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.

Mass Flow Rate Measurements Through Metallic Microtubes in the Slip and Transition Regimes

2015 ◽  
Author(s):  
Ernane Silva ◽  
Cesar J. Deschamps ◽  
Marcos Rojas-Cárdenas
Keyword(s):  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Rarefied Gas ◽  
Mean Free Path ◽  
Accommodation Coefficient ◽  
Transitional Flow ◽  
Gas Flows ◽  
Slip Regime ◽  
Non Equilibrium

The exchange of momentum and energy in gas flows through microchannels is significantly influenced by the gas-surface interaction. At this scale often the gas is rarefied and therefore non-equilibrium effects in the fluid flow can arise in a layer which extends for a distance equivalent to the mean free path from the walls. Typical examples of non-equilibrium phenomena for rarefied gas flows are slip at the wall, thermal transpiration and temperature jump at the wall. The aim of the present study is to experimentally investigate the non-equilibrium effects present in an isothermal pressure induced flow for a large range of rarefaction conditions. The isothermal slip at the wall is usually characterized by the tangential momentum accommodation coefficient (TMAC). This coefficient depends on the molecular nature of the gas and on the physical characteristics of the surface, such as material and roughness. In particular this paper explores the influence of the surface material on the TMAC through measurements of the mass flow rate in capillaries for the special case of nitrogen. Commercially available microtubes of three different metallic materials — stainless steel, copper, and brass — were considered in the analysis. Measurements were performed with a dynamic measurement technique based on the constant volume method and comprehend the transitional flow regime and most part of the slip regime. Theoretical results obtained from the solution of the Boltzmann equation via the BGK kinetic model, which is a simplified approximation for the collisional term, were compared to the experimental results.

scholarly journals Torque on a Rotating Ellipsoid in a Rarefied Gas

1974 ◽  
Vol 29 (12) ◽  
pp. 1717-1722 ◽  
Author(s):  
J. Halbritter
Keyword(s):  
Rarefied Gas ◽  
Specular Reflection ◽  
Mean Free Path ◽  
Accommodation Coefficient ◽  
Ellipsoid Of Revolution ◽  
Ellipsoidal Surface ◽  
The Mean ◽  
The Impact ◽  
Arbitrary Axis ◽  
Monatomic Gas

A particle, shaped as an ellipsoid of revolution and rotating about an arbitrary axis, experiences a torque in a rarefied monatomic gas because of the impact with the gas atoms. This torque is calculated for the case where the linear dimensions of the ellipsoid are small compared with the mean free path of the gas. The interaction of the gas atoms with the ellipsoidal surface is taken into account by means of the boundary condition for the distribution function in terms of an accommodation coefficient (diffuse and specular reflection). The torque is considered for prolate and oblate ellipsoids. The formulae obtained are of interest in the theory of the Brownian motion of a rotating particle in a rarefied gas.

An Investigation on Micro Slip Flows in Micro Channels

2010 ◽  
Author(s):  
Gh. Reza Salehi ◽  
Masoud JalaliBidgoli ◽  
Saeed ZeinaliDanaloo ◽  
Kazem HasanZadeh
Keyword(s):  
Flow Rate ◽  
Pressure Ratio ◽  
Slip Flow ◽  
Accommodation Coefficient ◽  
Flow Rate Ratio ◽  
Numerical Representation ◽  
Micro Channel ◽  
Parallel Plates ◽  
Dimensionless Numbers ◽  
Micro Channels

In this paper, distributions of velocity and flow rate of micro channels are studied. Moreover, the parameters which influence them were also discussed, as well as their effects and relevant curves. In the Analytical study, the governing equation in specific micro flows is obtained. This equation is specifically investigated for slip flow in two micro parallel plates (micro channel).At the next step numerical representation shows the influence of the related parameters in micro channel flow such as Knudsen number, thermal -accommodation coefficient, mass flow rate ratio and pressure ratio (outlet to inlet), Tangential Momentum Accommodation Coefficient with relative curves, and flow rate distribution in slippery state to no slip state has been compared as the another part of this solution. Finally, the results of investigating parameters and dimensionless numbers in micro channels are reviewed.

On Turbulent Flow Between Parallel Plates

1953 ◽  
Vol 20 (1) ◽  
pp. 109-114
Author(s):  
S. I. Pai
Keyword(s):  
Turbulent Flow ◽  
Velocity Distribution ◽  
Poiseuille Flow ◽  
The Other ◽  
Turbulent Velocity ◽  
Parallel Plates ◽  
Mean Velocity ◽  
Reynolds Equations ◽  
Mean Pressure ◽  
The Mean

Abstract The Reynolds equations of motion of turbulent flow of incompressible fluid have been studied for turbulent flow between parallel plates. The number of these equations is finally reduced to two. One of these consists of mean velocity and correlation between transverse and longitudinal turbulent-velocity fluctuations u 1 ′ u 2 ′ ¯ only. The other consists of the mean pressure and transverse turbulent-velocity intensity. Some conclusions about the mean pressure distribution and turbulent fluctuations are drawn. These equations are applied to two special cases: One is Poiseuille flow in which both plates are at rest and the other is Couette flow in which one plate is at rest and the other is moving with constant velocity. The mean velocity distribution and the correlation u 1 ′ u 2 ′ ¯ can be expressed in a form of polynomial of the co-ordinate in the direction perpendicular to the plates, with the ratio of shearing stress on the plate to that of the corresponding laminar flow of the same maximum velocity as a parameter. These expressions hold true all the way across the plates, i.e., both the turbulent region and viscous layer including the laminar sublayer. These expressions for Poiseuille flow have been checked with experimental data of Laufer fairly well. It also shows that the logarithmic mean velocity distribution is not a rigorous solution of Reynolds equations.

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.

Solution with Third-order Accuracy for the Electron Distribution Function in Weakly Ionized Gases (or in Intrinsic Semiconductors): Application to the Drift Velocity

1981 ◽  
Vol 34 (4) ◽  
pp. 361 ◽  
Author(s):  
G Cavalleri
Keyword(s):  
Distribution Function ◽  
Legendre Polynomials ◽  
Taylor Expansion ◽  
Electron Distribution ◽  
Electron Distribution Function ◽  
Mean Free Path ◽  
Third Order ◽  
Order Accuracy ◽  
Weakly Ionized ◽  
The Mean

The first four components 10, I" 12 and 13 of the expansion in Legendre polynomials of the electron distribution function I are shown to be of order t:D, et, e2 and e3 respectively, with e = (m/M)'/2 where m and M are the masses of the electron and molecule respectively. This allows the solution of the so-called P3 approximation to the Boltzmann equation applied to a weakly ionized gas (or to an intrinsic semiconductor) in steady-state and uniform conditions and for dominant elastic collisions. However, nonphysical divergences appear in 10 and in the drift velocity W. This can be understood by the equivalence of the Boltzmann-Legendre formulation and the mean free path formulation in which a Taylor expansion is performed around the 'origin', i.e. for a -+ 0, where a = eE/m is the acceleration due to an external electric field E. Indeed, one sees that the expansion under the integral sign (integrals appear in the evaluation of transport quantities) leads to divergent integrals if the expansion is around a = O. Fortunately, it is easy to perform a Taylor expansion around a oft 0 in the mean free path formulation and then to find the corresponding expansion in Legendre polynomials outside the origin. In this way, explicit convergent expressions are found for 10, I" 12, 13 and W, with third-order accuracy in e = (m/M)'/2. This is better than the best preceding expression, that by Davydov-Chapman-Cowling, which has first-order accuracy only (it is the solution of the P, approximation to the Boltzmann equation).

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