Free Molecule Flow Through a Vacuum Seal

1970 ◽  
Vol 92 (3) ◽  
pp. 405-410
Author(s):  
H. S. Yu ◽  
E. M. Sparrow
Keyword(s):  
Mass Flow ◽  
Numerical Solutions ◽  
Rarefied Gas ◽  
Coupled System ◽  
Mass Fluxes ◽  
Wide Range ◽  
Flow Through ◽  
Molecule Flow ◽  
Range Of Values

An analysis is made of the rate of the mass flow through a vacuum seal separating two rarefied gas environments. The determination of the mass throughflow characteristics involves the formulation and solution of a coupled system of six integral equations. The formulation is performed using the methods of kinetic theory. Numerical solutions are carried out for a wide range of values of the seal geometrical parameter. Mass flow results evaluated from these solutions are presented graphically. In addition, representative distributions of the mass fluxes at the participating surfaces are given.

Free Molecule Flow Through Slit and Annular Orifices in the Presence of Participating Bounding Walls

1969 ◽  
Vol 36 (4) ◽  
pp. 715-722
Author(s):  
E. M. Sparrow ◽  
H. S. Yu ◽  
T. S. Lundgren
Keyword(s):  
Integral Equations ◽  
Approximate Model ◽  
Geometrical Parameters ◽  
Free Molecule ◽  
Closed Form Solutions ◽  
Wide Range ◽  
Flow Through ◽  
Bounding Surfaces ◽  
Molecule Flow ◽  
Range Of Values

The effect of actively participating bounding surfaces on the free molecule flow through a slit or an annular orifice situated in a wall separating two regions of different pressure is analyzed. The flow through the slit or orifice depends on the distributions of the flux of mass leaving the bounding surfaces. These distributions are found by formulating and solving pairs of integral equations. In the case of the slit, the integral equations are formulated by employing kinetic theory methods, while for the annular orifice it was found advantageous to use the techniques of radiative transfer. In addition to exact solutions, closed-form solutions based on an approximate model are derived. Results are presented for a wide range of values of the relevant geometrical parameters.

scholarly journals Field and Laboratory-based Approach for the Determination of Friction Angle of Geological Discontinuities of Malaysian Granites

2011 ◽  
Vol 28 (2) ◽  
pp. 151 ◽  
Author(s):  
R. A Ghani ◽  
T. L Goh ◽  
A. M Hariri ◽  
Y. N Baizura
Keyword(s):  
Friction Angle ◽  
Roughness Coefficient ◽  
Average Value ◽  
Peak Friction Angle ◽  
Maximum Value ◽  
Wide Range ◽  
Discontinuity Surfaces ◽  
Geological Discontinuities ◽  
Range Of Values

The basic friction angle, Φb for artificially sawn discontinuity planes for fresh granite, as determined by tilt testing, has an average value of 30º. For the natural rough discontinuity surfaces, a wide range of values have been determined for the peak friction angle, Φpeak ranging from 47º to a maximum value of 80º, depending on the joint roughness coefficient (JRC). The average values of the friction angles for the different degrees of roughness were as follows: JRC 2–4 = 58°; JRC 6–8 = 60°; JRC 8–10 = 47°; JRC 12–14 = 60°; JRC 14–16 = 71° ; JRC 18–20 = 80°.

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.

Experimental determination of thermal conductivity of composite materials in a wide range of values at room temperature

2019 ◽  
Author(s):  
A.N. Chistov ◽  
M.Yu. Kladov ◽  
I.B. Pronin ◽  
A.S. Smirnov
Keyword(s):  
Thermal Conductivity ◽  
Composite Materials ◽  
Room Temperature ◽  
Measurement Procedure ◽  
Thermal Mode ◽  
Wide Range ◽  
Measurement Results ◽  
Transfer Problems ◽  
Range Of Values

In developing new composite materials and solving heat transfer problems, the thermal conductivity is an important characteristic that must be reliably determined. This often requires samples of the smallest dimensions, which is relevant for the production of pilot batches of material, as well as if they are taken directly from the product, when the amount of material is very limited. Most common methods for determining thermal conductivity require samples of relatively large sizes. To measure thermal conductivity on small-sized samples, an upgraded benchtop instrument is introduced. The instrument uses the relative method of longitudinal heat flux, which consists in a comparative measurement of a sample located between the heater and the standard in a stationary thermal mode. This paper presents the instrument design details, the requirements for the samples, explains the calibration features and the measurement procedure. The measurement results in a number of composite materials, as well as in materials with well-studied properties are analyzed. Findings show that the error of determining the thermal conductivity on a modernized instrument does not exceed several percent.

The Determination of Mass Flow in the Vapour-Compression Refrigerator

1935 ◽  
Vol 129 (1) ◽  
pp. 477-505 ◽  
Author(s):  
E. C. Smith
Keyword(s):  
Experimental Determination ◽  
Mass Flow ◽  
The State ◽  
Volumetric Efficiency ◽  
Coefficient Of Performance ◽  
Flow Meter ◽  
Wide Range ◽  
Liquid Portion ◽  
Vapour Compression

The paper describes an experimental determination of the mass flow of refrigerant per minute and refrigerating effect per minute in a vapour-compression refrigerator, when the state of the refrigerant at the exit from the evaporator was varied over a wide range of superheat temperatures and dryness fractions. The usual methods of measuring the flow of liquids in pipes were not suitable for the present work and a special type of flow meter, described in the text, was developed. The results obtained were not as theory would tend to suggest, but were substantially modified by practical conditions, particularly for dryness fractions between 0·97 and 0·87. The volumetric efficiency changed abruptly over this range from a higher to a lower value. The reduction was attributed to the effect of re-evaporation of. the liquid portion of the refrigerant in the compressor during the suction stroke, as it was found that the higher volumetric efficiency was obtained when the refrigerant was superheated throughout most of the delivery stroke, and the lower volumetric efficiency occurred when the state of the refrigerant on entering the compressor resulted in liquid being present in the cylinder at the end of the delivery stroke. The reduction in the volumetric efficiency resulted in a corresponding reduction in the mass flow, the refrigerating effect, and the heat rejected by the condenser per minute, and in the coefficient of performance for dryness fractions ranging between 0·97 and 0·87.

Low-Permeability Laboratory Measurements by Nonsteady-State and Conventional Methods

1983 ◽  
Vol 23 (06) ◽  
pp. 928-936 ◽  
Author(s):  
David Louis Freeman ◽  
Darrell Cleo Bush
Keyword(s):  
Mass Flow ◽  
Numerical Solutions ◽  
Gas Permeability ◽  
Laboratory Data ◽  
Test Method ◽  
Low Permeability ◽  
Well Completion ◽  
Pore Pressures ◽  
Nonsteady State ◽  
Flow Through

Abstract Evaluation of tight gas reservoirs requires an accurate but rapid and practical method to determine permeability. Such a method is presented for determining both specific and effective gas permeability in the 0.0001- to 0.35-md range for plug-size core samples. Equipment is described that meets the requirements for calculation of nonsteady-state flow and incorporates the capability of simulation, high net overburden pressures by either hydrostatic or triaxial confining pressures with ease of operation. The time required to collect data and calculate Klinkenberg permeability is typically less than 6 minutes per sample. Values normally differ by less than + 5 % from those obtained by steady-state methods. This method is well suited for routine laboratory determinations of permeability on samples from reservoirs with tight or very low gas permeability. Effective gas permeabilities on samples containing nearly irreducible water saturations and the water permeabilities presented are closer to the Klinkenberg permeability values in low-permeability samples than most previously reported. Introduction Substantial price incentives exist in the U.S. to make it attractive for producers to recover gas from tight formations that are less than 15,000 ft 14572 mi deep and have no more than 0.1 md in-situ permeability. This incentive, plus the need for a rapid method to obtain accurate laboratory data on low-permeability samples for well completion and gas reservoir engineering, made it desirable to develop the subject equipment and test method. Various methods used to determine limiting permeability were investigated. The conventional method of determining three specific gas permeabilities and using the Klinkenberg relation to determine a limiting permeability is laborious. Methods involving numerical solutions of one-dimensional (ID) gas-flow equations such as those proposed by Aronofsky and Jenkins and Bruce et al. involve solutions by finite differences. This approach required long calculation times, which made it too cumbersome. Methods such as those proposed by Brace et al. and Walls et al. require pore pressures of the sample to be brought to equilibrium at values close to the reservoir pressure before analysis of the sample, and thus excessive time is required in approaching equilibrium. Jones suggested accounting for the non steady mass flow through the sample during an upstream pressure drawdown test. Such an approach may be used with relatively low mean pore pressures ( - 100 psig ( 690 kPa). The number of calculations was not large, while the reported accuracy was good. The method described in this paper accounts for the nonsteady mass flow through a sample during a downstream pressure-buildup test. The downstream approach allows the smallest possible downstream volumes to be used and ensures flow through the sample. These small downstream volumes allow the detection of very small flow rates in a relatively short time. SPEJ P. 928^

scholarly journals Immobilized Luminescent Bacteria for the Detection of Mycotoxins under Discrete and Flow-Through Conditions

Biosensors ◽  
2019 ◽  
Vol 9 (2) ◽  
pp. 63 ◽  
Author(s):  
Olga Senko ◽  
Nikolay Stepanov ◽  
Olga Maslova ◽  
Rashid Akhundov ◽  
Anvar Ismailov ◽  
...  
Keyword(s):  
Aqueous Media ◽  
Photobacterium Phosphoreum ◽  
Poly Vinyl Alcohol ◽  
Bacterial Cells ◽  
Flow Conditions ◽  
Luminescent Bacteria ◽  
Wide Range ◽  
Order Of Magnitude ◽  
Flow Through

A biosensitive element in the form of bacterial Photobacterium phosphoreum cells immobilized in poly(vinyl alcohol) cryogel was tested for the determination of different mycotoxins under discrete and flow-through analysis conditions. The immobilized bioluminescent cells made it possible to quantify the presence of Ochratoxin A, Sterigmatocystin, Zearalenone, and Deoxynivalenon in aqueous media in a wide range of their concentrations (0.017–56 mg/L, 0.010–33 mg/L, 0.009–14 mg/L, and 0.026–177 mg/L, respectively) via measuring the quenching of cell luminescence. The flow conditions allowed the analysis sensitivity to be improved by an order of magnitude in terms of detected concentrations. Using the immobilized luminescent bacterial cells, we have shown the possibility of evaluating the efficiency of the mycotoxins’ hydrolysis under the action of enzymes. In this way, a 94 ± 4.5% efficiency of Zearalenone hydrolysis with hexahistidine-containing organophosphorus hydrolase for 1h-long treatment of the mycotoxin solution (100 mg/L) was shown.

Simultaneous Heat and Mass Transfer in Film Absorption With the Presence of Non-Absorbable Gases

2000 ◽  
Vol 123 (5) ◽  
pp. 984-989 ◽  
Author(s):  
Hamza M. Habib ◽  
Byard D. Wood
Keyword(s):  
Mass Transfer ◽  
Water Vapor ◽  
Heat And Mass Transfer ◽  
Lithium Chloride ◽  
Numerical Solutions ◽  
Adiabatic Wall ◽  
Average Mass ◽  
Mass Fluxes ◽  
Wide Range ◽  
Aqueous Lithium Bromide

Numerical solutions are presented for the effect of a non-absorbable gas on the heat and mass transfer rates during the absorption of water vapor by a falling laminar smooth film of an aqueous lithium bromide or aqueous lithium chloride solution (absorbent). The geometry consists of a vertical channel with two walls, one of which is isothermal and the other adiabatic. The liquid film of an absorbent flows down over the isothermal wall, while a mixture of water vapor and air flows between the liquid free-surface and the adiabatic wall. The whole system is kept under vacuum pressure. Water vapor is absorbed by the film and air is the non-absorbable gas. The momentum, energy, and concentration equations are written with a set of interfacial and boundary conditions and solved numerically for the two phases. Variable property effects are included, as well as the interfacial shear. Heat and mass transfer results are presented over a wide range of inlet air concentrations. The average mass fluxes showed a continuous reduction with an increase in the amount of air for a concentration of air as high as 40 percent by weight. But the local mass fluxes showed a different behavior from the absorption of a pure vapor case. The decrease was much higher at the entrance than in a pure vapor case. The numerical results are in good agreement with the experimental data available for lithium chloride. The model has promise as means of predicting the heat and mass transfer characteristics of falling film absorber.

scholarly journals Bending of Rectangular Plates With Finite Deflections

1965 ◽  
Vol 32 (4) ◽  
pp. 821-825 ◽  
Author(s):  
Frances Bauer ◽  
Louis Bauer ◽  
William Becker ◽  
Edward L. Reiss
Keyword(s):  
Aspect Ratio ◽  
Numerical Solutions ◽  
Approximate Solutions ◽  
Normal Pressure ◽  
Rectangular Plates ◽  
Membrane Stress ◽  
Wide Range ◽  
Loading Parameter ◽  
Range Of Values ◽  
Membrane Displacement

A previously developed iterative procedure is applied to obtain numerical solutions of the von Ka´rma´n equations for rectangular plates subjected to a uniform normal pressure. On the simply supported boundary, it is assumed that the normal membrane stress and the tangential membrane displacement vanish. Solutions are obtained for a wide range of values of the loading parameter and the aspect ratio. Boundary layers develop both as the loading parameter and the aspect ratio increase. The stresses and deflections are examined and compared with an “asymptotic” solution which can be valid only in the interiors of long plates. A comparison is also made with previously obtained approximate solutions.

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