Computational study of a novel Knudsen pump design exploiting drilling and 3D printing techniques in low thermal conductivity materials

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Computation of the effective area and associated uncertainties of non-rotating piston gauges FPG and FRS

The effective areas of three force-balanced piston gauges (FPGs) and two Furness Rosenberg standards (FRS) in the operating pressure range of each device varying for 1 Pa–15 kPa have been accurately computed both in the gauge and absolute modes. Geometrical data for the non-rotating piston-cylinder assemblies (PCAs) have been provided by the National Metrology Institutes (NMIs) of PTB, RISE, INRiM and CMI. Since the flow is in a wide range of the Knudsen number, simulations have been based on the Batnagar–Gross–Krook (BGK) kinetic model equation, while the typical Dadson and CFD approaches have been complimentary applied only in the viscous regime. Furthermore, an uncertainty analysis has been performed. The effective area is strongly affected by the PCA geometry and the flow conditions, while its dependency on pressure may be different even for devices of the same type. The main source of uncertainty is the dimensional measurements of the piston and the cylinder, followed by the accommodation coefficient characterizing the gas-surface interaction, while the effect of other flow and modeling parameters is negligible. The total relative standard uncertainty of the effective area has been always found to be less than 1 · 10−5 indicating that pressure measurements of high accuracy can be ensured. Since the effective area is estimated based solely on computations the FPG and the FRS assemblies may be characterized as primary pressure standards

Uncertainty propagation analysis of the computed ITER torus effective pumping speed during the dwell phase

At the University of Thessaly the ARIADNE code for modeling complex gas distribution systems operating under any vacuum conditions has been developed by integrating a kinetic database to a typical gas network solver. The ARIADNE code has been successfully implemented to model the ITER primary pumping system providing the torus effective pumping speed, as well as the pressure evolution during the dwell phase. However, the computed results are subject to the input data, which include the pipe network geometry, approximating the real geometry of the ITER primary pumping system and the operating data, such as the torus pressure, gas temperature and cryopump pumping speed. The effect of the aforementioned input quantity uncertainties to the torus effective pumping speed is investigated via an uncertainty propagation analysis by coupling the Monte Carlo method (MCM) with the ARIADNE code. Documenting the propagation of each input parameter uncertainty to the torus effective pumping speed uncertainty is beneficial for judging the accuracy of the modeling and simulation results, as well as for identifying the most important sources of uncertainty. Furthermore, the presented methodology can be used to investigate the uncertainty propagation of any input quantity to any output quantity for vacuum systems of arbitrary complexity

Modeling of time-dependent gas pumping networks in the whole range of the Knudsen number: simulation of the ITER dwell phase

A hybrid time-dependent algorithm to simulate the transient response of gas distribution systems of arbitrary size and complexity, in the whole range of the Knudsen number, is proposed. The pressure evolution in the vessels is described by a simple macro model derived via mass conservation principals, while the pressure and mass flow rates in the pipe network are described by a micro model, consisting of the in-house steady-state gas network code “ARIADNE”, based on kinetic theory. The two models are explicitly coupled, i.e. at each time step the gas network is solved via ARIADNE and the computed node pressures and pipe flow rates are provided to the macroscale evolution equations to update the vessel pressures. The proposed methodology and code are successfully validated by solving two prototype problems and comparing the results with corresponding ones available in the literature or obtained by Molflow+. The computational effectiveness and efficiency of the proposed approach to model large size networks is demonstrated by simulating the transient response of the ITER torus primary pumping system in the dwell phase. Interesting findings for the torus effective pumping speed and pressure evolution, including the final pressure at the end of the dwell phase are provided

Author's personal copy A fast iterative model for discrete velocity calculations on triangular grids

a b s t r a c t A fast synthetic type iterative model is proposed to speed up the slow convergence of discrete velocity algorithms for solving linear kinetic equations on triangular lattices. The efficiency of the scheme is verified both theoretically by a discrete Fourier stability analysis and computationally by solving a rarefied gas flow problem. The stability analysis of the discrete kinetic equations yields the spectral radius of the typical and the proposed iterative algorithms and reveal the drastically improved performance of the latter one for any grid resolution. This is the first time that stability analysis of the full discrete kinetic equations related to rarefied gas theory is formulated, providing the detailed dependency of the iteration scheme on the discretization parameters in the phase space. The corresponding characteristics of the model deduced by solving numerically the rarefied gas flow through a duct with triangular cross section are in complete agreement with the theoretical findings. The proposed approach may open a way for fast computation of rarefied gas flows on complex geometries in the whole range of gas rarefaction including the hydrodynamic regime

Modeling of ITER related vacuum gas pumping distribution systems

A novel algorithm recently developed to solve steady-state isothermal vacuum gas dynamics flows through pipe networks consisting of long tubes is extended to include, in addition to long channels, channels of moderate length 10 < LID< 50. This is achieved by implementing the so-called end effect treatment/correction. Analysis and results are based on kinetic theory as described by the Boltzmann equation or associated reliable kinetic model equations. For a pipe network of known geometry the algorithm is capable of computing the mass flow rates (or the conductance) through the pipes as well as the pressure heads at the nodes of the network. The feasibility of the approach is demonstrated by simulating two ITER related vacuum distribution systems, one in the viscous regime and a second one in a wide range of Knudsen numbers. Since a kinetic approach is implemented, the algorithm is valid and the results are accurate in the whole range of the Knudsen number, while the involved computational effort remains small. (c) 2013 Elsevier B.V. All rights reserved

Gas Mixing and Final Mixture Composition Control in Simple Geometry Micro-mixers via DSMC Analysis

The mixing process of two pressure driven steady-state rarefied gas streams flowing between two parallel plates was investigated via DSMC (Direct Simulation Monte Carlo) for different combinations of gases. The distance from the inlet, where the associated relative density difference of each species is minimized and the associated mixture homogeneity is optimized, is the so-called mixing length. In general, gas mixing progressed very rapidly. The type of gas surface interaction was clearly the most important parameter affecting gas mixing. As the reflection became more specular, the mixing length significantly increased. The mixing lengths of the HS (hard sphere) and VHS (variable hard sphere) collision models were higher than those of the VSS (variable soft sphere) model, while the corresponding relative density differences were negligible. In addition, the molecular mass ratio of the two components had a minor effect on the mixing length and a more important effect on the relative density difference. The mixture became less homogenous as the molecular mass ratio reduced. Finally, varying the channel length and/or the wall temperature had a minor effect. Furthermore, it was proposed to control the output mixture composition by adding in the mixing zone, the so-called splitter, separating the downstream flow into two outlet mainstreams. Based on intensive simulation data with the splitter, simple approximate expressions were derived, capable of providing, once the desired outlet mixture composition was specified, the correct position of the splitter, without performing time consuming simulations. The mixing analysis performed and the proposed approach for controlling gas mixing may support corresponding experimental work, as well as the design of gas micro-mixers

Flow Rate Measurement of Rarefied Binary Gases in Long Rectangular Microchannels

Abstract The flow rate of binary gas mixtures through rectangular long microchannels is measured and compared to the numerical solution of the McCormack kinetic model. The microchannels are etched in silicon, and each individual channel has width=21, height=1.15, length=5000 μm. The measurement refers to He/Ar and He/Kr gas mixtures and are based on the constant volume method. The microchannel is placed between an upstream and a downstream reservoir having different pressures. The flow through the microsystem is maintained by the pressure drop between the containers and the flow rate is determined from the pressure variations in the reservoirs. In the case of He/Ar, measurements have been performed for several values of its concentration varying between zero and one, while in the case of He/Kr only a concentration equal to 0.5 is considered. The pressure ratio between the two containers is in the range of 3-7 and the corresponding average Knudsen numbers are in the range of 0.12-0.98. The results of the flow rate measurement are compared to the discrete velocity solution of the McCormack kinetic model and very good agreement between experiment and simulation has been obtained for all flow configurations. The relative discrepancy between the experimental and numerical results is in the range of the experimental uncertainty

Validity range of linear kinetic modeling in rarefied pressure driven single gas flows through circular capillaries

The range of validity of various linear kinetic modeling approaches simulating rarefied pressure driven gas flow through circular tubes is computationally investigated by comparing the flowrates obtained by the linear approaches with the corresponding nonlinear ones. The applicability margins of the linear theories in terms of the parameters determining the flow (gas rarefaction, pressure ratio, tube aspect ratio) are specified, provided that the introduced deviation norm is smaller than a specific value. The work is motivated by the fact that computational effort is significantly reduced when linear, instead of nonlinear, kinetic modeling is implemented. It is found that the range of validity of the linear solutions is much wider than the expected one, as defined by their formal mathematical constrains and it remains valid in a range of parameters, where the DSMC method and nonlinear kinetic modeling become computationally inefficient, resulting in great computational savings