Squeeze Film Flow Between Arbitrary Two-Dimensional Surfaces Subject to Normal Oscillations

1978 ◽  
Vol 100 (3) ◽  
pp. 316-322 ◽  
Author(s):  
J. A. Tichy ◽  
M. F. Modest
Keyword(s):  
Thrust Bearing ◽  
Analytic Solution ◽  
Film Flow ◽  
Oscillation Amplitude ◽  
Reynolds Numbers ◽  
Lubrication Theory ◽  
Squeeze Film ◽  
Two Dimensional ◽  
Surface Geometry ◽  
Inertia Effects

An analytic solution is presented for squeeze film flow with smooth, arbitrary, two-dimensional surface geometry. One surface undergoes sinusoidal oscillation toward the other. The oscillation amplitude is much smaller than the film thickness, which is in turn much smaller than the bearing length. The solution improves on the lubrication theory due to the inclusion of inertia effects. The solution to an illustrative problem is presented—the thrust bearing. The velocity field, pressure distribution and load differ significantly from those predicted by lubrication theory. The results show the lubrication solution for load and pressure to be in error by over 100 percent for Reynolds numbers as low as 5.

Squeeze Film Flow in Arbitrarily Shaped Journal Bearings Subject to Oscillations

1978 ◽  
Vol 100 (3) ◽  
pp. 323-329 ◽  
Author(s):  
M. F. Modest ◽  
J. A. Tichy
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Film Flow ◽  
Linear Partial Differential Equation ◽  
Journal Bearings ◽  
Lubrication Theory ◽  
Squeeze Film ◽  
Solution Technique ◽  
Practical Applications ◽  
High Reynolds

Squeeze film flow in smooth but arbitrarily shaped infinite journal bearings is considered. The nonrotating shaft is subject to small sinusoidal oscillations. An analytic solution is presented which improves on the lubrication theory by including inertia terms in the equations of motion. The solution technique is to introduce a stream function by which the problem can be reduced to a linear partial differential equation, with time varying boundary conditions, which can be solved by conventional means. The solution to an illustrative problem is presented—the circular journal and bearing. The velocity field and pressure distribution differ qualitatively from those predicted by lubrication theory due to the existence of out-of-phase components. The results show that the lubrication solution for the amplitude of load and pressure can be significantly in error for high Reynolds number operation of a bearing at low eccentricity ratio. At high eccentricity ratios, however, the lubrication theory can be used with confidence, even at very extreme (high Reynolds number) conditions. Simple approximate closed form expressions for pressure and load are presented which are sufficiently accurate for engineering use (error <3 percent) in the range of practical applications.

On Squeeze Film Damping in Microsystems

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Victor Marrero ◽  
Diana-Andra Borca-Tasciuc ◽  
John Tichy
Keyword(s):  
Hydrodynamic Lubrication ◽  
Reynolds Numbers ◽  
Lubrication Theory ◽  
Squeeze Film ◽  
Solution Technique ◽  
Parallel Plates ◽  
Damping Force ◽  
Aspect Ratios ◽  
Squeeze Film Damping ◽  
High Reynolds

Classical hydrodynamic lubrication theory has been one of the most successful and widely used theories in all of engineering and applied science. This theory predicts that the force resisting the squeezing of a fluid between two parallel plates is inversely proportional to the cube of the fluid thickness. However, recent reports on liquid squeeze film damping in microsystems appear to indicate that experimentally measured damping force is proportional to the inverse of the fluid thickness to the first power—a large fundamental discrepancy from classical theory. This paper investigates potential limitations of lubrication theory in microsystems by theoretical and computational methods. The governing equations for a Newtonian incompressible fluid are solved subject to two-dimensional, parallel surface squeezing by an open-source computational fluid dynamics program called parallel hierarchic adaptive stabilized transient analysis (PHASTA), and by a classical similarity solution technique. At low convective Reynolds numbers, the damping force is determined as a function of the ratio of a reference film thickness H to a reference direction B along the film. Good agreement with classical lubrication theory is found for aspect ratios H/B as high as 1 despite the fact that lubrication theory requires that this ratio be “small.” A similarity analysis shows that when instantaneous convective Reynolds number is of order 10–100 (a range present in experiment), calculated damping deviates significantly from lubrication theory. This suggests that nonlinearity associated with high Reynolds numbers could explain the experimentally observed discrepancy in damping force. Dynamic analysis of beams undergoing small vibrations in the presence of a liquid medium further supports this finding.

Numerical Solution for Laminar Two Dimensional Flow About a Cylinder Oscillating in a Uniform Stream

1982 ◽  
Vol 104 (2) ◽  
pp. 214-220 ◽  
Author(s):  
S. E. Hurlbut ◽  
M. L. Spaulding ◽  
F. M. White
Keyword(s):  
Reynolds Numbers ◽  
Quantitative Agreement ◽  
Two Dimensional ◽  
Inertia Effects ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Vortex Shedding Frequency ◽  
Shedding Frequency ◽  
Lock In ◽  
Uniform Stream

A finite difference model is presented for viscous two dimensional flow of a uniform stream past an oscillating cylinder. A noninertial coordinate transformation is used so that the grid mesh remains fixed relative to the accelerating cylinder. Three types of cylinder motion are considered: oscillation in a still fluid, oscillation parallel to a moving stream, and oscillation transverse to a moving stream. Computations are made for Reynolds numbers between 1 and 100 and amplitude-to-diameter ratios from 0.1 to 2.0. The computed results correctly predict the lock-in or wake-capture phenomenon which occurs when cylinder oscillation is near the natural vortex shedding frequency. Drag, lift, and inertia effects are extracted from the numerical results. Detailed computations at a Reynolds number of 80 are shown to be in quantitative agreement with available experimental data for oscillating cylinders.

The Gaseous Squeeze-Film at Moderately Large Squeeze Numbers

1970 ◽  
Vol 92 (4) ◽  
pp. 766-781 ◽  
Author(s):  
C. H. T. Pan
Keyword(s):  
Edge Effects ◽  
Lubrication Theory ◽  
Point Of View ◽  
Squeeze Film ◽  
Universal Functions ◽  
Inertia Effects ◽  
Gas Lubrication ◽  
Spherical Bearing ◽  
Squeeze Number ◽  
Isothermal Gas

The asymptotic analysis of the gaseous squeeze-film bearing has been extended to obtain 0 {σ−1/2} effects in accordance with the isothermal gas lubrication theory and the method of singular perturbation. 0 {σ−1/2} corrections are identified to contain not only edge effects (inner problem) but also edge-interior interactions which are analogous to the boundary layer displacement effects in aerodynamics. The latter features can further be recognized to be related to mean-gap taper, squeeze taper, and cross-edge sliding. These results are discussed from the point of view of “global bearing properties” including the temporal mean as well as the in-phase and quadrature synchronous components of the fluid film force and moment. The edge effects are presented in terms of universal functions which can be used directly as corrections in the global properties. The edge-interior interactions must be determined by solving the asymptotic p.d.e. with boundary condition also expressed in terms of universal functions. Formulations applicable to cylindrical, conical, and spherical bearing geometries are outlined. Illustrative numerical examples are provided. Conditions affecting the validity of the isothermal gas lubrication theory (neglecting inertia effects) as related to the magnitude of the squeeze number are discussed.

Inertia Effects in Thin Film Flow With a Corrugated Boundary

1991 ◽  
Vol 58 (1) ◽  
pp. 272-277 ◽  
Author(s):  
Ilter Serbetci ◽  
John A. Tichy
Keyword(s):  
Pressure Distribution ◽  
Film Flow ◽  
Stokes Equations ◽  
Lubrication Theory ◽  
Navier Stokes ◽  
Thin Film Flow ◽  
Perturbation Expansions ◽  
Navier Stokes Equations ◽  
Inertia Effects ◽  
Grooved Surface

An analytical solution is presented for two-dimensional, incompressible film flow between a sinusoidally grooved (or rough) surface and a flat surface. The upper grooved surface is stationary whereas the lower, smooth surface moves with a constant speed, The Navier-Stokes equations were solved employing both mapping techniques and perturbation expansions. Due to the inclusion of the inertia effects, a different pressure distribution is obtained than predicted by the classical lubrication theory. In particular, the amplitude of the pressure distribution of the classical lubrication theory is found to be in error by over 100 percent (for modified Reynolds number of 3–4).

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.

Two-dimensional flow under gravity in a jet of viscous liquid

1968 ◽  
Vol 31 (3) ◽  
pp. 481-500 ◽  
Author(s):  
N. S. Clarke
Keyword(s):  
Flow Region ◽  
Reynolds Numbers ◽  
Asymptotic Solutions ◽  
Perturbation Scheme ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Secondary Importance ◽  
Inertia Effects ◽  
Dimensional Flow ◽  
Two Dimensional Flow

This paper is concerned with the steady, symmetric, two-dimensional flow of a viscous, incompressible fluid issuing from an orifice and falling freely under gravity. A Reynolds number is defined and considered to be small. Due to the apparent intractability of the problem in the neighbourhood of the orifice, interest is confined to the flow region below the orifice, where the jet is bounded by two free streamlines. It is assumed that the influence of the orifice conditions will decay exponentially, and so the asymptotic solutions sought have no dependence upon the nature of the flow at the orifice. In the region just downstream of the orifice, it is expected that the inertia effects will be of secondary importance. Accordingly the Stokes solution is sought and a perturbation scheme is developed from it to take account of the inertia effects. It was found possible only to express the Stokes solution and its perturbations in the form of co-ordinate expansions. This perturbation scheme is found to be singular far downstream due to the increasing importance of the inertia effects. Far downstream the jet is expected to be very thin and the velocity and stress variations across it to be small. These assumptions are used as a basis in deriving an asymptotic expansion for small Reynolds numbers, which is valid far downstream. This expansion also has the appearance of being valid very far downstream, even for Reynolds numbers which are not necessarily small. The method of matched asymptotic expansions is used to link the asymptotic solutions in the two regions. An extension of the method deriving the expansion far downstream, to cover the case of an axially-symmetric jet, is given in an appendix.

scholarly journals Measurements of Squeeze Film Bearing Forces to Demonstrate the Effect of Fluid Inertia

1984 ◽  
Author(s):  
John A. Tichy
Keyword(s):  
Dynamic Systems ◽  
High Speed ◽  
Hydrodynamic Lubrication ◽  
Reynolds Numbers ◽  
Lubrication Theory ◽  
Squeeze Film ◽  
Fluid Inertia ◽  
Viscous Forces ◽  
Rotor Dynamic ◽  
Inertia Forces

Squeeze film dampers are commonly applied to high speed rotating machinery, such as aircraft engines, to reduce vibration problems. The theory of hydrodynamic lubrication has been used for the design and modeling of dampers in rotor dynamic systems despite typical modified Reynolds numbers in applications between ten and fifty. Lubrication theory is strictly valid for Reynolds numbers much less than one, which means that fluid viscous forces are much greater than inertia forces. Theoretical papers which account for fluid inertia in squeeze films have predicted large discrepancies from lubrication theory, but these results have not found wide acceptance by workers in the gas turbine industry. Recently, experimental results on the behavior of rotor dynamic systems have been reported which strongly support the existence of large fluid inertia forces. In the present paper direct measurements of damper forces are presented for the first time. Reynolds numbers up to ten are obtained at eccentricity ratios 0.2 and 0.5. Lubrication theory underpredicts the measured forces by up to a factor of two (100% error). Qualitative agreement is found with predictions of earlier improved theories which include fluid inertia forces.

Theoretical Analysis of the Incompressible Laminar Flow in a Macro-Roughness Cell

2003 ◽  
Vol 125 (2) ◽  
pp. 309-318 ◽  
Author(s):  
Mihai Arghir ◽  
Nicolas Roucou ◽  
Mathieu Helene ◽  
Jean Frene
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Lubrication Theory ◽  
Textured Surface ◽  
Relative Importance ◽  
Two Dimensional ◽  
Textured Surfaces ◽  
Simplified Models ◽  
Inertia Effects ◽  
Laminar Shear

The present work deals with the analysis of the incompressible laminar shear driven flow in a channel of which one of the walls carries a macro roughness pattern while the opposite one has a parallel velocity. The problem is discussed from the standpoint of lubrication theory and it is shown that the usual simplified models as the Reynolds or the Stokes equations are not applicable. Numerical results are presented for three types of two dimensional macro-roughness and two versions of a three dimensional one. It is shown that a pressure generation effect occurs with increasing the relative importance of convective inertia. Previous analyses found in the literature discussed only the increase of the shear stress due to the presence of the macro roughness but the lift effect due to the pressure generation has never been enlightened up to now. It is further discussed that, extrapolated to a very large number of macro roughness characterizing a textured surface, this new effect could be added to the other lift generating mechanisms of the lubrication theory. It could thus bring a different light on inertia effects stemming from the use of textured surfaces.

Inertial Considerations in Parallel Circular Squeeze Film Bearings

1970 ◽  
Vol 92 (4) ◽  
pp. 588-592 ◽  
Author(s):  
J. A. Tichy ◽  
W. O. Winer
Keyword(s):  
Newtonian Fluid ◽  
Film Flow ◽  
Momentum Equation ◽  
Lubrication Theory ◽  
Squeeze Film ◽  
Experimental Measurements ◽  
Inertial Effects ◽  
Regular Perturbation ◽  
Parallel Surfaces ◽  
Good Agreement

A second order regular perturbation solution for squeeze film flow of a Newtonian fluid between circular parallel surfaces is presented. All the inertial terms are included in the momentum equation. Experimental measurements of pressure in a squeeze film at high squeeze rates are shown to be in good agreement with the solution. The solution is particularly useful in assessing the extent to which fluid inertial effects would cause the classical lubrication theory to be in error for any particular squeeze film. The inertial effects are shown to be functions of two readily determined dimensionless parameters, the squeeze Reynold’s number Res and the squeeze acceleration number A.

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