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.

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.

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.

Slip Flow in the Hydrodynamic Entrance Region of Circular and Noncircular Microchannels

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Zhipeng Duan ◽  
Y. S. Muzychka
Keyword(s):  
Friction Factor ◽  
Slip Flow ◽  
Velocity Slip ◽  
Mean Free Path ◽  
Momentum Equation ◽  
Linearization Method ◽  
Asymptotic Results ◽  
Cross Sectional ◽  
Practical Applications ◽  
Continuum Flow

Microscale fluid dynamics has received intensive interest due to the emergence of micro-electro-mechanical systems (MEMS) technology. When the mean free path of the gas is comparable to the channel’s characteristic dimension, the continuum assumption is no longer valid and a velocity slip may occur at the duct walls. Noncircular cross sections are common channel shapes that can be produced by microfabrication. The noncircular microchannels have extensive practical applications in MEMS. The paper deals with issues of hydrodynamic flow development. Slip flow in the entrance of circular and parallel plate microchannels is first considered by solving a linearized momentum equation. It is found that slip flow is less sensitive to analytical linearized approximations than continuum flow and the linearization method is an accurate approximation for slip flow. Also, it is found that the entrance friction factor Reynolds product is of finite value and dependent on the Kn and tangential momentum accommodation coefficient but independent of the cross-sectional geometry. Slip flow and continuum flow in the hydrodynamic entrance of noncircular microchannels has been examined and a model is proposed to predict the friction factor and Reynolds product f Re for developing slip flow and continuum flow in most noncircular microchannels. It is shown that the complete problem may be easily analyzed by combining the asymptotic results for short and long ducts. Through the selection of a characteristic length scale, the square root of cross-sectional area, the effect of duct shape has been minimized. The proposed model has an approximate accuracy of 10% for most common duct shapes.

Computational Study on a Novel Micropump Driven by a Built-In Thermal Bimorph Microvalve

2014 ◽  
Author(s):  
Yen-Lin Han
Keyword(s):  
Free Path ◽  
Rarefied Gas ◽  
Computational Study ◽  
Pressure Ratio ◽  
Flow Characteristics ◽  
Direct Simulation Monte Carlo ◽  
Mean Free Path ◽  
Narrow Channel ◽  
Monte Carlo Simulation Technique ◽  
Edge Flow

Using the rarefied gas dynamic phenomenon of thermal edge flow, a micropump with a built-in thermal bimorph microvalve is proposed to provide pumping needs for systems such as micro fuel cells. A thermal bimorph cantilever used as a microvalve is located within one gas molecular mean free path away from a narrow flow channel, which connects two larger size connectors on either side. The sharp edge of the heated microvalve, whose length is several times of the gas molecular mean free path, can induce flows along its surface and into the narrow channel. Using the DSMC (Direct Simulation Monte Carlo) simulation technique, the thermal edge flow characteristics are studied computationally to determine the feasibility of the proposed design. The result for a closed simulation domains at steady state determined that a pressure ratio of 1.22 can be achieved by the proposed design. The average flow velocities in open simulation domains were found to be closely related to the heater location. This preliminary computational study has proven that with particular parameters, such as the microvalve’s size and location, matching the gas mean free path, the proposed micropump with a built-in microvalve design appears to be viable to drive the thermal edge gas flows and create noticeable pressure difference to serve as a micropump.

Elastohydrodynamic Lubrication of Air-Lubricated Rollers

1996 ◽  
Vol 118 (3) ◽  
pp. 623-628 ◽  
Author(s):  
Y. B. Chang ◽  
F. W. Chambers ◽  
J. J. Shelton
Keyword(s):  
Numerical Model ◽  
Film Thickness ◽  
Free Path ◽  
Close Contact ◽  
Slip Flow ◽  
Elastohydrodynamic Lubrication ◽  
Mean Free Path ◽  
Pressure Profiles ◽  
The Mean ◽  
Air Film

The lubricating air film between two rotating rollers in close contact was studied numerically. The numerical model used in this study accounts for the effects of air compressibility, material deformation, and the slip flow which occurs when the air film thickness is not much larger than the mean-free-path of the air molecules. The air film profiles and the pressure profiles for the nip region between the rollers were calculated. It was found that the calculated air film thicknesses are lower than predicted by the liquid elastohydrodynamic calculation. From this study, equations for the minimum air film thickness, the air film thickness at the center of contact, and the amount of air that passes through the nip were obtained. This study has application to the prediction of the amount of air entrained in a winding roll.

scholarly journals Planetesimals in rarefied gas: wind erosion in slip flow

2020 ◽  
Vol 493 (4) ◽  
pp. 5456-5463 ◽  
Author(s):  
Tunahan Demirci ◽  
Niclas Schneider ◽  
Tobias Steinpilz ◽  
Tabea Bogdan ◽  
Jens Teiser ◽  
...  
Keyword(s):  
Shear Stress ◽  
Wind Erosion ◽  
Rarefied Gas ◽  
Ambient Pressure ◽  
Slip Flow ◽  
Critical Shear Stress ◽  
Mean Free Path ◽  
The Mean ◽  
Gas Molecules ◽  
First Time

ABSTRACT A planetesimal moves through the gas of its protoplanetary disc where it experiences a head wind. Though the ambient pressure is low, this wind can erode and ultimately destroy the planetesimal if the flow is strong enough. For the first time, we observe wind erosion in ground-based and microgravity experiments at pressures relevant in protoplanetary discs, i.e. down to $10^{-1}\, \rm mbar$. We find that the required shear stress for erosion depends on the Knudsen number related to the grains at the surface. The critical shear stress to initiate erosion increases as particles become comparable to or larger than the mean free path of the gas molecules. This makes pebble pile planetesimals more stable at lower pressure. However, it does not save them as the experiments also show that the critical shear stress to initiate erosion is very low for sub-millimetre-sized grains.

New slip boundary condition in high-speed rarefied gas flow simulations

2019 ◽  
Vol 234 (3) ◽  
pp. 840-856
Author(s):  
Nam TP Le ◽  
Nam H Tran ◽  
Thoai N Tran ◽  
Toan T Tran
Keyword(s):  
Boundary Condition ◽  
High Speed ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Slip Boundary Condition ◽  
Mean Free Path ◽  
Slip Condition ◽  
Monte Carlo Data ◽  
Flow Simulations ◽  
Slip Boundary

In this paper, we propose a new slip boundary condition in hypersonic gas flow simulations. It is derived by considering the Langmuir isotherm adsorption into the Kaniadarkis et al. model of the kinetic theory of gas. Moreover, the motion of the adsorbed molecules over the surface (i.e. surface diffusion) is considered for the calculation of the mean free path in new slip condition. Three aerodynamic configurations are selected for evaluating new slip condition such as (1) the sharp-leading-edge flat plate, (2) circular cylinder in cross-flow, and (3) the sharp 25°–55° biconic cases. Hypersonic gas flows have the Mach number ranging from 6.1 to 15.6, and the working gases are argon and nitrogen. The simulation results show that new slip condition predicts better slip velocity than the Maxwell slip condition and gives good agreement with the direct simulation Monte-Carlo data for all cases considered in the present work.

Sound Propagation Through a Gas in Microscale

2009 ◽  
Author(s):  
Felix Sharipov ◽  
Denize Kalempa
Keyword(s):  
Kinetic Equation ◽  
Free Path ◽  
Sound Wave ◽  
Gas Flow ◽  
Sound Propagation ◽  
Rarefied Gas ◽  
Mean Free Path ◽  
Sound Waves ◽  
Wave Source ◽  
Wide Range

A sound wave propagation through a rarefied gas is investigated on the basis of the linearized kinetic equation by taking into account the influence of the receptor of sound waves on the solution of the problem. In order to do so, a plate oscillating in the normal direction to its own plane is considered as a sound wave source while a stationary one is considered as being the receptor of sound waves. The distance between the plates can be of the order of the molecular mean free path. It is assumed a fully established oscillation so that the solution of the kinetic equation depends on time harmonically. The main parameters of the problem are the oscillation speed parameter, defined as the ratio of intermolecular collision frequency to the sound frequency, and the Knudsen number, defined as the ratio of the molecular mean free path to a characteristic scale of the gas flow. The problem is solved over a wide range of both parameters and the amplitudes and phases of all the macrocharacteristics of the gas flow are calculated.

On Slip Flow Considerations in Gas-Lubricated Porous Bearings

1984 ◽  
Vol 106 (4) ◽  
pp. 484-491 ◽  
Author(s):  
M. Malik ◽  
Cz. M. Rodkiewicz
Keyword(s):  
Free Path ◽  
Reynolds Equation ◽  
Slip Flow ◽  
Mean Free Path ◽  
Journal Bearings ◽  
Numerical Results ◽  
Static Characteristics ◽  
Flow Conditions ◽  
Porous Shell ◽  
Sliding Surfaces

A modified form of Reynolds equation is derived for the compressible lubrication of porous bearings. The analysis takes into account two kinds of nonadherence conditions on the sliding surfaces, namely, the slip flow under the influence of molecular mean free path and the slip flow at gas film-porous shell interface. Numerical results are presented to illustrate the relative effects of the two kinds of slip flow conditions on static characteristics of self acting journal bearings.

The distribution of temperature along electrically heated tubes and coils I. Theoretical

1960 ◽  
Vol 257 (1290) ◽  
pp. 302-315 ◽  
Keyword(s):  
Differential Equation ◽  
Thermal Conductivity ◽  
Free Path ◽  
Rarefied Gas ◽  
Mean Free Path ◽  
Temperature Dependent ◽  
Narrow Tube ◽  
Annular Ring ◽  
The Core ◽  
Thin Walled Tube

The distribution of temperature along a filament electrically heated in vacuo has been studied in detail in previous papers, both theoretically and experimentally. The investigations are extended in the present paper to the case of a thin-walled tube. The major new factor that appears here is the radiational transfer of energy in the core of the tube, and if one can evaluate the rate of gain in energy by a given annular ring on this account one can readily formulate the differential equation governing the distribution of temperature along the tube. Taking ε to be the emissivity, and hence also the absorptivity , of the surface, and taking the fraction (1 – ε) of the radiation incident on the surface that is not absorbed by it to be specularly reflected, we have calculated the radiational gain by the annular ring per second; the expression consists of two terms, proportional to (dT/dx) 2 and to d 2 T/ d x 2 respectively, and their coefficients point to a temperature-dependent thermal conductivity of the core equal to 16/3σDT 3 (2─ε)/ε. It is as though the conduction is due to the thermal diffusion of the photons, and they had a mean free path equal to the diameter D of the tube, enhanced by a factor (2 – ε )/ε as a result of the specular reflexions, in the same manner in which the ‘coefficient of slip' of the molecules of a rarefied gas in its passage through a narrow tube is enhanced by the specular reflexions of the molecules from the walls of the tube. The expression for the conductivity of the core bears a close analogy to the corresponding expression for other transport phenomena in which the mean free path of the diffusing particle is limited by the dimensions of the medium or of the enclosure, e. g. the thermal conductivity of a hot gas in a narrow tube due to the diffusion of the photons emitted by the molecules, or the thermal conductivity of a dielectric cylinder a t low temperatures due to the diffusion of thermal phonons. Though the differential equation determining the temperature distribution along a tube is more complicated than that for a filament, a practically general solution can be obtained; it is found to be similar to that for the filament, except that the natural length is now considerably greater, and the longitudinal variation of the temperature considerably flatter, than in the filament. The case of a closely wound coil is very similar to that of the tube, except that the conductivity through the material of the walls is now through the wire and hence much smaller than in the tube.

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