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A backward facing micro-step is a building block for many microfluidic devices. Due to micron sized characteristic dimensions, the gas flow in such a geometry is rarefied in nature. Such rarefied gas flows are widely solved using the Direct Simulation Monte Carlo (DSMC) technique. Flow separation, circulation and re-attachment are some of the basic characteristics of step flows. The objective of this study is to analyze the effect of rarefaction on the flow properties and the separation of the flow. The range of selected Knudsen number (Kn) covers the slip and transition regime from a value of 0.0311–13.25. The pressure ratios employed are 3 and 5. It is observed that the slip velocity continuously increases while the centre-line velocity first decreases, then remains constant and finally increases with increase in Kn. At the step, separation of the flow is seen for Kn < 0.1325 while no such separation is observed in the range of Kn from 0.198 to 13.25. The corresponding Re for these ranges are 6.43 to 0.67 and 0.392 to 0.012 respectively. The re-attachment length decreases with increase in Kn whereas it increases with increase in Re. A stronger pressure force and a weaker diffusion effect leads to flow separation in the slip regime whereas stronger diffusion and weaker pressure force lead to an absence of flow separation in the transition regime. Finally, this work presents for the first time the existence of the Knudsen minimum for such a backward step geometry. [ABSTRACT FROM AUTHOR]

A major challenge for the conventional Direct Simulation Monte Carlo ( DSMC ) technique lies in the fact that its computational cost becomes prohibitive in the near continuum regime, where the Knudsen number ( Kn )—characterizing the degree of rarefaction—becomes small. In contrast, the Fokker–Planck ( FP ) based particle Monte Carlo scheme allows for computationally efficient simulations of rarefied gas flows in the low and intermediate Kn regime. The Fokker–Planck collision operator—instead of performing binary collisions employed by the DSMC method—integrates continuous stochastic processes for the phase space evolution in time. This allows for time step and grid cell sizes larger than the respective collisional scales required by DSMC . Dynamically switching between the FP and the DSMC collision operators in each computational cell is the basis of the combined FP-DSMC method, which has been proven successful in simulating flows covering the whole Kn range. Until recently, this algorithm had only been applied to two-dimensional test cases. In this contribution, we present the first general purpose implementation of the combined FP-DSMC method. Utilizing both shared- and distributed-memory parallelization, this implementation provides the capability for simulations involving many particles and complex geometries by exploiting state of the art computer cluster technologies. [ABSTRACT FROM AUTHOR]

In this paper, the influence of the gas-surface interaction on the time-dependent rarefied gas flow through a short tube into vacuum is investigated. Due to a significant scale separation, the flow is simulated using a hybrid scheme proposed by Vargas et al. [1, 2], in which the pressure change in the upstream chamber is coupled to the flow rate obtained by the Direct Simulation Monte Carlo (DSMC) computations. First, the influence of gas-surface interaction is demonstrated through comparison of DSMC simulation results obtained for different values of accommodation coefficients. The obtained dataset is then used to show how the boundary conditions can affect the time-dependent gas flow, even when applied on the small surface area of the device. It is argued that the domain of possible solutions is bounded by the cases of specular and diffuse scattering. Furthermore, it is investigated how this domain can be affected by measurement uncertainties present in the experimental setup. Next, the analysis of the gas-surface interaction is extended to binary mixtures. In the end, it is discussed how the obtained results can be used in order to improve the efficiency of gas separation mechanisms. [ABSTRACT FROM AUTHOR]

Recently, Fokker–Planck based particle Monte Carlo schemes have been proposed and evaluated for simulations of rarefied gas flows [1–3] . In this paper, the variance reduction for particle Monte Carlo simulations based on the Fokker–Planck model is considered. First, deviational based schemes were derived and reviewed, and it is shown that these deviational methods are not appropriate for practical Fokker–Planck based rarefied gas flow simulations. This is due to the fact that the deviational schemes considered in this study lead either to instabilities in the case of two-weight methods or to large statistical errors if the direct sampling method is applied. Motivated by this conclusion, we developed a novel scheme based on correlated stochastic processes. The main idea here is to synthesize an additional stochastic process with a known solution, which is simultaneously solved together with the main one. By correlating the two processes, the statistical errors can dramatically be reduced; especially for low Mach numbers. To assess the methods, homogeneous relaxation, planar Couette and lid-driven cavity flows were considered. For these test cases, it could be demonstrated that variance reduction based on parallel processes is very robust and effective. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the effects of convective heat transfer on the argon gas flow through micro/nanochannels subject to uniform wall heat flux (UWH) boundary condition using the direct simulation Monte Carlo (DSMC) method. Both the hot wall (qwall > 0) and the cold wall (qwall < 0) cases are considered. We consider the effect of wall heat flux on the centerline pressure, velocity profile and mass flow rate through the channel in the slip regime. The effects of rarefaction, property variations and compressibility are considered. We show that UWH boundary condition leads to the thermal transpiration. Our investigations showed that this thermal transpiration enhances the heat transfer rate at the walls in the case of hot walls and decreases it where the walls are being cooled. We also show that the deviation of the centerline pressure distribution from the linear distribution depends on the direction of the wall heat flux. [ABSTRACT FROM AUTHOR]

A Fokker–Planck based particle Monte Carlo algorithm was devised recently for simulations of rarefied gas flows by the authors [1–3] . The main motivation behind the Fokker–Planck (FP) model is computational efficiency, which could be gained due to the fact that the resulting stochastic processes are continuous in velocity space. This property of the model leads to simulations where the computational cost becomes independent of the Knudsen number (Kn) [3] . However, the Fokker–Planck model which can be seen as a diffusion approximation of the Boltzmann equation, becomes less accurate as Kn increases. In this study we propose a hybrid Fokker–Planck–Direct Simulation Monte Carlo (FP–DSMC) solution method, which is applicable for the whole range of Kn. The objective of this algorithm is to retain the efficiency of the FP scheme at low Kn ( Kn ≪ 1 ) and to employ conventional DSMC at high Kn ( Kn ≫ 1 ). Since the computational particles employed by the FP model represent the same data as in DSMC, the coupling between the two methods is straightforward. The new ingredient is a switching criterion which would ideally result in a hybrid scheme with the efficiency of the FP method and the accuracy of DSMC for the whole Kn-range. Here, we adopt the number of collisions in a given computational cell and for a given time step size as a decision criterion in order to switch between the FP model and DSMC. For assessment of the hybrid algorithm, different test cases including flow impingement and flow expansion through a slit were studied. Both accuracy and efficiency of the model are shown to be excellent for the presented test cases. [ABSTRACT FROM AUTHOR]

The NACA 0012 airfoil and the sharp 25–55-deg biconic cases are usually considered in evaluating the accuracy of new forms of velocity slip and temperature jump wall boundary conditions in the Navier–Stokes–Fourier equations. These cases have been investigated by many researchers in previous works with the first order Maxwell slip and Smoluchowski jump boundary conditions. Recently, we proposed a new form of the second order temperature jump for simulating rarefied gas flows and obtained accurate results for low-speed microflows. The current work is an extension of our previous CFD work where we applied both the second order velocity slip condition and the second order temperature jump boundary condition in new forms to simulate rarefied external gas flows for these cases. The second order boundary conditions are implemented into the rhoCentralFoam solver in the OpenFOAM software. The NACA 0012 airfoil case is investigated with angles-of-attack of 0 and 10 degrees and Mach numbers of 0.8 and 2. The sharp 25–55-deg biconic case is simulated at Mach of 15.6. The simulation results obtained for the NACA 0012 airfoil show that the combination of the second order slip/jump boundary conditions gives suitable agreements with DSMC for surface gas temperature and drag coefficients in comparison with those of the first order conditions. However, the results of the biconic case figure out that the second order conditions are not superior to the first order conditions. [ABSTRACT FROM AUTHOR]

Molecular distillation process is a type of vapors transport process at high vacuum in the distillation space between evaporator and condenser. To get a better understanding of vapor flow characteristics in molecular distillation, vapor phase behavior is simulated using the direct simulation Monte Carlo (DSMC) method. The variable hard sphere (VHS) model is adopted to calculate molecular collisions. Molecular rotation and translation have both been taken into account while dealing with molecular energy distribution after collisions. Flow characteristics obtained for velocity distribution and number density are used to calculate the collision frequency and mean free path in the distillation space. The effects of evaporating temperature, condensing temperature and distillation gap on the vapors flow characteristics are discussed. It is found that for gas molecules by increasing the evaporating temperature, the number density and velocity, collision frequency in distillation space increase, while the mean free path decreases. As the condensing temperature increases, the number density and collision frequency in the distillation space increases, while velocity and mean free path decreases. It is also observed that much narrower distillation gap results in steeper variation tendency of flow characteristics. [ABSTRACT FROM AUTHOR]

An air data sensor (ADS) system is one of the key components in space transports. It can provide precious information on the pressure and the Mach number data that cannot be obtained from internal motion sensors. When a spaceship or a reentry vehicle is cruising at a very high altitude, the ADS will suffer problem of the time-delay in its pressure signals that propagates through a thin pressure tube. In this study, the time delay of the pressure propagation inside a thin tube under a low-pressure environment is evaluated based on the direct-simulation Monte-Carlo (DSMC) method. A CFD analysis based on axisymmetric Navier-Stokes equations is also conducted to evaluate the contribution of rarefied gas effects to the pressure propagation speed. These results are compared with experimental results. Based on the DSMC and CFD analyses, the time constant for the pressure change is determined to be around 0.013 seconds whereas the experimental results yielded 0.12 seconds when the pressure at the exit of the tube increases for about 20 to 40 Pa starting from 30 Pa. These results suggest that the propagation delay observed in the flight test of the atmospheric-entry capsule descending at an altitude of 79 km with Mach-4.5 flight velocity was partly caused by the rarefied gas effect. [ABSTRACT FROM AUTHOR]

Preliminary studies are made to determine the aerodynamic and accommodation characteristics of the wind tunnel model under hypersonic rarefied flow. In the method, the wind tunnel models are exposed to the test flow in the hypersonic rarefied wind tunnel in JAXA. The displacements of the models due to the aerodynamic forces are measured during the testing. The flowfield around the wind tunnel model in the test section is also analyzed by using the numerical calculation. In the calculation, the accommodation coefficient of wind tunnel model surface is parametrically changed. The accommodation parameter of the wind tunnel model surface is then deduced from the comparison between the calculation and the measurement. For the sphere wind tunnel model, agreement between measurement and calculation could be obtained by present method with the accommodation coefficient from 0.8 to 0.9. It is also found that the determination of accommodation parameter becomes more achievable by using the displacement along the flow direction rather than that along the horizontal direction. On the other hand, further detailed modeling is required in the numerical analysis for the flat plate model. The uncertainties in the force measurement in the HRWT are discussed in this paper. [ABSTRACT FROM AUTHOR]