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One of the important tasks of space flight safety is the ability of a wing to maintain stability in an oncoming turbulent flow. In this case, the spacecraft must move the greatest distance. The paper studies the motion of a thin plate near a boundary in an oncoming flow of rarefied gas. At low Reynolds numbers, the effect of the boundary on the plate is studied, and the possibility of self-propulsion is shown. • The drag force of the plate increases sharply as the distance to the boundary decreases. • The lifting force and moment change from the center of the plate to the boundary decreases. • The point of application of the resultant force shifts to the rear edge of the plate. • Self-motion is possible for plates that have a common rib. [ABSTRACT FROM AUTHOR]

On 13–15 January 2022, the Hunga Tonga–Hunga Ha'apai underwater volcano erupted. This powerful eruption generated infrasonic waves with amplitudes of thousands of Pascals in the near field. The ground infrasonic stations in China, located approximately 10 000 km from the Hunga volcano, also received waves with frequencies from 0.01 to 0.05 Hz. However, the amplitude reached 17 Pa, which is higher than the predicted amplitude using the absorption model without considering the dispersion effect in the thin thermosphere. At high altitudes, dispersion exists and the sound speed depends on the ratio of the molecular mean collision ratio to sound frequency, which is proportional to the ratio (frequency/pressure). And attenuation coefficients are complex to model. We simulate dispersive sound speeds and attenuation coefficients at different frequencies according to theory and our experimental data. In the thermosphere, the dispersion effect causes noticeable changes of sound speed and then affects wave propagation paths in the far field. The abnormal attenuation coefficient has a smaller impact on thermospheric returns than that of the dispersive sound speed, but it is also not negligible. It explains the large amplitude of thermospheric signals received in our infrasound stations. This article is part of the theme issue 'Celebrating the 15th anniversary of the Royal Society Newton International Fellowship'. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Ordnance Equipment Engineering is the property of Chongqing University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Application of two-dimensional lattice Boltzmann equations of various orders on standard lattices to the description of slow isothermal rarefied flows is considered. A two-dimensional Poiseuille flow at different Knudsen numbers is used as a test problem. This problem is solved numerically using several lattice Boltzmann equations of low and high orders that have from nine to 53 discrete velocities. The results are compared with the solutions to the linearized Boltzmann and Bhatnagar–Gross–Crook equations, which are used as test ones. Numerical experiments showed that increasing the order of the lattice Boltzmann equation (i.e., the number of first moments of the local Maxwell distribution reproduced by the discrete local equilibrium of the lattice Boltzmann equation) does not always lead to improved accuracy. In particular, a new low-order LB model with 16 velocities which reproduces diffuse reflection boundary conditions at a qualitative level is proposed. It is shown that for this model it is possible to obtain accurate values of the volumetric flow rate slip velocities for a wide range of Knudsen numbers in comparison with other models under consideration. [ABSTRACT FROM AUTHOR]

We present a brief survey of problem formulations related to high-speed beams with emphasis on analytical solutions. Additionally, numerical solutions for some problems of this class are described. Within the framework of kinetic theory, the analytical method is used to consider the interaction of groups of particles (molecules) assuming that the particles' velocities are highly correlated (delta function is used as a distribution density). The problems of beam interaction with and without loss of particles are studied numerically using direct statistical Monte Carlo simulation. For the problem with loss of particles (intersection and interaction of thin beams), good agreement with the analytical solution is obtained. For the problem without loss of particles (collision of flows), we obtain a numerical solution of the type of a traveling shock wave of limiting compression that is formed when the flow collides with a wall. The role of collision transforms at the initial stage of the process is shown. The problem of beam penetration into a stationary gas up to the stage of plume formation is considered, and a similarity of its initial stage with the problem of thin beams is noted. It is emphasized that analytical methods are fruitful as applied to primary analysis of problems and to the verification of numerical solutions. [ABSTRACT FROM AUTHOR]

Copyright of Journal of National University of Defense Technology / Guofang Keji Daxue Xuebao is the property of NUDT Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Numerical investigations of high-speed rarefied gas outflow into a vacuum through channels with a forward- or backward-facing step have been conducted using the direct simulation Monte Carlo method. Calculations have been performed for various free-stream Mach numbers, covering transonic, supersonic, and hypersonic flow regimes, and over a wide range of gas rarefaction from free molecular to near hydrodynamic conditions. Mass flow rates through the channel and the gas flow field have been accurately calculated both inside the channel and in the regions upstream and downstream. It has been established that channel geometry, the free-stream velocity, and gas rarefaction strongly influence the gas flow. In the flow field, in front of the channel, a phenomenon known as a detached shock occurs, while inside the channel, a gas recirculation zone may form. [ABSTRACT FROM AUTHOR]

Copyright of Journal of National University of Defense Technology / Guofang Keji Daxue Xuebao is the property of NUDT Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Abstract Highly rarefied gas flows through a rough channel of finite length with small bumps appended to its surfaces are investigated, by varying the accommodation coefficient $$\alpha$$ α in Maxwell’s diffuse-specular boundary condition, the characteristic size and position of the bumps, and the channel length. First, we study the influence of the surface bumps and consider the rarefied gas flow in a unit channel with periodic boundary conditions to remove the end effect. It is found that the surface bumps have a significant impact on the flow permeability. When $$\alpha$$ α is very small (i.e., nearly specular reflection of gas molecules at the channel surface), the apparent gas permeability is dramatically reduced, even in the presence of small bumps, to a value that is almost comparable to the one when fully diffuse gas-surface scattering is assumed. This impact can be taken into account through an effective accommodation coefficient, i.e., the permeability of the rough channel is taken equivalently as that of a smooth channel without bumps but having gas-surface scattering under the effective accommodation coefficient. Second, we study the end effect by connecting a smooth channel of length $$L_0$$ L 0 to two huge gas reservoirs. It is found that (i) the end correction length is large at small $$\alpha$$ α . Consequently, the mass flow rate barely reduces with increasing $$L_0$$ L 0 rather than scales down by a factor of $$1/L_0$$ 1 / L 0 as predicted by the classical Knudsen diffusion theory; and (ii) the end correction is related to the channel’s aspect ratio. Finally, based on the effective accommodation coefficient and end correction, we explain the exotic flow enhancement in graphene angstrom-scale channels observed by Geim’s research group (Keerthi et al, Nature 558:420–424, 2018).

Numerical simulations of an underexpanded supersonic jet exhausting from a circular nozzle are reported. The study is performed in a three-dimensional formulation using two different approaches: Navier–Stokes equations and Direct Simulation Monte Carlo method. In both cases, a reverse flow zone is formed behind the Mach disk in the first shock cell. Thus, this phenomenon, which was previously observed in axisymmetric simulations, cannot be attributed to inaccuracies of approximation of these equations near the axis of symmetry. [ABSTRACT FROM AUTHOR]

A nitrogen jet expanding during its exhaustion from a nozzle into a vacuum chamber is numerically simulated by a hybrid approach. The flow parameters in the nozzle and in the near field of the jet are determined by solving the Navier–Stokes equations by using the ANSYS Fluent software. The gas flow at large distances from the nozzle exit is modeled by the Direct Simulation Monte Carlo method by using the SMILE software system. Such an approach makes it possible to perform sufficiently accurate simulations in the near field of the jet; moreover, the temperature nonequilibrium of the expanding gas jet and other effects of rarefaction in the far field of the jet are taken into account. The approach is verified by using various approximate analytical models of gas exhaustion into vacuum. A comparison of the numerical results with available experimental data shows that they are in good agreement. [ABSTRACT FROM AUTHOR]

Flow around a body moving at a high subsonic velocity in a tube filled with rarefied gas is studied. This aerodynamic problem is considered as applied to the task of designing a high-speed vacuum transport at finite Knudsen numbers. Parameters that are close to target characteristics of such systems are chosen, more precisely, speed of about 1000 km/h, significant transverse size of the body, and nitrogen–oxygen mixture (air) as the filling gas are chosen. The problem was solved in a three-dimensional statement. [ABSTRACT FROM AUTHOR]

The S-model kinetic equation is used to study the rarefied gas flow from a high-pressure tank to a low-pressure one through a flat membrane with a finite number of pores. The kinetic equation is solved numerically using a second-order accurate implicit conservative method implemented in the in-house code Nesvetay. For transitional and continuum flow regimes, numerical solutions of the compressible Navier–Stokes equations are obtained. The gas flow rate through the system of pores and the forces acting on the membrane bars are investigated as functions of the Knudsen number (Kn) at a pressure ratio of 2 : 1 in the tanks. The features of the flow field near the membrane and away from it are described. [ABSTRACT FROM AUTHOR]

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

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

Highly rarefied gas flows through a rough channel of finite length with small bumps appended to its surfaces are investigated, by varying the accommodation coefficient α in Maxwell's diffuse-specular boundary condition, the characteristic size and position of the bumps, and the channel length. First, we study the influence of the surface bumps and consider the rarefied gas flow in a unit channel with periodic boundary conditions to remove the end effect. It is found that the surface bumps have a significant impact on the flow permeability. When α is very small (i.e., nearly specular reflection of gas molecules at the channel surface), the apparent gas permeability is dramatically reduced, even in the presence of small bumps, to a value that is almost comparable to the one when fully diffuse gas-surface scattering is assumed. This impact can be taken into account through an effective accommodation coefficient, i.e., the permeability of the rough channel is taken equivalently as that of a smooth channel without bumps but having gas-surface scattering under the effective accommodation coefficient. Second, we study the end effect by connecting a smooth channel of length L 0 to two huge gas reservoirs. It is found that (i) the end correction length is large at small α . Consequently, the mass flow rate barely reduces with increasing L 0 rather than scales down by a factor of 1 / L 0 as predicted by the classical Knudsen diffusion theory; and (ii) the end correction is related to the channel's aspect ratio. Finally, based on the effective accommodation coefficient and end correction, we explain the exotic flow enhancement in graphene angstrom-scale channels observed by Geim's research group (Keerthi et al, Nature 558:420–424, 2018). [ABSTRACT FROM AUTHOR]

Supersonic gas flow from an annular nozzle into a low-pressure chamber is studied numerically using kinetic and continuum approaches. Such flows find applications in gas-jet plasma-chemical technologies using an electron beam passing through an axial channel. The study is performed by using the direct simulation Monte Carlo method and by solving continuum equations using ANSYS Fluent software. It is shown that the solutions obtained are in good agreement with each other even in low-density regions of the electron beam channel. This leads to the conclusion that ANSYS Fluent software is suitable for simulating flows of this type. [ABSTRACT FROM AUTHOR]

Rarefied gas flow into a vacuum through short linearly diverging and converging channels has been examined with the direct simulation Monte Carlo method. Solution to the problem has been suggested using complete geometric setup with quite large areas on inlet and outlet of a model channel in examined geometry. A mass flow rate through the channel and flow field both inside the channel and upstream and downstream have been calculated in a wide range of gas rarefaction. These calculation results are comparable to corresponding data for the channel with constant cross section. A strong impact of channel geometry and gas rarefaction has been proved. [ABSTRACT FROM AUTHOR]

Copyright of Journal of National University of Defense Technology / Guofang Keji Daxue Xuebao is the property of NUDT Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, the influence of the tangential momentum accommodation coefficient α v (TMAC) on an assumed planar, compressible, and slightly rarefied nitrogen gas flow through a microchannel was numerically investigated. Given the small values of Knudsen numbers (0. 04 < K n < 0. 07) and the low Mach number ( M a < 0. 3), the 2 D governing equations were solved using the finite element method with first-order slip boundary conditions using the COMSOL Multiphysics software. The obtained results were presented and discussed. Those results are in good agreement compared to analytical solutions and to the DSMC results obtained by the literature, which confirms the validity of the present model. A comparison with experimental data provided from the literature for pressure distribution of airflow through a long microchannel was also presented and comparable results were found. It has been proved that COMSOL is faster in resolving such problems compared to DSMC method. It has been shown that decreasing the tangential momentum accommodation coefficient α v values increases the gas velocity and the velocity jump near walls, while the pressure gradient is reduced for the given α v values. It has been also shown that for tending to zero values of α v , vortices in the inlet chamber become more intense. [ABSTRACT FROM AUTHOR]

A highly underexpanded jet outflow into the background in transition and scattering regimes is studied computationally. The direct simulation Monte Carlo method and Navier–Stokes equations are used. The main parameters’ impact on the jet flow is analyzed. It is shown that a drastic flow structure transformation occurs in a relatively narrow Reynolds numbers’ range, 5 ≤ ReL ≤ 30, featuring the jet–surrounding gas interaction. At ReL = 5, a shock wave structure that is typical for the underexpanded jet degenerates completely. The existing empirical expressions application for the estimation of the characteristic dimensions of the shock wave structure in the transition regime leads to significant inaccuracy. For the considered parameters’ range, the approaches based on the direct simulation Monte Carlo method and Navier–Stokes (NS) equations’ solution lead to similar results in the nozzle region, where the flow regime is hydrodynamic. Nevertheless, the NS approach employment for the assessment of flow parameters within rarefied shock layers is debatable.

The work aims to find and substantiate a new approach to hot separation of liquid-propellant rocket stages. This separation method is the most energy-efficient when combined with the gas-jet braking and tilting the previous stage. It allows to simplify and reduce the weight of the separation system by tens of kilograms. The research showed a significantly lower effect of the engine combustion products jet on the reflective screen than according to the calculation methods of other authors. An increase in the ratio of fuel components completely excludes the possibility of an explosion. There are no theoretical prerequisites for the ignition and explosion of incompletely oxidized combustion products with the oxidizer vapor of the lower tank under high vacuum conditions. The authors showed that the Knudsen number is bigger than one, and the branched-chain combustion does not happen. Moreover, there are no conditions for fire in case of accidental burn-through of the separated stage upper tank. The practical significance of the work lies in a significant reduction in the weight of the protective screen and increasing the reliability of the hot stage separation system. The proposed method allows safely using in practice the most energy-efficient stage separation scheme. [ABSTRACT FROM AUTHOR]

Present paper uses Direct Simulation Monte Carlo method to perform a numerical assessment of applicability of turbomolecular-pump-like device to separation of gas mixtures. Device is represented by several rows of inclined moving (rotors) and stationary (stators) blades. Neon-Argon mixture flow is considered. Separation effect was obtained when rotors operate in counter-flow mode, i.e. pump gas against external pressure gradient. Parametric study of the influence of device operation parameters (rotors speed, blades inclination and length, number of stages in the device, rarefaction regime) was performed. It was shown that increase of these parameters leads to increase of separation factor and decrease of gas flowrate, and vice versa. Non-monotonic dependence on rotors speed with local maxima was observed. It was shown that separation effect is present even at low rotation speeds (around 10 m/s) and transitional rarefaction regime, which are not typical for classic turbomolecular pumps. [ABSTRACT FROM AUTHOR]

In this study, we theoretically explore the impact of tilt on the switching dynamics of a MEMS device operated by a pair of electrostatic actuators and subject to pronounced squeeze-film damping in the transition and free molecular flow regimes. Our investigation reveals that inducing tilt, achieved through the application of uneven voltages on the electrodes, introduces additional source terms in the modified Reynolds equation governing the pressure distribution in the squeeze-film gap. These added terms result in an accelerated decay of the squeeze film force, facilitating faster device switching between the initial and target configurations. To analyze the device dynamics, we develop a coupled numerical model and employ evolutionary multi-objective optimization to determine an optimal actuation scheme. This optimization is carried out for scenarios where initially different voltages are applied to the electrodes during a certain pre-defined time interval before transitioning to the steady voltage corresponding to the target gap size at equilibrium. Our findings highlight that the suggested actuation strategy leads to substantial improvements in the switching time of the device. Furthermore, we provide insights into the conditions favoring tilt actuation over parallel-motion actuation where the initially applied voltages are equal. [Display omitted] • Tilt, induced by uneven voltage actuation, accelerates squeeze film force decay and shortens MEMS device switching time. • Tilt effect on squeeze film force decay is expressed by additional source terms in the modified Reynolds equation. • A coupled numerical model was developed and used for evolutionary multi-objective optimization of the MEMS actuation scheme. • A criterion is established for tilt effectiveness in optimal actuation scenarios. [ABSTRACT FROM AUTHOR]

The Direct Simulation Monte Carlo (DSMC) method is used to study rarefaction effects on the structure of an axisymmetric underexpanded jet. A comparison with the data of other researchers shows that DSMC simulations accurately reproduce the features of the steady shock-wave structure of the jet. Rarefaction produces a noticeable effect on the jet flow. In particular, it makes the barrel shock in the first shock cell change the type of its reflection from the axis, which leads to vanishing of the developed Mach disk and to the changes in the structure of other shock cells. For the first time, the formation of a closed reverse flow region behind the Mach disk is observed in a molecular-kinetic simulation. This phenomenon has been earlier observed only in continuum simulations. [ABSTRACT FROM AUTHOR]

A computational investigation of the dynamics of gas expansion due to intense nanosecond laser evaporation into vacuum has been carried out. The problem is solved in a one-dimensional approximation, which simplifies calculations and at the same time allows one to analyze the main features of the expansion dynamics. For analysis we use three different approaches. Two of them are based on kinetic analysis via the direct simulation Monte Carlo (DSMC) method and numerical solution of the model Bhatnagar–Gross–Krook (BGK) equation. The third one focuses on derivation of an analytical continuum solution. Emphasis is placed on the analysis of the velocity distribution function and the average energy of particles passing through the time-of-flight detector on the normal to the evaporation surface, which is important for interpreting experimental measurements. The formulated problem is quite difficult as the considered flow is time-dependent, contains discontinuities in boundary conditions and involves large variations of local Knudsen numbers as well as steep gradients of the velocity distribution function. Data were obtained on the particle energy in the time-of-flight distribution for the range of regimes from the free molecular flow to continuum one. The maximum attainable average energy of particles in the time-of-flight distribution is determined. The non-monotonicity of the energy increase was found, which is explained based on analysis of the velocity distribution of particles. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we refer previously reported numerical data to design a new analytic equation for Poiseuille flow in a circular channel. Superposition of the continuum, slip, and free-molecular flow equations provides a versatile solution for the entire Knudsen range; however, it is not accurate in the transition regime. Adding correction factors and modifications to the existing flow-rate model enhances the precision and validity for wide flow ranges. Parameters of each equation are fitted for the collected data with Levenberg–Marquardt algorithm and compared in each regime; subsequently, the equation with the best accuracy and simplicity is selected. The newly suggested formula fits well for the referred data by correlating with the dimensionless flow rate, Knudsen number, and tangential momentum accommodation coefficient (TMAC). Furthermore, we calculate the TMAC using previous experimental data, which reflects the reflective interactions between the channel surfaces and gas molecules. Our newly suggested formula demonstrates effectively that the TMAC is significantly affected not only by the channel surface roughness but also by the molecular structure of gas.

Gas species in high altitude plume flow are all exposed to low temperature, thus making possible phase change processes on those other than H 2 O vapor. In order to obtain saturated threshold of gas species, which is normally abundant in plume flow, this study establishes Gibbs phase calculation method for CO 2 , CO, H 2 , and N 2. The non-continuum effect caused by rarefied gas environment is quantitatively calculated by ratio between molecular free path scale and characteristic length of investigated object. Validation on Gibbs method is guaranteed by comparison between calculated results and data from American National Standards Institute (ANSI), while non-continuum effect method is verified by revealing essential reason for gas-solid phase change processes resembling droplet condensation phenomenon observed in high altitude environment. According to the results, non-continuum effect only influences gas-solid boundary. Phase change for rarefied gas species can only occur under low temperature. Saturated threshold deflects toward solid phase region below specific molecules number density, thus decreasing gas to solid phase change trend. Both increasing on characteristic length and existence of other gas components contamination decreases non-continuum effect. Variation on non-continuum effect shows biggest influence on CO 2 saturated phase change threshold, while shows smallest influence on that of N 2. • A calculating model for CO 2 , CO, H 2 , N 2 is established. • The non-continuum effect saturated threshold is quantitatively calculated. • Gas species tend to exist in gas phase under influence of non-continuum effect. • Increase on characteristic length and other gas components contamination decreases influence of non-continuum effect. • Non-continuum effect shows biggest influence on phase change threshold of CO 2 , while smallest influence on that of N 2. [ABSTRACT FROM AUTHOR]

In this paper, a topology optimization method for rarefied gas flows is proposed. We use the discrete velocity method (DVM) to solve the Boltzmann equation, and construct an extension of the standard DVM algorithm in order to model gas flow in a domain of mixed materials. The proposed extension consists of a correction in convection fluxes as well as an extra source term which mimics reflection boundary conditions, so that the presence of fluid or solid can be characterized by a pseudo density. To evaluate the change in objective functional due to the design variable, an adjoint problem is derived from the steady state condition of the extended DVM, which forms a linear system of equations that can be solved using iterative methods like in standard DVM. Using the design sensitivity obtained from the adjoint system, optimization of flow structures can be achieved. Validity of the proposed method is demonstrated through several numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we propose that thermally induced Knudsen forces in a rarefied gas can be exploited to achieve a tweezer-like mechanism that can be used to trap and grasp a micro-object without physical contact. Using the direct simulation Monte Carlo (DSMC) method, we showed that the proposed mechanism is achieved when a heated thin plate, mounted perpendicularly on a flat substrate, is placed close to a colder object; in this case, a beam. This mechanism is mainly due to the pressure differences induced by the thermal edge flows at the corners of the beam and the thermal edge flow at the tip of the thin plate. Specifically, the pressure on the top surface of the beam is smaller than that on its bottom surface when the thin plate is above the beam, while the pressure on the right side of the beam is smaller than that on its left side when the thin plate is located near the right side of the beam. These differences in pressure generate a force, which attracts the beam to the plate horizontally and vertically. Furthermore, this phenomenon is enhanced when the height of the beam is shorter, such that the horizontal and vertical net forces, which attract the beam to the plate, become stronger. The mechanism proposed here was also found to depend significantly on the height of the beam, the temperature difference between the thin plate and the beam, and the Knudsen number. [ABSTRACT FROM AUTHOR]

In micro/nano-scale systems where the characteristic length is in the order of or less than the mean free path for gas molecules, an object placed close to a heated substrate with a surface microstructure receives a propulsive force. In addition to the induced forces on the boundaries, thermally driven flows can also be induced in such conditions. As the force exerted on the object is caused by momentum brought by gas molecules impinging on and reflected at the surface of the object, reproducing molecular gas flows around the object is required to investigate the force on it. Using the direct simulation Monte Carlo (DSMC) method to resolve the flow, we found that by modifying the conventional ratchet-shaped microstructure into different configurations, a stronger propulsive force can be achieved. Specifically, the tip angle of the microstructure is an important parameter in optimizing the induced force. The increase in the propulsive force induced by the different microstructures was also found to depend on the Knudsen number, i.e., the ratio of the mean free path to the characteristic length and the temperature difference between the heated microstructure and the colder object. Furthermore, we explained how this force is formed and why this force is enhanced by the decreasing tip angle, considering the momentum brought onto the bottom surface of the object by incident molecules. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The rarefied gas flow in the microscopic thermal transpiration pump fabricated by micro/nano-electro-mechanical systems is investigated. The numerical analysis is carried out by the direct simulation Monte Carlo (DSMC) method of the Boltzmann equation since the thermal transpiration phenomena are unique to the rarefied gas. The values of mass flow rate and pressure difference induced by the device are obtained by the DSMC method. The simulation adopts the three-dimensional numerical model that strictly follows the shape of the microchannel of the fabricated device. The numerical results can reproduce the experimental data by selecting the appropriate values of the Knudsen number and the accommodation coefficient on the surface. The simulation also clarifies the details of the three-dimensional flow structures for a wide range of Knudsen numbers. [ABSTRACT FROM AUTHOR]

The work is devoted to study 2D pressure driven rarefied gas flow in a microchannel having an elastic obstacle. The elastic obstacle is clamped at the bottom channel wall and its length is half of the channel height. The gas flow is simulated by Direct Simulation Monte Carlo (DSMC) method applying the advanced Simplified Bernoulli Trial (SBT) collision scheme. The elastic obstacle is modelled as geometrically nonlinear Euler Bernoulli beam. A reduced 3 modes reduction model of the beam is created. The influence of the gas flow on the beam vibration is studied, considering the linear and nonlinear beam theories.

Abstract We investigate the gas flows near to solid surfaces in terms of the local spatial variation in the molecular mean free path (MFP). Molecular dynamics (MD) is the appropriate scientific tool for obtaining molecularly-accurate dynamic information in micro and nano-scale gas flows, and has been used to evaluate the molecular mean free path of gases. In the calibration procedure, the viscosity of a gas in the homogeneous case can be recovered in our MD simulations and reach good agreement with the theoretical prediction and data from NIST. In surface-bounded gas flows, if the collisions between gas molecules and walls are counted, a spatially-varying mean free path is presented, and for the first time we have observed that the distribution of the free paths deviates from the exponential one and spikes appear in their distributions at larger Kn, i.e. in the transition flow regime. Based on elementary kinetic theory, the effective viscosity of the gas derived from the mean free path has been incorporated into the framework of the continuum-fluid dynamics equations, and micro-Couette flows are performed to demonstrate this potential application.

In this paper we present simulations of moving rigid bodies immersed in a rarefied gas. The rarefied gas is simulated by solving the Bhatnager-Gross-Krook (BGK) model for the Boltzmann equation. The Newton-Euler equations are solved to simulate the rigid body motion. The force and the torque on the rigid body is computed from the surrounded gas. An explicit Euler scheme is used for the time integration of the Newton-Euler equations. The BGK model is solved by the semi-Lagrangian method suggested by Russo & Filbet [22]. Due to the motion of the rigid body, the computational domain for the rarefied gas (and the interface between the rigid body and the gas domain) changes with respect to time. To allow a simpler handling of the interface motion we have used a meshfree method for the interpolation procedure in the semi-Lagrangian scheme. We have considered a one way, as well as a two-way coupling of rigid body and gas flow. We use diffuse reflection boundary conditions on the rigid body and also on the boundary of the computational domain. In one space dimension the numerical results are compared with analytical as well as with Direct Simulation Monte Carlo (DSMC) solutions of the Boltzmann equation. In the two-dimensional case results are compared with DSMC simulations for the Boltzmann equation and with results obtained by other researchers. Several test problems and applications illustrate the versatility of the approach.

The impetus of the this study is to investigate flow and thermal field in rarefied gas flows inside a trapezoidal micro/nano-cavity using the direct simulation Monte Carlo (DSMC) technique. The investigation covers the hydrodynamic properties and thermal behavior of the flow. The selected Knudsen numbers for this study are arranged in the slip and transition regimes. The results show the center of the vortex location moves by variation in the Knudsen numbers. Also, as the Knudsen number increases, the non-dimensional shear stress increases, but the distribution deviates from a symmetrical profile. The cold to hot transfer, which is in contrast with the conventional Fourier law, is observed. We show that the heat transfer is affected by the second derivative of the velocity. By increasing the Knudsen number, the transferred heat through the walls decreases, but the contraction/expansion effects on the temperature in the corner of the cavity become higher. [ABSTRACT FROM AUTHOR]

A computational investigation of the dynamics of gas expansion due to intense nanosecond laser evaporation into vacuum has been carried out. The problem is solved in a one-dimensional approximation, which simplifies calculations and at the same time allows one to analyze the main features of the expansion dynamics. For analysis we use three different approaches. Two of them are based on kinetic analysis via the direct simulation Monte Carlo (DSMC) method and numerical solution of the model Bhatnagar–Gross–Krook (BGK) equation. The third one focuses on derivation of an analytical continuum solution. Emphasis is placed on the analysis of the velocity distribution function and the average energy of particles passing through the time-of-flight detector on the normal to the evaporation surface, which is important for interpreting experimental measurements. The formulated problem is quite difficult as the considered flow is time-dependent, contains discontinuities in boundary conditions and involves large variations of local Knudsen numbers as well as steep gradients of the velocity distribution function. Data were obtained on the particle energy in the time-of-flight distribution for the range of regimes from the free molecular flow to continuum one. The maximum attainable average energy of particles in the time-of-flight distribution is determined. The non-monotonicity of the energy increase was found, which is explained based on analysis of the velocity distribution of particles.

We study a liquid droplet moving inside a rarefied gas. In other words, we consider a two-phase flow with liquid and rarefied gas phases and an interface between the two phases which deforms with respect to time and space. The gas phase is modelled by the Bhatanager–Gross–Krook (BGK) model of the Boltzmann equation. The liquid phase is modelled by the incompressible Navier–Stokes equations. Interface boundary conditions for the liquid and gas phases are presented. The BGK model is solved by a semi-Lagrangian scheme with a meshfree reconstruction procedure. A similar meshfree particle method is used to solve the incompressible Navier–Stokes equations for the liquid phase. In 1D the solutions of the BGK-Navier-Stokes equations and the Boltzmann-Navier-Stokes equations are compared, where the Boltzmann equation is solved by a direct simulation Monte Carlo method. Results in 1 D and 2 D physical spaces are presented. [ABSTRACT FROM AUTHOR]

The study of nonstationary rarefied gas flows is currently paid much attention. Such interest to these problems is caused by the creation of pulsed jets used for the deposition of thin films and special coatings on solid surfaces. However the problems of nonstationary rarefied gas flows have not been studied sufficiently fully because of their large computational complexity. In this paper the computational aspects of investigating the nonstationary flows of a reflected gas from a wall and flowing through a suddenly formed gap is considering. The objective of this study is to analyze the possible numerical kinetic approaches for solving such nonstationary problems and to identify the difficulties encountered in solving.When studying the gas flows in strong rarefaction regimes one should consider the Boltzmann kinetic equation, but its numerical implementation is rather laborious. In order to use more simple approaches based for example on approximation kinetic equations (Ellipsoidal-Statistical model, Shakhov model), it is important to estimate the difference of the solutions of the model equations and the Boltzmann equation. For this purpose two auxiliary problems are considered: reflection of the gas flow from the wall and outflow of the free jet into the rarefied background gas. Numerical solution of these problems shows a weak dependence of the solution on the type of the collision operator in the rarefied region, but a strong dependence on the velocity grid step . The detailed velocity grid is necessary to avoid non-monotonous behavior of macroparameters caused by the “ray effect”. To reduce numerical costs on detailed grid a hybrid method based on the synthesis of model equation and the Boltzmann equation is proposed. Such approach can be promising since it reduces the domain in which the Boltzmann collision integral should be used.The results presented in this paper were obtained using two different software packages Unified Flow Solver (UFS) [13] and Nesvetay 3D [14-15]. Note that UFS uses the discrete ordinate method for velocity space on a uniform grid and a hierarchical adaptive mesh refinement in physical space. The possibility of calculating both the Boltzmann equation and model equations is realized. The Nesvetay 3D complex was created to solve the Shakhov model equation, (S-model) and makes it possible to calculate on non-structured non uniform grids in velocity and physical spaces.Translated from Russian. Original text: Mathematics and Mathematical Modeling. 2018. no. 4. Pp. 27-44.

This paper is devoted to the application of the method of numerical solution of the Boltzmann equation for the solution of the problem of modeling the behavior of radionuclides in the cavity of the interelectric gap of a multielement electrogenerating channel. The analysis of gas-kinetic processes of thermionic converters is important for proving the design of the power-generating channel. The paper reviews two constructive schemes of the channel: with one- and two-way withdrawal of gaseous fission products into a vacuum-cesium system. The analysis uses a two-dimensional transport equation of the second-order accuracy for the solution of the left-hand side and the projection method for solving the right-hand side - the collision integral. In the course of the work, a software package was implemented that makes it possible to calculate on the cluster architecture by using the algorithm of parallelizing the left-hand side of the equation; the paper contains the results of the analysis of the dependence of the calculation efficiency on the number of parallel nodes. The paper contains calculations of data on the distribution of pressures of gaseous fission products in the gap cavity, calculations use various sets of initial pressures and flows; the dependency of the radionuclide pressure in the collector region was determined as a function of cesium pressures at the ends of the gap. The tests in the loop channel of a nuclear reactor confirm the obtained results.

A method is proposed to solve the linearized ellipsoidal-statistical Holway equation in the classical problem of a rarefied gas flow between two parallel planes. To approximate the desired solution, the function is expanded in a series in Chebyshev polynomials of the first kind for each variable. The Holway model kinetic equation is reduced by the collocation method to a linear matrix equation. The values of the mass and heat flows of gas are calculated. [ABSTRACT FROM AUTHOR]