Evaluation of Various Approximate Solutions for Fluid Inertia Effects on the Dynamic Performance of a Stepped Thrust Bearing

1985 ◽  
Vol 107 (1) ◽  
pp. 39-45 ◽  
Author(s):  
Y. Haruyama ◽  
T. Kazamaki ◽  
A. Mori ◽  
H. Mori
Keyword(s):  
Film Thickness ◽  
Thrust Bearing ◽  
Stokes Equations ◽  
Dynamic Performance ◽  
Approximate Solutions ◽  
Time Dependent ◽  
Fluid Inertia ◽  
Inertia Effects ◽  
Dependent Term ◽  
Wide Range

Based on the Navier-Stokes equations in which the pressure is assumed to be constant across the film thickness, various approximate solutions and the exact one for the dynamic performance of an infinitely wide, stepped thrust bearing in a laminar flow regime are presented under the assumption of a small harmonic vibration. From comparison of the approximate solutions with the exact one, it is concluded that some kind of averaging approach in which the time dependent term is treated exactly while the convective inertia terms are averaged out across the film thickness gives close approximations in a wide range of designing conditions, and that the other kind of averaging approach in which all the inertia terms including the time dependent term are averaged out across the film thickness gives fairly good approximations.

scholarly journals On Fluid Inertia Effects in Infinitely Wide Foil Bearings

1970 ◽  
Vol 92 (3) ◽  
pp. 490-493 ◽  
Author(s):  
A. Eshel
Keyword(s):  
Film Thickness ◽  
Approximate Solutions ◽  
Fluid Film ◽  
Fluid Inertia ◽  
Inertia Effects ◽  
Foil Bearings ◽  
Lubricating Film ◽  
Fluid Film Thickness ◽  
Fluid Compressibility

Equations for a foil over a lubricating film in which the effects of fluid inertia are taken into account are derived. Approximate solutions showing the effect of inertia and fluid compressibility are obtained. The effect of inertia is to increase considerably the fluid-film thickness.

Dynamic Characterization of an Integral Squeeze Film Bearing Support Damper for a Supercritical CO2 Expander

2017 ◽  
Author(s):  
Bugra Ertas ◽  
Adolfo Delgado ◽  
Jeffrey Moore
Keyword(s):  
High Speed ◽  
Dynamic Performance ◽  
Mechanical Impedance ◽  
Squeeze Film ◽  
Fluid Inertia ◽  
Inertia Effects ◽  
Damping Behavior ◽  
Impedance Testing ◽  
Stiffness And Damping ◽  
Onset Of Cavitation

The present work advances experimental results and analytical predictions on the dynamic performance of an integral squeeze film damper (ISFD) for application in a high-speed super-critical CO2 (sCO2) expander. The test campaign focused on conducting controlled orbital motion mechanical impedance testing aimed at extracting stiffness and damping coefficients for varying end seal clearances, excitation frequencies, and vibration amplitudes. In addition to the measurement of stiffness and damping; the testing revealed the onset of cavitation for the ISFD. Results show damping behavior that is constant with vibratory velocity for each end seal clearance case until the onset of cavitation/air ingestion, while the direct stiffness measurement was shown to be linear. Measurable added inertia coefficients were also identified. The predictive model uses an isothermal finite element method to solve for dynamic pressures for an incompressible fluid using a modified Reynolds equation accounting for fluid inertia effects. The predictions revealed good correlation for experimentally measured direct damping, but resulted in grossly overpredicted inertia coefficients when compared to experiments.

Effects of Fluid Inertia Forces on the Performance of a Plane Inclined Sector Pad for an Annular Thrust Bearing Under Laminar Condition

1985 ◽  
Vol 107 (1) ◽  
pp. 46-52 ◽  
Author(s):  
Atsunobu Mori ◽  
Katsuyuki Tanaka ◽  
Haruo Mori
Keyword(s):  
Stokes Equations ◽  
Ambient Pressure ◽  
Dynamic Performance ◽  
Leading Edge ◽  
Navier Stokes ◽  
Frictional Torque ◽  
Fluid Inertia ◽  
Thin Film Lubrication ◽  
Navier Stokes Equations ◽  
Inertia Forces

The hydrodynamic wedge of a plane inclined sector pad is analyzed in relation to the lubricant inertia forces under incompressible laminar conditions. Based on the usual assumptions of thin film lubrication theory without the thermal effects, modified Reynolds equations are derived by averaging out all the inertia terms of the Navier-Stokes equations across the film thickness. The equations are linearized with respect to the inertia parameter, and solved numerically for a plane inclined, sectorial configuration. The boundary value of the film pressure at the leading edge is set at the ambient pressure, under the assumption of a negligibly small rampressure thereat. The inertial effects on the static and dynamic performance such as the load carrying capacity, flow rate, frictional torque, position of pressure center, film stiffness, and damping coefficient are discussed, in which the effects of the centrifugal force and those of the other convective inertia forces are compared with each other.

Externally Pressurized Bearings as Servomechanisms. I—The Simple Thrust Bearing

1967 ◽  
Vol 89 (4) ◽  
pp. 418-424 ◽  
Author(s):  
Donald F. Wilcock
Keyword(s):  
Transfer Function ◽  
Film Thickness ◽  
Closed Loop ◽  
Thrust Bearing ◽  
The Other ◽  
Time Dependent ◽  
Dependent Flow ◽  
Bearing Behavior ◽  
Fresh Insight ◽  
Insight Into

The externally pressurized bearing may be considered and analyzed as an hydraulic closed-loop servomechanism. The use of restrictor feed devices introduces an inner loop that reduces the gain. The time-dependent flow due to the change in volume with film thickness creates a “lead” break frequency favorable to stability. Fluid compressibility, on the other hand, leads to a “lag” break frequency which, if it approaches or becomes less than the “lead” frequency, results in bearing instability. Analysis by transfer function furnishes fresh insight into EP bearing behavior.

scholarly journals Fluid inertia effects in a squeeze film. Evaluation of various approximate solutions in a large sinusoidal squeezing motion.

1988 ◽  
Vol 54 (500) ◽  
pp. 919-926
Author(s):  
Yoshio HARUYAMA ◽  
Atsunobu MORI ◽  
Haruo MORI ◽  
Fusao MIKAMI ◽  
Tsuneji KAZAMAKI ◽  
...  
Keyword(s):  
Approximate Solutions ◽  
Squeeze Film ◽  
Fluid Inertia ◽  
Inertia Effects

Magnetohydrodynamic lubrication flow between parallel plates

1966 ◽  
Vol 26 (3) ◽  
pp. 537-543 ◽  
Author(s):  
E. Roland Maki ◽  
Dennis C. Kuzma ◽  
Russell J. Donnelly
Keyword(s):  
Thrust Bearing ◽  
Lubrication Theory ◽  
Parallel Plates ◽  
Fluid Inertia ◽  
Inertia Effects ◽  
Theory And Experiment ◽  
Good Agreement

The magnetohydrodynamic lubrication flow in an externally pressurized thrust bearing is investigated both theoretically and experimentally. The ordinary magnetohydrodynamic lubrication theory for this bearing is extended to include fluid inertia effects. Very good agreement is obtained between theory and experiment.

Comparison of Experimental and Numerical Obtained Velocity Fields in a Single-Blade Centrifugal Pump

2006 ◽  
Author(s):  
Friedrich-Karl Benra ◽  
Hans Josef Dohmen ◽  
Marcel Zwingenberg
Keyword(s):  
Numerical Simulations ◽  
Centrifugal Pump ◽  
Transient Flow ◽  
Stokes Equations ◽  
Reverse Flow ◽  
Strong Dependence ◽  
Time Dependent ◽  
Wide Range ◽  
Operating Points ◽  
Blade Pump

The development of a pressure and a suction surface of a single-blade pump impeller leads to a strong asymmetric pressure distribution at the perimeter of the rotor outlet. The interaction of the impeller flow with the pump casing produces a flow field which is periodic with the impeller turning. In a numerical approach the transient flow in a complete single-blade centrifugal pump has been calculated by solving the 3-dimensional time dependent Reynolds averaged Navier-Stokes equations (URANS) with a commercial CFD code for a wide range of pump operation. A strong dependence from the impeller position has been recognized for all flow parameters. Especially at off-design conditions the flow in the impeller and in the casing showed stall and reverse flow at particular impeller positions. Experiments have been used to validate the numerical investigations of the time dependent flow in the single-blade pump. The submersible pump, completely made of transparent plastic, has been investigated in detail by the Particle Image Velocimetry. The phase averaged 2D-velocity field inside the pump was measured for the same operating points which were investigated by numerical methods in advance. Measurement planes near the hub and the shroud disc and also at mid-span of the blade were chosen to expose the 3D-character of the flow inside the pump. The measured velocities were compared to the results from numerical simulations in detail. The good agreement between measurements and calculations, which was obtained for all investigated operating points, certifies the numerical simulations a high accuracy.

Fluid-Inertia Effects in Radial Flow Between Oscillating, Rotating Parallel Disks

1981 ◽  
Vol 103 (1) ◽  
pp. 144-149
Author(s):  
D. K. Warinner ◽  
J. T. Pearson
Keyword(s):  
Turbulent Flows ◽  
Radial Flow ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Fluid Inertia ◽  
Rotating Disks ◽  
Spiral Flow ◽  
Navier Stokes Equations ◽  
Inertia Effects

An order-of-magnitude analysis is applied to the Navier-Stokes equations and the continuity equation for isothermal, radial fluid flow between oscillating and rotating disks. This analysis investigates the four basic cases of 1) steady, radial flow, 2) unsteady, radial flow, 3) steady, spiral flow, and 4) unsteady, spiral flow. It is shown that certain values of particular dimensionless parameters for general cases will reduce the Navier-Stokes equations to simplified forms and thus render them amenable to closed-form solutions for, say, the pressure distribution between oscillating, rotating disks. The analysis holds for laminar and turbulent flows and compressible and incompressible flows. The conditions that must be satisfied for one to reasonably neglect 1) rotation, 2) unsteady terms, and 3) convective terms are set forth. One result shown is that only rarely could one reasonably neglect the radial convective acceleration while retaining the radial local acceleration.

Effects of Surfactant on the Motion of a Large Bubble in a Capillary Tube

2011 ◽  
Author(s):  
Gokalp Gursel ◽  
Ufuk Olgac ◽  
Metin Muradoglu
Keyword(s):  
Film Thickness ◽  
Liquid Film ◽  
Evolution Equations ◽  
Stokes Equations ◽  
Capillary Tube ◽  
Navier Stokes ◽  
Large Bubble ◽  
Front Tracking Method ◽  
Wide Range ◽  
Soluble Surfactants

The finite-difference/front-tracking method is used to study the motion and deformation of a large bubble moving through a capillary tube in the presence of both insoluble and soluble surfactants. Emphasis is placed on the effects of surfactant on the liquid film thickness between the bubble and the tube wall. The numerical method is designed to solve the evolution equations of the interfacial and bulk surfactant concentrations coupled with the incompressible Navier-Stokes equations. A non-linear equation of state is used to relate interfacial surface tension to surfactant concentration at the interface. The film thickness is first computed for the clean bubble case and the results are compared with the lubrication theory in the limit of small capillary numbers, i.e., Ca ≪ 1, and found to be in good agreement with the predictions of Bretherton [1]. Thereafter, the method is used to investigate the effects of insoluble and soluble surfactants on the film thickness for a wide range of governing non-dimensional numbers. It is found that both the insoluble and soluble surfactants have a thickening effect on the liquid film, which compares well with both the experimental results of Krechetnikov and Homsy [2] and analytical predictions of Daripa and Pasa [3].

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