The Effect of Lubricant Inertia Near the Leading Edge of a Plane Slider Bearing

1987 ◽  
Vol 109 (1) ◽  
pp. 60-64 ◽  
Author(s):  
R. H. Buckholz
Keyword(s):  
Reynolds Number ◽  
Leading Edge ◽  
Lubrication Theory ◽  
Major Conclusion ◽  
Fluid Inertia ◽  
Slider Bearing ◽  
Flux Balance ◽  
Analytical Results ◽  
Pressure Boundary Condition ◽  
Flow Through

The influence of fluid inertia on a plane slider bearing that operates at a 0(1) modified Reynolds number is examined in this study. The flow is laminar, and the Reynolds number—based on the slider velocity, lubricant kinematic viscosity, and leading-edge slider height—can be as high as 1000. Our major conclusion is that the primary effect of fluid inertia is to raise the pressure boundary condition near the bearing leading-edge. Lubrication theory is used to determine the pressure in the fluid film in the region downstream of the bearing entry. The leading-edge pressure increase caused by convective inertia is determined by a mass-flux balance between the flow near the leading-edge, and the flow through the bearing gap, which is determined by lubrication theory. Analytical results are obtained both for the convective-inertia pressure at the bearing entrance and for the pressure under the slider bearing. Results are compared to other numerical calculations and to analytical results, where the fluid inertia terms were kept throughout the bearing gap.

Approximations in Hydrodynamic Lubrication

1992 ◽  
Vol 114 (1) ◽  
pp. 14-25 ◽  
Author(s):  
R. X. Dai ◽  
Q. Dong ◽  
A. Z. Szeri
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Numerical Study ◽  
Hydrodynamic Lubrication ◽  
Lubrication Theory ◽  
Navier Stokes ◽  
Fluid Inertia ◽  
Navier Stokes Equations ◽  
Number Range ◽  
Bearing Stiffness

In this numerical study of the approximations that led Reynolds to the formulation of classical Lubrication Theory, we compare results from (1) the full Navier-Stokes equations, (2) a lubrication theory relative to the “natural,” i.e., bipolar, coordinate system of the geometry that neglects fluid inertia, and (3) the classical Reynolds Lubrication Theory that neglects both fluid inertia and film curvature. By applying parametric continuation techniques, we then estimate the Reynolds number range of validity of the laminar flow assumption of classical theory. The study demonstrates that both the Navier-Stokes and the “bipolar lubrication” solutions converge monotonically to results from classical Lubrication Theory, one from below and the other from above. Furthermore the oil-film force is shown to be invariant with Reynolds number in the range 0 < R < Rc for conventional journal bearing geometry, where Rc is the critical value of the Reynolds number at first bifurcation. A similar conclusion also holds for the off-diagonal components of the bearing stiffness matrix, while the diagonal components are linear in the Reynolds number, in accordance with the small perturbation theory of DiPrima and Stuart.

Plane Slider Bearing Load Due to Fluid Inertia—Experiment and Theory

1985 ◽  
Vol 107 (1) ◽  
pp. 32-38 ◽  
Author(s):  
J. A. Tichy ◽  
S.-H. Chen
Keyword(s):  
Reynolds Number ◽  
Reynolds Numbers ◽  
Pressure Jump ◽  
Experimental Measurements ◽  
Small Reynolds Number ◽  
Inertia Effect ◽  
Fluid Inertia ◽  
Slider Bearing ◽  
Bearing Load ◽  
Slow Velocity

Experimental measurements of load in a simulated plane slider bearing have been performed. The flow is laminar but modified Reynolds numbers up to 30 are obtained. In comparison with actual bearings, large film thickness and slow velocity are used to avoid experimental difficulties and isolate the inertia effect. The load is found to have increased by 100 percent relative to lubrication theory at modified Reynolds number about ten. Most existing inertia theories predict only a small effect at this Reynolds number. A simple theory is proposed to account for this discrepancy, combining existing models which have considered an inlet pressure jump and small Reynolds number perturbation analysis.

Experimental Evaluation of Sector-Shaped Hydrodynamic Thrust Bearings Under Translation and Transverse Vibration

1994 ◽  
Vol 116 (3) ◽  
pp. 521-527 ◽  
Author(s):  
Y. K. Wang ◽  
C. D. Mote
Keyword(s):  
Reynolds Number ◽  
Transverse Vibration ◽  
Thrust Bearing ◽  
Lubrication Theory ◽  
Fluid Inertia ◽  
Thrust Bearings ◽  
Spring Force ◽  
Bearing Load ◽  
The Mean ◽  
Simultaneous Translation

The bearing load of a plane inclined sector-shaped hydrodynamic thrust bearing, under simultaneous translation and transverse vibration, is measured experimentally. The results are used to evaluate the lubrication theory solutions. Consequently, both the influences of the unsteady film inertia, measured by the squeeze Reynolds number Res, and the convective film inertia, measured by the modified Reynolds number Re*, on load amplitude and phase are investigated. It is found that the inertia-neglected lubrication solutions underestimate: (1) the oscillatory component of the bearing load by 6.5 percent at Res = 1.0 and by 1.4 percent at Re* = 1.0, and (2) the mean component of the bearing load by 0.7 percent at Res = 1.0 and by 2.0 percent at Re* = 1.0 Moreover, the fluid inertia induces an equivalent negative spring force component which shifts the phase of the bearing load by 9.5 deg at Res =1.0 and by 4 deg at Re* = 1.0 as compared to the lubrication theory predictions. Hence it can be an important consideration when designing bearings for vibration control purposes.

scholarly journals Settling of an asymmetric dumbbell in a quiescent fluid

2016 ◽  
Vol 802 ◽  
pp. 174-185 ◽  
Author(s):  
F. Candelier ◽  
B. Mehlig
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Size Difference ◽  
Fluid Inertia ◽  
Horizontal Orientation ◽  
Vertically Aligned ◽  
Rigid Rod ◽  
Quiescent Fluid

We compute the hydrodynamic torque on a dumbbell (two spheres linked by a massless rigid rod) settling in a quiescent fluid at small but finite Reynolds number. The spheres have the same mass densities but different sizes. When the sizes are quite different, the dumbbell settles vertically, aligned with the direction of gravity, the largest sphere first. But when the size difference is sufficiently small, then its steady-state angle is determined by a competition between the size difference and the Reynolds number. When the sizes of the spheres are exactly equal, then fluid inertia causes the dumbbell to settle in a horizontal orientation.

Radial lift on a suspended finite-sized sphere due to fluid inertia for low-Reynolds-number flow through a cylinder

2013 ◽  
Vol 722 ◽  
pp. 159-186 ◽  
Author(s):  
Sukalyan Bhattacharya ◽  
Dil K. Gurung ◽  
Shahin Navardi
Keyword(s):  
Reynolds Number ◽  
Particle Diameter ◽  
Axial Direction ◽  
Perturbation Scheme ◽  
Fluid Inertia ◽  
Regular Perturbation ◽  
Cross Sectional ◽  
First Order ◽  
Reynolds Number Flow ◽  
Freely Suspended

AbstractThis article describes the radial drift of a suspended sphere in a cylinder-bound Poiseuille flow where the Reynolds number is small but finite. Unlike past studies, it considers a circular narrow conduit whose cross-sectional diameter is only $1. 5$–$6$ times the particle diameter. Thus, the analysis quantifies the effect of fluid inertia on the radial motion of the particle in the channel when the flow field is significantly influenced by the presence of the suspended body. To this end, the hydrodynamic fields are expanded as a series in Reynolds number, and a set of hierarchical equations for different orders of the expansion is derived. Accordingly, the zeroth-order fields in Reynolds number satisfy the Stokes equation, which is accurately solved in the presence of the spherical particle and the cylindrical conduit. Then, recognizing that in narrow vessels Stokesian scattered fields from the sphere decrease exponentially in the axial direction, a simpler regular perturbation scheme is used to quantify the first-order inertial correction to hydrodynamic quantities. Consequently, it is possible to obtain two results. First, the sphere is assumed to follow the axial motion of a freely suspended sphere in a Stokesian condition, and the radial lift force on it due to the presence of fluid inertia is evaluated. Then, the approximate motion is determined for a freely suspended body on which net hydrodynamic force including first-order inertial lift is zero. The results agree well with the available experimental results. Thus, this study along with the measured data would precisely describe particle dynamics inside narrow tubes.

scholarly journals Flow past a square-section cylinder with a wavy stagnation face

2001 ◽  
Vol 426 ◽  
pp. 263-295 ◽  
Author(s):  
RUPAD M. DAREKAR ◽  
SPENCER J. SHERWIN
Keyword(s):  
Reynolds Number ◽  
Cross Flow ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Physical Structure ◽  
Near Wake ◽  
Hairpin Vortices ◽  
Independent State ◽  
Flow Past ◽  
Edge Surface

Numerical investigations have been performed for the flow past square-section cylinders with a spanwise geometric deformation leading to a stagnation face with a sinusoidal waviness. The computations were performed using a spectral/hp element solver over a range of Reynolds numbers from 10 to 150.Starting from fully developed shedding past a straight cylinder at a Reynolds number of 100, a sufficiently high waviness is impulsively introduced resulting in the stabilization of the near wake to a time-independent state. It is shown that the spanwise waviness sets up a cross-flow within the growing boundary layer on the leading-edge surface thereby generating streamwise and vertical components of vorticity. These additional components of vorticity appear in regions close to the inflection points of the wavy stagnation face where the spanwise vorticity is weakened. This redistribution of vorticity leads to the breakdown of the unsteady and staggered Kármán vortex wake into a steady and symmetric near-wake structure. The steady nature of the near wake is associated with a reduction in total drag of about 16% at a Reynolds number of 100 compared with the straight, non-wavy cylinder.Further increases in the amplitude of the waviness lead to the emergence of hairpin vortices from the near-wake region. This wake topology has similarities to the wake of a sphere at low Reynolds numbers. The physical structure of the wake due to the variation of the amplitude of the waviness is identified with five distinct regimes. Furthermore, the introduction of a waviness at a wavelength close to the mode A wavelength and the primary wavelength of the straight square-section cylinder leads to the suppression of the Kármán street at a minimal waviness amplitude.

Heat Transfer and Flowfield Measurements in the Leading Edge Region of a Stator Vane Endwall

1999 ◽  
Vol 121 (3) ◽  
pp. 558-568 ◽  
Author(s):  
M. B. Kang ◽  
A. Kohli ◽  
K. A. Thole
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Secondary Flows ◽  
Edge Region ◽  
Leading Edge Vortex ◽  
Stator Vane ◽  
Edge Vortex ◽  
The Mean

The leading edge region of a first-stage stator vane experiences high heat transfer rates, especially near the endwall, making it very important to get a better understanding of the formation of the leading edge vortex. In order to improve numerical predictions of the complex endwall flow, benchmark quality experimental data are required. To this purpose, this study documents the endwall heat transfer and static pressure coefficient distribution of a modern stator vane for two different exit Reynolds numbers (Reex = 6 × 105 and 1.2 × 106). In addition, laser-Doppler velocimeter measurements of all three components of the mean and fluctuating velocities are presented for a plane in the leading edge region. Results indicate that the endwall heat transfer, pressure distribution, and flowfield characteristics change with Reynolds number. The endwall pressure distributions show that lower pressure coefficients occur at higher Reynolds numbers due to secondary flows. The stronger secondary flows cause enhanced heat transfer near the trailing edge of the vane at the higher Reynolds number. On the other hand, the mean velocity, turbulent kinetic energy, and vorticity results indicate that leading edge vortex is stronger and more turbulent at the lower Reynolds number. The Reynolds number also has an effect on the location of the separation point, which moves closer to the stator vane at lower Reynolds numbers.

Comparison of Two Active Flow Control Mechanisms of Pure Blowing and Pure Suction on a Pitching NACA0012 Airfoil at Reynolds Number of 1 × 106

2018 ◽  
Author(s):  
Ehsan Asgari ◽  
Mehran Tadjfar
Keyword(s):  
Reynolds Number ◽  
Flow Control ◽  
Active Flow Control ◽  
Hysteresis Loops ◽  
Leading Edge ◽  
Control Mechanisms ◽  
Airfoil Surface ◽  
Naca0012 Airfoil ◽  
Maximum Angle ◽  
Active Flow

In this study, we have applied and compared two active flow control (AFC) mechanisms on a pitching NACA0012 airfoil at Reynolds number of 1 × 106 using 2-D computational fluid dynamics (CFD). These mechanisms are continuous blowing and suction which are applied separately on the airfoil which pitches around its quarter-chord in a sinusoidal motion. The location for suction and blowing was determined in our previous study based on the formation of a counter clock-wise vortex near the leading-edge. In our current study, we have compared the effectiveness of pure blowing and pure suction in suppressing the dynamic stall vortex (DSV) which is the main contributor to the drag increase, particularly near the maximum angle of attack (AOA) and in early downstroke motion. The blowing/suction slot is considered as a dent on the airfoil surface which enables the AFC to perform in a tangential manner. This configuration would allow blowing jet to penetrate further downstream and was shown to be more effective compared to a cross-flow orientation. We have compared the two aforementioned mechanisms in terms of hysteresis loops of lift and drag coefficients and have demonstrated the dynamics of flow in controlled and uncontrolled situations.

scholarly journals Oscillating foils of high propulsive efficiency

1998 ◽  
Vol 360 ◽  
pp. 41-72 ◽  
Author(s):  
J. M. ANDERSON ◽  
K. STREITLIEN ◽  
D. S. BARRETT ◽  
M. S. TRIANTAFYLLOU
Keyword(s):  
Reynolds Number ◽  
High Efficiency ◽  
Leading Edge ◽  
Half Cycle ◽  
Trailing Edge ◽  
Propulsive Efficiency ◽  
Principal Characteristics ◽  
Theoretical Predictions ◽  
Power Measurements ◽  
Oscillating Foils

Thrust-producing harmonically oscillating foils are studied through force and power measurements, as well as visualization data, to classify the principal characteristics of the flow around and in the wake of the foil. Visualization data are obtained using digital particle image velocimetry at Reynolds number 1100, and force and power data are measured at Reynolds number 40 000. The experimental results are compared with theoretical predictions of linear and nonlinear inviscid theory and it is found that agreement between theory and experiment is good over a certain parametric range, when the wake consists of an array of alternating vortices and either very weak or no leading-edge vortices form. High propulsive efficiency, as high as 87%, is measured experimentally under conditions of optimal wake formation. Visualization results elucidate the basic mechanisms involved and show that conditions of high efficiency are associated with the formation on alternating sides of the foil of a moderately strong leading-edge vortex per half-cycle, which is convected downstream and interacts with trailing-edge vorticity, resulting eventually in the formation of a reverse Kármán street. The phase angle between transverse oscillation and angular motion is the critical parameter affecting the interaction of leading-edge and trailing-edge vorticity, as well as the efficiency of propulsion.

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