Analysis of Bearings Operating in Turbulent Regime

1962 ◽  
Vol 84 (1) ◽  
pp. 139-151 ◽  
Author(s):  
V. N. Constantinescu
Keyword(s):  
Three Dimensional ◽  
Lubricant Layer ◽  
Turbulent Regime ◽  
Mixing Length ◽  
Thrust Bearings ◽  
Mixing Length Theory

Proceeding from the results obtained previously [5] this paper analyzes theoretically the three-dimensional motion in the lubricant layer by using Prandtl’s mixing length theory. Formulas and diagram are presented for calculating journal and thrust bearings subjected to turbulent lubrication.

Analysis of Thrust Bearings Operating in Turbulent Regime

1988 ◽  
Vol 110 (3) ◽  
pp. 555-560 ◽  
Author(s):  
M. Harada ◽  
H. Aoki
Keyword(s):  
Steady State ◽  
Thrust Bearing ◽  
Three Dimensional ◽  
Cross Coupling ◽  
Fluid Film ◽  
Turbulent Regime ◽  
Pressure Gradients ◽  
Mixing Length ◽  
Thrust Bearings ◽  
Mixing Length Theory

This paper relates to the turbulent motion in the lubricant fluid film with centrifugal effects and the lubrication theory for thrust bearings operating in turbulent regime. Using Prandtl’s mixing-length theory, three-dimensional turbulent velocity distributions, including pressure gradients and centrifugal effects, are calculated, and the cross-coupling of nonplanar flow of the lubricant fluid film is discussed. From these results, turbulent lubrication equations with centrifugal effects are derived. Applying these lubrication equations to a sectorial inclined thrust bearing, the steady-state characteristics and the dynamic ones are calculated.

Solution for the Pressure and Temperature in Thrust Bearings Operating in the Thermohydrodynamic Turbulent Regime

1974 ◽  
Vol 96 (1) ◽  
pp. 58-68 ◽  
Author(s):  
K. H. Huebner
Keyword(s):  
Thermal Effects ◽  
Eddy Viscosity ◽  
Turbulent Transport ◽  
Three Dimensional ◽  
Turbulent Shear ◽  
Turbulent Regime ◽  
Reynolds Analogy ◽  
Thrust Bearings ◽  
Law Of The Wall ◽  
Lubricant Viscosity

A numerical solution is developed for the equations governing the turbulent thermohydrodynamic flow in a sector shaped thrust bearing. The lubricant viscosity is taken as a function of the three-dimensional temperature distribution in the fluid-film. Three-dimensional heat transfer between the lubricant and both the moving and stationary solids is included in the analysis. Isotropy of the turbulent mixing process is assumed. The “law of the wall” for turbulent shear flows is used to define an eddy viscosity based on the local wall shear stress and the viscosity within the film. A modified Reynolds analogy is assumed to relate the turbulent transport of heat and momentum. According to the Ng-Pan theory the momentum transport equations are linearized by assuming the nonplanar flow is a small perturbation of turbulent Couette flow. Thermal effects are shown to be less pronounced in turbulent flow than in laminar flow.

scholarly journals Convection with misaligned gravity and rotation: simulations and rotating mixing length theory

2020 ◽  
Vol 493 (4) ◽  
pp. 5233-5256 ◽  
Author(s):  
Laura K Currie ◽  
Adrian J Barker ◽  
Yoram Lithwick ◽  
Matthew K Browning
Keyword(s):  
Temperature Gradient ◽  
Heat Transport ◽  
Three Dimensional ◽  
Single Mode ◽  
Small Region ◽  
Spatial Spectrum ◽  
Mixing Length ◽  
Zonal Flows ◽  
Polar Latitude ◽  
Mixing Length Theory

ABSTRACT We present numerical simulations, using two complementary set-ups, of rotating Boussinesq thermal convection in a three-dimensional Cartesian geometry with misaligned gravity and rotation vectors. This model represents a small region at a non-polar latitude in the convection zone of a star or planet. We investigate the effects of rotation on the bulk properties of convection at different latitudes, focusing on determining the relation between the heat flux and temperature gradient. We show that our results may be interpreted using rotating mixing length theory (RMLT). The simplest version of RMLT (due to Stevenson) considers the single mode that transports the most heat. This works reasonably well in explaining our results, but there is a systematic departure from these predictions (up to approximately $30{{\ \rm per\ cent}}$ in the temperature gradient) at mid-latitudes. We develop a more detailed treatment of RMLT that includes the transport afforded by multiple modes, and we show that this accounts for most of the systematic differences. We also show that convectively generated zonal flows and meridional circulations are produced in our simulations, and that their properties depend strongly on the dimensions of the box. These flows also affect the heat transport, contributing to departures from RMLT at some latitudes. However, we find the theoretical predictions of the multi-mode theory for the mid-layer temperature gradient, the root-mean-square (rms) vertical velocity, the rms temperature fluctuation, and the spatial spectrum of the heat transport at different latitudes are all in reasonably good agreement with our numerical results when zonal flows are small.

A Transition-Turbulent Lubrication Theory Using Mixing Length Concept

1993 ◽  
Vol 115 (4) ◽  
pp. 591-596
Author(s):  
P. B. Kosasih ◽  
A. K. Tieu
Keyword(s):  
Reynolds Stress ◽  
Stress Gradient ◽  
Three Dimensional ◽  
Turbulent Regime ◽  
Transition Regime ◽  
Mixing Length ◽  
Parallel Plates ◽  
Pressure Distributions ◽  
Load Carrying ◽  
Local Shear

This paper applies the recently introduced Reynolds stress expression (Tieu and Kosasih, 1992) in the transition-turbulent lubrication analysis. The Reynolds stress is modeled using the mixing length expression which is able to account for the effect of local shear stress gradient, and it can be extended to apply in the transition regime. This theory is then used to determine three-dimensional velocity distributions between parallel plates. From the results, a set of coefficients covering transition-turbulent regime used in conjunction with the modified Reynolds equation is presented. It is shown that the resulting coefficients agree well with results of Elrod and Ng (1967) in the fully turbulent regime while differences are shown in the transition regime. Pressure distributions and load carrying capacity of superlaminar journal bearing are compared with available experimental data.

scholarly journals The Mixing Length Ratio, Eddy Diffusivity and Acoustic Waves

1988 ◽  
Vol 108 ◽  
pp. 191-192
Author(s):  
Kwing L. Chan ◽  
Sabatino Sofia
Keyword(s):  
Acoustic Waves ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Eddy Diffusivity ◽  
Rectangular Domain ◽  
Numerical Results ◽  
Length Ratio ◽  
Mixing Length ◽  
Mixing Length Theory

Many processes in the convection zone of a star affect the evolution and the atmospheric diagnostics. Here, a progress report is given on our numerical study of some convection related phenomena. The numerical results are obtained by solving the Navier Stokes equations in a three dimensional rectangular domain. The units are chosen such that the initial temperature, pressure, density, and the depth of the domain are all normalized to 1.The mixing length theory relates the convective (enthalpy) flux FC to the envelope structure quite well (Chan and Sofia 1987). For efficient convection that occurs in deep convective regions, the numerical results are compatible with a mixing length ratio of 2.1. The mixing length theory fails to address the significance of the flux of kinetic energy FKE (see Figure 1). FKE is negative and has a magnitude comparable to the total flux. These results are qualitatively similar to those of two dimensional computations (Hurlburt et. al. 1984).

Pulsating white dwarfs and convection

2019 ◽  
Vol 15 (S357) ◽  
pp. 127-130
Author(s):  
J. L. Provencal ◽  
M. H. Montgomery ◽  
H. L. Shipman ◽  
Keyword(s):  
Local Time ◽  
White Dwarfs ◽  
Recent Progress ◽  
Three Dimensional ◽  
Theoretical Uncertainty ◽  
Mixing Length ◽  
Mixing Length Theory

AbstractConvection is a highly turbulent, three dimensional process that is traditionally treated using a simple, local, time independent description. Convection is one of the largest sources of theoretical uncertainty in stellar modeling. We outline recent progress in studies using pulsating white dwarfs to constrain convection and calibrate mixing length theory.

A Liquid Metal Flow Between Two Coaxial Cylinders System

2019 ◽  
Vol 11 (1) ◽  
pp. 79-86
Author(s):  
Abdelkrim Merah ◽  
Ridha Kelaiaia ◽  
Faiza Mokhtari
Keyword(s):  
Couette Flow ◽  
Metal Flow ◽  
Three Dimensional ◽  
Liquid Sodium ◽  
Taylor Vortex ◽  
Turbulent Regime ◽  
Coaxial Cylinders ◽  
Concentric Cylinders ◽  
Ideal Tool ◽  
The Stability

Abstract The Taylor-Couette flow between two rotating coaxial cylinders remains an ideal tool for understanding the mechanism of the transition from laminar to turbulent regime in rotating flow for the scientific community. We present for different Taylor numbers a set of three-dimensional numerical investigations of the stability and transition from Couette flow to Taylor vortex regime of a viscous incompressible fluid (liquid sodium) between two concentric cylinders with the inner one rotating and the outer one at rest. We seek the onset of the first instability and we compare the obtained results for different velocity rates. We calculate the corresponding Taylor number in order to show its effect on flow patterns and pressure field.

EXPERIMENTAL INVESTIGATION OF FLOW RESPONSE TO STATIONARY DISTURBANCE IN ROTATING-DISK FLOW

2019 ◽  
Vol XVI (2) ◽  
pp. 13-22
Author(s):  
Muhammad Ehtisham Siddiqui
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Three Dimensional ◽  
Rotating Disk ◽  
Careful Analysis ◽  
Laboratory Frame ◽  
Transition To Turbulence ◽  
Turbulent Regime ◽  
Mean Velocity ◽  
Layer Flow

Three-dimensional boundary-layer flow is well known for its abrupt and sharp transition from laminar to turbulent regime. The presented study is a first attempt to achieve the target of delaying the natural transition to turbulence. The behaviour of two different shaped and sized stationary disturbances (in the laboratory frame) on the rotating-disk boundary layer flow is investigated. These disturbances are placed at dimensionless radial location (Rf = 340) which lies within the convectively unstable zone over a rotating-disk. Mean velocity profiles were measured using constant-temperature hot-wire anemometry. By careful analysis of experimental data, the instability of these disturbance wakes and its estimated orientation within the boundary-layer were investigated.

Turbulent three-dimensional dielectric electrohydrodynamic convection between two plates

2012 ◽  
Vol 696 ◽  
pp. 228-262 ◽  
Author(s):  
A. Kourmatzis ◽  
J. S. Shrimpton
Keyword(s):  
Spatial Data ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Energy Budgets ◽  
Turbulent Regime ◽  
Scalar Flux ◽  
Wide Range ◽  
Scalar Variance

AbstractThe fundamental mechanisms responsible for the creation of electrohydrodynamically driven roll structures in free electroconvection between two plates are analysed with reference to traditional Rayleigh–Bénard convection (RBC). Previously available knowledge limited to two dimensions is extended to three-dimensions, and a wide range of electric Reynolds numbers is analysed, extending into a fully inherently three-dimensional turbulent regime. Results reveal that structures appearing in three-dimensional electrohydrodynamics (EHD) are similar to those observed for RBC, and while two-dimensional EHD results bear some similarities with the three-dimensional results there are distinct differences. Analysis of two-point correlations and integral length scales show that full three-dimensional electroconvection is more chaotic than in two dimensions and this is also noted by qualitatively observing the roll structures that arise for both low (${\mathit{Re}}_{E} = 1$) and high electric Reynolds numbers (up to ${\mathit{Re}}_{E} = 120$). Furthermore, calculations of mean profiles and second-order moments along with energy budgets and spectra have examined the validity of neglecting the fluctuating electric field ${ E}_{i}^{\ensuremath{\prime} } $ in the Reynolds-averaged EHD equations and provide insight into the generation and transport mechanisms of turbulent EHD. Spectral and spatial data clearly indicate how fluctuating energy is transferred from electrical to hydrodynamic forms, on moving through the domain away from the charging electrode. It is shown that ${ E}_{i}^{\ensuremath{\prime} } $ is not negligible close to the walls and terms acting as sources and sinks in the turbulent kinetic energy, turbulent scalar flux and turbulent scalar variance equations are examined. Profiles of hydrodynamic terms in the budgets resemble those in the literature for RBC; however there are terms specific to EHD that are significant, indicating that the transfer of energy in EHD is also attributed to further electrodynamic terms and a strong coupling exists between the charge flux and variance, due to the ionic drift term.

scholarly journals Run-Up Simulation of a Semi-Floating Ring Supported Turbocharger Rotor Considering Thrust Bearing and Mass-Conserving Cavitation

Lubricants ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 44
Author(s):  
Christian Ziese ◽  
Cornelius Irmscher ◽  
Steffen Nitzschke ◽  
Christian Daniel ◽  
Elmar Woschke
Keyword(s):  
Reynolds Equation ◽  
Energy Equation ◽  
Thrust Bearing ◽  
Three Dimensional ◽  
Reliable Prediction ◽  
Two Phase ◽  
Hydrodynamic Bearings ◽  
Thrust Bearings ◽  
Run Up ◽  
The Impact

The vibration behaviour of turbocharger rotors is influenced by the acting loads as well as by the type and arrangement of the hydrodynamic bearings and their operating condition. Due to the highly non-linear bearing behaviour, lubricant film-induced excitations can occur, which lead to sub-synchronous rotor vibrations. A significant impact on the oscillation behaviour is attributed to the pressure distribution in the hydrodynamic bearings, which is influenced by the thermo-hydrodynamic conditions and the occurrence of outgassing processes. This contribution investigates the vibration behaviour of a floating ring supported turbocharger rotor. For detailed modelling of the bearings, the Reynolds equation with mass-conserving cavitation, the three-dimensional energy equation and the heat conduction equation are solved. To examine the impact of outgassing processes and thrust bearing on the occurrence of sub-synchronous rotor vibrations separately, a variation of the bearing model is made. This includes run-up simulations considering or neglecting thrust bearings and two-phase flow in the lubrication gap. It is shown that, for a reliable prediction of sub-synchronous vibrations, both the modelling of outgassing processes in hydrodynamic bearings and the consideration of thrust bearing are necessary.

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