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Resonant gas oscillation in a closed tube bounded by an oscillating plate and a vaporliquid interface is theoretically analyzed by applying the asymptotic theory to the ES-BGK Boltzmann equation for the case of M2≃Kn≪1 and a small evaporation coefficient α = O(Kn), where M and Kn are the typical Mach number and the Knudsen number, respectively. As a result, we derive a nonlinear integro-differential equation for determining the wave profile with the evaporation and condensation in the form including α.

The hypersonic rarefied gas flow over blunt bodies in the transitional flow regime, typical of the reentry flight of space vehicles at altitudes higher 90-100 km, is investigated. As an example, the problem of hypersonic flows over long blunt wings and axisymmetric bodies is considered. It is analyzed in a wide range of the free stream Knudsen number by using various approaches: the continuum approach - numerical and analytical solutions, the direct simulation Monte Carlo method and the direct numerical solution of the Boltzmann kinetic equation with the S-model collision integral. The efficiency, domain of applicability, advantages and disadvantages of various approaches in the transitional flow regime are considered.

New kinetic effects and new types of Knudsen boundary layers in a gas flows near permeable membranes with uniform temperature and with temperature difference between the surfaces were studied. Two flows were considered. The first one is a pressure driven gas flow through the membrane, and the second one is a pressure difference driven flow through the membrane, due to the temperature difference across it (thermomolecular pressure difference at zero flow through the membrane). The results of theoretical research of gas flow through the membranes with extremely thin perforated channels (pores) are considered. It is assumed that the gas flow regime inside the pores is a free-molecular one and is a transition one outside the membrane. Mathematical tool are DSMC and other Monte-Carlo methods that describe the molecular motion outside the membrane and inside the membrane pores. The quantitative relationship between the flow parameters and the membrane properties is established. A new test for numerical methods ...

Results of Couette flow investigation are given for the free-molecule flow regime as well as or the transitional one. The numerical solution of Boltzmann equation by the direct Monte Carlo simulation method is used in our paper for investigating the Couette flow in a wide range of values of plate temperatures ratio, Knudsen number and the upper plate velocity. The dependences of the energy flux transferred towards the lower plate, of the shear stress, and of the flux of normal momentum on the Knudsen number are considered. It is found that for any Mach number there exists the interval of plate temperatures ratios such that the energy flux towards the plate changes the sign if the Knudsen number increases, previously reaching a local extremum. It is demonstrated as well that the effect of nonmonotonicity at high Mach number is observed not only for the shear stress and the energy flux but for the normal momentum flux as well. We also found the cases where the energy flux varies monotonically or even has a deep negative minimum, but the shear stress has a maximum.

In this paper we present the results of numerical simulations, based on a Monte Carlo procedure (DSMC), aimed at the analysis of the flow of a binary gas mixture issuing from a circular jet and impinging on a flat plate perpendicular to the jet axis.

28TH INTERNATIONAL SYMPOSIUM ON RAREFIED GAS DYNAMICS 2012(July 9-13, 2012.), Zaragoza, Spain, 資料番号: ARDS12018000

The direct simulation Monte Carlo (DSMC) method is a powerful particle-based method for modeling gas flows. It works well for relatively large Knudsen (Kn) numbers, typically larger than 0.01, but quickly becomes computationally intensive as Kn decreases due to its time step and cell size limitations. An alternative approach was proposed to relax or remove these limitations, based on replacing pairwise collisions with a stochastic model corresponding to the Fokker-Planck equation [J. Comput. Phys., 229, 1077 (2010); J. Fluid Mech., 680, 574 (2011)]. Similar to the DSMC method, the downside of that approach suffers from computationally statistical noise. To solve the problem, a diffusion-based information preservation (D-IP) method has been developed. The main idea is to track the motion of a simulated molecule from the diffusive standpoint, and obtain the flow velocity and temperature through sampling and averaging the IP quantities. To validate the idea and the corresponding model, several benchmark problems with Kn similar to 10(-3)-10(-4) have been investigated. It is shown that the IP calculations are not only accurate, but also efficient because they make possible using a time step and cell size over an order of magnitude larger than the mean collision time and mean free path, respectively.

Hypersonic vehicles travel across the atmosphere at very high speed, and the surrounding gas experiences complicated physical and chemical processes. These processes produce real gas effects at high temperature and rarefied gas effects at high altitude where the two effects are coupled through molecular collisions. In this study, we aim to identify the individual real gas and rarefied gas effects by simulating hypersonic flow over a 2D cylinder, a sphere and a blunted cone using a continuum-based CFD approach and the direct simulation Monte Carlo method. It is found that physical processes such as vibrational excitation and chemical reaction will reduce significantly the shock stand-off distance and flow temperature for flows having small Knudsen number. The calculated skin friction and surface heat flux will decrease when the real gas effects are considered in simulations. The trend, however, gets weakened as the Knudsen number increases. It is concluded that the rarefied gas effects weaken the real gas effects on hypersonic flows.

The present paper is devoted to simulating the compressible turbulent flows at the new level. The principal importance of the kinetic approach for description of turbulence is discussed. An explicit-implicit numerical scheme in the framework of the direct approach for the Boltzmann kinetic equation is examined. Numerical investigation of supersonic jets and the supersonic turbulent separated flow in the vicinity of backward/forward-facing step with leeward-face angle equals to 8°, 25°, 45° and 90° and Ma ≈ 3 for a model 2D case is made. At lower Knudsen number values (starting from 0.001) instabilities in the jet flow is observed. The comparison with available experimental and numerical results is performed in terms of the pressure and skin friction distributions over the body surface and the distribution of heat-transfer coefficient. A good agreement with the experimental heat-transfer coefficient is observed.

Functional structure of relations between the Poiseuille gas flow rate through the capillaries and rarefaction parameter (Knudsen number), the gas/surface interaction parameter (accommodation coefficient) and cross-sectional shape of the capillaries is established. For this purpose, the numerical solutions of the relaxation kinetic equation and the Boltzmann equation with specular-diffuse boundary condition for the interaction of gas molecules with the inner surface of the capillary are used. Asymptotic expansion of the gas flow rate depending on the Knudsen number at small value of it is used also.

DSMC algorithm for calculation of cluster formation and growth based on classical nucleation theory (CNT) and size-corrected CNT (SCCNT) was developed. Using the proposed algorithm 1D copper vapour flow simulations in the transient Knudsen number regime were carried out. The sufficient difference in the clusterization degree was observed when comparing the results of CNT and SCCNT simulations. Impact of the internal energy release on monomer and cluster parameters within nucleation was analyzed.

A model for flows around moving vanes in a Crookes radiometer is proposed. More precisely, a series of uniformly spaced parallel flat plates heated on their single sides, moving in a channel at a constant speed, is considered in the case where the direction of motion is perpendicular to the plates. The flow around the plates is investigated numerically on the basis of the ellipsoidal statistical (ES) model of the Boltzmann equation and the diffuse reflection boundary condition by means of an accurate finite-difference method. Special attention is paid to the discontinuity contained in the velocity distribution function. The pressure distribution around the edge is found to be different from that reported previously [S. Taguchi and K. Aoki, J. Fluid Mech. 694, 191-224 (2012)], in which the plate is assumed to have a stationary position in a closed container. The force exerted on the plates is obtained as a function of the plate velocity. The terminal velocity of the plates is also determined for several Knudsen numbers.

Rapidly emerging micro-electro-mechanical devices create new potential microfluidic applications. A simulation of an internal and external gas flows is important for their design. For small Knudsen number Kn < 0.1 (Kn = l0/L, where l0 is the mean free path of the gas molecules and L is the characteristic length), a continuum approach based on modified Navier-Stokes-Fourier or extended hydrodynamic continuum models with corresponding velocity-slip and temperature-jump boundary conditions is still applicable and, respectively, preferable. We restrict ourself to the use of Navier-Stokes-Fourier continuum model. A development of the algorithm to solve a specific class of problems is closely related to numerical schemes used for approximation of equations terms. Higher-order approximation schemes can reduce the number of mesh nodes and respectively computational time, but it is possible to obtain physical unrealistic results. In this paper we study influence of some approximation schemes for convective terms o...

The assumptions are discussed under which the equations of the generalized non-equilibrium thermodynamics obtained by the moment and the Chapman-Enskog methods agree. The Chapman-Enskog method is known to be based on the perturbation theory with the Knudsen number as a small parameter. The parameter is introduced in the kinetic equation and the distribution function is expanded into a series in the small Knudsen number. We apply this procedure not to the distribution function, but to the expansion coefficients of the moment series. It can be shown that under special convolution of the resulting system of equations, one can pass from the moment equations to the Chapman-Enskog equations both in hydrodynamic and Burnett approximations. Here is exactly the same transition in the equations of generalized non-equilibrium thermodynamics. The structure of the heat and momentum fluxes, and non-physical fluxes entered into the Chapman-Enskog method is reproduced from the moment equations.

A systematic study on the goodness of Maxwell model in the modeling of micro/nano gas flows in the entire Knudsen range is presented. We evaluate the model by examining key macroscopic properties such as temperature, density and pressure, in a couple classical benchmark problems namely thermal Couette and thermal transpiration problems. Our reference solutions are obtained from a hybrid DSMC/MD algorithm developed in house. We have found that while the extended Maxwell model, that is, the Maxwell model with three accommodation coefficients, is in general more accurate than the classical Maxwell model, the differences in the magnitudes of the predicted macroscopic quantities are quite small except the pressure profile of the thermal Couette problem, in which case the classical Maxwell model predicts a pressure trend that is opposite to that predicted by both the extended Maxwell model and the hybrid MD/DSMC simulations. This fact is also demonstrated in our study of the thermal transpiration coefficient, γ. The value predicted by the extended Maxwell model depends highly on the tangential accommodation coefficient which is consistent with the experimental findings, while the classical Maxwell model, as is well known, predicts a coefficient that is independent of the accommodation coefficient. We have also found that there is a correlation between the reflected velocity components. Neither the extended Maxwell model nor the CL model is able to capture this correlation.

Hypersonic flow over a flat plate is investigated under a wide range of Mach and Knudsen numbers using both continuum-based approach and DSMC method. The simulated gas is argon thus to isolate the high temperature effects. The Mach number of the flow lies between 5 and 30 whereas the Knudsen number covers the entire flow regime. It is learned that local rarefaction is observed near the leading edge even when the Knudsen number is around 0.001. The continuum breakdown can be identified using a nonequilibrium parameter that evaluates the difference among the temperature components. It is also learned that there is competition between viscous effects and rarefied effects on the skin friction. The total drag on the plate can be well estimated using a bridging formula that connects the results from the continuum and free molecular expressions. In addition, the value of drag depends on the surface temperature. The drag coefficient increases with the surface temperature when the Knudsen number is less than 0.01 but decreases when the Knudsen number is larger than 1.0.

To understand the molecular behaviour of gases in high speed rarefied conditions, we perform molecular dynamics (MD) numerical experiments using the open source code Open FOAM. We use shear-driven Couette flows as test cases, where the two parallel plates are moving with a speed of Uw in opposite directions with their temperatures set to Tw. The gas rarefaction conditions vary from slip to transition, and compressibility conditions vary from low speed isothermal to hypersonic flow regimes, i.e. Knudsen number (Kn) from 0.01 to 1 and Mach number (Ma) from 0.05 to 10. We measure the molecular velocity distribution functions, the spatial variation of gas mean free path profiles and other macroscopic properties. Our MD results convey that flow properties in the near-wall non-equilibrium region do not merely depend on Kn, but they are also significantly affected by Ma. These results may yield new insight into diffusive transport in rarefied gases at high speeds.

Lattice group models (LGpM) are kinetic models on integer lattices derived from the automorphism group of the lattice. In the last decades it was too expensive to simulate large systems (100 - 1000 velocities in a 2D or 3D model), with complex physical two or three dimensional domains, on normal computers or clusters within an acceptable amount of time. That changed due to the fast growth of the computing power of modern processing units. We briefly introduce lattice group models and then describe the main parallelization and optimization strategies for an efficient implementation on NVIDIA® graphics cards and INTEL® processors. Afterwards we present the achieved speedups and discuss some results from numerical simulations of physical phenomena (shock waves, Knudsen pump, Karman vortex street) in two and three dimensions at high, transitional and low Knudsen numbers.

The interaction of a diffusing outgas flow from a sphere nose opposing a hypersonic free stream is studied numerically using the direct simulation Monte-Carlo technique under the transitional rarefied-gas-flow regime conditions at Knudsen numbers from 0.016 to 1.5 and blowing factors from 0.15 to 1.5. Strong influences of the blowing factor (the ratio of outgas mass flux to upstream mass flux) and the Knudsen number on the flow structure about a sphere (temperature fields and the configuration of mixing flow zones) and on heat distributions along the spherical surface have been found. At large blowing factors, the injected gas significantly reduces heat flux in wide area near the spherical nose. This effect is more pronounced for light gas (helium) injection in the near-continuum flow.

Resonant gas oscillation in a closed tube bounded by an oscillating plate and a vapor-liquid interface is theoretically analyzed by applying the asymptotic theory to the ES-BGK Boltzmann equation for the case of MP ∼ Kn ≪ 1 and a small evaporation coefficient α = O(Kn), where MP and Kn are the Mach number of the plate and the Knudsen number, respectively. As a result, we derive a nonlinear integro-differential equation for determining the wave profile with the evaporation and condensation including α. We numerically solve the integro-differential equation with the method of Fourier series, and obtain a parameter plane for shock formation conditions and also the prediction of critical condition for shock formation.

Recently, the DSBGK method (Note: the original name DS-BGK is changed to DSBGK for simplicity) was proposed to reduce the stochastic noise in simulating rarefied gas flows at low velocity. Its total computational time is almost independent of the magnitude of deviation from equilibrium state. It was verified by the DSMC method in different benchmark problems over a wide range of Kn number. Some simulation results of the closed lid-driven cavity flow, thermal transpiration flow and the open channel flow by the DSBGK method are given here to show its efficiency and numerical stability. In closed problems, the density distribution is subject to unphysical fluctuation due to the absence of density constraint at the boundary. Thus, many simulated molecules are employed by DSBGK simulations to improve the stability and reduce the magnitude of fluctuation. This increases the memory usage remarkably but has small influence to the efficiency of DSBGK simulations. In open problems, the DSBGK simulation remains stable when using about 10 simulated molecules per cell because the fixed number densities at open boundaries eliminate the unphysical fluctuation. Small modification to the CLL reflection model is introduced to further improve the efficiency slightly.

Micro/nano geometries with specified wall heat flux are widely encountered in electronic cooling and micro-/nano-fluidic sensors. We introduce a new technique to impose the desired (positive/negative) wall heat flux boundary condition in the DSMC simulations. This technique is based on an iterative progress on the wall temperature magnitude. It is found that the proposed iterative technique has a good numerical performance and could implement both positive and negative values of wall heat flux rates accurately. Using present technique, rarefied gas flow through micro-/nanochannels under specified wall heat flux conditions is simulated and unique behaviors are observed in case of channels with cooling walls. For example, contrary to the heating process, it is observed that cooling of micro/nanochannel walls would result in small variations in the density field. Upstream thermal creep effects in the cooling process decrease the velocity slip despite of the Knudsen number increase along the channel. Similarl...

A hypersonic flow about a cylindrically blunted thick plate at a zero angle of attack is numerically studied with the kinetic (DSMC) and continuum (Navier‐Stokes equations) approaches. The Navier‐Stokes equations with velocity slip and temperature jump boundary conditions correctly predict the flow fields and surface parameters for values of the Knudsen number (based on the radius of leading edge curvature) smaller than 0.1. The results of computations demonstrate significant effects of the entropy layer on the boundary layer characteristics.

Performance of the Knudsen pump is studied numerically to find out effective configurations not only for the finally achieved separation and compression rates, but also for its time efficiency. A system of convection–diffusion equations with transmission conditions, which have been derived from the Boltzmann equation under the narrow channel approximation, is used for simulations of various configurations. A comparison with the experiment of evacuation from a tank is also made to demonstrate the practical ability of that system.

The moment method of Grad is used to derive macroscopic conservation equations for multicomponent plasmas for small and moderate Knudsen numbers, accounting for the electromagnetic field influence and thermal nonequilibrium. In the low Knudsen number limit, the equations derived are fully consistent with those obtained by means of the Chapman‐Enskog method. In particular, we have retieved the Kolesnikov effect coupling electrons and heavy particles in the case of the Boltzmann moment systems. Finally, a regularization procedure is proposed to achieve continuous shock structures at all Mach numbers.

The two-dimensional Kolmogorov flow generated by an imposed unidirectional forcing varying sinusoidally in space is simulated by using direct simulation Monte Carlo method. Our simulation is performed under the condition of Knudsen number Kn=0.005 and forcing wave number k(f) = 4. When the Reynolds number Re exceeds the critical value Re(c) = root 2, the basic shear flow becomes instable and changes to cellular structures. As Re increases, two main regimes of the flow have been observed: small scale structure (Re(c) 7Re(c)). When large scale structure is formed, the energy is inversely transferred from small scale forcing to large scale structure. As Re continues to increase, the evolution of flow field successively becomes quasi-periodical and irregular. This behavior provides a reasonable transition to turbulence with further increase of Re.

The flow of a rarefied gas through tubes of circular cross‐section and finite length, driven by arbitrarily large gradients of pressure is simulated in a computationally efficient manner based on kinetic model equations. The governing Ellipsoidal model kinetic equation is discretized in the phase space by a finite difference scheme and the discrete velocity method. It is seen that good agreement is obtained with corresponding DSMC results in the literature. Due to the five‐dimensional nature of the problem, various techniques have been used to reduce the computational effort. Convergence has been accelerated for small Knudsen flows using the Wynn‐epsilon algorithm while memory usage optimization, grid refinement and parallelization have been introduced. Overall, a highly efficient deterministic algorithm has been developed.

A gas separator that makes use of the thermal transpiration in a rarefied gas is proposed, and its gas separation performance is investigated numerically. The separator consists of two kinds of flow channels with different length scales. An array of micro‐channels is used to induce the gas separation effect by the thermal transpiration at intermediate Knudsen number, and two larger channels are used to accumulate the extracted molecules by the gas flows with larger flow velocities. Numerical example shows that the molar fractions of a gas in the two larger channels differ by several percent when the Mach numbers are approximately 0.2 there. The possibility of larger concentration difference is also discussed.

We show how to accelerate the numerical solution of the Boltzmann equation for a binary gas mixture by using Graphics Processing Units (GPUs). In order to fully exploit the computational power of the GPU, we adopt a semi‐regular method of solution which combines a finite difference discretization of the free‐streaming term with a Monte Carlo evaluation of the collision integral. The efficiency of the code is demonstrated by studying the propagation of plane harmonic waves of small amplitude in a binary gas mixture of hard spheres for a wide range of Knudsen numbers and wave frequencies. The GPU‐based code is about two order of magnitudes faster than the CPU version thus proving that GPUs can substantially speedup the numerical solution of kinetic equations.

Adaptive Cartesian mesh methods have demonstrated unique abilities for automated mesh generation and dynamic mesh adaptation to flow solution and moving boundaries. However Navier‐Stokes (NS) solvers with Cartesian mesh often produce large fluctuations of surface quantities (pressure, skin friction, and heat flux) at solid boundaries. We show that the Immersed Boundary Method (IBM) with adaptive octree Cartesian mesh allows one to eliminate unphysical fluctuations of skin friction and heat flux at solid boundaries for viscous flow simulations. Implementation of IBM for deterministic Boltzmann solvers with adaptive Cartesian mesh is described.

The paper is devoted to the nature of the recirculation zone behind a Mach disk in an underexpanded jet predicted by CFD at some range of determining parameters. The free jet flow behind the axisymmetric sonic nozzle was simulated by two approaches—in the frames of the full set of Navier‐Stokes (NS) equations and by the DSMC approach. No recirculation zone predicted by NS algorithm was observed in the flow field obtained by the DSMC approach. The nature of the discussed effect, therefore, seems to be purely computational and caused by limited applicability of the Navier‐Stokes equations for the description of the flow in the vicinity of the Mach disk with the high gradients of the flow parameters at that location.

The flow in conical supersonic micronozzles and behind them by deposition of pentacene accelerated by helium was studied with the use of direct simulation Monte-Carlo method. The Knudsen number in critical cross-section of nozzles is 0.0043. A directedness of resulting accelerated pentacene flow was studied as a function of cone angle and geometrical Mach number of the nozzle. The intensity of heavy gas flow in the hypersonic region can be elevated by one order using supersonic nozzles.

Relations between different problems described by the linearized Boltzmann equation (LBE) are discussed on the basis of the classical symmetry of LBE and kinetic boundary condition. The theory is developed for the system of arbitrary Knudsen number (Kn) from the view point of the Green function. After showing the main idea of the approach to steady problems for bounded and unbounded domains, its extension to unsteady problems in a fixed bounded domain is given. In particular, in the latter, recovery of Kubo formula for the viscosity and thermal conductivity in the fluctuation–dissipation theorem and its extension to the systems of arbitrary Kn are shown. A comment on the extension to gas mixtures is also given.

The impact of the radiometer vane thickness and edge geometry on the total radiometric force is examined numerically solving the ES BGK model kinetic equation. The flow of argon over a single vane and a multi‐vane configurations is considered in the range of Knudsen numbers from 0.02 to 1. The shear force is found to reduce the total radiometric force for most vane configurations. It is shown that a change in the vane shape may offset the losses due to the shear force in a multi‐vane geometry.

Having a very good mixture is a problem in MEMS devices because of their miniaturized dimensions for which the flows are always laminar. The gas flows in micro‐channels are rarefied and characterized by Knudsen numbers in the range of transition flows. In the present paper, Direct Simulation of Monte Carlo method is used to analyze some factors affecting the gas mixture within a micro‐channel with a splitter plate. Our purpose is to numerically simulate the flow of a gas mixture in a micro channel, in order to analyse the evolution of the mixing length in several configurations.

The radiometric force produced by a linear array of three radiometer vanes has been assessed numerically using an argon carrier gas and experimentally using air. The separation distance between the three vanes of the array was varied between 0 and 120 percent based on the height of an individual radiometer vane of 40 mm. Qualitative agreement between the numerical and experimental results is shown as a function of operating Knudsen number, vane separation distance, and surrounding chamber geometry. Both sets of results indicate an asymptotic trend in maximum force as the separation distance increases as well as a shift in the maximum force Knudsen number. Small chamber effects for both numerical and experimental results indicate an increase of the total force ranging from a factor of 2.5 to 4. Quantitatively, however, the numerical simulations yield forces approximately an order of magnitude higher than observed in the experiments due to differences in carrier gas and accommodation coefficient as well as the two dimensional nature of the numerical simulations versus the three dimensional experiment.

The ‘piston effect’, namely the time response of a fluid to an instantaneous change in the temperature of its boundaries, is studied for a rarefied gas confined in a slab. The problem is solved for the entire range of Knudsen numbers in the case where the prescribed temperature jumps at the walls are small. Analytic solutions are obtained in both collisionless and continuum limits and compared with low‐variance direct Monte Carlo simulations (LVDSMC) of the Boltzmann equation. The collisionless analysis captures well the early‐time dynamics of the system (at times t of the order of the mean collision time τcoll), where the gas motion is essentially ballistic, and the continuum‐limit analysis agrees with LVDSMC predictions at times t≥50τcoll, where the system behaviour is dominated by molecular collisions. Between these two limits, the dynamics of the system is governed by the solution of the complete linearized Boltzmann equation. The results supply insight into the mechanism of continuum breakdown in hea...

The outflow of gas into a vacuum from a supersonic nozzle with a screen mounted at the nozzle exit has been investigated both experimentally and numerically. The level of back flux was estimated by the pressure inside the probe placed in the backflow region. The obtained results indicate a possibility to decrease the back flux by putting a screen on the exit part of the nozzle, though improper screen geometry may cause even the back flux to increase.

In this paper we investigate the problem of isothermal pressure driven gas flow through a channel using a continuum equations set with a mass diffusion correction to the mass-density equation. The additional term is invoked as a way of releasing the local-equilibrium assumption in the presence of strong local gradients. Then the dissipative mass flux is proportional to local density/pressure gradient which is constant in a cross section and results in a correction to the velocity profile. Subsequently, better mass-flow rate predictions are obtained than those obtained using Maxwell-type first order slip boundary conditions. Results indicate that the mass diffusion correction captures the "Knudsen paradox" and change in curvature of the streamwise pressure profile without the need for setting higher order slip boundary conditions.

Stability analyses of two‐dimension conventional Burnett and Woods equations were carried out. The characteristic stability equations of these two equations were first derived and the characteristic curves were achieved. The linearized stability analyses show that the two‐dimension conventional Burnett and Woods equations are not stable. The critical Knudsen numbers for these two extended hydrodynamic equations are 0.353 and 0.130, respectively. The critical Knudsen numbers are smaller than those of one‐dimension equations. The two‐dimension extended hydrodynamic equations are more unstable than one‐dimension equations.

Utilizing a recently developed 3D smart wall molecular dynamics algorithm, we investigate argon flow in a 5.4 nm channel, which corresponds to the free molecular flow regime. Simulation results are compared with the linearized Boltzmann equation solutions. Significant deviations from the kinetic theory predictions are observed for the velocity, density and average normal stress profiles in the near wall region, where the wall force field effects are dominant. The results clearly show incomplete similitude between the rarefied and nano‐scale gas flows, if solely based on the Knudsen number.

The mechanisms and formulations of gas transfer under different conditions in tight porous media are reviewed. The characteristic features of the fundamental flow mechanisms are examined. The essential parameters of relevant modeling approaches are identified and discussed. The present formulations are modified for real gas conditions.

Energy is one of the biggest concerns in the 21st century. In this paper, a new energy harvest method is proposed. The key component of the new method is the Knudsen compressor which is based on the rarefied flow phenomenon of thermal creep. In this study, the possibility of Knudsen compressor filled with nano scale aerogel working at atmosphere pressure is first studied by Direct Simulation Monte Carlo (DSMC) method. The simulation results provide the information for design and fabricate a Knudsen compressor. The numerical analysis estimates that at the day time of summer, an array of multi‐stages Knudsen compressor in 1 m2 area could capture energy of 74 W.

Several modifications aimed at improving physical accuracy are proposed for solving axially symmetric problems building on the DSMC (2007) algorithms introduced by Bird. Originally developed to solve nonequilibrium, rarefied flows, the DSMC method is now regularly used to solve complex problems over a wide range of Knudsen numbers. These new algorithms include features such as nearest neighbor collisions excluding the previous collision partners, separate collision and sampling cells, automatically adaptive variable time steps, a modified no-time counter procedure for collisions, and discontinuous and event-driven physical processes. Axially symmetric solutions require radial weighting for the simulated molecules since the molecules near the axis represent fewer real molecules than those farther away from the axis due to the difference in volume of the cells. In the present methodology, these radial weighting factors are continuous, linear functions that vary with the radial position of each simulated molecule. It is shown that how one defines the number of tentative collisions greatly influences the mean collision time near the axis. The method by which the grid is treated for axially symmetric problems also plays an important role near the axis, especially for scalar pressure. A new method to treat how the molecules are traced through the grid is proposed to alleviate the decrease in scalar pressure at the axis near the surface. Also, a modification to the duplication buffer is proposed to vary the duplicated molecular velocities while retaining the molecular kinetic energy and axially symmetric nature of the problem.

The pressure‐sensitive paint (PSP) has potential as a diagnostic tool for pressure measurement in the high Knudsen number regime because it works as a so‐called “molecular sensor.” However, there are few reports concerning application of the PSP to micro devices, because the conventional PSP is too thick owing to the use of polymer binder. In our previous work, we have adopted Langmuir‐Blodgett (LB) technique to fabricate pressure sensitive molecular films (PSMFs) using Pd(II) Mesoporphyrin IX (PdMP). The PSMF based on PdMP has pressure sensitivity only at low pressure range (below 3 kPa). In this study, we have constructed PSMF composed of Pt(II) Mesoporphyrin IX (PtMP) to be applied to pressure measurement near atmospheric pressure. The pressure sensitivity of PSMF based on PtMP has been tested, and it is clarified that the PSMF of PtMP has equivalent pressure sensitivity of polymer PSP. Moreover, we have applied PSMF to measurement of pressure distribution of micro‐channel gas flow, showing its usefulness.

A rarefied gas flow through the infinite expanse of an in‐line array of circular cylinders is considered on the basis of kinetic theory. The temperature of the cylinder, which is uniform in each cylinder and is common in one direction of the array, varies from one cylinder after another with a constant increment in the other direction. A pressure gradient is imposed in the gas in the same direction as the cylinder‐temperature variation. A steady flow caused by the pressure gradient and that caused by the temperature variation of the array are investigated numerically on the basis of the linearized Bhatnagar‐Gross‐Krook (BGK) equation and the diffuse reflection boundary condition. The integral equation approach has been employed in the numerical computation. The mass‐flow rate as well as the energy‐flow rate of the gas through the periodic unit cell is obtained as a function of the Knudsen number.

A set of local Knudsen numbers are defined, which are demonstrated to be more appropriate than conventional ones for the purposes of identifying gas flow non‐equilibrium. The problematic area of choosing an appropriate switching criteria is addressed by adopting a local Knudsen number definition based on higher‐order constitutive relations; the R13 equations are chosen. A procedure is then described that allows the estimation of the R13 local Knudsen number within a Navier‐Stokes solver, and the efficacy of this as a switching criterion is tested within an illustrative hybrid BGK/Navier‐Stokes procedure. For the test case investigated, the results from the hybrid procedure compare very well with the full BGK solution, and are obtained at a fraction (depending on the global Kn) of the computational cost.

A computational model of a rotating microactuator with a four blade rotor system immersed in a low density gas is analyzed by using DSMC method. The rotor system is rotated by a driving force of rarefied dynamic effects arising around each blade due to the temperature difference between front and rear blade sides created and held by a given source of local gas heating. Three models of microactuators with different design are considered: a rotor system with inclined under certain angle blades with different temperatures of the front and rear surface of each blade; a rotor system with inclined blades immersed in low density gas under temperature gradient held between two hot and cold plates, and finally, a rotor system with blades having a fancy surface with anisotropic reflection of the gas molecules. The DSMC analysis is performed at Knudsen numbers (based on the blade size) in the range Kn = 0.1–0.2 close to the experimentally established values, for which the rotation rate reached its maximum. The resul...

Mass flow rate measurements in a single silicon micro channel were carried out for various gases in isothermal steady flows. The results obtained, from hydrodynamic to near free molecular regime by using a powerful experimental platform, allowed us to deduce interesting information, notably about the reflection/accommodation process at the wall. In the 0–0.3 Knudsen range, a continuum approximated analytic approach was derived from NS equations, associated to first or second order slip boundary conditions. Identifying the experimental mass flow rate curves to the theoretical ones the TMAC of various gases were extracted. Over all the Knudsen range [0–50] the experimental results were compared with theoretical values calculated from kinetic approaches: using variable TMAC values as fitting parameter, the theoretical curves were fitted to the experimental ones. Whatever the Knudsen range and the theoretical approach, the TMAC values are found decreasing when the molecular weights of the gas considered increase (as long as the different gases are compared using the same approach). Moreover, the values of the various accommodation coefficients are rather close one to other but sufficiently smaller than unity to conclude that the full accommodation modelling is not satisfactory to describe the gas/wall interaction.

The gas flows in a microchannel are rarefied and characterized by Knudsen numbers in the range of transition flows. The introduction of a small parameter related to the geometry and the application of the Principle of Least Degeneracy to the dimensionless Navier‐Stokes or Burnett equations allow to yield models for the study of flows with small Mach number and with small or moderate Knudsen number. On the other hand, Direct Simulation of Monte Carlo method is used to analyze the flow within a microchannel connecting two open areas containing the same gas under different thermodynamic equilibrium conditions. Some comparisons are presented.