A Theory of Lubrication With Turbulent Flow and Its Application to Slider Bearings

1960 ◽  
Vol 27 (1) ◽  
pp. 1-4 ◽  
Author(s):  
L. N. Tao
Keyword(s):  
Exact Solution ◽  
Reynolds Number ◽  
Turbulent Flow ◽  
Closed Form ◽  
Governing Equation ◽  
Reynolds Equation ◽  
Three Dimensions ◽  
Slider Bearing ◽  
Numerical Example ◽  
Special Case

The governing equation of turbulent lubrication in three dimensions, equivalent to the Reynolds equation of laminar lubrication, is derived. The problem of a slider bearing with no side leakage is then analyzed. An exact solution is found in closed form. Bearing characteristics are also established. It is found that the Reynolds number is an important parameter in the problem of turbulent lubrication. Furthermore, it is shown that the laminar lubrication may be considered as the special case of the present study. A numerical example is also included.

THREE-BODY FORCE MODELS OF NONHYPERCENTRAL HARMONIC AND ANHARMONIC POTENTIALS IN THREE-DIMENSIONAL POTENTIALS

2008 ◽  
Vol 23 (40) ◽  
pp. 3411-3417 ◽  
Author(s):  
M. R. SHOJAEI ◽  
A. A. RAJABI
Keyword(s):  
Exact Solution ◽  
Body Force ◽  
Three Dimensional ◽  
Hyperspherical Harmonic ◽  
Three Dimensions ◽  
Systematic Analysis ◽  
Relative Coordinates ◽  
Internal Particle ◽  
Three Body ◽  
Special Case

We present a theoretical approach to the internal motion of a system based on three-body forces among particles in a special case, using three-body potentials. The three-body force models are more easily introduced and treated within the hyperspherical harmonic formalism. The internal particle motion is usually described by means of the Jacobian relative coordinates ρ, λ and R. The problems related to three-body nonhypercentral potentials in three dimensions are investigated. While the difficulties that arise in the study of nonhypercentral potentials are explicitly shown, we discuss some results obtained using nonhypercentral harmonic and anharmonic and some inverse power terms; however the potential can be easily generalized in order to allow a systematic analysis, which presents an exact solution to the wave function. The method is also applied to some other types of potentials.

Numerical and Experimental Analysis of Turbulent Flow in Corrugated Pipes

2010 ◽  
Vol 132 (7) ◽  
Author(s):  
Henrique Stel ◽  
Rigoberto E. M. Morales ◽  
Admilson T. Franco ◽  
Silvio L. M. Junqueira ◽  
Raul H. Erthal ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Turbulence Models ◽  
Reynolds Numbers ◽  
Velocity Magnitude ◽  
Geometric Configurations ◽  
Corrugated Surfaces ◽  
Friction Factors

This article describes a numerical and experimental investigation of turbulent flow in pipes with periodic “d-type” corrugations. Four geometric configurations of d-type corrugated surfaces with different groove heights and lengths are evaluated, and calculations for Reynolds numbers ranging from 5000 to 100,000 are performed. The numerical analysis is carried out using computational fluid dynamics, and two turbulence models are considered: the two-equation, low-Reynolds-number Chen–Kim k-ε turbulence model, for which several flow properties such as friction factor, Reynolds stress, and turbulence kinetic energy are computed, and the algebraic LVEL model, used only to compute the friction factors and a velocity magnitude profile for comparison. An experimental loop is designed to perform pressure-drop measurements of turbulent water flow in corrugated pipes for the different geometric configurations. Pressure-drop values are correlated with the friction factor to validate the numerical results. These show that, in general, the magnitudes of all the flow quantities analyzed increase near the corrugated wall and that this increase tends to be more significant for higher Reynolds numbers as well as for larger grooves. According to previous studies, these results may be related to enhanced momentum transfer between the groove and core flow as the Reynolds number and groove length increase. Numerical friction factors for both the Chen–Kim k-ε and LVEL turbulence models show good agreement with the experimental measurements.

Closed-Form Displacement Relations of a Five-Link R-R-C-C-R Spatial Mechanism

1971 ◽  
Vol 93 (1) ◽  
pp. 221-226 ◽  
Author(s):  
A. H. Soni ◽  
P. R. Pamidi
Keyword(s):  
Closed Form ◽  
Polynomial Equation ◽  
Input Output ◽  
Degree Polynomial ◽  
Spatial Mechanism ◽  
Dual Number ◽  
Numerical Example

Using (3 × 3) matrices with dual-number elements, closed form displacement relationships are derived for a spatial five-link R-R-C-C-R mechanism. The input-output closed form displacement relationship is an eighth degree polynomial equation. A numerical example is presented.

Turbulent flow between concentric rotating cylinders at large Reynolds number

1992 ◽  
Vol 68 (10) ◽  
pp. 1515-1518 ◽  
Author(s):  
Daniel P. Lathrop ◽  
Jay Fineberg ◽  
Harry L. Swinney
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Large Reynolds Number ◽  
Rotating Cylinders

Parameter Extension Simulation of Turbulent Flows in a Compressor Cascade With a High Reynolds Number

2020 ◽  
Author(s):  
Yan Jin
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Simulation Method ◽  
Potential Method ◽  
Navier Stokes ◽  
Reference Solution ◽  
Compressor Cascade ◽  
High Reynolds

Abstract The turbulent flow in a compressor cascade is calculated by using a new simulation method, i.e., parameter extension simulation (PES). It is defined as the calculation of a turbulent flow with the help of a reference solution. A special large-eddy simulation (LES) method is developed to calculate the reference solution for PES. Then, the reference solution is extended to approximate the exact solution for the Navier-Stokes equations. The Richardson extrapolation is used to estimate the model error. The compressor cascade is made of NACA0065-009 airfoils. The Reynolds number 3.82 × 105 and the attack angles −2° to 7° are accounted for in the study. The effects of the end-walls, attack angle, and tripping bands on the flow are analyzed. The PES results are compared with the experimental data as well as the LES results using the Smagorinsky, k-equation and WALE subgrid models. The numerical results show that the PES requires a lower mesh resolution than the other LES methods. The details of the flow field including the laminar-turbulence transition can be directly captured from the PES results without introducing any additional model. These characteristics make the PES a potential method for simulating flows in turbomachinery with high Reynolds numbers.

Do We Need Higher Dose Scale Inhibitors to Inhibit Scale under Turbulent Conditions? Insight into Mechanisms and New Test Methodology

2014 ◽  
Author(s):  
Tao Chen ◽  
Ping Chen ◽  
Harry Montgomerie ◽  
Thomas Hagen ◽  
Ronald Benvie ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Growth Inhibitor ◽  
Test Method ◽  
Bulk Precipitation ◽  
Scale Inhibitor ◽  
Surface Deposition ◽  
Test Methodology ◽  
The Relationship ◽  
Scale Deposition

Abstract Turbulent flow, especially around chokes, downhole safety valves and inflow control devices, favors scale deposition potentially leading to severe loss of production. Recently, scale formation under turbulent conditions has been studied and progressed, focused on the bulk precipitation (SPE164070) and a small bore valve loop test (SPE 155428). However, bulk precipitation is not fully representative the surface deposition in the fields and the Reynolds number of modified loop is unknown. The relationship between a measured Reynolds number and surface deposition up until this study has not been addressed. A newly developed test methodology with rotating cylinder has been applied to generate high shear rate and evaluate surface deposition with Reynolds numbers up to ~41000. The relationship between Reynolds number and surface deposition is addressed. Using this highly representable test method for BaSO4 scale deposition, several different generic types of inhibitor chemistries, including polymers and phosphonates, were assessed under different levels of turbulence to evaluate their performance on surface deposition. The results showed it is not always true that higher turbulence results in higher dose of inhibitor being required to control scale. It is inhibitor chemistry and mechanisms dependent. The scale inhibitorscan be classified as three types when evaluating the trend of mass deposition versus Reynolds number and the morphology of the crystals deposited on the metal surface. ➢ Type 1: Crytal growth inhibitors. The mass of surface deposition increases with the increase of turbulence, along with smaller crystals.➢ Type 2: Dispersion and crystal growth inhibitor. The higher the turbulence, the less mass deposition, along with smaller crystals.➢ Type 3: Dispersion scale inhibitors. The higher the turbulence, the less mass deposition. The size of the crystals has no major change. This paper gives a comprehensive study of the effect of flow condition on the scale surface deposition and inhibition mechanisms. In addition, it details how this methodology and new environmentally acceptable inhibitor chemistry can be coupled to develop a chemical technology toolbox that also includes techniques for advanced scale inhibitor analysis and improved scale inhibitor retention, to design optimum scale squeeze packages for the harsh scaling conditions associated with turbulent flow conditions.

The Effect of Lubricant Inertia in Journal-Bearing Lubrication

1957 ◽  
Vol 24 (4) ◽  
pp. 494-496
Author(s):  
J. F. Osterle ◽  
Y. T. Chou ◽  
E. A. Saibel
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Hydrodynamic Theory ◽  
Simple Relationship ◽  
Inertia Effect ◽  
Laminar Regime ◽  
Steady State Operation

Abstract The Reynolds equation of hydrodynamic theory, modified to take lubricant inertia into approximate account, is applied to the steady-state operation of journal bearings to determine the effect of lubricant inertia on the pressure developed in the lubricant. A simple relationship results, relating this “inertial” pressure to the Reynolds number of the flow. It is found that the inertia effect can be significant in the laminar regime.

Sign in / Sign up

Export Citation Format

Share Document