Rarefied Gas Flow Research Articles

DSMC simulation of rarefied gas flow over a 2D backward-facing step in the transitional flow regime: Effect of Mach number and wall temperature

Rarefied gas flow over a backward-facing step (BFS) is often encountered in separating flows prevalent in aerodynamic flows, engine flows, condensers, space vehicles, heat transfer systems, and microflows. Direct Simulation Monte Carlo (DSMC) is a powerful tool to investigate such flows. The purpose of this research is to assess the impact of Mach number and wall temperature on the flow and surface properties in the transitional flow regime. The Mach numbers considered are 5, 10, 25, 30, and the ratio of the temperature of the wall to that of freestream considered are 1, 2, 4, 8. The Reynolds number for the cases studied is 8.6, 17.2, 43, and 51.7, respectively. Typically the flow properties near the wall are found to increase with both Mach number and wall temperature owing to compressibility and viscous dissipation effects. The variation in flow properties is more sensitive to Mach number than the wall temperature. The surface properties are found to decrease with Mach number and increase with wall temperature. Moreover, in the wake of the step, the vortex’s recirculation length is reasonably independent of both free stream Mach number and wall temperature, whereas it decreases with Knudsen number.

A Stochastic Two-Scale Model for Rarefied Gas Flow in Highly Heterogeneous Porous Media

This paper presents the development of a model enabling the analysis of rarefied gas flow through highly heterogeneous porous media. To capture the characteristics associated with the global- and the local-scale topology of the permeable phase in a typical porous medium, the heterogeneous multi-scale method, which is a flexible framework for constructing two-scale models, was employed. The rapid spatial variations associated with the local-scale topology are accounted for stochastically, by treating the permeability of different local-scale domains as a random variable. The results obtained with the present model show that an increase in the spatial variability in the heterogeneous topology of the porous medium significantly reduces the relevance of rarefaction effects. This clearly shows the necessity of considering a realistic description of the pore topology and questions the applicability of the results obtained for topologies exhibiting regular pore patterns. Although the present model is developed to study low Knudsen number flows, i.e. the slip-flow regime, the same development procedure could be readily adapted for other regimes as well.

Rarefied gas flow into vacuum through a channel with sudden contraction or expansion

Based on the direct simulation Monte Carlo method, we have simulated a flow of rarefied gas into vacuum through a channel with sudden contraction or expansion in cross section. The nonequilibrium effects at the input and output of the channel have been taken into account by including certain pre- and post-channel regions into the geometry under consideration. In a wide range of gas rarefaction, the mass flow rate through the channel and the flow field both inside the channel and in the upstream and downstream regions have been calculated. The results have been compared with the characteristics of a channel with the constant cross section. A significant effect of the channel geometry has been established. The Knudsen minimum has been found in the mass flow rate as a function of gas rarefaction, while a compression zone and a circulation zone have been discovered in the flow field.

A novel hybrid DSMC-Fokker Planck algorithm implemented to rarefied gas flows

In this article, a new hybrid approach combining Fokker Planck (FP) and Direct Simulation Monte Carlo (DSMC) is introduced. The FP approach, which is an approximation of the Boltzmann equation, has been recently introduced for modeling rarefied gas flows. Compared to standard molecular methods like DSMC, it has a lower computational cost. However, the FP model may provide erroneous results in modeling some flow features, including vortex region and shock waves. The DSMC approach is accurate enough; yet, it has a high computational cost, especially at low Knudsen/low Mach number conditions. The purpose of this article is to suggest an optimized hybrid algorithm to benefit from high-speed modeling and sufficient accuracy simultaneously. We show a modified form of the gradient length Knudsen number, i.e., KnGL/Kn, must be considered to define the range of accuracy of the FP method. We used KnGL/Kn as a parameter for switching between DSMC and FP. The cavity flow and the nozzle flow are considered for the investigation of the proposed hybrid algorithm. The dependence of the accuracy and computational cost on KnGL/Kn is reported. The results demonstrate that the optimized KnGL/Kn is between 3 and 4, which gives suitable computational cost and acceptable accuracy.

Molecular dynamics study on scattering characteristics of nitrogen molecules from platinum surface by molecular beam method

Rarefied gas flow has received wide attention due to the booming of micro/nano-electromechanical systems and aerospace engineering. Under such rarefied conditions, the frequency of intermolecular collisions is sharply reduced, so the impacts of interactions between gas molecules and the wall surface on flow states become non-negligible. Owing to the complexity of theoretical research and the poor reproducibility of experimentation, molecular dynamics simulation has developed into an effective method to study the interplay between gases and solid surfaces. In this study, molecular dynamics simulations on the scattering process of nitrogen molecules from a platinum surface are conducted in a three-dimensional system. The dependences of scattering angle distributions and momentum/energy variations on the incident velocity, angles, and surface roughness are obtained. The results of this paper are not only an attempt to reveal the mechanisms of gas–surface interactions but can also be used as necessary reference data for the development of appropriate gas–surface interaction models.

Preface

XIII International Conference on Applied Mathematics and Mechanics in the Aerospace Industry (AMMAI’2020) http://www.npnj.ru/index_e.htm 6-13 September 2020 Alushta, Russia The Thirteenth International Conference on Applied Mathematics and Mechanics in the Aerospace Industry (AMMAI’2020) will be held on 6-13 September 2020 at Alushta Health and Educational Center, Russia. AMMAI’2020 is dedicated to the 90th anniversary of Moscow Aviation Institute and the 100th anniversary of the birth of academician I.F. Obraztsov.The conference deals with the topical issues of the aerospace industry, including methods of applied mathematics and mechanics, as well as computer modeling. The conference focuses on solving the problems associated with modeling the flows of liquid, gas and plasma in combustion chambers, nozzles, jets and flow paths of power plants, as well as the interaction of gas and gas-dust flows with the aircraft surface. The participants of AMMAI’2020 will discuss the numerical methods, computational algorithms and software systems that allow solving problems of general mechanics, mechanics of continuous media and deformable solids, tribology in application to aviation, rocketry and astronautics. Information systems and technologies, in particular, high-performance computing technologies, will be also discussed at the conference.This year the conference was planned to be held on 24-31 May 2020, but due to COVID-19 it was put forward to September 2020. The conference will be organized partially by personal attendance of participants as well as virtually using Internet communication technologies (Zoom, Skype). The conference attendance will be organized in compliance with all sanitary standards and safety requirements. The majority of participants will take part in the Conference virtually. It is worth noting that the option of virtual participation allows expanding significantly the geography and increasing the number of participants. More than 320 participants from different regions of Russian Federation as well as from Asia and Europe will present their reports during the Conference sessions.The conference has already received 194 submissions that were reviewed. Finally, 85 papers were accepted for publication in IOP Conference Series: Materials Science and Engineering. The papers cover the conference topics; they present results of theoretical and experimental studies in such areas as hypersonic aerothermodynamics, combustion, detonation, multiphase flows and heat and mass transfer processes, nonequilibrium processes in nozzles and jets, plasma aerodynamics, rarefied gas flows, interaction of flows with the surface, solid mechanics, tribology. Among the accepted papers, there are some devoted to modern methods of numerical modeling, high performance computing, artificial intelligence algorithms, machine learning and big data processing.The Organizing Committee of AMMAI’2020 acknowledges the financial support from Russian Foundation for Basic Research and the technical support from Moscow Aviation Institute.We would like to thank reviewers for their time and effort in reviewing the papers, as well as authors, which took into account the reviewers recommendations and improved their papers to insure high quality of the AMMAI’2020 Proceedings.Chair of the AMMAI’2020 Technical Programs Committee: Dr. Natalia SeverinaEditor of AMAI’2020 Conference Proceedings: Anna Bogdan

Highly dilute gas flows over an ellipse

This paper presents recent investigation results on free molecular flows over a diffusely or specularly reflective ellipse, by using the gaskinetic theory. A virtual density distribution along the diffusely reflective surface is introduced to aid the investigations. Many local surface properties are obtained, including the surface slip velocity and coefficients for pressure, friction, and heat flux. Global coefficients for aerodynamic forces and moments and mass center–force center distances are also obtained by integrating the local surface distributions. In the end, analytical expressions for the flowfields around a diffusely or specularly reflective ellipse are also obtained. Special non-dimensional parameters, such as temperature and speed ratios, are explicitly embedded in these expressions. Particle simulations with the direct simulation Monte Carlo (DSMC) method are performed to validate the above results. Those expressions need computers for evaluations; however, the cost is very minor when compared with DSMC simulations. The approaches are heuristic to investigate other external collisionless flows, and the load coefficients can be considered as baseline references at the high Knudsen number limit. By using these collisionless flow results, it is feasible to further study less rarefied gas flows over an ellipse, for example, with an asymptotic method. Swift parameter studies based on these solutions can be performed to study their effect.

DSMC investigation of rarefied gas flow over a 2D forward-facing step: Effect of Knudsen number

A Forward-Facing Step (FFS) can be approximated as a simplified geometry for modeling the irregularities around space vehicles, the flow around which is often rarefied. These irregularities lead to flow separation, circulation, and re-attachment. This study aims to examine one of the fundamental surface irregularities that can have a significant effect on the design of space vehicles. In this article, Direct Simulation Monte Carlo (DSMC), an effective method for studying rarefied flows, is used to investigate the role of rarefaction on the non-reacting hypersonic rarefied gas flow over a forward-facing step. A comprehensive analysis of the effects of Knudsen number on the on flow-field properties, i.e., velocity, pressure, temperature, density, and surface properties, i.e., pressure coefficient, skin friction coefficient, and heat transfer coefficient is performed. The selected Knudsen number range from 0.05 to 21.33, covering the various rarefaction regimes. The Mach number of the free-stream flow employed was 25. The sections in the vicinity and downstream of the step are examined in-depth, describing the predominant nonequilibrium aspects. The normalized flow properties increased with Knudsen number and are primarily affected by the interplay of compressibility and viscous dissipation effects. Flow recirculation occurred in the slip and transition regime, whereas it was absent in the free-molecular regime; moreover, the recirculation lengths decreased with rarefaction. The surface properties were found to increase with Knudsen number with peak magnitudes located on the upstream and frontal face of the step.

Modified lattice Boltzmann solution for non-isothermal rarefied gas flow through microchannel utilizing BSR and second-order implicit schemes

Thermal microscale gas flow was simulated into a coplanar microchannel was simulated at a broad range of Knudsen numbers. Attempts were made to improve the accuracy of slip velocity on walls using a modified model with two relaxation times based upon the mesoscopic method. The temperature jump of fluid flow at the wall was captured by a model with a single relaxation time using a second-order implicit method. The Zou–He boundary conditions were employed at both inlet and outlet boundaries, and bounce-back/specular reflection distribution functions were applied to the impermeable walls. The non-equilibrium distribution functions were also used as the inlet temperature boundary condition. A fully developed temperature profile was considered at the microchannel outlet. A pressure ratio of 2 was considered in the simulations, and various parameters such as dimensionless pressure, pressure deviation from the linear pressure, dimensionless velocity at various Knudsen numbers, centerline velocity and slip velocity of the fluid, centerline temperature and fluid temperature on the wall, Nusselt number with changing Knudsen and Prandtl numbers, parameter k along the microchannel length and Cf·Re values were evaluated in the slip and transition flow regimes. The results of the direct simulation Monte Carlo were used to evaluate the correctness of the numerical model. The consistency of the two methods indicated the accuracy of the proposed method.

Rarefied flow separation in microchannel with bends

Abstract

Ray effect in rarefied flow simulation

Ray effect usually appears in the computation of radiative transfer when discrete ordinates method (DOM) is used. The cause and remedy for the ray effect have been intensively investigated in the radiation community. For rarefied gas flow, the ray effect is also associated with the discrete velocity method (DVM). However, few studies have been carried out in the rarefied community. In this paper, we make a detailed investigation of the ray effect in the rarefied flow simulation. Starting from a few commonly used benchmark tests, the root of the ray effect will be analyzed theoretically and validated numerically. The mitigation strategy by adjusting the discretization in the particle velocity space is studied as well. The guidelines are proposed to optimize the velocity space discretization for effectively reducing the ray effect. However, the design of optimal velocity space discretization is problem dependent and it can be hardly obtained in a highly rarefied flow simulation with complicated geometry. Due to the intrinsic self-adaptation of particle velocity, the stochastic particle method could automatically provide an optimized velocity discretization and avoid the ray effect. In the term of ray effect mitigation, the use of stochastic particle method is recommended in the numerical simulation of highly rarefied flow.

Rarefied gas flow past a flat plate at zero angle of attack

We consider subsonic, transonic, and moderate supersonic rarefied monatomic gas flows past a flat plate at zero angle of attack in the transitional regime. The influence of the rarefaction on the flow pattern is investigated mainly by the direct simulation Monte Carlo method. We study the shear stress, normal momentum flux transferred to the plate, and energy flux transferred to the plate at various Knudsen numbers, Mach numbers, and plate temperatures. We show that if the plate temperature is equal to the temperature of the undisturbed gas, then at any Mach number of the incoming flow, the average dimensionless normal momentum transferred to the plate has at least one extreme with respect to the Knudsen number. Specifically, in the supersonic and sonic cases, these dependences have a maximum. In the case of subsonic transonic Mach number M = 0.8, the dependence has a weak maximum and a weak minimum. At M = 0.5, it has weak minimum. We show that in a wide temperature range at subsonic and moderate supersonic Mach numbers in the transitional regime, the plate temperature very weakly affects the average friction force acting on the plate. We show that there exist certain intervals of plate temperatures ratios and Mach numbers such that the average dimensionless energy flux transferred to the plate changes the sign if the Knudsen number increases, previously reaching a local negative minimum.

Variance-reduction kinetic simulation of low-speed rarefied gas flow through long microchannels of annular cross sections

In micro/nano-devices, the low-speed transport of mass, momentum, and energy through long-ducts is frequently encountered, thereby necessitating scientific investigations. Here, long-ducts of various annular cross sections conducting low-speed gas flows under the influence of a small pressure gradient are considered, in order to understand how the mass flow rate is affected by rarefaction, variations in the radius ratio, and eccentricity of annular geometries. The Boltzmann model equation is treated by a low-variance formulation and simulated by a stochastic kinetic particle-based approach, which addresses the deviation of the molecular distribution function from equilibrium to reduce computational cost significantly. An efficient parallel solver has also been developed and utilized in this research, which is validated against the reported results in the literature. The efficient kinetic particle treatment provides a powerful simulation tool to reveal multi-scale flow physics, which is essential to develop and optimize micro/nano-fluidic devices.

A kinetic Fokker–Planck approach for modeling variable hard-sphere gas mixtures

Kinetic Fokker–Planck (FP) methods for modeling rarefied gas flows have received increasing attention over the last few years. However, formulating such models for realistic multi-species gases is still an open subject of research. Therefore, in this letter, we develop a kinetic FP model for describing gas mixtures with particles interacting according to the variable hard-sphere interaction potential. In accordance with the kinetic FP framework, a stochastic solution algorithm is employed in order to solve the model on a particle level. Different test cases are carried out, and the performance of the proposed method is compared with the direct simulation Monte Carlo algorithm.

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.

Comparison of the Shakhov and ellipsoidal models for the Boltzmann equation and DSMC for ab initio-based particle interactions

In this paper, we consider the capabilities of the Boltzmann equation with the Shakhov and ellipsoidal models for the collision term to capture the characteristics of rarefied gas flows. The benchmark is performed by comparing the results obtained using these kinetic model equations with direct simulation Monte Carlo (DSMC) results for particles interacting via ab initiopotentials. The analysis is restricted to channel flows between parallel plates and we consider three flow problems, namely: the heat transfer between stationary plates, the Couette flow and the heat transfer under shear. The simulations are performed in the non-linear regime for the 3He, 4He, and Ne gases. The reference temperature ranges between 1 K and 3000 K for 3He and 4He and between 20 K and 5000 K for Ne. While good agreement is seen up to the transition regime for the direct phenomena (shear stress, heat flux driven by temperature gradient), the relative errors in the cross phenomena (heat flux perpendicular to the temperature gradient) exceed 10% even in the slip-flow regime. The kinetic model equations are solved using the finite difference lattice Boltzmann algorithm based on half-range Gauss-Hermite quadratures with the third order upwind method used for the implementation of the advection.

Numerical study of conduction and radiation heat losses from vacuum annulus in parabolic trough receivers

Parabolic trough receiver is a key component to convert solar energy into thermal energy in the parabolic trough solar system. The heat loss of the receiver has an important influence on the thermal efficiency and the operating cost of the power station. In this paper, conduction and radiation heat losses are analyzed respectively to identify the heat loss mechanism of the receiver. A 2-D heat transfer model is established by using the direct simulation Monte Carlo method for rarefied gas flow and heat transfer within the annulus of the receiver to predict the conduction heat loss caused by residual gases. The numerical results conform to the experimental results, and show the temperature of the glass envelope and heat loss for various conditions in detail. The effects of annulus pressure, gas species, temperature of heat transfer fluid, and annulus size on the conduction and radiation heat losses are systematically analyzed. Besides, the main factors that cause heat loss are analyzed, providing a theoretical basis for guiding the improvement of receiver, as well as the operation and maintenance strategy to reduce heat loss.

One-dimensional simulation of Couette–Poiseuille flow with variable cross section for the full range of gas rarefaction

Clearance mass flows are a major loss mechanism in dry running rotatory positive displacement vacuum pumps. Therefore, a detailed knowledge of the clearance mass flow is crucial to calculate the operation of those pumps. The small clearance heights and the large pressure range of such pumps require a wide range of gas rarefaction parameters to be taken into account. The flow in the clearance can be described as a combined Couette–Poiseuille flow with variable cross section. This is typically done by solving the Stokes equation, but especially at high gas rarefaction parameters, the inertia cannot be neglected any more, which can lead to choking of the flow. A one-dimensional approach for the compressible fluid flow was provided by Shapiro. It is shown that this approach can be carried over for the rarefied gas flow. The problem is solved in bounds for the constant total temperature and compared to experimental investigations by varying the pressure ratio and the circumferential speed of the clearance boundary in a wide range of gas rarefaction parameters.

A collocation method for linear ellipsoidal model kinetic equation in a circular tube

A rarefied gas flow trough a long circular tube due to pressure is studied on the basis of the Holway linear ellipsoidal model kinetic equation. The diffuse reflection model is used as the boundary condition on the channel walls. The mass flow rate is calculated as a function of the small pressure gradient. Similar results presented in the literature are compared.

Reduced order modeling-based discrete unified gas kinetic scheme for rarefied gas flows

Boltzmann solvers face significant difficulty in simulating rarefied flows at high Knudsen numbers. In this flow regime, the gas distribution function is widely scattered and highly concentrated with a very steep slope in the particle velocity space. In order to capture the feature of such a flow, the Boltzmann solvers such as the Discrete Unified Gas Kinetic Scheme (DUGKS) discretize the particle velocity space with a very fine mesh (many discrete particle velocities) using the Discrete Velocity Method (DVM) due to which the load for computation becomes unendurable. In this paper, a Reduced Order Modeling (ROM) method is used to generate a reduced discrete velocity space for the DUGKS. More specifically, the discrete empirical interpolation method [S. Chaturantabut and D. C. Sorensen, SIAM J. Sci. Comput. 32, 2737–2764 (2010)] is used to select the dominant nodes in the original discrete velocity space to form a reduced discrete velocity space, which represents important dynamical characteristics. In this way, most grid points in the discrete velocity space, which are of negligible importance on the integration, are removed in practical computation, which yields a significant improvement in computational efficiency. The proposed ROM approach is not limited to a specific DVM-based solver. For illustration, in this paper, we developed the Reduced Order Modeling-based Discrete Unified Gas Kinetic Scheme (ROM-DUGKS) by applying the reduced velocity space to the conventional DUGKS. Validations are performed in both low-speed and hypersonic rarefied flows at various Knudsen numbers. The results show that the ROM-DUGKS is much more efficient than the original DUGKS while still maintaining high accuracy. This significant improvement in computational efficiency will unleash the potential of the DVM-based solvers such as the DUGKS for practical applications to rarefied flow problems.