Dimitris Valougeorgis

Rarefied gas flow through short tubes into vacuum

A rarefied gas flow into vacuum through a tube of finite length is investigated over the whole range of gas rarefaction by the direct simulation Monte Carlo method. The nonequilibrium effects at the inlet and outlet of the tube have been considered by including in the computational domain large volumes of the upstream and downstream reservoirs. Results for the dimensionless flow rate and for the flow field are presented for a wide range of the gas rarefaction and for various values of the length to radius ratio in the range from 0 to 10. The influence of the gas-surface interaction model, as well as the effect of the intermolecular potential model on the gas flow, is examined. A good agreement has been obtained between the present numerical results and the corresponding experimental ones available in the literature.A rarefied gas flow into vacuum through a tube of finite length is investigated over the whole range of gas rarefaction by the direct simulation Monte Carlo method. The nonequilibrium effects at the inlet and outlet of the tube have been considered by including in the computational domain large volumes of the upstream and downstream reservoirs. Results for the dimensionless flow rate and for the flow field are presented for a wide range of the gas rarefaction and for various values of the length to radius ratio in the range from 0 to 10. The influence of the gas-surface interaction model, as well as the effect of the intermolecular potential model on the gas flow, is examined. A good agreement has been obtained between the present numerical results and the corresponding experimental ones available in the literature.

Flow of gaseous mixtures through rectangular microchannels driven by pressure, temperature, and concentration gradients

The flow of binary gaseous mixtures through rectangular microchannels due to small pressure, temperature, and molar concentration gradients over the whole range of the Knudsen number is studied. The solution is based on a mesoscale approach, formally described by two coupled kinetic equations, subject to diffuse scattering boundary conditions. The model proposed by McCormack substitutes the complicated collision term and the resulting kinetic equations are solved by an accelerated version of the discrete velocity method. Typical results are presented for the flow rates and the heat fluxes of two different binary mixtures (Ne–Ar and He–Xe) with various molar concentrations, in two-dimensional microchannels of different aspect (height to width) ratios. The formulation is very efficient and can be used instead of the classical method of solving the Navier–Stokes equations with slip boundary conditions, which is restricted by the hydrodynamic regime. Moreover, the present formulation is a good alternative to the direct simulation Monte Carlo method, which often becomes computationally inefficient.

Computational and experimental study of gas flows through long channels of various cross sections in the whole range of the Knudsen number

A computational and experimental study has been performed for the investigation of fully developed rarefied gas flows through channels of circular, orthogonal, triangular, and trapezoidal cross sections. The theoretical-computational approach is based on the solution of the Bhatnagar-Gross-Krook kinetic equation subject to Maxwell diffuse-specular boundary conditions by the discrete velocity method. The experimental work has been performed at the vacuum facility “TRANSFLOW,” at Forschungszentrum Karlsruhe and it is based on measuring, for assigned flow rates, the corresponding pressure differences. The computed and measured mass flow rates and conductance are in all cases in very good agreement. In addition, in order to obtain some insight in the flow characteristics, the reference Knudsen, Reynolds, and Mach numbers characterizing the flow at each experimental run have been estimated. Also, the pressure distribution along the channel for several typical cases is presented. Both computational and experime...

The driven cavity flow over the whole range of the Knudsen number

The flow of a rarefied gas in a rectangular enclosure due to the motion of the upper wall is solved over the whole range of the Knudsen number. The formulation is based on the two–dimensional linearized Bhatnagar-Gross-Krook (BGK) kinetic equation with Maxwell diffuse-specular boundary conditions. The integro-differential equations are solved numerically implementing the discrete velocity method. The discontinuity at the boundaries between stationary and moving walls is treated accordingly. A detailed investigation of the rarefaction effects on the flow pattern and quantities is presented over the whole range of the Knudsen number and various aspect (height/width) ratios. Numerical results of flow characteristics, including the streamlines, the velocity profiles, the pressure and temperature contours, and the drag force of the moving wall, are presented for different aspect ratios and various degrees of gas rarefaction from the free molecular through the transition up to the continuum limit. On several oc...

Simulation of gas flow through tubes of finite length over the whole range of rarefaction for various pressure drop ratios

The rarefied gas flow through circular tubes of finite length has been investigated computationally by the direct simulation Monte Carlo method. The reduced flow rate and the flow field have been calculated as functions of the gas rarefaction, the length-to-radius ratio, and the pressure ratio along the tube. The gas rarefaction, which is inversely proportional to the Knudsen number, is varied from 0 to 2000, i.e., the free-molecular, transitional, and hydrodynamic regimes are embraced. A wide range of the length-to-radius ratio, namely, from 0 corresponding to the orifice flow up to 10 representing a sufficiently long tube, has been considered. Several values of the pressure ratio between 0 and 0.7 have been regarded. This pressure range covers both gas flow into vacuum and into a background gas. It has been found that the rarefaction parameter has the most significant effect on the flowfield characteristics and patterns, followed by the pressure ratio drop, while the length-to-radius ratio has a rather ...

Acceleration Schemes of the Discrete Velocity Method: Gaseous Flows in Rectangular Microchannels

The convergence rate of the discrete velocity method (DVM), which has been applied extensively in the area of rarefied gas dynamics, is studied via a Fourier stability analysis. The spectral radius of the continuum form of the iteration map is found to be equal to one, which justifies the slow convergence rate of the method. Next the efficiency of the DVM is improved by introducing various acceleration schemes. The new synthetic-type schemes speed up significantly the iterative convergence rate. The spectral radius of the acceleration schemes is also studied and the so-called H1 acceleration method is found to be the optimum one. Finally, the two-dimensional flow problem of a gas through a rectangular microchannel is solved using the new fast iterative DVM. The number of required iterations and the overall computational time are significantly reduced, providing experimental evidence of the analytic formulation. The whole approach is demonstrated using the BGK and S kinetic models.

Rarefied gas flow in a rectangular enclosure induced by non-isothermal walls

The flow of a rarefied gas in a rectangular enclosure due to the non-isothermal walls with no synergetic contributions from external force fields is investigated. The top and bottom walls are maintained at constant but different temperatures and along the lateral walls a linear temperature profile is assumed. Modeling is based on the direct numerical solution of the Shakhov kinetic equation and the Direct Simulation Monte Carlo (DSMC) method. Solving the problem both deterministically and stochastically allows a systematic comparison and verification of the results as well as the exploitation of the numerical advantages of each approach in the investigation of the involved flow and heat transfer phenomena. The thermally induced flow is simulated in terms of three dimensionless parameters characterizing the problem, namely, the reference Knudsen number, the temperature ratio of the bottom over the top plates, and the enclosure aspect ratio. Their effect on the flow configuration and bulk quantities is thoroughly examined. Along the side walls, the gas flows at small Knudsen numbers from cold-to-hot, while as the Knudsen number is increased the gas flows from hot-to-cold and the thermally induced flow configuration becomes more complex. These flow patterns with the hot-to-cold flow to be extended to the whole length of the non-isothermal side walls may exist even at small temperature differences and then, they are enhanced as the temperature difference between the top and bottom plates is increased. The cavity aspect ratio also influences this flow configuration and the hot-to-cold flow is becoming more dominant as the depth compared to the width of the cavity is increased. To further analyze the flow patterns a novel solution decomposition into ballistic and collision parts is introduced. This is achieved by accordingly modifying the indexing process of the typical DSMC algorithm. The contribution of each part of the solution is separately examined and a physical interpretation of the flow configuration, including the hot-to-cold flow close to the side walls, in the whole range of the Knudsen number is provided.

The friction factor of a rarefied gas flow in a circular tube

An expression for the estimation of the Poiseuille number for internal rarefied flows is developed. The derived formula is given in terms of dimensionless quantities, which are obtained by the solution of the flow based on kinetic theory. The formulation is applied to the fully developed flow of a gas in a circular tube, and tabulated results of the Poiseuille number are presented in the whole range of the Knudsen number and for various values of the accommodation coefficient. Also, in the slip regime, a closed-form expression for the Poiseuille number is derived and a brief discussion on the proper estimation of the viscous slip coefficient is provided.

A fast iterative model for discrete velocity calculations on triangular grids

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.

Application of the integro-moment method to steady-state two-dimensional rarefied gas flows subject to boundary induced discontinuities

The computational efficiency of the integro-moment method for solving steady-state two-dimensional rarefied gas flows is investigated. The two-dimensional boundary driven flow of a single gas in a cavity is used as a model problem, because the kinetic equations and the boundary conditions describing this flow contain most of the terms and features, which might appear in problems modeled by kinetic equations. Following a detailed quantitative comparison with the discrete velocity method, it is concluded that the integro-moment method may be considered as a alternative reliable and efficient computational scheme for solving rarefied (or non-equilibrium) flows in the whole range of the Knudsen number. Even more, it is shown that by implementing the integro-moment method the propagation of any discontinuities, which may exist at the boundaries, inside the computational domain and the production of an unphysical oscillatory behavior in the macroscopic quantities, are completely eliminated. The proposed integro-moment methodology is general and may be applied to any multidimensional non-equilibrium flow described by linear kinetic model equations.