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.

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.

scholarly journals Solitary waves on falling liquid films in the inertia-dominated regime

2018 ◽  
Vol 837 ◽  
pp. 491-519 ◽  
Author(s):  
Fabian Denner ◽  
Alexandros Charogiannis ◽  
Marc Pradas ◽  
Christos N. Markides ◽  
Berend G. M. van Wachem ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Solitary Waves ◽  
Reynolds Numbers ◽  
Liquid Films ◽  
Flow Reversal ◽  
Experimental Measurements ◽  
Flow Recirculation ◽  
High Reynolds Numbers ◽  
High Reynolds ◽  
Falling Liquid Films

We offer new insights and results on the hydrodynamics of solitary waves on inertia-dominated falling liquid films using a combination of experimental measurements, direct numerical simulations (DNS) and low-dimensional (LD) modelling. The DNS are shown to be in very good agreement with experimental measurements in terms of the main wave characteristics and velocity profiles over the entire range of investigated Reynolds numbers. And, surprisingly, the LD model is found to predict accurately the film height even for inertia-dominated films with high Reynolds numbers. Based on a detailed analysis of the flow field within the liquid film, the hydrodynamic mechanism responsible for a constant, or even reducing, maximum film height when the Reynolds number increases above a critical value is identified, and reasons why no flow reversal is observed underneath the wave trough above a critical Reynolds number are proposed. The saturation of the maximum film height is shown to be linked to a reduced effective inertia acting on the solitary waves as a result of flow recirculation in the main wave hump and in the moving frame of reference. Nevertheless, the velocity profile at the crest of the solitary waves remains parabolic and self-similar even after the onset of flow recirculation. The upper limit of the Reynolds number with respect to flow reversal is primarily the result of steeper solitary waves at high Reynolds numbers, which leads to larger streamwise pressure gradients that counter flow reversal. Our results should be of interest in the optimisation of the heat and mass transport characteristics of falling liquid films and can also serve as a benchmark for future model development.

Motion of spheroid particles in shear flow with inertia

2014 ◽  
Vol 749 ◽  
pp. 145-166 ◽  
Author(s):  
Wenbin Mao ◽  
Alexander Alexeev
Keyword(s):  
Reynolds Number ◽  
Angular Velocity ◽  
Shear Flow ◽  
Rotation Period ◽  
Reynolds Numbers ◽  
Stokes Number ◽  
Simple Shear Flow ◽  
Fluid Inertia ◽  
Particle Rotation ◽  
Particle Inertia

AbstractIn this article, we investigate the motion of a solid spheroid particle in a simple shear flow. Using a lattice Boltzmann method, we examine individual effects of fluid inertia and particle rotary inertia as well as their combination on the dynamics and trajectory of spheroid particles at low and moderate Reynolds numbers. The motion of a single spheroid is shown to be dependent on the particle Reynolds number, particle aspect ratio, particle initial orientation and the Stokes number. Spheroids with random initial orientations are found to drift to stable orbits influenced by fluid inertia and/or particle inertia. Specifically, prolate spheroids drift towards the tumbling mode of motion, whereas oblate spheroids drift to the rolling mode. The rotation period and the variation of angular velocity of tumbling spheroids decrease as Stokes number increases. With increasing Reynolds number, both the maximum and minimum values of angular velocity decrease, whereas the particle rotation period increases. We show that particle inertia does not affect the hydrodynamic torque on the particle. We also demonstrate that superposition can be used to estimate the combined effect of fluid inertia and particle inertia on the dynamics of spheroid particles at sufficiently low Reynolds numbers.

Inertia Effect in Hydrodynamic Lubrication With Film Rupture

1987 ◽  
Vol 109 (1) ◽  
pp. 86-90 ◽  
Author(s):  
H. I. You ◽  
S. S. Lu
Keyword(s):  
Reynolds Number ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Hydrodynamic Lubrication ◽  
Inertia Effect ◽  
Fluid Inertia ◽  
Film Rupture ◽  
Minimum Film Thickness ◽  
Rupture Model ◽  
Modified Reynolds Equation

The modified Reynolds equation in conjunction with the modified Coyne-Elrod rupture model is used to investigate the inertia effect on the pressure distribution in converging-diverging bearings. The modified Reynolds equation is solved analytically for infinitely long bearings, including the cylinder-plane bearing and the journal bearing. The results showed that the fluid inertia tends to stretch the fluid film and to move the film rupture point farther downstream. The effects are profound even at a moderate value of the reduced Reynolds number, Re* ≈ 0.13 based on the minimum film thickness.

Heat transfer from a sphere at low Reynolds numbers

1973 ◽  
Vol 60 (2) ◽  
pp. 273-283 ◽  
Author(s):  
S. C. R. Dennis ◽  
J. D. A. Walker ◽  
J. D. Hudson
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Viscous Incompressible Fluid ◽  
Reynolds Numbers ◽  
Experimental Measurements ◽  
Low Reynolds Numbers ◽  
Nusselt Numbers ◽  
The Mean ◽  
Low Reynolds ◽  
Prandtl Numbers

The heat transfer due to forced convection from an isothermal sphere in a steady stream of viscous incompressible fluid is calculated for low values of the Reynolds number and Prandtl numbers ofO(1). The mean Nusselt number is compared with the results of experimental measurements. At very low Reynolds numbers, both the local and mean Nusselt numbers are compared with the results obtained from the theory of matched asymptotic expansions.

Flow past a sphere with an oscillation in the free-stream velocity and unsteady drag at finite Reynolds number

1992 ◽  
Vol 237 ◽  
pp. 323-341 ◽  
Author(s):  
Renwei Mei ◽  
Ronald J. Adrian
Keyword(s):  
Reynolds Number ◽  
Finite Difference ◽  
Unsteady Flow ◽  
Large Time ◽  
Free Stream ◽  
Reynolds Numbers ◽  
Stream Velocity ◽  
Small Reynolds Number ◽  
Dependent Part ◽  
History Force

Unsteady flow over a stationary sphere with a small fluctuation in the free-stream velocity is considered at small Reynolds number, Re. A matched asymptotic solution is obtained for the frequency-dependent (or the acceleration-dependent) part of the unsteady flow at very small frequency, ω, under the restriction St [Lt ] Re [Lt ] 1, where St is the Strouhal number. The acceleration-dependent part of the unsteady drag is found to be proportional to St ∼ ω instead of the ω½ dependence predicted by Stokes’ solution. Consequently, the expression for the Basset history force is incorrect for large time even for very small Reynolds numbers. Present results compare well with the previous numerical results of Mei, Lawrence & Adrian (1991) using a finite-difference method for the same unsteady flow at small Reynolds number. Using the principle of causality, the present analytical results at small Re, the numerical results at finite Re for low frequency, and Stokes’ results for high frequency, a modified expression for the history force is proposed in the time domain. It is confirmed by comparing with the finite-difference results at arbitrary frequency through Fourier transformation. The modified history force has an integration kernel that decays as t−2, instead of t½, at large time for both small and finite Reynolds numbers.

Moderate-Reynolds-number flows in ordered and random arrays of spheres

2001 ◽  
Vol 448 ◽  
pp. 243-278 ◽  
Author(s):  
REGHAN J. HILL ◽  
DONALD L. KOCH ◽  
ANTHONY J. C. LADD
Keyword(s):  
Reynolds Number ◽  
Drag Force ◽  
Volume Fraction ◽  
Reynolds Numbers ◽  
Hydrodynamic Dispersion ◽  
Fluid Inertia ◽  
Volume Fractions ◽  
Moderate Reynolds Number ◽  
Random Arrays ◽  
Arrays Of Spheres

Lattice-Boltzmann simulations are used to examine the effects of fluid inertia, at moderate Reynolds numbers, on flows in simple cubic, face-centred cubic and random arrays of spheres. The drag force on the spheres, and hence the permeability of the arrays, is calculated as a function of the Reynolds number at solid volume fractions up to the close-packed limits of the arrays. At Reynolds numbers up to O(102), the non-dimensional drag force has a more complex dependence on the Reynolds number and the solid volume fraction than suggested by the well-known Ergun correlation, particularly at solid volume fractions smaller than those that can be achieved in physical experiments. However, good agreement is found between the simulations and Ergun's correlation at solid volume fractions approaching the close-packed limit. For ordered arrays, the drag force is further complicated by its dependence on the direction of the flow relative to the axes of the arrays, even though in the absence of fluid inertia the permeability is isotropic. Visualizations of the flows are used to help interpret the numerical results. For random arrays, the transition to unsteady flow and the effect of moderate Reynolds numbers on hydrodynamic dispersion are discussed.

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.

Low Reynolds number flow around and heat transfer from a heated circular cylinder

2010 ◽  
Vol 1 (1-2) ◽  
pp. 15-20 ◽  
Author(s):  
B. Bolló
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Reynolds Number Flow ◽  
Two Dimensional Flow ◽  
Number Flow ◽  
Low Reynolds ◽  
Increasing Temperature

Abstract The two-dimensional flow around a stationary heated circular cylinder at low Reynolds numbers of 50 < Re < 210 is investigated numerically using the FLUENT commercial software package. The dimensionless vortex shedding frequency (St) reduces with increasing temperature at a given Reynolds number. The effective temperature concept was used and St-Re data were successfully transformed to the St-Reeff curve. Comparisons include root-mean-square values of the lift coefficient and Nusselt number. The results agree well with available data in the literature.

scholarly journals Turbulence model performance for ventilation components pressure losses

2021 ◽  
Author(s):  
Karsten Tawackolian ◽  
Martin Kriegel
Keyword(s):  
Reynolds Number ◽  
Turbulence Model ◽  
Pressure Loss ◽  
Low Reynolds Number ◽  
Turbulence Models ◽  
Reynolds Numbers ◽  
Test Case ◽  
Pressure Losses ◽  
Loss Coefficients ◽  
Near Wall

AbstractThis study looks to find a suitable turbulence model for calculating pressure losses of ventilation components. In building ventilation, the most relevant Reynolds number range is between 3×104 and 6×105, depending on the duct dimensions and airflow rates. Pressure loss coefficients can increase considerably for some components at Reynolds numbers below 2×105. An initial survey of popular turbulence models was conducted for a selected test case of a bend with such a strong Reynolds number dependence. Most of the turbulence models failed in reproducing this dependence and predicted curve progressions that were too flat and only applicable for higher Reynolds numbers. Viscous effects near walls played an important role in the present simulations. In turbulence modelling, near-wall damping functions are used to account for this influence. A model that implements near-wall modelling is the lag elliptic blending k-ε model. This model gave reasonable predictions for pressure loss coefficients at lower Reynolds numbers. Another example is the low Reynolds number k-ε turbulence model of Wilcox (LRN). The modification uses damping functions and was initially developed for simulating profiles such as aircraft wings. It has not been widely used for internal flows such as air duct flows. Based on selected reference cases, the three closure coefficients of the LRN model were adapted in this work to simulate ventilation components. Improved predictions were obtained with new coefficients (LRNM model). This underlined that low Reynolds number effects are relevant in ventilation ductworks and give first insights for suitable turbulence models for this application. Both the lag elliptic blending model and the modified LRNM model predicted the pressure losses relatively well for the test case where the other tested models failed.

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