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Abstract Fokker-Planck kinetic models have been devised as an approximation of the Boltzmann collision operator. Cubic Fokker-Planck-DSMC hybrid method is employed to simulate the diatomic gas flow through a thin slit and a thin orifice. Pressure driven nitrogen expansion gas flows with two different pressure ratios are investigated at Knudsen number 0.001. The DSMC method is physically accurate for all flow regime; however it is computationally expensive in high density or near continuum regions. The Fokker-Planck-DSMC hybrid scheme employs DSMC in rarefied regions and Fokker-Planck method in near continuum flow regions for an efficient and accurate solution. Numerical procedures of the cubic Fokker-Planck method are implemented within the framework of an existing DSMC-solver, SPARTA. The Fokker-Planck-DSMC hybrid solution reproduces pure DSMC solution with improved computational efficiency up to a factor of five for vacuum flow through a thin orifice. In addition, breakdown of translational equilibrium is investigated. Domain criterion of FP-DSMC is safely smaller than Bird's breakdown criterion. Highlights • Rarefied diatomic gas flow through a thin slit and a thin orifice. • Access of accuracy and efficiency of cubic FP-DSMC for diatomic gas flow. • Investigation of breakdown of translational equilibrium on cubic FP-DSMC hybrid. • Comparison of diatomic and monoatomic flow through a thin slit and a thin orifice. [ABSTRACT FROM AUTHOR]

An integrated software tool for modeling and simulation of complex gas distribution systems operating under any vacuum conditions is presented and validated. The algorithm structure includes (a) the input geometrical and operational data of the network, (b) the definition of the fundamental set of network loops and pseudoloops, (c) the formulation and solution of the mass and energy conservation equations, (d) the kinetic data base of the flow rates for channels of any length in the whole range of the Knudsen number, supporting, in an explicit manner, the solution of the conservation equations and (e) the network output data (mainly node pressures and channel flow rates/conductance). The code validity is benchmarked under rough vacuum conditions by comparison with hydrodynamic solutions in the slip regime. Then, its feasibility, effectiveness and potential are demonstrated by simulating the ITER torus vacuum system with the six direct pumps based on the 2012 design of the ITER divertor. Detailed results of the flow patterns and paths in the cassettes, in the gaps between the cassettes and along the divertor ring, as well as of the total throughput for various pumping scenarios and dome pressures are provided. A comparison with previous results available in the literature is included. [ABSTRACT FROM AUTHOR]

Abstract: A method to take into account the influence of the inlet/outlet ends on rarefied gas flows through moderately long capillaries proposed previously [Vacuum 97, 26 (2013)] is applied to gas flows through circular tubes. The method is based on the concept of effective tube length, representing a sum of its real length and an increment. To calculate the length increment, a flow field near the inlet/outlet of tube is calculated on the basis of the linearized kinetic equation. It is shown that the value of the length increment is independent of the tube length, but depends only on the rarefaction parameter so that it can be used to obtain accurate predictions of the mass flow rate and the axial pressure distribution without great computational effort. Comparisons with results obtained by considering the complete flow domain have shown the efficiency of the end correction concept. [Copyright &y& Elsevier]

Abstract: Flow of a rarefied gas through a cylindrical tube connecting two reservoirs maintained at a small pressure difference is considered using the axisymmetric version of the linearised BGK kinetic model equation subject to Maxwell diffuse–specular boundary conditions. This is a problem of five dimensions in phase space, solved in a fully deterministic manner using a parallelised discrete velocity algorithm. Results include flow rates as well as distributions of density and velocity perturbations, from the free molecular up to the slip regime and for length-over-radius () ratios ranging from zero (orifice flow) up to 20. The dependency of the results on gas rarefaction, wall accommodation and tube length is analysed and discussed. It is found that the Knudsen minimum appears only at . Furthermore, in the case of it is confirmed that the results are practically independent of the accommodation coefficient. Comparing the present linear results with corresponding non-linear ones, it is seen that linearised analysis can capture the correct behaviour of the flow field not only for infinitesimally small but also for small but finite pressure differences and that its range of applicability is wider than expected. Also, the error introduced by the assumption of fully developed flow for channels of moderate length is estimated through a comparison with the present corresponding results. [Copyright &y& Elsevier]

Abstract: A rarefied gas flow through channels (i.e. flow through parallel plates) of finite length has been modeled based on the direct simulation Monte Carlo method. The reduced flow rate and the flow field have been calculated as function of the gas rarefaction, the length-to-height ratio and the pressure ratio upstream and downstream of the channel. The whole range of the gas rarefaction including the free-molecular, transitional and hydrodynamic regimes and a wide range of the length-to-height ratio representing both short and long channels have been considered. Several values of the pressure ratio between 0 and 0.5 have been used in the calculations. It is shown that the rarefaction parameter has the most significant effect on the flow field characteristics and patterns, followed by the pressure ratio, while the length-to-height ratio has a rather modest impact. The Mach belt phenomenon is discussed in detail. [Copyright &y& Elsevier]

Abstract: The flow of a monatomic gas through a slit and an orifice due to an arbitrarily large pressure difference is examined on the basis of the nonlinear Bhatnagar–Gross–Krook (BGK) model equation, subject to Maxwell diffuse boundary conditions. The governing kinetic equation is discretized by a second-order control volume scheme in the physical space and the discrete velocity method in the molecular velocity space. The nonlinear fully deterministic algorithm is optimized to reduce the computational effort by introducing memory usage optimization, grid refinement and parallelization in the molecular velocity space. Results for the flow rates and the macroscopic distributions of the flow field are presented in a wide range of the Knudsen number for several pressure ratios. The effect of the various geometric and physical parameters on the flow field is examined. Comparison with previously reported corresponding Direct Simulation Monte Carlo (DSMC) results indicates a very good agreement, which clearly demonstrates the accuracy of the kinetic algorithm and furthermore the reliability of the BGK model for simulating pressure driven flows. [Copyright &y& Elsevier]

Abstract: The starting gas flow in a cylindrical channel is investigated in the whole range of the Knudsen number by numerically solving the governing time dependent kinetic equations in a fully deterministic manner. The gas is initially at rest and then due to a suddenly imposed uniform pressure gradient, is starting to flow. The motion is time dependent up to the point where the steady-state flow conditions are recovered. The flow field is modeled by the linearized unsteady BGK equation subject to Maxwell purely diffuse boundary conditions. The solution provides a detailed description of the evolution of the flow field with regard to time from the starting point, where the gas is at rest up to a certain time where almost steady-state conditions are recovered. Based on the results some insight of how rapidly a vacuum flow will respond to a sudden change, related to an externally imposed pressure gradient coming from a vacuum pump or a valve, is obtained. The total time to recover the stationary solution in terms of the rarefaction parameter exhibits a minimum close to the well known Knudsen minimum. [Copyright &y& Elsevier]

Abstract: Vacuum flows in various configurations, which are related to fusion reactors are simulated using linear kinetic theory and the direct simulation Monte Carlo method (DSMC), in the whole range of the Knudsen number. In the case of flows through channels of infinite length, even for large pressure differences, the flow is linear (fully developed) and linearized kinetic theory has been applied with considerable success. In the case of flows through channels of finite length, the flow is strongly non-equilibrium and has to be tackled by the DSMC method. In the present work we present a comparative study between experimental and computational results for the case of circular channels of finite length. Experimental data and corresponding computational results are provided for the conductance of channels with different lengths and several downstream to upstream pressure ratios, covering a wide range of the Knudsen number. In addition, a brief review of some recent work related to the case of long channels is presented and general remarks related to the overall flow conditions and characteristics for flows through channels of various lengths and cross sections are stated. [ABSTRACT FROM AUTHOR]

Abstract: The problem of nonlinear heat transfer through a rarefied gas confined between concentric cylinders maintained at different temperatures is investigated. The formulation is based on the nonlinear Shakhov kinetic model subject to Cercignani–Lampis boundary conditions, while molecular interaction is modelled by the inverse power law. The detailed behaviour of the radial heat flow, density, temperature and pressure distributions in terms of the normalized temperature difference between the cylindrical walls, the ratio of the two cylindrical radii and the gas rarefaction is investigated and certain interesting characteristics are revealed. The study includes small, moderate and large temperature differences and various radius ratios and is extended in the whole range of the Knudsen number. It is verified that the type of molecular interaction plays an important role when the heat transfer configuration becomes strongly nonlinear, while the influence of the gas–surface scattering law has similar effects both in linear and nonlinear conditions. By comparing linear and nonlinear results corresponding to the same conditions, it is concluded that linearized analysis can capture the correct behaviour of the heat flow configuration not only for infinitesimally small but also for finite temperature differences and that its range of applicability is wider than expected. [Copyright &y& Elsevier]

Abstract: The fully developed flow of rarefied gases through circular ducts of concentric annular cross sections is solved via kinetic theory. The flow is due to an externally imposed pressure gradient in the longitudinal direction and it is simulated by the BGK kinetic equation, subject to Maxwell diffuse-specular boundary conditions. The approximate principal of the hydraulic diameter is investigated for first time in the field of rarefied gas dynamics. For the specific flow pattern, in addition to the flow rates, results are reported for the Poiseuille number and the exact hydraulic diameter. The corresponding parameters include the whole range of the Knudsen number and various values of the accommodation coefficient and the ratio of the inner over the outer radius. The accuracy of the results is validated in several ways, including the recovery of the analytical solutions at the hydrodynamic and free molecular limits. [Copyright &y& Elsevier]