffuse. The capture efficiency is 65.79% with a high compression ratio of 210.2.

Data-driven nonlinear constitutive relations for rarefied flow computations

To overcome the defects of traditional rarefied numerical methods such as the Direct Simulation Monte Carlo (DSMC) method and unified Boltzmann equation schemes and extend the covering range of macroscopic equations in high Knudsen number flows, data-driven nonlinear constitutive relations (DNCR) are proposed first through the machine learning method. Based on the training data from both Navier-Stokes (NS) solver and unified gas kinetic scheme (UGKS) solver, the map between responses of stress tensors and heat flux and feature vectors is established after the training phase. Through the obtained off-line training model, new test cases excluded from training data set could be predicated rapidly and accurately by solving conventional equations with modified stress tensor and heat flux. Finally, conventional one-dimensional shock wave cases and two-dimensional hypersonic flows around a blunt circular cylinder are presented to assess the capability of the developed method through various comparisons between DNCR, NS, UGKS, DSMC and experimental results. The improvement of the predictive capability of the coarse-graining model could make the DNCR method to be an effective tool in the rarefied gas community, especially for hypersonic engineering applications.

Theoretical and numerical study of nanoporous evaporation with receded liquid surface: effect of Knudsen number

The liquid evaporation from nanoscale pores has attracted much attention from researchers due to its importance in water treatment and device cooling related applications. It is crucial to investigate the receded liquid case as the vapour flow resistance in a nanopore has high impacts on the evaporation rate. This paper proposed a semi-empirical analysis on nanoporous evaporation with a receded liquid surface under the influence of the Knudsen number. The vapour flow dynamics in a nanopore was examined considering the multiple reflections of vapour molecules. We calculated the value of pore transmissivity based on transitional gas flow correlation which incorporated the effect of the Knudsen number. Direct simulation Monte Carlo method was employed to provide validation for the present model. The vapour density jump near the liquid surface and the pressure ratio between the far field and saturation value were predicted by our model with good precision. It was shown that the vapour flow resistance in the nanopore accounted for more than 90 % of the total resistance in present cases. With increasing Knudsen number, the pressure ratio gradually drops and reaches an asymptotic level. This suggested a relatively higher evaporation resistance in free molecular regimes. The present work revealed the importance of the Knudsen number in nanoporous evaporation with receded liquids, providing insights into the governing factors under various Knudsen regimes.

Nonequilibrium effects in high enthalpy gas flows expanding through nozzles

An approach based on the direct simulation Monte Carlo method is proposed to model a core flow in a converging–diverging nozzle. The area of applicability of this approach is defined by the Boltzmann equation, which allows fully kinetic models that accurately capture thermal and chemical nonequilibrium to be applied to gas flows where the flow regime rapidly changes from continuum to transitional. The approach is validated through comparison with available experimental data. The examination of nonequilibrium and reaction rate effects for Caltech's T5 shock tunnel condition has shown little impact of nonequilibrium but demonstrated significant sensitivity of nitric oxide (NO) density to all exchange reaction and NO recombination rates. The use of the most recent theoretical and experimental rates results in a factor of two lower NO density at the nozzle exit as compared to the conventional Park rates, which indicates that re-visiting of the latter may be necessary. Multi-parametric sensitivity study of T5 conditions has not provided an explanation for a large drop in free-stream temperature and NO density over time, under constant flow velocity, observed recently in T5. Modeling of High Enthalpy Shock Tunnel Göttingen conditions has demonstrated considerable nonequilibrium between vibrational modes of N2, NO, and O2; it has also shown that the vibration–dissociation coupling strongly influences mole fractions of NO and O2.

Уточненная оценка аэродинамических характеристик наноспутника сложной геометрии

The paper presents an approach to refine the aerodynamic characteristics (drag coefficient, aerodynamic torque) of a complex-geometry nanosatellite. The approach is based on the direct simulation Monte-Carlo method. The calculations took into account gas−surface interaction according to Cercignani—Lampis—Lord model, chemical composition of atmosphere on the orbit altitude and particle thermal velocity. The nanosatellite complex geometry was described as a finite-element grid with the cell size of 5 mm. The results of the engineering and numerical methods were compared. The differences in drag coefficient and aerodynamic torque between the two methods reached 20%.

Multiscale mechanics of yttria film formation during plasma spray coating

In this study, we proposed a multiscale analysis method that integrates the direct simulation Monte Carlo (DSMC) method and all-atom molecular dynamics (MD) simulation to comprehend the process of unsteady plasma spray coating of yttria nanoparticles (YNPs) on an alumina substrate. The correlation between the increase in the powder feed rate and growth mechanism of the film microstructure was obtained by solving the collisions of the sprayed YNPs and corresponding spatial trajectories. The results showed that higher powder feed rates form a wider spray cone angle, and a reduction in spray distance increased the probability of powder impinging normal to the substrate. This also explained the changes in the interfacial adhesion and hardness of the films with the powder feed rate and spray distance observed in the experiments. In particular, vertically incident YNPs not only constituted the densest bulk layer, but also contributed to strong adhesion by increasing the probability of generating Y-O-Al binding structures at the interface. The findings were the first to examine the complexity of chemo-mechanical behavior between spatial particle trajectories and facing material, thus throwing light on an important factor in the quality of sprayed ceramic coatings.

Performance Analyses of Fluidic Thrust Vector Control System Using Dual Throat Nozzle

Flows in the rocket engine nozzles have been numerically analyzed to assess the performance of thrust vector control system of fluidic type by the direct simulation Monte Carlo method. Secondary jet is injected through a small port at one side of two-dimensional dual throat nozzle wall. If the cross-sectional areas of both throats are identical (nozzle A), and the injection port is near the first throat, the main flow separation caused by the secondary jet is observed, and a steady-state thrust deflection of about 18° is obtained when the flow rate of the secondary jet is 5% of the total fluid. However, the deflection also occurs randomly when the secondary jet is stopped. To avoid it, the second throat is widened to 1.50 times the cross-sectional area of the first throat (nozzle B), and it is observed that the thrust deflection is nearly zero for all cases without secondary jet injection. However, the thrust deflection is only about 5° when the secondary jet is injected near the first throat of nozzle B. When the injection port is placed further downstream of the first throat in nozzle B, thrust deflections between 14 and 15° are obtained.

Numerical investigation of gas separation via thermally induced flows in ratchet-like patterned microchannels

Gas separation can be achieved via thermally induced flows inside a microchannel. To obtain the optimum parameters for the best gas-separation efficiency, the direct simulation Monte Carlo (DSMC) method is used to numerically simulate a ratchet-like patterned microchannel with triangular hot plates. The analysis is based on the molar fraction of binary gas mixtures (He–Xe) in a steady state. The influence of temperature, Knudsen number, surface accommodation coefficient, and geometric parameters of the microchannel on its gas separation efficiency are studied using the controlled variable method. Results show that the separated heavier gas species (Xe) is mainly accumulated in wide or narrow microchannel at the last stage of the microchannel. The gas-accumulating position can be controlled by changing the microchannel width, microchannel length, and ratchet angle. The lighter gas moves from the cold to the hot side and concentrates in the hot region, while the heavier gas concentrates in the cold region. The gas separation efficiency improves as the temperature difference increases and the surface accommodation coefficient of the inclined surface decreases. The surface accommodation coefficient directly affects the transition between the thermal edge flow and radiometric flow near the upper tip of the triangle in the microchannel. The gas separation efficiency with a radiometric flow at the upper tip of the triangle is better than that with a thermal edge flow. In addition, the study gives the optimum parameter values for the best gas separation efficiency. These results can be applied to the realization and design of gas separators in various industry fields.