Rarefied gas flow of binary mixtures through long channels with triangular and trapezoidal cross sections

Szalmás, Lajos; Valougeorgis, Dimitris

doi:10.1007/s10404-010-0564-9

Cited by 30 publications

(20 citation statements)

References 35 publications

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“…It is emphasized, that although the concentration of the mixture at the two reservoirs is the same, a variation of the mixture concentration along the channel may appear due to the fact that the particles of the two species are traveling with different molecular speeds. This phenomenon, known as separation effect, has been discussed in the past by several authors Takata et al 2007;Szalmas and Valougeorgis 2010). It is also noted that during the flow process the concentration of the mixture in the reservoirs is considered as constant, since the number of gas molecules flowing through the channel is negligible compared to the gas molecules in the reservoirs.…”

Section: Definition Of the Problemmentioning

confidence: 96%

Comparative study between computational and experimental results for binary rarefied gas flows through long microchannels

Szalmás

Pitakarnnop

Geoffroy

et al. 2010

Microfluid Nanofluid

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A comparative study between computational and experimental results for pressure-driven binary gas flows through long microchannels is performed. The theoretical formulation is based on the McCormack kinetic model and the computational results are valid in the whole range of the Knudsen number. Diffusion effects are taken into consideration. The experimental work is based on the Constant Volume Method, and the results are in the slip and transition regime. Using both approaches, the molar flow rates of the He-Ar gas mixture flowing through a rectangular microchannel are estimated for a wide range of pressure drops between the upstream and downstream reservoirs and several mixture concentrations varying from pure He to pure Ar. In all cases, a very good agreement is found, within the margins of the introduced modeling and measurement uncertainties. In addition, computational results for the pressure and concentration distributions along the channel are provided. As far as the authors are aware of, this is the first detailed and complete comparative study between theory and experiment for gaseous flows through long microchannels in the case of binary mixtures.

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Section: Definition Of the Problemmentioning

confidence: 96%

Comparative study between computational and experimental results for binary rarefied gas flows through long microchannels

Szalmás

Pitakarnnop

Geoffroy

et al. 2010

Microfluid Nanofluid

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“…In the accelerated method, an additional moment equation is derived and solved parallel with the kinetic equation. The accelerated method for the BGK linearized kinetic equation is welldocumented in the literature [5,8,12,14]; hence, its description is omitted here for brevity. In the numerical solution, the molecular velocity and spatial spaces are discretized.…”

Section: Second Eq (5) Is Integrated To Yield _mentioning

confidence: 99%

“…For this reason, Eq. (6) is solved by using a variant of the accelerated discrete velocity method [5,8,12,14]. It is known that this method is superior to the standard kinetic solver at very small Knudsen numbers.…”

Section: Second Eq (5) Is Integrated To Yield _mentioning

confidence: 99%

Analysis of the diodic effect of flows of rarefied gases in tapered rectangular channels

Szalmás

Veltzke

Thöming

2015

Vacuum

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“…The virtue of Eq. (43) is that the resulting diffusion equations will be very simple (compared to those in Refs [28,32]. for the McCormack kinetic model), but without any loss of efficiency of the SIS.…”

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confidence: 99%

A fast iterative scheme for the linearized Boltzmann equation

Zhang

Liu

et al. 2017

Journal of Computational Physics

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Iterative schemes to find steady-state solutions to the Boltzmann equation is efficient for highly rarefied gas flows, but can be very slow to converge in the near-continuum flow regime. In this paper, a synthetic iterative scheme is developed to speed up the solution of the linearized Boltzmann equation by penalizing the collision operator $L$ into the form $L=(L+N\delta{h})-N\delta{h}$, where $\delta$ is the gas rarefaction parameter, $h$ is the velocity distribution function, and $N$ is a tuning parameter controlling the convergence rate. The velocity distribution function is first solved by the conventional iterative scheme, then it is corrected such that the macroscopic flow velocity is governed by a diffusion-type equation that is asymptotic-preserving into the Navier-Stokes limit. The efficiency of this new scheme is assessed by calculating the eigenvalue of the iteration, as well as solving for Poiseuille and thermal transpiration flows. We find that the fastest convergence of our synthetic scheme for the linearized Boltzmann equation is achieved when $N\delta$ is close to the average collision frequency. The synthetic iterative scheme is significantly faster than the conventional iterative scheme in both the transition and the near-continuum gas flow regimes. Moreover, due to its asymptotic-preserving properties, the synthetic iterative scheme does not need high spatial resolution in the near-continuum flow regime, which makes it even faster than the conventional iterative scheme. Using this synthetic scheme, with the fast spectral approximation of the linearized Boltzmann collision operator, Poiseuille and thermal transpiration flows between two parallel plates, through channels of circular/rectangular cross sections and various porous media are calculated over the whole range of gas rarefaction. Finally, the flow of a Ne-Ar gas mixture is solved based on the linearized Boltzmann equation with the Lennard-Jones intermolecular potential for the first time, and the difference between these results and those using the hard-sphere potential is discussed

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Rarefied gas flow of binary mixtures through long channels with triangular and trapezoidal cross sections

Cited by 30 publications

References 35 publications

Comparative study between computational and experimental results for binary rarefied gas flows through long microchannels

Comparative study between computational and experimental results for binary rarefied gas flows through long microchannels

Analysis of the diodic effect of flows of rarefied gases in tapered rectangular channels

A fast iterative scheme for the linearized Boltzmann equation

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