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Abstract The Katrin experiment aims to measure the effective mass of the electron antineutrino from the analysis of electron spectra stemming from the β -decay of molecular tritium with a sensitivity of 200 meV/c2. Therefore, a cumulative amount of about 40 g of gaseous tritium is circulated daily in a windowless source section. An accurate description of the gas flow through this section is of fundamental importance for the neutrino mass measurement as it significantly influences the generation and transport of β -decay electrons through the experimental setup. In this paper we present a comprehensive model consisting of calculations of rarefied gas flow through the different components of the source section ranging from viscous to free molecular flow. By connecting these simulations with a number of experimentally determined operational parameters the gas model can be refreshed regularly according to the measured operating conditions. In this work, measurement and modelling uncertainties are quantified with regard to their implications for the neutrino mass measurement. We find that the magnitude of systematic uncertainties related to the source model is represented by | Δ m ν 2 | = (3.06 ± 0.24) ⋅ 10 − 3 eV 2 / c 4 , and that the gas model is ready to be used in the analysis of upcoming Katrin data. Highlights • Description of gas flow in the KATRIN windowless gaseous tritium source. • Improved gas model allows experimental verification and neutrino mass analysis. • Description of measurements to monitor and determine the amount of gas in the KATRIN source, using an angular-selective electron gun. • Quantification of neutrino mass systematic uncertainty related to the description of gas flow in the KATRIN source. [ABSTRACT FROM AUTHOR]

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]

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]

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]

Transient flow of rarefied gas through an orifice caused by various pressure ratios between the reservoirs is investigated for a wide range of the gas rarefaction, varying from the free molecular to continuum regime. The problem is studied on the basis of the numerical solution of unsteady S-model kinetic equation. It is found that the mass flow rate takes from 2.35 to 30.37 characteristic times, which is defined by orifice radius over the most probable molecular speed, to reach its steady state value. The time of steady flow establishment and the steady state distribution of the flow parameters are compared with previously reported data obtained by the Direct Simulation Monte Carlo (DSMC) method. A simple fitting expression is proposed for the approximation of the mass flow rate evolution in time. [ABSTRACT FROM AUTHOR]

Abstract: The method, proposed previously by other authors, is applied here to calculate a mass flow rate of rarefied gas through a long rectangular channel of variable cross-section aspect ratio. The gas flow through this channel is generated by the pressure and/or temperature gradient. The method is based on the results obtained previously on the basis of the kinetic equation and it requires very modest computational efforts. As a demonstration of its application some examples of the mass flow rate calculations for the isothermal and non-isothermal flows through the channels with variable rectangular cross sections are given. The analytical expressions in the case of the hydrodynamic and free molecular flow regimes are proposed. [Copyright &y& Elsevier]

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: A transient gas flow through a rectangular slit is simulated on the basis of unsteady S-model kinetic equation. The flow into vacuum and at two pressure ratios between the reservoirs are considered for a wide range of the rarefaction parameter lying from the free molecular to the near continuum regime. The time of steady flow establishment is obtained and it is found that this time depends on the pressure ratio between the reservoirs and on the gas rarefaction. The time evolution of the macroscopic flow parameters is analyzed in detail. The present results are compared with the results on the orifice flow previously obtained by other authors. [Copyright &y& Elsevier]

Abstract: The paper is devoted to the study of a rarefied gas flow through a finite length conical pipe into vacuum. The problem is solved in the complete geometrical setup, which included not only the pipe, but also high- and low-pressure reservoirs. The analysis is based on the direct numerical solution of the Boltzmann kinetic equation with the S-model collision integral in three space dimensions. The method of the solution is based on the recent implicit total variation diminishing (TVD) method on unstructured spatial meshes. It is conservative with respect to the collision integral and work across all flow regimes. The results are provided for various ratios of the outlet and inlet diameters, pipe's lengths and Knudsen numbers. The computed flow rates are compared with the case of the circular pipe of constant radius as well as an approximate method for very long pipes. The influence of the pipe geometry on the flow field is also examined. The presented results can be used as a benchmark for calculations by other methods and codes. [Copyright &y& Elsevier]