Derivation of a Closed Form Expression for Estimating the Reduced Flow Rate for Pressure Driven Rarefied Gas Flow Through Circular Nano/Micro Pores

In this paper, a new model to predict the gas flow rate through short tubes under rarefied condition based on the sigmoidal bahaviour of gas reduced flow rate (W) versus the rarefaction parameter (d) under rarefied condition was developed. The data produced by Varoutis et al. via Direct Simulation Monte Carlo (DSMC) method were utilised to obtain the model coefficients as functions of tube length to radius (w) and pressure ratio (Pr). Then, the model was tested against the published experimental data.There was a high degree of agreement between the model predictions and the experimental data. Moreover, the new model was capable to predict the reduced flow rate of rarefied systems, not only at free molecular region and hydrodynamic region, but also at transition region, hence covering all the Knudsen number domain within the utilised data. Therefore, the proposed model was capable to make predictions as well as meet all the criteria of the rarefied gas flow within the following conditions: 0<Pr<0.9, 0.01<d<1000 and 0.0<w<20. Thus, the proposed model provides a useful tool to make a valid prediction of the rarefied gas flow behavior in a wide range of gas transport regime.

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Rarefied gas flow rate in poiseuille flow through a circular capillary

Fluid Dynamics ◽

10.1134/s0015462815050130 ◽

2015 ◽

Vol 50 (5) ◽

pp. 711-720

Author(s):

V. V. Zhvick

Keyword(s):

Flow Rate ◽

Poiseuille Flow ◽

Gas Flow ◽

Rarefied Gas ◽

Gas Flow Rate ◽

Rarefied Gas Flow ◽

Flow Through ◽

Circular Capillary

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Rarefied gas flow around a sharp edge induced by a temperature field

Journal of Fluid Mechanics ◽

10.1017/jfm.2011.536 ◽

2012 ◽

Vol 694 ◽

pp. 191-224 ◽

Cited By ~ 26

Author(s):

Satoshi Taguchi ◽

Kazuo Aoki

Keyword(s):

Knudsen Number ◽

Gas Flow ◽

Rarefied Gas ◽

Structural Similarity ◽

Rarefied Gas Flow ◽

Bgk Model ◽

Thermally Induced ◽

Wide Range ◽

Flow Features ◽

Limiting Behaviour

AbstractA rarefied gas flow thermally induced around a heated (or cooled) flat plate, contained in a vessel, is considered in two different situations: (i) both sides of the plate are simultaneously and uniformly heated (or cooled); and (ii) only one side of the plate is uniformly heated. The former is known as the thermal edge flow and the latter, typically observed in the Crookes radiometer, may be called the radiometric flow. The steady behaviour of the gas induced in the container is investigated on the basis of the Bhatnagar–Gross–Krook (BGK) model of the Boltzmann equation and the diffuse reflection boundary condition by means of an accurate finite-difference method. The flow features are clarified for a wide range of the Knudsen number, with a particular emphasis placed on the structural similarity between the two flows. The limiting behaviour of the flow as the Knudsen number tends to zero (and thus the system approaches the continuum limit) is investigated for both flows. The detailed structure of the normal stress on the plate as well as the cause of the radiometric force (the force acting on the plate from the hotter to the colder side) is also clarified for the present infinitely thin plate.

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One-way flow over uniformly heated U-shaped bodies driven by thermal edge effects

10.21203/rs.3.rs-970317/v1 ◽

2021 ◽

Author(s):

Satoshi Taguchi ◽

Tetsuro Tsuji

Keyword(s):

Mass Flow Rate ◽

Mass Flow ◽

Flow Rate ◽

Gas Flow ◽

Microelectromechanical Systems ◽

Rarefied Gas ◽

Shaped Body ◽

Knudsen Numbers ◽

Wide Range ◽

Edge Flow

Abstract The thermal edge flow is a gas flow typically induced near a sharp edge (or a tip) of a uniformly heated flat plate. This flow has potential applicability as a nonmechanical flow controller in microelectromechanical systems (MEMS). However, it has a shortcoming: the thermal edge flows from each edge cancel out, resulting in no net flow. In this study, to circumvent this difficulty, the use of a U-shaped body is proposed and is examined numerically. More specifically, a rarefied gas flow over an array of U-shaped bodies, periodically arranged in a straight channel, is investigated using the direct simulation Monte-Carlo (DSMC) method. The U-shaped bodies are kept at a uniform temperature different from that of the channel. Two types of U-shaped bodies are considered, namely, a square-U shape and a round-U shape. It is demonstrated that a steady one-way flow is induced in the channel for both types. The mass flow rate is obtained for a wide range of the Knudsen numbers, i.e., the ratio of the molecular mean free path to the characteristic size of the U-shape body. For the square-U type, the direction of the overall mass flow is in the same direction for the entire range of the Knudsen numbers investigated. For the round-U type, the direction of the total mass flux is reversed when the Knudsen number is moderate or larger. This reversal of the mass flow rate is attributed to a kind of thermal edge flow induced over the curved part of the round-U-shaped body, which overwhelms the thermal edge flow induced near the tip. The force acting on each of the bodies is also investigated.

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