Steryios Naris

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...

Hybrid modeling of time-dependent rarefied gas expansion

The time evolution of the flow parameters in a system where gas is expanded from a high pressure chamber through a tube toward a low pressure chamber is investigated. During the process, the pressure in the two chambers is changing in the opposite direction, while the flow rate is reduced until the system reaches its equilibrium state. Rarefied conditions may be present. Based on the observation that the characteristic time in the chambers is several orders of magnitude larger than that in the tube, the evolution of the flow is modeled in a hybrid manner. At each time step, based on kinetic theory, a steady-state flow configuration is solved to estimate the amount of gas passing through the tube (micromodel) and then the pressure of the two vessels is updated by applying the mass conservation principle and the equation of state (macromodel). The pressure and the flow rate variation with respect to time are provided for several time-dependent configurations and the dependency of the results on the initial Knudsen number and pressure ratio as well as on the length of the tube is analyzed. The proposed methodology, which is applicable when the volume of the chambers is significantly larger than the volume of the tube, is valid in the whole range of the Knudsen number and computationally very efficient.The time evolution of the flow parameters in a system where gas is expanded from a high pressure chamber through a tube toward a low pressure chamber is investigated. During the process, the pressure in the two chambers is changing in the opposite direction, while the flow rate is reduced until the system reaches its equilibrium state. Rarefied conditions may be present. Based on the observation that the characteristic time in the chambers is several orders of magnitude larger than that in the tube, the evolution of the flow is modeled in a hybrid manner. At each time step, based on kinetic theory, a steady-state flow configuration is solved to estimate the amount of gas passing through the tube (micromodel) and then the pressure of the two vessels is updated by applying the mass conservation principle and the equation of state (macromodel). The pressure and the flow rate variation with respect to time are provided for several time-dependent configurations and the dependency of the results on the initial ...

Boundary-driven nonequilibrium gas flow in a grooved channel via kinetic theory

The nonequilibrium flow of a gas in a two-dimensional grooved channel, due to the motion of the wall of the channel, is investigated based on kinetic theory. The presence of the rectangular grooves that are placed periodically on the stationary wall results in a two-dimensional flow pattern. The problem is modeled by the linearized Bhatnagar-Gross-Krook (BGK) and S-model kinetic equations, which are solved for the corresponding perturbed distribution functions by the discrete velocity method. Maxwell diffuse type reflecting boundary conditions are used to model the gas-surface interaction, while periodic boundary conditions are imposed at the inlet and outlet of the channel. The computed macroscopic quantities of practical interest include velocity profiles, contours of pressure, density, and temperature, as well as the flow rate and the heat flux through the channel and the drag coefficient along the moving boundary. The results are valid in the whole range of the Knudsen number, from the free molecular ...

Rarefied gas mixture flow between plates of arbitrary length due to small pressure difference

The linearized flow of a binary gas mixture between two parallel plates of any length driven by a small pressure difference is numerically solved based on the McCormack kinetic model. In this case the flow is not fully developed and the simulated flow field includes, in addition to the channel, efficiently large upstream and downstream regions significantly increasing the required computational effort. In the present work results are provided for one gas mixture, namely He-Ne with a specific concentration of 0.5 in a wide range of gas rarefaction. The ratio of the length over the height of the channel is taken to be equal to 0, 1 and 5 corresponding to flow through channels of very short (slit), short and moderate lengths respectively. Results are provided for the two kinetic coefficients related to Poiseuille and barodiffusion flow rates and the velocity profiles of each species. The effect of the length to height ratio and of the gas rarefaction on the flow quantities is investigated deducing that as the ratio in increased the separation phenomenon becomes more dominant, while a Knudsen minimum is observed at the ratio equal to 5.

Design and optimization of a Holweck pump via linear kinetic theory

The Holweck pump is widely used in the vacuum pumping industry. It can be a self standing apparatus or it can be part of a more advanced pumping system. It is composed by an inner rotating cylinder (rotor) and an outer stationary cylinder (stator). One of them, has spiral guided grooves resulting to a gas motion from the high towards the low vacuum port. Vacuum pumps may be simulated by the DSMC method but due to the involved high computational cost in many cases manufactures commonly resort to empirical formulas and experimental data. Recently a computationally efficient simulation of the Holweck pump via linear kinetic theory has been proposed by Sharipov et al [1]. Neglecting curvature and end effects the gas flow configuration through the helicoidal channels is decomposed into four basic flows. They correspond to pressure and boundary driven flows through a grooved channel and through a long channel with a T shape cross section. Although the formulation and the methodology are explained in detail, results are very limited and more important they are presented in a normalized way which does not provide the needed information about the pump performance in terms of the involved geometrical and flow parameters. In the present work the four basic flows are solved numerically based on the linearized BGK model equation subjected to diffuse boundary conditions. The results obtained are combined in order to create a database of the flow characteristics for a large spectrum of the rarefaction parameter and various geometrical configurations. Based on this database the performance characteristics which are critical in the design of the Holweck pump are computed and the design parameters such as the angle of the pump and the rotational speed, are optimized. This modeling may be extended to other vacuum pumps.