Some Remarks on the Validity of Reynolds Equation in the Modeling of Lubricant Film Flows on the Surface Roughness Scale

2004 ◽  
Vol 126 (4) ◽  
pp. 703-710 ◽  
Author(s):  
T. Almqvist ◽  
R. Larsson
Keyword(s):  
Surface Roughness ◽  
Reynolds Equation ◽  
Numerical Solutions ◽  
Fluid Dynamic ◽  
Lubricant Film ◽  
Continuity Equations ◽  
Newtonian Case ◽  
Eyring Model ◽  
Wavelength Scale ◽  
Film Flows

The objective of this paper is to investigate the flow in a lubricant film on the surface roughness scale and to compare the numerical solutions obtained by two different solution approaches. This is accomplished firstly by the CFD-approach (computational fluid dynamic approach) where the momentum and continuity equations are solved separately, and secondly the Reynolds equation approach, which is a combination and a simplification of the above equations. The rheology is assumed to be both Newtonian and non-Newtonian. An Eyring model is used in the non-Newtonian case. The result shows that discrepancies between the two approaches may occur, primarily due to a singularity which appears in the momentum equations when the stresses in the lubricant attain magnitudes that are common in EHL. This singularity is not represented by the Reynolds equation. If, however, the rheology is shifted to a non-Newtonian Eyring model the deviations between the two solution approaches is removed or reduced. The second source of discrepancies between the two approaches is the film thickness to wavelength scale ω. It will be shown that the Reynolds equation is valid until this ratio is approximately O10−2.

Calculation of Surface Roughness Effects on Air-Riding Seals

2002 ◽  
Author(s):  
C. Guardino ◽  
J. W. Chew ◽  
N. J. Hills
Keyword(s):  
Surface Roughness ◽  
Compressible Flows ◽  
Reynolds Equation ◽  
Incompressible Flows ◽  
Numerical Solutions ◽  
Cfd Analysis ◽  
Roughness Effects ◽  
Stationary Wall ◽  
Comparative Results ◽  
Effect Of Surface

The effects of surface roughness on air-riding seals are investigated here using the Rayleigh-pad as an example. Both incompressible and compressible flows are considered using both CFD analysis and analytical/numerical solutions of the Reynolds equation for various 2D or 3D roughness patterns on the stationary wall. A ‘unit-based’ approach for incompressible flows has also been employed and is shown to be computationally much less expensive than the full-geometry solution. Results are presented showing the effect of surface roughness on the net lift force. The effects of varying the Reynolds number are demonstrated, as well as comparative results for static stiffness.

Calculation of Surface Roughness Effects on Air-Riding Seals

2004 ◽  
Vol 126 (1) ◽  
pp. 75-82 ◽  
Author(s):  
C. Guardino ◽  
J. W. Chew ◽  
N. J. Hills
Keyword(s):  
Surface Roughness ◽  
Compressible Flows ◽  
Reynolds Equation ◽  
Incompressible Flows ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Roughness Effects ◽  
Stationary Wall ◽  
Comparative Results ◽  
Effect Of Surface

The effects of surface roughness on air-riding seals are investigated here using the Rayleigh pad as an example. Both incompressible and compressible flows are considered using both CFD analysis and analytical/numerical solutions of the Reynolds equation for various two-dimensional or three-dimensional roughness patterns on the stationary wall. A “unit-based” approach for incompressible flows has also been employed and is shown to be computationally much less expensive than the full-geometry solution. Results are presented showing the effect of surface roughness on the net lift force. The effects of varying the Reynolds number are demonstrated, as well as comparative results for static stiffness.

A Reynolds-Eyring Equation for Elastohydrodynamic Lubrication in Line Contacts

1987 ◽  
Vol 109 (4) ◽  
pp. 648-654 ◽  
Author(s):  
T. F. Conry ◽  
S. Wang ◽  
C. Cusano
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Numerical Solutions ◽  
Elastohydrodynamic Lubrication ◽  
Newtonian Flow ◽  
Line Contacts ◽  
Different Temperatures ◽  
Eyring Model ◽  
Eyring Theory ◽  
New Equation

A new Reynolds equation, based on the Eyring theory of non-Newtonian flow, is derived for flow in one dimension. It is shown that this new equation reduces to the traditional Reynolds equation as the Eyring model approaches the Newtonian model in the limit. Numerical solutions are presented for a selected oil at two different temperatures. The central film thickness decreases with increasing dimensionless viscosity parameter and slide/roll ratios. A transition zone is noted through which the ratio of minimum to central film thickness passes as the pressure distribution goes from near Hertzian to a distribution that appreciably deviates from Hertzian.

scholarly journals Experimental Investigation and Comparison of the Thermal Performance of Additively and Conventionally Manufactured Heat Exchangers

Metals ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 574
Author(s):  
Ana Vafadar ◽  
Ferdinando Guzzomi ◽  
Kevin Hayward
Keyword(s):  
Surface Roughness ◽  
Thermal Performance ◽  
Heat Exchangers ◽  
High Efficiency ◽  
Cooling System ◽  
Fluid Dynamic ◽  
Dynamic Performance ◽  
Experimental Studies ◽  
Manufacturing Method ◽  
Industrial Sectors

Air heat exchangers (HXs) are applicable in many industrial sectors because they offer a simple, reliable, and cost-effective cooling system. Additive manufacturing (AM) systems have significant potential in the construction of high-efficiency, lightweight HXs; however, HXs still mainly rely on conventional manufacturing (CM) systems such as milling, and brazing. This is due to the fact that little is known regarding the effects of AM on the performance of AM fabricated HXs. In this research, three air HXs comprising of a single fin fabricated from stainless steel 316 L using AM and CM methods—i.e., the HXs were fabricated by both direct metal printing and milling. To evaluate the fabricated HXs, microstructure images of the HXs were investigated, and the surface roughness of the samples was measured. Furthermore, an experimental test rig was designed and manufactured to conduct the experimental studies, and the thermal performance was investigated using four characteristics: heat transfer coefficient, Nusselt number, thermal fluid dynamic performance, and friction factor. The results showed that the manufacturing method has a considerable effect on the HX thermal performance. Furthermore, the surface roughness and distribution, and quantity of internal voids, which might be created during and after the printing process, affect the performance of HXs.

The Effect of Journal Bearing Misalignment on Load and Cavitation for Non-Newtonian Lubricants

1986 ◽  
Vol 108 (4) ◽  
pp. 645-654 ◽  
Author(s):  
R. H. Buckholz ◽  
J. F. Lin
Keyword(s):  
Reynolds Equation ◽  
Numerical Solutions ◽  
Journal Bearings ◽  
Surface Boundary ◽  
Film Rupture ◽  
Aspect Ratios ◽  
Free Surface Boundary Condition ◽  
Load Carrying ◽  
Boundary Location ◽  
Surface Boundary Condition

An analysis for hydrodynamic, non-Newtonian lubrication of misaligned journal bearings is given. The hydrodynamic load-carrying capacity for partial arc journal bearings lubricated by power-law, non-Newtonian fluids is calculated for small valves of the bearing aspect ratios. These results are compared with: numerical solutions to the non-Newtonian modified Reynolds equation, with Ocvirk’s experimental results for misaligned bearings, and with other numerical simulations. The cavitation (i.e., film rupture) boundary location is calculated using the Reynolds’ free-surface, boundary condition.

Dynamic Characteristics of a Hydrostatic Gas Bearing Driven by Oscillating Exhaust Pressure

1984 ◽  
Vol 106 (4) ◽  
pp. 477-483 ◽  
Author(s):  
C. B. Watkins ◽  
H. D. Branch ◽  
I. E. Eronini
Keyword(s):  
Reynolds Equation ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Source Model ◽  
Regular Perturbation ◽  
Response Characteristics ◽  
Finite Difference Approximations ◽  
Bode Plots ◽  
Gas Bearing

Vibration of a statically loaded, inherently compensated hydrostatic journal bearing due to oscillating exhaust pressure is investigated. Both angular and radial vibration modes are analyzed. The time-dependent Reynolds equation governing the pressure distribution between the oscillating journal and sleeve is solved together with the journal equation of motion to obtain the response characteristics of the bearing. The Reynolds equation and the equation of motion are simplified by applying regular perturbation theory for small displacements. The numerical solutions of the perturbation equations are obtained by discretizing the pressure field using finite-difference approximations with a discrete, nonuniform line-source model which excludes effects due to feeding hole volume. An iterative scheme is used to simultaneously satisfy the equations of motion for the journal. The results presented include Bode plots of bearing-oscillation gain and phase for a particular bearing configuration for various combinations of parameters over a range of frequencies, including the resonant frequency.

Modular Turbulence Modeling Applied to an Engine Intake

2013 ◽  
Vol 136 (5) ◽  
Author(s):  
Ugochukwu R. Oriji ◽  
Paul G. Tucker
Keyword(s):  
Surface Roughness ◽  
Turbulence Modeling ◽  
Fluid Dynamic ◽  
Navier Stokes ◽  
Test Cases ◽  
Laminar Separation ◽  
Streamline Curvature ◽  
Favorable Pressure Gradient ◽  
Flow Features ◽  
The One

The one equation Spalart–Allmaras (SA) turbulence model in an extended modular form is presented. It is employed for the prediction of crosswind flow around the lip of a 90 deg sector of an intake with and without surface roughness. The flow features around the lip are complex. There exists a region of high streamline curvature. For this, the Richardson number would suggest complete degeneration to laminar flow. Also, there are regions of high favorable pressure gradient (FPG) sufficient to laminarize a turbulent boundary layer (BL). This is all terminated by a shock and followed by a laminar separation. Under these severe conditions, the SA model is insensitive to capturing the effects of laminarization and the reenergization of eddy viscosity. The latter promotes the momentum transfer and correct reattachment prior to the fan face. Through distinct modules, the SA model has been modified to account for the effect of laminarization and separation induced transition. The modules have been implemented in the Rolls-Royce HYDRA computational fluid dynamic (CFD) solver. They have been validated over a number of experimental test cases involving laminarization and also surface roughness. The validated modules are finally applied in unsteady Reynolds-averaged Navier–Stokes (URANS) mode to flow around an engine intake and comparisons made with measurements. Encouraging agreement is found and hence advances made towards a more reliable intake design framework.

CFD Prediction of the Effects of Surface Roughness on Elastohydrodynamic Lubrication under Rolling/Sliding Conditions

2012 ◽  
Vol 184-185 ◽  
pp. 86-89 ◽  
Author(s):  
Shian Gao ◽  
Sutthinan Srirattayawong
Keyword(s):  
Surface Roughness ◽  
Shear Stress ◽  
Fluid Dynamic ◽  
Flow Behavior ◽  
Elastohydrodynamic Lubrication ◽  
Pressure Profile ◽  
Hertzian Contact ◽  
Pure Rolling ◽  
Large Fluctuations ◽  
Two Parameters

The surface roughness plays an important role in elastohydrodynamic lubrication (EHL). To improve the lubrication system the flow behavior and lubrication mechanism must be understood, especially in the thin film classification. The effects of surface roughness in the EHL problem are complicated and difficult to measure by experiment. Therefore numerical simulation using the computational fluid dynamic (CFD) approach is proposed in this research. The CFD model developed has taken the arbitrary surface roughness into consideration, and has been used to predict the characteristics of fluid flow, such as the pressure distribution, the minimal film thickness and the shear stress. The cylinder is considered to be under elastic deformation according to the theory of Hertzian contact and the surface of cylinder is defined to have an arbitrary roughness. The simulation results show that the surface roughness has significant effects on the pressure profile and shear stress, especially in the case of pure rolling, where the two parameters in the rough surface case show large fluctuations that are much higher than the corresponding smooth surface case.

On the effects of two-dimensional Reynolds roughness in hydrodynamic lubrication

1978 ◽  
Vol 364 (1716) ◽  
pp. 89-106 ◽  
Keyword(s):  
Surface Roughness ◽  
Numerical Computation ◽  
Autocorrelation Function ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
The Other ◽  
Roughness Height ◽  
Two Dimensional ◽  
Roughness Effects ◽  
Dimensional Surface

The hydrodynamic lubrication of rough surfaces is analysed with the Reynolds equation, whose application requires the roughness spacing to be large, and the roughness height to be small, compared with the thick­ness of the fluid film. The general two-dimensional surface roughness is considered, and results applicable to any roughness structure are obtained. It is revealed analytically that two types of term contribute to roughness effects: one depends on the shape of the autocorrelation function and the other does not. The former contribution was neglected by previous workers. The numerical computation of an example shows that these two contributions are comparable in magnitude.

Sign in / Sign up

Export Citation Format

Share Document