Direct Simulation Monte Carlo Method Research Articles

Investigation of local Nusselt number in a rarefied microchannel gas flow using Direct Simulation Monte Carlo method

Heat transfer in microscale and rarefied gaseous flows has been investigated for high Knudsen number (Kn) flows using the Direct Simulation Monte Carlo (DSMC) method. A wide range of Kn [0.05 – 5], pressure ratio [1.2 – 4] and wall temperature [323 K – 723 K] is studied. The heat flux and local Nusselt number (Nu) are found to exhibit three distinct sections along the length of the microchannel – heat transfer-dominated section, constant heat transfer section and exit section. The defining roles of different effects such as non-equilibrium conditions at the wall, viscous dissipation, axial conduction, pressure work, and shear work have been considered implicitly in the DSMC method. These parameters are seen to influence the heat transfer differently at lower and higher Kn. These results help to quantify the fraction of total heat exchange and reveals the complex interplay of various terms of the energy equation in gas flow in microchannels.

An improved continuum model for hypersonic thermal nonequilibrium flow in the near-continuum regime

In this work, the rarefied Couette flow of diatomic gases with thermal nonequilibrium effects is investigated by the direct simulation Monte Carlo (DSMC) method, and a macroscopic computational model is developed to consider the local rarefaction effects for diatomic gases in the near-continuum regime. The nonlinear transport properties of the diatomic gases are studied, indicating that effective viscosity and effective translational thermal conductivity in the shear nonequilibrium state are affected by translational nonequilibrium effects, which obey the same laws for both monatomic and diatomic gases. The transport coefficients of internal energy modes are affected by both translational nonequilibrium and internal energy relaxation, therefore, the effective rotational and vibrational thermal conductivities are related to the effective viscosity through a modified Eucken relation that accounts for internal energy relaxation. Conclusively, effective constitutive relations are newly established as a function of the shear nonequilibrium parameter and the modified Eucken factors for thermal nonequilibrium flows, and these are integrated into the macroscopic two-temperature model. Subsequently, it is assessed in the simulation of hypersonic flows over flat plates and cylinders at various Knudsen numbers. The results show that the surface shear stress and heat flux obtained by the proposed model agree well with the DSMC results, indicating significantly improved performance compared to the conventional Navier–Stokes two-temperature model for hypersonic flows in the near-continuum regime.

Generation and Applications of a Broad Atomic Oxygen Beam with a High Flux‐Density via Collision‐Induced Dissociation of O2

Generation and Applications of a Broad Atomic Oxygen Beam with a High <scp>Flux‐Density</scp> via <scp>Collision‐Induced</scp> Dissociation of <scp>O₂</scp>

Inflatable aerodynamic decelerators for CubeSat reentry and recovery: Surface properties

In this investigation, Direct Simulation Monte Carlo Method is used to compute the surface properties of inflatable aerodynamic decelerators (IAD) applied for the reentry, recovery, and reuse of cubeSats. Surface properties calculation is of fundamental importance for flexible thermal protection system materials selection that withstand the harsh reentry environment. Furthermore, simulations are extremely important to detect possible hot spots at the IAD before design and flight. In this work, three IAD configurations are exposed to a rarefied hypersonic flow with freestream conditions that correspond to those found at reentry conditions at 105 km altitude. All geometries are assumed to be axisymmetric and have a maximum radius of 0.3 m from the center line to the shoulder edge. The main differences between the geometries are the angle between the IAD and cubeSat body and the IAD curvature for geometry 3. According to the results, all IAD geometries are effective in protecting the cubeSat during the reentry phase. It is shown that the IAD geometry has a significant influence on the heat transfer, pressure, and skin friction coefficient distribution over the flexible heat shield. The maximum heat transfer coefficient computed for geometry 1, 2, and 3 is 0.90, 0.97, and 0.84, respectively.

Numerical study on drag and heat flux reduction induced by a counterflowing jet for rarefied hypersonic flow over a blunt body

This paper focuses on the drag and heat flux reduction induced by a counterflowing jet located on the leading edge of the blunt body head in rarefied hypersonic flows using the direct simulation Monte Carlo method. Flow structures in the flowfield, such as detached shock wave, Mach disk, contact surface, jet layer, and recompression shock wave, are all weakened gradually with the increase in the freestream altitude, and they eventually disappear at the altitude of 90 km. The increase in the jet pressure provides a great drag reduction by up to 53% when it increases from 800 to 1600 Pa, but the proportion of drag on the blunt body head to the total drag is only affected slightly by the jet pressure. A noteworthy finding is that further increasing jet pressure almost have no effect on heat flux variation when it is larger than 1200 Pa. On the whole, jet temperature has a quite weak influence on both flow structures and drag, while heat flux on the blunt body head is closely related to jet temperature. The results suggest that jet temperature should vary with that of blunt body surface, and moreover, the optimal jet temperature should be moderately lower than the wall surface temperature. In addition, increasing freestream altitude can provide excellent performance of drag reduction, but it causes non-monotonic variation of heat flux. In view of this, it is worth noting that heat flux on the blunt body head actually increases with altitude when the blunt body is in a severely rarefied atmospheric environment, such as the altitude H &amp;gt; 70 km.

Rarefied Flow Simulations of Heat Transfer Across Evacuated Cryogenic Tank Insulation Structures

The Direct Simulation Monte Carlo Method computations are performed to investigate the heat transfer across highly evacuated cryogenic tank insulation structures. These structures usually consist of one cold and one hot wall with a temperature difference up to 260 K surrounding a rarefied gas which originates from permeating or leaking propellant. To validate the flow solver PICLas for this application, heat transfer results across parallel flat plates with nonflowing gaseous hydrogen and methane are compared to empirical relations of rarefied gas heat transfer and reference computations, showing good agreement with a deviation of less than 11%. Because gas flow usually occurs during and after evacuation, the heat transfer and skin friction coefficient in a symmetrical hydrogen channel flow with a wall distance of 30 mm is compared with literature data, showing a good match with a Nusselt number deviation of less than 20%. Furthermore, honeycomb tank insulation structures are analyzed, which can be used for future cryogenic liquid rocket tanks. Here, rarefied flow simulations are performed for slitted honeycomb structures with and without throughflow of hydrogen gas at a Knudsen number of 1.5 and transitional flow conditions at a Knudsen number of 0.1. The heat transfer results at the honeycomb sandwich are 50 to 70% below empirical relations for heat transfer across flat plates. Throughflow does not affect the heat transfer across the honeycomb because the Peclet number is less than 0.01.

An improved DSMC method for acoustic agglomeration of solid particles assisted by spray droplets

The direct simulation Monte Carlo (DSMC) method was improved for describing the process of acoustic agglomeration assisted by spray droplets. The agglomeration and rebound as consequences of inter-particle collisions were modeled by considering all possible particle types, in particular, mixed-phase particles associated with the immersion and distribution mechanisms. Numerical predictions by the present method were validated by both analytical solutions and experimental data. The dynamic process of the acoustic agglomeration in terms of the size and type evolution as well as the evolution of number concentration of different particle types were examined. Results suggest that the strong interaction between the solid particles and the spray droplets causes the significant enhancement of acoustic agglomeration. Furthermore, the effect of frequency varying from audible to ultrasonic range on the acoustic agglomeration was evaluated. Overall, a better performance of acoustic agglomeration can be achieved at a lower frequency, regardless of addition of spray droplets. Agglomeration efficiency of 64.8% can be achieve at acoustic frequency of 1000 Hz in case with spray droplets. This study provides not only a numerical model for describing the agglomeration of complex particles in particle-laden gas flows, but also important insights into the acoustic agglomeration assisted by spray droplets.

Regular reflection of shock waves in steady flows: viscous and non-equilibrium effects

Numerical analysis of a steady monatomic gas flow about the point of the regular reflection of a strong oblique shock wave from the symmetry plane is conducted with the Navier–Stokes–Fourier (NSF) equations, the regularized Grad 13-moment (R13) equations and the direct simulation Monte Carlo (DSMC) method. In contrast to the inviscid solution to this problem completely defined by the Rankine–Hugoniot (RH) relations, all three models predict a complicated flow structure with strong thermal non-equilibrium and a long wake with flow parameters not predicted by the RH relations. The temperature $T_y$ related to thermal motion of molecules in the direction normal to the symmetry plane has a maximum inside the reflection zone while in a planar shock wave the maximum is observed for the $T_x$ temperature. The R13 equations predict these features much better than the NSF equations and are in good agreement with the benchmark DSMC results. An analysis of the flow with the conservation equations was conducted in order to evaluate the effects of various processes on a fluid element moving along the symmetry plane. In contrast to the shock wave where effects of viscosity and heat conduction are one-dimensional with zeroth net contribution to the fluid-element energy across the shock, the flow across the zone of the shock reflection is dominated by two-dimensional effects with positive net contribution of viscosity and negative contribution of heat conduction to the fluid-element energy. These effects are believed to be the main source of the wake with parameters deviating from the RH values.

Localised sublimation under cometary dust mantles

Observations of cometary surfaces have indicated that the amount of exposed surficial water ice is insufficient to supply the measured water production rates within the inner solar system. The measured water production rates are also a small fraction of that which would arise from freely subliming pure water ice bodies of similar surface area. A plausible mechanism, given the now well-established, high porosity of comets is that water ice is subliming below the visible surface with the produced gas escaping through the pores in a non-subliming hot dust matrix. If this process leads to an additional heating of the evolving gas, this may provide an elegant explanation for the temperature of the gas required to match measured terminal velocities. We investigate this process using a series of numerical models based on the Direct Simulation Monte Carlo (DSMC) method for rarified gas dynamics. We show that inhomogeneities in the source are not evident in the flow field once the thickness of the porous layer reaches a specific size and that lateral flow through the porous layer (parallel to the surface) can broaden the apparent source size when the source is small and isolated. The temperatures of the gas flow at the visible surface can be significantly increased and will respond to the temperature distribution within the non-volatile porous layer. The influence of the structural properties of the porous layer (how the porous layer is mechanically constructed) is shown to have only limited influence on the final gas parameters at the surface.

A stochastic Fokker–Planck–Master model for diatomic rarefied gas flows

The direct simulation Monte Carlo (DSMC) method is widely used for numerical solutions of the Boltzmann equation. However, the associated computational cost becomes prohibitive in the near-continuum regime. To address this limitation, the particle-based Fokker–Planck (FP) method has been extensively studied in the past decade. The FP equation, which describes Brownian motion, does not require resolution of the collisional time and length scales. While several monatomic FP models have been proposed, the modeling of diatomic gases within the FP framework has received limited attention. In this paper, we propose a new diatomic kinetic model, named the Fokker–Planck–Master (FPM) model, which can accurately describe energy exchanges between translational-rotational and translational-vibrational modes. The FPM model combines the FP equation to describe the evolution of translational and rotational modes, and the master equation to describe the evolution of the vibrational modes. The numerical test cases include relaxation problems, Couette flows, and hypersonic flows past a vertical flat plate. The results demonstrate that the FPM model shows good agreement with both analytical and DSMC solutions.

Study of the spike-aerodisk-opposing jet on heat protection to both the spike-aerodisk and the blunt body and overall drag reduction in rarefied hypersonic flow in near space

The Direct Simulation Monte Carlo method (DSMC) is utilized in this study to investigate the flowfield surrounding the spike-aerodisk without and with an opposing jet under rarefied hypersonic conditions within near space (altitudes of 60∼90 km and Mach numbers 7∼20). As the flight altitude increases, the incoming flow gradually becomes rarefied, weakening the drag reduction effect of the spike-aerodisk model. At altitudes reaching 90 km, the spike-aerodisk loses its drag reduction effect due to the increasing proportion of the viscous drag coefficient. At a flight altitude of 70 km, as flight Mach numbers increase, the drag reduction and thermal protection performance of the spike-aerodisk remains unchanged, mainly demonstrating the excellent performance of the spike-aerodisk model at high Mach numbers. However, the peak wall heat flux coefficient on the aerodisk can be 4.8 times higher than on the blunt body. Therefore, an opposing jet is introduced to protect the spike-aerodisk from overheating and further improve the spike-aerodisk's drag and heat reduction efficiency. Within the investigated parameter range, when the opposing-jet pressure ratio is 0.02, the peak wall heat flux coefficient of the aerodisk can decrease from 0.58 to a level similar to that of the blunt body, approximately 0.12. To make the aerodisk more certain from overheating, choosing the opposing-jet pressure ratio of 0.08 can improve drag reduction and heat prevention on the blunt body by 60.9 % and 59.7 %, respectively, compared to the spike-aerodisk model without an opposing jet.

Numerical study of microscale gas pump based on surface acoustic waves

The concept of microscale fluidic pump based on microchannel with surface acoustic waves (SAWs), propagating along one of its walls, has been extensively studied in the last decade with possible application to lab-on-chip projects. Meanwhile, any mentions of the application of such device to gas medium seem absent in the literature. The present paper aims to fill this gap by investigating the possibility of using microchannel with SAWs as a microscale gas pump. The numerical study is performed using the modification of the direct simulation Monte Carlo method. It was shown that the pumping effect occurs mainly in the area covered by SAW, while the upper layers of gas are almost still in average. The pumping effect demonstrates weak dependence on gas rarefaction, decreases with the SAW speed, and is lower for a low amplitude to channel height ratios. Finally, it is shown that the propulsion intensity in the open system decreases with a decreasing microchannel height, while the compression ratio in the closed system, on the contrary, increases.

Non-equilibrium and anisotropy in Titan atmosphere entry

Titan is the largest moon of Saturn. It is the only moon in our solar system provided with atmosphere. Therefore, exploration of Titan demands aerodynamic computations aimed at a proper design of space vehicles that will bring instruments to its surface. To this purpose, the aerodynamic computing methodologies are Computational Fluid Dynamics (CFD) for the solution of continuum flow fields and Direct Simulation Monte Carlo (DSMC) method for the solution of rarefied flow fields. The failure of the Navier-Stokes equations at high altitude is due to non-equilibrium (different translational, rotational and vibrational temperatures) and to anisotropy (different components in the x, y and z direction of the translational temperature). The limitations in using DSMC at low altitudes are due to technical limitations of the computer, i.e. memory capacity and processing speed. In the present work, non-equilibrium has been quantified by the relative differences between translational and rotational (θt-r), translational and vibrational (θt-v) temperatures. Similarly, the relative differences between the translational temperature component along x and those along y (θx-y) and z (θx-z) quantified anisotropy. For each test condition, the maximum values of θ are representative of non-equilibrium and anisotropy. Computations have been carried out considering the Huygens capsule in axial-symmetric flow, along Titan atmospheric entry in the altitude interval 100–470 km by means of the commercial codes: 1) Fluent v18.1 in the interval 100–295 km, 2) DS2V-4.5 64 bits in the interval 295–470 km. The present computations stated that in the Titan entry of a capsule of dimension comparable with that of Huygens, the altitude of about 182 km should be the limit altitude for a proper use of a CFD code.

Mobility and diffusion of intruders in granular suspensions: Einstein relation

The Enskog kinetic equation is considered to determine the diffusion D and mobility λ transport coefficients of intruders immersed in a granular gas of inelastic hard spheres (grains). Intruders and grains are in contact with a thermal bath, which plays the role of a background gas. As usual, the influence of the latter on the dynamics of intruders and grains is accounted for via a viscous drag force plus a stochastic Langevin-like term proportional to the background temperature T b. In this case, the starting kinetic equations are the Enskog and Enskog–Lorentz equations for grains and intruders, respectively, with the addition of Fokker–Planck terms to each one of the above equations. The transport coefficients λ and D are determined by solving the Enskog–Lorentz kinetic equation by means of the Chapman–Enskog method adapted to inelastic collisions. As for elastic collisions, both transport coefficients are given in terms of the solutions of two integral equations, which are approximately solved up to the second order in a Sonine polynomial expansion. Theoretical results are compared against numerical solutions of the inelastic Enskog equation by means of the direct simulation Monte Carlo method. In general, good agreement between theory and simulations is found, especially in the case of the second Sonine approximation. Knowledge of the coefficients λ and D allows us to assess the departure of the (conventional) Einstein relation ϵ=D/(Tbλ) from 1. As expected from previous results for driven granular gases, it is shown that when the bath temperature T b is replaced by the intruder temperature T 0 in the Einstein relation, the origin of the deviation of ε from 1 is only due to the non-Maxwellian behavior of the reference state of intruders (measured by the cumulant c 0). Since the magnitude of c 0 is in general very small, deviations of the (modified) Einstein relation ϵ0=D/(T0λ) from 1 cannot be detected in computer simulations of dilute granular gases. This conclusion agrees well with previous computer simulation results.

Direct numerical simulation of supersonic nanoparticles flow in free-molecule regime using the angular coefficient method

We employ molecular flow methods to numerically simulate the supersonic nanoparticles flow in free-molecule regime. To streamline the computational complexity, interaction forces between the gas and solid particles are disregarded. We first develop a discrete phase model (DPM) method that integrates the non-rigid body collision model, enabling an accurate simulation of nanoparticle diffusion under the influence of the drag force and Brownian motion force. The nanoparticles considered in this study have sizes below 10 nm, and the accuracy of the DPM method is verified by comparing its results with experimental data. Subsequently, we theoretically and numerically investigate the transmission probability and number density of N2 molecules flowing through two-dimensional (2D) channels and three-dimensional (3D) tubes by using the angular coefficient (AC) method and the direct simulation Monte Carlo (DSMC) method. The findings indicate that as the diameter of the nanoparticle (dp) decreases to 1 nm, the diffusion coefficient (D) and the root mean square displacement (x) of nanoparticles approach the N2 molecules. The microscopic velocity of most N2 molecules falls within the range of 62–1400 m/s, and the macroscopic velocity of N2 flow falls within the range of Ma = 1.28–1.35. In contrast to the DSMC method, the AC method exhibits enhanced accuracy even with a reduced number of grids and obviates the process for large-scale sampling. Additionally, the solution time required by the AC method is approximately 1/10 and 1/13–1/32 of the DSMC method in 3D cylindrical tubes and 2D channels, respectively. Moreover, the AC method demonstrates superior adaptability when dealing with complex geometries.

Evaluation of stochastic particle Bhatnagar–Gross–Krook methods with a focus on velocity distribution function

For precise application of Bhatnagar–Gross–Krook (BGK) methods, assessing its accuracy in non-equilibrium flows is necessary. Generally, this assessment relies on macroscopic parameters, which are moments of the velocity distribution function (VDF). However, in non-equilibrium flows, the significance of each moment diminishes as the VDF deviates from the Maxwellian VDF. This study investigates the VDF in non-equilibrium flows. Two Prandtl-corrected BGK methods, the ellipsoidal statistical BGK and Shakhov BGK (SBGK), are compared with the direct simulation Monte Carlo method. To observe the VDF while excluding the effects of convection, the homogeneous relaxation of the initial non-equilibrium state is analyzed. The VDF in Couette flow and normal shock waves, where collision and convection coexist, is then examined. When comparing the accuracy of the BGK methods using higher-order moments, inconsistencies are observed. However, when comparing the VDFs, the SBGK method reproduces the non-equilibrium VDF more accurately. The results demonstrate the importance of the VDF in the evaluation of non-equilibrium flows.

The direct Monte Carlo simulation of microchannel flows for a large Knudsen number range

In recent years, porous materials containing micro- and nano-scale pores have found widespread applications. As the pore size decreases in such materials, rarefaction effects become significant in the pore flow, making the study of flow characteristics under higher Knudsen number conditions particularly crucial. In this work, through a direct simulation Monte Carlo (DSMC) method, an in-depth investigation is conducted into the gas flow characteristics and Klinkenberg effect in porous media with pore sizes ranging from 1 nm to 50 μm and Knudsen numbers spanning from 0.02 (slip flow) to 1200 (free molecular flow). The feasibility of using the DSMC method to simulate an internal free molecular flow in a porous medium under extreme rarefaction conditions with a Knudsen number of 1200 is validated. Furthermore, the impact of the gas pressure and porous medium pore size on the permeability is examined. The results reveal that with an increase in the Knudsen number, the dominant forces in the flow field transition from viscous forces to Knudsen diffusion, leading to a gradual increase in permeability. A comparative analysis reveals that existing apparent permeability models only provide satisfactory descriptions under certain Knudsen number conditions. Re-fitting the coefficient of the Kawagoe model and incorporating viscosity corrections leads to an apparent permeability model that can provide good predictions over a broader range of Knudsen numbers.

Investigation of the Inverse Magnus Effect on a Rotating Sphere in Hypersonic Rarefied Flow

Explorations involving long-endurance and maneuvering flights in the upper atmosphere, as well as research on atmospheric entries of space debris or asteroids, call for a full understanding of hypersonic rarefied flows. The inverse Magnus effect occurs in the hypersonic rarefied flow past a rotating sphere, but the aerodynamic behavior is contrary to the Magnus effect in the continuum flow regime. In this article, a series of such flows are numerically studied using the direct simulation Monte Carlo (DSMC) method. By analyzing the flow fields, as well as the distributions of pressure and shear stress on the sphere, the formation of the inverse Magnus force can be attributed to the tangential momentum transfer between incident gas molecules and the windward surface. The variation laws of aerodynamic parameters with the rotation rate are presented and discussed.

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.