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 Non-equilibrium dynamics of dense gas under tight confinement

2016 ◽  
Vol 794 ◽  
pp. 252-266 ◽  
Author(s):  
Lei Wu ◽  
Haihu Liu ◽  
Jason M. Reese ◽  
Yonghao Zhang
Keyword(s):  
Boltzmann Equation ◽  
Flow Regime ◽  
Mass Flow Rate ◽  
Knudsen Number ◽  
Mass Flow ◽  
Flow Rate ◽  
Transitional Flow ◽  
Molecular Flow ◽  
Parallel Plates ◽  
The Boltzmann Equation

The force-driven Poiseuille flow of dense gases between two parallel plates is investigated through the numerical solution of the generalized Enskog equation for two-dimensional hard discs. We focus on the competing effects of the mean free path ${\it\lambda}$, the channel width $L$ and the disc diameter ${\it\sigma}$. For elastic collisions between hard discs, the normalized mass flow rate in the hydrodynamic limit increases with $L/{\it\sigma}$ for a fixed Knudsen number (defined as $Kn={\it\lambda}/L$), but is always smaller than that predicted by the Boltzmann equation. Also, for a fixed $L/{\it\sigma}$, the mass flow rate in the hydrodynamic flow regime is not a monotonically decreasing function of $Kn$ but has a maximum when the solid fraction is approximately 0.3. Under ultra-tight confinement, the famous Knudsen minimum disappears, and the mass flow rate increases with $Kn$, and is larger than that predicted by the Boltzmann equation in the free-molecular flow regime; for a fixed $Kn$, the smaller $L/{\it\sigma}$ is, the larger the mass flow rate. In the transitional flow regime, however, the variation of the mass flow rate with $L/{\it\sigma}$ is not monotonic for a fixed $Kn$: the minimum mass flow rate occurs at $L/{\it\sigma}\approx 2{-}3$. For inelastic collisions, the energy dissipation between the hard discs always enhances the mass flow rate. Anomalous slip velocity is also found, which decreases with increasing Knudsen number. The mechanism for these exotic behaviours is analysed.

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

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.

scholarly journals Experimental Investigation and Modeling of Inertance Tubes

2005 ◽  
Vol 127 (5) ◽  
pp. 1029-1037 ◽  
Author(s):  
L. O. Schunk ◽  
G. F. Nellis ◽  
J. M. Pfotenhauer
Keyword(s):  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Acoustic Power ◽  
Operating Conditions ◽  
Thermodynamic Efficiency ◽  
Pulse Tube ◽  
Design Charts ◽  
Wide Range ◽  
Pulse Tube Refrigerators

Growing interest in larger scale pulse tubes has focused attention on optimizing their thermodynamic efficiency. For Stirling-type pulse tubes, the performance is governed by the phase difference between the pressure and mass flow, a characteristic that can be conveniently adjusted through the use of inertance tubes. In this paper we present a model in which the inertance tube is divided into a large number of increments; each increment is represented by a resistance, compliance, and inertance. This model can include local variations along the inertance tube and is capable of predicting pressure, mass flow rate, and the phase between these quantities at any location in the inertance tube as well as in the attached reservoir. The model is verified through careful comparison with those quantities that can be easily and reliably measured; these include the pressure variations along the length of the inertance tube and the mass flow rate into the reservoir. These experimental quantities are shown to be in good agreement with the model’s predictions over a wide range of operating conditions. Design charts are subsequently generated using the model and are presented for various operating conditions in order to facilitate the design of inertance tubes for pulse tube refrigerators. These design charts enable the pulse tube designer to select an inertance tube geometry that achieves a desired phase shift for a given level of acoustic power.

Mass Flow Rate Measurements in Microchannels

2009 ◽  
Author(s):  
Irina A. Graur ◽  
Pierre Perrier ◽  
J. G. Me´olans
Keyword(s):  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Accommodation Coefficient ◽  
Steady Flows ◽  
Molecular Weights ◽  
Slip Boundary ◽  
Accommodation Coefficients ◽  
Accommodation Process ◽  
Wall Interaction

Mass flow rate measurements in a single silicon micro channel were carried out for various gases in isothermal steady flows. The results obtained from hydrodynamic to near free molecular regime by using a powerful experimental platform, allowed us to deduce interesting information, notably about the reflection/accommodation process at the wall. In the 0 – 0.3 Knudsen range, a continuum analytic approach was derived from NS equations, associated to first or second order slip boundary conditions. Identifying the experimental mass flow rate curves to the theoretical ones the tangential momentum accommodation coefficient (TMAC) of various gases was extracted. Over all the Knudsen range [0 – 50] the experimental results were compared with theoretical values calculated from the kinetic approaches: using variable accommodation coefficient values as fitting parameter, the theoretical curves were fitted to the experimental ones. Whatever the Knudsen range and whatever the theoretical approach, the TMAC values are found decreasing when the molecular weights of the gas increase (as long as the different gases are compared using the same approach). Moreover, the values of the various accommodation coefficients are rather close one to other but sufficiently smaller than unity to conclude that the full accommodation modelling is not satisfactory to describe the gas/wall interaction.

Assessment of Dimensionless Correlations for Prediction of Refrigerant Mass Flow Rate Through Capillary Tubes — A Review

2017 ◽  
Vol 25 (04) ◽  
pp. 1730004 ◽  
Author(s):  
Mehdi Rasti ◽  
Ji Hwan Jeong
Keyword(s):  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Capillary Tube ◽  
Capillary Tubes ◽  
Two Phase ◽  
Comprehensive Review ◽  
Wide Range ◽  
Inlet Conditions ◽  
Dimensionless Correlations

Capillary tubes are widely used as expansion devices in small-capacity refrigeration systems. Since the refrigerant flow through the capillary tubes is complex, many researchers presented empirical dimensionless correlations to predict the refrigerant mass flow rate. A comprehensive review of the dimensionless correlations for the prediction of refrigerants mass flow rate through straight and coiled capillary tubes depending on their geometry and adiabatic or diabatic capillary tubes depending on the flow configurations has been discussed. A comprehensive review shows that most of previous dimensionless correlations have problems such as discontinuity at the saturated lines or ability to predict the refrigerant mass flow rate only for the capillary tube subcooled inlet condition. The correlations suggested by Rasti et al. and Rasti and Jeong appeared to be general and continuous and these correlations can be used to predict the refrigerant mass flow rate through all the types of capillary tubes with wide range of capillary tube inlet conditions including subcooled liquid, two-phase mixture, and superheated vapor conditions.

Mass Flow Rate Measurements: From Hydrodynamic to Free Molecular Regime

2008 ◽  
Author(s):  
Timothe´e Ewart ◽  
Irina A. Graour ◽  
Pierre Perrier ◽  
J. Gilbert Me´olans
Keyword(s):  
Mass Flow Rate ◽  
Knudsen Number ◽  
Mass Flow ◽  
Flow Rate ◽  
Stationary Flow ◽  
Small Mass ◽  
Accommodation Coefficient ◽  
Navier Stokes ◽  
Number Range ◽  
Free Molecular Regime

An experimental investigation in a single silica microtube in isothermal stationary flow for various gases is made from the hydrodynamic to the near free molecular regime to study the reflection/accommodation process at the wall. This kind of investigation requires, more than other Micro-Electro-Mechanical-Systems (MEMS) experiments, a powerful experimental platform to measure very small mass flow rate. A global analytic expression, based on the Navier-Stokes (NS) equations with second order boundary conditions, is used to yield the Tangential Momentum Accommodation Coefficient (TMAC) in 0.003–0.3 Knudsen number range. Otherwise, the experimental results of the mass flow rate is compared with theoretical values calculated from kinetic approaches using variable TMAC as fitting parameter over the 0.3–30 Knudsen number range. Finally, whatever the theoretical approach the TMAC values obtained from the different gas-surface pairs are rather close one to other, but the TMAC values seem decreasing when the molecular mass increases.

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.

Optimization of the process of reproducing units of mass and volume of liquid in a stream, mass and volumetric flow rates of liquid for calibration units with weighing devices

2020 ◽  
pp. 60-64
Author(s):  
R. A. Korneev ◽  
A. R. Tukhvatullin ◽  
V. A. Fafurin ◽  
R. R. Nigmatullin ◽  
A. V. Shchelchkov
Keyword(s):  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Storage Tank ◽  
Experimental Studies ◽  
Working Fluid ◽  
Time Interval ◽  
Flow Rates ◽  
Wide Range ◽  
Flow Switch

The publication presents an experimental method for estimating the minimum time interval for filling a storage tank with a working fluid with a fixed geometry of the nozzle of the flow switch of the calibration plant when playing units of mass and volume of fluid in the flow, mass and volumetric flow rates of the fluid. Experimental studies were performed in a wide range of mass flow rate 11,10–83,26 kg/s (40–300 t/h) with repeated static weighing of the working fluid. The flow switch is made with a fixed geometry of the flow part of the nozzle exit, which is typical for a large number of calibration units in use in our country with weighing devices. The graphical dependences of the mass flow rate on the time of filling the storage capacity obtained from the research results are the basis for optimizing the process of reproducing units of mass and volume of liquid in the flow, mass and volumetric flow rates of the liquid for calibration plants with weighing devices. These graphical dependencies made it possible to formulate recommendations on the reasonable choice of the minimum interval for filling the storage tank with working fluid in the studied range of mass flow rate. Optimization has been tested and can be extended to calibration units with weighing devices from various manufacturers with individual design and operating parameters.

Efficiency Improvement of Industrial Fans if Operating at Off-Design Modes

2019 ◽  
Vol 7 (3) ◽  
pp. 43-51
Author(s):  
Глеб Замолодчиков ◽  
Gleb Zamolodchikov ◽  
Р. Тумашев ◽  
R. Tumashev ◽  
Н. Щеголев ◽  
...  
Keyword(s):  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
High Efficiency ◽  
Operating Mode ◽  
Rotor Blades ◽  
Aerodynamic Load ◽  
Axial Fan ◽  
Performance Factor ◽  
Wide Range

This paper’s aim is enhancement of efficiency for fans adjusting by turn of rotor blades. A high load axial fan and a fan with decreased rotor’s pitch chord ratio by reduction of blades number were investigated. Have been performed tests of the fan with design characteristics as follows: theoretical head coefficient Ht = 0,3, mass flow rate Ca = 0,4, hub’s relative diameter ν = 0.6, and with blades, graded on the law of permanent circulation. The area of effective adjustment was estimated by the performance factor value η* ≥ 0,8. When changing the stagger angles in a wide range from 26° to 70°, the area of highly economical work was in variation ranges 0,26–0,78 for the mass flow rate Ca , and 0,24–0,5 for the theoretical head coefficient Ht accordingly. Tests of fans with a reduced blades number in the rotor (12 instead of 16 for the original fan) has showed that under the same stagger angles the fan’s high-efficiency operating mode is approximately in the same range of Ca variation at slightly reduced values of theoretical head coefficient. Maximal performance factor has increased on 2.5%. Decreasing the number of rotary blades, simplifying the turning mechanism and reducing the weight are possible in the design of fans with increased values of aerodynamic load coefficients.

Experimental Investigation on Swirl and Heat Transfer Within a Rotor-Stator Cavity

2016 ◽  
Author(s):  
Daniele Massini ◽  
Bruno Facchini ◽  
Mirko Micio ◽  
Riccardo Da Soghe
Keyword(s):  
Heat Transfer ◽  
Experimental Investigation ◽  
Mass Flow Rate ◽  
Working Conditions ◽  
Mass Flow ◽  
Flow Rate ◽  
System Effect ◽  
Flow Measurements ◽  
Wide Range ◽  
Admission System

A rotating test rig, reproducing a rotor-stator cavity with an axial admission system, has been exploited for an experimental investigation on the internal flow field and its effect on heat transfer on the stator side. Working conditions were varied in a wide range of rotating velocities and superposed mass flow rates. 2D PIV flow measurements were performed in order to obtain a radial distribution of the tangential velocity, results were used to validate numerical simulations aimed at understanding the admission system effect on the swirl distribution. Heat transfer coefficient distribution along the stator disk has been evaluated performing a steady state technique exploiting Thermo-chromic Liquid Crystals (TLC). Tests have been performed varying the superposed mass flow rate up to reaching the condition of cavity completely sealed, further increase of the mass flow rate showed to reduce the effect of the rotation. Working conditions were set in order to investigate cases missing in open literature, however few tests performed in similarity with other researches provided comparable results.

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