Nonisothermal motion of a rarefied gas in a short planar channel over a wide range of knudsen number

1990 ◽  
Vol 59 (1) ◽  
pp. 869-875 ◽  
Author(s):  
F. M. Sharipov ◽  
V. D. Seleznev ◽  
A. M. Makarov
Keyword(s):  
Knudsen Number ◽  
Rarefied Gas ◽  
Planar Channel ◽  
Wide Range ◽  
Nonisothermal Motion

Plane Thermal Transpiration of a Rarefied Gas Between Two Walls of Maxwell-Type Boundaries With Different Accommodation Coefficients

2014 ◽  
Vol 136 (8) ◽  
Author(s):  
Toshiyuki Doi
Keyword(s):  
Boltzmann Equation ◽  
Mass Flow Rate ◽  
Knudsen Number ◽  
Mass Flow ◽  
Flow Rate ◽  
Poiseuille Flow ◽  
Rarefied Gas ◽  
Thermal Transpiration ◽  
Wide Range ◽  
Accommodation Coefficients

Plane thermal transpiration of a rarefied gas between two walls of Maxwell-type boundaries with different accommodation coefficients is studied based on the linearized Boltzmann equation for a hard-sphere molecular gas. The Boltzmann equation is solved numerically using a finite difference method, in which the collision integral is evaluated by the numerical kernel method. The detailed numerical data, including the mass and heat flow rates of the gas, are provided over a wide range of the Knudsen number and the entire range of the accommodation coefficients. Unlike in the plane Poiseuille flow, the dependence of the mass flow rate on the accommodation coefficients shows different characteristics depending on the Knudsen number. When the Knudsen number is relatively large, the mass flow rate of the gas increases monotonically with the decrease in either of the accommodation coefficients like in Poiseuille flow. When the Knudsen number is small, in contrast, the mass flow rate does not vary monotonically but exhibits a minimum with the decrease in either of the accommodation coefficients. The mechanism of this phenomenon is discussed based on the flow field of the gas.

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

2012 ◽  
Vol 694 ◽  
pp. 191-224 ◽  
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.

scholarly journals Inversion of the transverse force on a spinning sphere moving in a rarefied gas

2021 ◽  
Vol 933 ◽  
Author(s):  
Satoshi Taguchi ◽  
Tetsuro Tsuji
Keyword(s):  
Boltzmann Equation ◽  
Knudsen Number ◽  
Rarefied Gas ◽  
Mean Free Path ◽  
Transverse Force ◽  
Surface Velocity ◽  
Translational Velocity ◽  
The Boltzmann Equation ◽  
Wide Range ◽  
The Continuum

The flow around a spinning sphere moving in a rarefied gas is considered in the following situation: (i) the translational velocity of the sphere is small (i.e. the Mach number is small); (ii) the Knudsen number, the ratio of the molecular mean free path to the sphere radius, is of the order of unity (the case with small Knudsen numbers is also discussed); and (iii) the ratio between the equatorial surface velocity and the translational velocity of the sphere is of the order of unity. The behaviour of the gas, particularly the transverse force acting on the sphere, is investigated through an asymptotic analysis of the Boltzmann equation for small Mach numbers. It is shown that the transverse force is expressed as $\boldsymbol{F}_L = {\rm \pi}\rho a^3 (\boldsymbol{\varOmega} \times \boldsymbol{v}) \bar{h}_L$ , where $\rho$ is the density of the surrounding gas, a is the radius of the sphere, $\boldsymbol {\varOmega }$ is its angular velocity, $\boldsymbol {v}$ is its velocity and $\bar {h}_L$ is a numerical factor that depends on the Knudsen number. Then, $\bar {h}_L$ is obtained numerically based on the Bhatnagar–Gross–Krook model of the Boltzmann equation for a wide range of Knudsen number. It is shown that $\bar {h}_L$ varies with the Knudsen number monotonically from 1 (the continuum limit) to $-\tfrac {2}{3}$ (the free molecular limit), vanishing at an intermediate Knudsen number. The present analysis is intended to clarify the transition of the transverse force, which is previously known to have different signs in the continuum and the free molecular limits.

Rarefied gas motion in a short planar channel over the entire knudsen number range

1990 ◽  
Vol 30 (5) ◽  
pp. 713-717 ◽  
Author(s):  
V. D. Akin'shin ◽  
A. M. Makarov ◽  
V. D. Seleznev ◽  
F. M. Sharipov
Keyword(s):  
Knudsen Number ◽  
Rarefied Gas ◽  
Planar Channel ◽  
Number Range

Study of Gas Flow in Micronozzles Using an Unstructured DSMC Method

2009 ◽  
Author(s):  
Ehsan Roohi ◽  
Masoud Darbandi ◽  
Vahid Mirjalili
Keyword(s):  
Boundary Layer ◽  
Knudsen Number ◽  
Gas Flow ◽  
Subsonic Flow ◽  
Flow Behavior ◽  
Boundary Layer Separation ◽  
Back Pressure ◽  
Viscous Force ◽  
Dsmc Method ◽  
Wide Range

The current research uses an unstructured direct simulation Monte Carlo (DSMC) method to numerically investigate supersonic and subsonic flow behavior in micro convergent–divergent nozzle over a wide range of rarefied regimes. The current unstructured DSMC solver has been suitably modified via using uniform distribution of particles, employing proper subcell geometry, and benefiting from an advanced molecular tracking algorithm. Using this solver, we study the effects of back pressure, gas/surface interactions (diffuse/specular reflections), and Knudsen number, on the flow field in micronozzles. We show that high viscous force manifesting in boundary layers prevents supersonic flow formation in the divergent section of nozzles as soon as the Knudsen number increases above a moderate magnitude. In order to accurately simulate subsonic flow at the nozzle outlet, it is necessary to add a buffer zone to the end of nozzle. If we apply the back pressure at the outlet, boundary layer separation is observed and a region of backward flow appears inside the boundary layer while the core region of inviscid flow experiences multiple shock-expansion waves. We also show that the wall boundary layer prevents forming shocks in the divergent part. Alternatively, Mach cores appear at the nozzle center followed by bow shocks and an expansion region.

The aerodynamic resistance to a rotating sphere in the transition régime between free molecule and continuum creep flow

1964 ◽  
Vol 279 (1376) ◽  
pp. 39-49 ◽  
Keyword(s):  
Rarefied Gas ◽  
Aerodynamic Drag ◽  
Aerodynamic Resistance ◽  
Reynolds Numbers ◽  
Approximate Theory ◽  
Drag Torque ◽  
Free Molecule ◽  
Steel Sphere ◽  
Creep Flow ◽  
Wide Range

An experimental and theoretical study has been made of the aerodynamic drag torque on a sphere rotating in a rarefied gas. The drag torque on a magnetically suspended polished steel sphere rotating in air was measured over a wide range of Knudsen numbers from continuum to free molecule flow and for several different Mach numbers up to ca . 1. The drag under free molecule conditions was found to be consistent with the assumption of perfectly diffuse reflexion of molecules at the surface of the rotor. An approximate theory is derived which is analogous to Millikan’s solution to the problem of plane Couette flow and is valid for low Mach and Reynolds numbers. Theory and experiment are found to agree to within 10 % in the range investigated, for Reynolds numbers less than ca . 20.

Modeling of Flow Characteristic and Heat Transfer for Micro Couette Flow

2001 ◽  
Author(s):  
Hong Xue ◽  
Ling Xie ◽  
S. K. Chou
Keyword(s):  
Heat Transfer ◽  
Couette Flow ◽  
Flow Characteristic ◽  
Rarefied Gas ◽  
Characteristic Length ◽  
Velocity Slip ◽  
Flow And Heat Transfer ◽  
Wide Range ◽  
Perturbation Velocity ◽  
Rarefaction Effects

Abstract Gaseous flow encountered in micro/nano electromechanical systems experiences change in Kn number across a wide range of flow regime due to variation in characteristic length in the system and significant compressibility of the rarefied gas. In this study, we attempt to develop a general, physics-based model to predict the flow and heat transfer in the slip and transition regimes. Such an extension is constructed on the fact that Chapman-Enskog’s approximation of the Boltzmann equation can be revised using a function of Kn number as a perturbation. Velocity slip and temperature jump at the solid boundaries are modified accordingly. Rarefaction effects on dynamic viscosity and thermal conductivity are considered. As a first step to evaluate the model, it is applied to the simplest shear-driven flow, micro Couette flow. Compared with the results of DSMC, satisfactory agreement has been achieved in a wide range of Kn and Ma numbers.

On the Rarefied Gas Flow in Pipes

2005 ◽  
Author(s):  
Vladan D. Djordjevic
Keyword(s):  
Knudsen Number ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Natural Extension ◽  
Slip Boundary Condition ◽  
Molecular Flow ◽  
Rarefied Gas Flow ◽  
Number Range ◽  
Average Value ◽  
Linearized Boltzmann Equation

Rarefied gas flow in a pipe is treated in the paper by modeling the slip boundary condition by means of a fractional derivative. At that the order of the derivative is conveniently chosen to be a function of the average value of the Knudsen number so that the entire Knudsen number range, from continuum flow to free molecular flow, is covered. Very good agreement with the solutions of linearized Boltzmann equation is achieved. The paper represents a natural extension of the work of the same author on the rarefied micro channel flow, published earlier.

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