Simulation of Rarefied Gas Flow in Microchannel Based on Vorticity-Stream Function Method

2007 ◽  
Author(s):  
Xueyong Wei ◽  
Mike C. L. Ward ◽  
Dejiang Lu ◽  
Zhuangde Jiang
Keyword(s):  
Stream Function ◽  
Function Method ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Taylor Series Expansion ◽  
Accommodation Coefficient ◽  
Parallel Plates ◽  
Slip Boundary ◽  
Tangential Momentum ◽  
New Formula

Vorticity-stream function method is successfully used to solve an incompressible gas flow in the parallel-plates micro-channel. A new formula in finite difference scheme is developed to describe the boundary vorticity based on the slip boundary theory and Taylor series expansion. Results show that the boundary vorticity are not only influenced by the Knudsen number (Kn) but also influenced by the tangential momentum accommodation coefficient (TMAC).

Rarefied gas flow between parallel plates

1969 ◽  
Vol 66 (1) ◽  
pp. 189-196 ◽  
Author(s):  
M. M. R. Williams
Keyword(s):  
Boundary Condition ◽  
Integral Equation ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Volumetric Flow Rate ◽  
Slip Boundary Condition ◽  
General Boundary Condition ◽  
Boltzmann Transport ◽  
Parallel Plates ◽  
Slip Boundary

AbstractThe flow of a rarefied gas between parallel plates has been studied via the linearized Boltzmann transport equation. Using a general boundary condition, which includes an arbitrary ratio of specular to diffuse reflection from the wall, we have derived an integral equation for the mass flow velocity. The integral equation is solved by using a replication property of the kernel and application of the method of Muskelishvili.The total volumetric flow rate is obtained and a slip boundary condition is deduced for use with the hydrodynamic equations.Certain aspects of the eigenvalue spectrum associated with the Boltzmann equation are discussed.

Poiseuille Flow and Thermal Transpiration of a Rarefied Gas Between Parallel Plates: Effect of Nonuniform Surface Properties of the Plates in the Transverse Direction

2015 ◽  
Vol 137 (10) ◽  
Author(s):  
Toshiyuki Doi
Keyword(s):  
Distribution Function ◽  
Flow Rate ◽  
Poiseuille Flow ◽  
Transverse Direction ◽  
Rarefied Gas ◽  
Mean Free Path ◽  
Accommodation Coefficient ◽  
Parallel Plates ◽  
Nonuniform Surface ◽  
The Mean

Poiseuille flow and thermal transpiration of a rarefied gas between parallel plates with nonuniform surface properties in the transverse direction are studied based on kinetic theory. We considered a simplified model in which one wall is a diffuse reflection boundary and the other wall is a Maxwell-type boundary on which the accommodation coefficient varies periodically and smoothly in the transverse direction. The spatially two-dimensional (2D) problem in the cross section is studied numerically based on the linearized Bhatnagar–Gross–Krook–Welander (BGKW) model of the Boltzmann equation. The flow behavior, i.e., the macroscopic flow velocity and the mass flow rate of the gas as well as the velocity distribution function, is studied over a wide range of the mean free path of the gas and the parameters of the distribution of the accommodation coefficient. The mass flow rate of the gas is approximated by a simple formula consisting of the data of the spatially one-dimensional (1D) problems. When the mean free path is large, the distribution function assumes a wavy variation in the molecular velocity space due to the effect of a nonuniform surface property of the plate.

Investigation of Wall Effect on Flow Characteristics in Supersonic Rarefied Gas Flow Past a Confined Square Cylinder Using the DSMC Method

2011 ◽  
Author(s):  
Mohamad M. Joneidipour ◽  
Reza Kamali
Keyword(s):  
Mach Number ◽  
Flow Field ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Blockage Ratio ◽  
Parallel Plates ◽  
Square Cylinder ◽  
Rarefied Gas Flow ◽  
Number Distribution ◽  
Mach Number Distribution

In the present study, the effect of wall in supersonic rarefied gas flow past a square cylinder is numerically studied. Therefore, a supersonic rarefied gas flow over a square cylinder is simulated first. Then, the simulations are repeated for a square cylinder confined between two parallel plates. In both cases, the Mach number distribution in the flow field of supersonic rarefied gas over the square cylinder is obtained using the direct simulation Monte Carlo method. Close inspection of contour lines of Mach number over the square cylinder shows that a discontinuity in the flow field occurs across the shock wave at the slip regime while there is no discontinuity at the transition flow regime. In the present paper, the effect of blockage ratio (defined as the distance between two parallel plates divided by the cylinder length) on the Mach number distribution in the flow field of supersonic rarefied gas over the square cylinder is also studied. Meanwhile, the obtained results from both mentioned cases are compared to each other. It is found that the deviation of two sets of data diminishes gradually as the blockage ratio increases.

scholarly journals A rarefied gas flow around a rotating sphere: diverging profiles of gradients of macroscopic quantities

2019 ◽  
Vol 862 ◽  
pp. 5-33 ◽  
Author(s):  
Satoshi Taguchi ◽  
Kazuyuki Saito ◽  
Shigeru Takata
Keyword(s):  
Gas Flow ◽  
Rarefied Gas ◽  
Velocity Distribution Function ◽  
Normal Derivative ◽  
Accommodation Coefficient ◽  
Jump Discontinuity ◽  
Rotating Sphere ◽  
Wide Range ◽  
Normal Distance ◽  
The Moment

The steady behaviour of a rarefied gas around a rotating sphere is studied numerically on the basis of the linearised ellipsoidal statistical model of the Boltzmann equation, also known as the ES model, and the Maxwell diffuse–specular boundary condition. It is demonstrated numerically that the normal derivative of the circumferential component of the flow velocity and that of the heat flux diverge on the boundary with a rate $s^{-1/2}$, where $s$ is the normal distance from the boundary. Further, it is demonstrated that the diverging term is proportional to the magnitude of the jump discontinuity of the velocity distribution function on the boundary, which originates from the mismatch of the incoming and outgoing data on the boundary. The moment of force exerted on the sphere is also obtained for a wide range of the Knudsen number and for various values of the accommodation coefficient.

scholarly journals Exact solutions for the axial pressure drop in isothermal channels with maxwell slip flow

2018 ◽  
Author(s):  
Alex Christian Hoffmann ◽  
Stamatina Karakitsiou ◽  
Bodil Holst
Keyword(s):  
Mass Flow ◽  
Gas Flow ◽  
Cylindrical Channel ◽  
Rectangular Channel ◽  
Slip Flow ◽  
Order Relation ◽  
Pressure Profile ◽  
Accommodation Coefficient ◽  
Parallel Plates ◽  
Axial Pressure

Expressions for the axial pressure profiles in a cylindrical channel and between parallel plates or a rectangular channel with large aspect ratio, with Maxwell slip gas flow are derived from first principles. The resulting expressions, which only involve the inlet and outlet pressures and the channel dimensions, will be useful in modelling or simulations of channel flows at Knudsen numbers in the range 0.001–0.1, such as in MEMS and NEMS. The expression for a cylindrical channel is validated by deriving from it an expression for the channel mass flow, which is shown to agree with a known expression for the mass flow through cylindrical channels with Maxwell slip flow. The expression for flow between parallel plates is found to agree with the zeroth order relation derived by Arkilic et al. using perturbation analysis. The effect of the accommodation coefficient on the pressure profile in a cylindrical channel is shown.

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