Low-Speed Slip Flow Over a Wedge

1970 ◽  
Vol 37 (2) ◽  
pp. 454-460 ◽  
Author(s):  
K. E. Kasza ◽  
W. L. Chow
Keyword(s):  
Boundary Layer ◽  
Free Path ◽  
Asymptotic Method ◽  
Slip Velocity ◽  
Rarefied Gas ◽  
Slip Flow ◽  
Velocity Slip ◽  
Mean Free Path ◽  
Low Speed ◽  
Boundary Layer Equations

The problem of low-speed slip flow of a rarefied gas over a wedge has been solved using Meksyn’s asymptotic method of integrating the boundary-layer equations. Detailed results are given for slip velocity and developing velocity profiles for various wedge angles. The solution tends far downstream asymptotically to the Falkner and Skan profiles of conventional nonslip flow. In addition, the first correction to the skin friction due to velocity slip is found to be of the order of the first power of the molecular mean free path of the gas.

scholarly journals Prediction of Windage Losses of an Enclosed High Speed Composite Rotor in Low Air Pressure Environments

2003 ◽  
Author(s):  
Hsing-Pang Liu ◽  
Mike Werst ◽  
Jonathan J. Hahne ◽  
David Bogard
Keyword(s):  
Free Path ◽  
High Speed ◽  
Rarefied Gas ◽  
Flow Instability ◽  
Slip Flow ◽  
Mean Free Path ◽  
Air Gap ◽  
Air Pressure ◽  
General Interest ◽  
Continuum Flow

The frictional windage losses associated with non-ventilated airflows in the air gaps between the rotor and stator of a high speed rotating machine can greatly influence the rotor outer and stator inner surface temperatures. The characteristics of the radial and axial air-gap flows have been of general interest in many engineering applications. A rotating air gap flow is very complex, and in general, can be categorized as a continuum flow, slip flow, and free molecule flow, depending on the ratio of its mean free path to the air gap dimension. For a continuum flow between concentric rotating cylinders, secondary flow of rows of circumferential Taylor vortices in the air gap due to centrifugal flow instability of a curved flow at relatively high rotating speeds will typically be formed. As the air pressure in the air gap drops significantly, rarefied gas flow, departure from continuum flow, occurs when the mean free path becomes relatively large compared to the air gap dimension. This paper has developed and summarized an analytical approach to predict high speed windage losses (rotor tip velocities up to 900 m/s) at low rotor cavity air pressures (0.1 torr to 10 torr). The predicted transient windage losses at various air pressures and high rotor speeds are compared with measured windage losses generated in continuum and slip flow regimes. The agreements between the predicted and measured windage losses are relatively well.

Lattice Boltzmann Simulation of Rarefied Gas Flow Along Moving Rigid Objects in Micro-Cavities

2015 ◽  
Author(s):  
Weilin Yang ◽  
Hongxia Li ◽  
TieJun Zhang ◽  
Ibrahim M. Elfadel
Keyword(s):  
Free Path ◽  
Lattice Boltzmann ◽  
Path Length ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Free Path Length ◽  
Mean Free Path ◽  
Fluid Simulation ◽  
Transition Flow ◽  
Rarefied Gas Flow

Rarefied gas flow plays an important role in the design and performance analysis of micro-electro-mechanical systems (MEMS) under high-vacuum conditions. The rarefaction can be evaluated by the Knudsen number (Kn), which is the ratio of the molecular mean free path length and the characteristic length. In micro systems, the rarefied gas flow usually stays in the slip- and transition-flow regions (10−3 < Kn < 10), and may even go into the free molecular flow region (Kn > 10). As a result, conventional design tools based on continuum Navier-Stokes equation solvers are not applicable to analyzing rarefaction phenomena in MEMS under vacuum conditions. In this paper, we investigate the rarefied gas flow by using the lattice Boltzmann method (LBM), which is suitable for mesoscopic fluid simulation. The gas pressure determines the mean free path length and Kn, which further influences the relaxation time in the collision procedure of LBM. Here, we focus on the problem of squeezed film damping caused by an oscillating rigid object in a cavity. We propose an improved LBM with an immersed boundary approach, where an adjustable force term is used to quantify the interaction between the moving object and adjacent fluid, and further determines the slip velocity. With the proposed approach, the rarefied gas flow in MEMS with squeezed film damping is characterized. Different factors that affect the damping coefficient, such as pressure of gas and frequency of oscillation, are investigated in our simulation studies.

scholarly journals Integration of the boundary-layer equations for a plane in a compressible fluid

1948 ◽  
Vol 195 (1041) ◽  
pp. 180-188 ◽  
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Prandtl Number ◽  
Incompressible Fluid ◽  
Satisfactory Agreement ◽  
Asymptotic Method ◽  
Compressible Fluid ◽  
Boundary Layer Equations ◽  
Rapid Calculation ◽  
Elementary Methods

The aim of this paper is to integrate Emmons & Brainerd’s equations analytically for arbitrary values of the Prandtl number and the Mach number, using the powerful asymptotic method of integration developed by the author in a previous paper (Meksyn 1948), dealing with the boundary layer in an incompressible fluid. It is shown here that in the first approximations the asymptotic integration gives ample accuracy and that it can be determined by simple and elementary methods. The results of this comparatively rapid calculation are in very satisfactory agreement with the results of the lengthy numerical calculations made by Emmons & Brainerd for certain specific values of Prandtl number and Mach number.

The Laminar Boundary Layer on a Hot Cylinder Fixed in a Fluctuating Stream

1961 ◽  
Vol 28 (3) ◽  
pp. 339-346 ◽  
Author(s):  
R. J. Gribben
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Laminar Boundary Layer ◽  
Small Amplitude ◽  
External Flow ◽  
Low Speed ◽  
Boundary Layer Equations ◽  
Special Cases ◽  
Exact Calculations ◽  
Small Amplitude Oscillation

The equations for nonsteady, two-dimensional low-speed compressible flow in the laminar boundary layer are solved approximately by use of the Pohlhausen technique with the assumption of quartic profiles for the velocity and temperature. The external flow considered is of the form of a steady basic velocity with a superimposed small amplitude oscillation such as may arise, for example, when a sound wave is present in a uniform incident stream. The analysis is then applicable to the case of a hot cylinder fixed in such a stream. Terms of the order of the incident stream Mach number are neglected in the expressions for external flow quantities (whereas the low-speed boundary-layer equations involve errors of the order of only the square of this Mach number). Two special cases are worked out—the flow over a flat plate for which there is fair agreement with available exact calculations, and the flow over a circular cylinder.

scholarly journals Influence of Variable Thermal Conductivity on MHD Boundary Layer Slip Flow of Ethylene-Glycol Based Cu Nanofluids over a Stretching Sheet with Convective Boundary Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
N. Bhaskar Reddy ◽  
T. Poornima ◽  
P. Sreenivasulu
Keyword(s):  
Thermal Conductivity ◽  
Boundary Layer ◽  
Boundary Condition ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Slip Flow ◽  
Velocity Slip ◽  
Convective Boundary Condition ◽  
Variable Thermal Conductivity ◽  
Convective Boundary

An analysis is carried out to investigate the influence of variable thermal conductivity and partial velocity slip on hydromagnetic two-dimensional boundary layer flow of a nanofluid with Cu nanoparticles over a stretching sheet with convective boundary condition. Using similarity transformation, the governing boundary layer equations along with the appropriate boundary conditions are transformed to a set of ordinary differential equations. Employing Runge-kutta fourth-order method along with shooting technique, the resultant system of equations is solved. The influence of various pertinent parameters such as nanofluid volume fraction parameter, the magnetic parameter, radiation parameter, thermal conductivity parameter, velocity slip parameter, Biot number, and suction or injection parameter on the velocity of the flow field and heat transfer characteristics is computed numerically and illustrated graphically. The present results are compared with the existing results for the case of regular fluid and found an excellent agreement.

scholarly journals Flow around a sphere in an oscillating stream of a dusty fluid

2006 ◽  
Vol 33 (1) ◽  
pp. 1-15
Author(s):  
A.C. Srivastava ◽  
P.K. Srivastava
Keyword(s):  
Boundary Layer ◽  
Relaxation Time ◽  
Secondary Flow ◽  
Mass Concentration ◽  
Slip Velocity ◽  
Main Flow ◽  
Dust Particles ◽  
Dusty Fluid ◽  
Boundary Layer Equations

The oscillation of a stream of dusty fluid in the presence of a sphere has been discussed. The effect of interaction of curvature and viscosity has been included in the boundary layer equations. The dust particles slip on the surface of the sphere and the slip velocity is a function of relaxation time of the dust particles but is independent of mass concentration of the gas. Dust particles shift the steady secondary flow towards the main flow and increase the resistance on the sphere. .

A boundary layer theorem, with applications to rotating cylinders

1957 ◽  
Vol 2 (1) ◽  
pp. 89-99 ◽  
Author(s):  
M. B. Glauert
Keyword(s):  
Boundary Layer ◽  
Circular Cylinder ◽  
Compressible Flow ◽  
Slip Flow ◽  
Three Dimensional ◽  
Time Dependent ◽  
Boundary Layer Equations ◽  
Rotating Circular Cylinder ◽  
Quantitative Results ◽  
Explicit Formulae

If, in a given solution of the boundary layer equations, the position of the wall is varied, then additional solutions of the boundary layer equations may be deduced. The theorem considers the nature of such solution, for the general case of time-dependent three-dimensional compressible flow.Applications of the theorem arise in several different fields, and it is shown that useful quantitative results can often be obtained with the minimum of calculation. In this paper, chief attention is focused on the case of a rotating circular cylinder, and explicit formulae are developed for the skin friction, valid for sufficiently low rotational speeds. The important results which the theorem gives for slip flow have been noted by previous extenions to these previous treatments are made. Other applications of the theorem are briefly mentioned.

MHD Slip Flow of Cu-Kerosene Nanofluid in a Channel with Stretching Walls Using 3-Stage Lobatto IIIA Formula

2018 ◽  
Vol 387 ◽  
pp. 51-62 ◽  
Author(s):  
Jawad Reza ◽  
Fateh Mebarek-Oudina ◽  
Oluwole Daniel Makinde
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Slip Flow ◽  
Transverse Magnetic ◽  
Numerical Results ◽  
Physical Parameters ◽  
Boundary Layer Equations ◽  
Energy Equations

In this paper, rheology of laminar incompressible Copper-Kerosene nanofluid in a channel with stretching walls under the influence of transverse magnetic field is investigated. The main structure of the partial differential equations was taken from the law of conservation of mass, momentum and energy equations. Governing boundary layer equations are transformed into nonlinear ordinary differential equations by using similarity variables and then solved with 3-stage Lobatto IIIA formula. Numerical results were compared with another numerical method (Runge-Kutta-Fehlberg) and found excellent agreement. The influence of physical parameters Reynolds number, magnetic number, solid volume fraction, momentum and thermal slip parameters on velocity and temperature profile considered. Numerical results revealed that solid volume fraction decreases the velocity of nanofluid particles near the lower wall of the channel and increase the thermal boundary layer thickness in the channel.

scholarly journals Velocity Measurements in Channel Gas Flows in the Slip Regime by means of Molecular Tagging Velocimetry

Micromachines ◽  
2020 ◽  
Vol 11 (4) ◽  
pp. 374 ◽  
Author(s):  
Dominique Fratantonio ◽  
Marcos Rojas-Cárdenas ◽  
Christine Barrot ◽  
Lucien Baldas ◽  
Stéphane Colin
Keyword(s):  
Slip Velocity ◽  
Rarefied Gas ◽  
Numerical Models ◽  
Slip Flow ◽  
Diagnostic Methods ◽  
Gas Flows ◽  
Reconstruction Method ◽  
Molecular Tagging Velocimetry ◽  
Molecular Tagging ◽  
Slip Regime

Direct measurements of the slip velocity in rarefied gas flows produced by local thermodynamic non-equilibrium at the wall represent crucial information for the validation of existing theoretical and numerical models. In this work, molecular tagging velocimetry (MTV) by direct phosphorescence is applied to argon and helium flows at low pressures in a 1-mm deep channel. MTV has provided accurate measurements of the molecular displacement of the gas at average pressures of the order of 1 kPa. To the best of our knowledge, this work reports the very first flow visualizations of a gas in a confined domain and in the slip flow regime, with Knudsen numbers up to 0.014. MTV is cross-validated with mass flowrate measurements by the constant volume technique. The two diagnostic methods are applied simultaneously, and the measurements in terms of average velocity at the test section are in good agreement. Moreover, preliminary results of the slip velocity at the wall are computed from the MTV data by means of a reconstruction method.

Hypersonic Rarefied Viscous Interaction Over a Semi-Infinite Flat Plate

1973 ◽  
Vol 40 (4) ◽  
pp. 857-862
Author(s):  
K. E. Kasza ◽  
W. L. Chow
Keyword(s):  
Flat Plate ◽  
Temperature Jump ◽  
Rarefied Gas ◽  
Velocity Slip ◽  
Boundary Layer Equations ◽  
Interaction Solutions ◽  
Viscous Interaction ◽  
Number Variation ◽  
Shock Location ◽  
Layer Region

The problem of hypersonic rarefied viscous interaction over a semi-infinite flat plate has been solved using Meksyn’s asymptotic method of integrating the full nonsimilar boundary-layer equations. The primary phenomena of “incomplete compression”, velocity slip, and temperature jump are incorporated into the analysis. Results are obtained for induced wall pressure, skin friction, and Stanton number variation along the plate. Detailed results are also obtained for developing velocity profiles and shock location. The pressure plateau within the merged layer region is correctly predicted and the solutions merge far downstream with the strong interaction solutions where rarefied gas effects become negligible.

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