Flow in Finite-Width, Thrust Bearings Including Inertial Effects: I—Laminar Flow

1978 ◽  
Vol 100 (3) ◽  
pp. 330-338 ◽  
Author(s):  
B. E. Launder ◽  
M. Leschziner
Keyword(s):  
Laminar Flow ◽  
Numerical Procedure ◽  
Solution Procedure ◽  
Finite Width ◽  
Inertial Effects ◽  
Full Inclusion ◽  
Thrust Bearings ◽  
Flow Problems ◽  
Differential Approach ◽  
Inertial Flow

Presented is a new numerical procedure for the calculation of flow in finite-width bearing films. The method, based on the integro-differential approach, is a development of schemes devised by Patankar and Spalding [8] and Gosman and Pun [9] for general flows occurring in fields other than tribology. Principal features of the method are: the full inclusion of inertial effects; the retention of “primitive” variables; the use of a marching solution procedure using line-by-line solution of the discretized conservation equations. Applications to several aspects of laminar inertial flow problems are discussed.

Flow in Finite-Width Thrust Bearings Including Inertial Effects: II—Turbulent Flow

1978 ◽  
Vol 100 (3) ◽  
pp. 339-345 ◽  
Author(s):  
B. E. Launder ◽  
M. A. Leschziner
Keyword(s):  
Turbulent Viscosity ◽  
Turbulence Energy ◽  
Finite Width ◽  
Fluid Inertia ◽  
Inertia Effects ◽  
Thrust Bearings ◽  
Inertial Flow ◽  
Transport Effects ◽  
Rate Of Dissipation ◽  
Selection Of

A new set of turbulent resistance laws for hydrodynamic lubricant films has been derived with the aid of a turbulence model which includes transport effects on two turbulence parameters. The model consists of two differential equations for the turbulence energy and its rate of dissipation and a constitutive equation for the turbulent viscosity. The model places no restrictions on the Reynolds number. An efficient finite-difference scheme, based on the integro-differential approach and incorporating the resistance laws and a set of accurate inertial coefficients, is applied to the solution of the turbulent inertial flow in finite-width slider bearings. A selection of predictions is presented for non-inertial and inertial flows. The former are compared with solutions obtained with alternative turbulent lubrication theories. The importance of including fluid inertia effects is demonstrated.

Numerical prediction of the performance of gas-lubricated spiral groove thrust bearings

1997 ◽  
Vol 211 (2) ◽  
pp. 117-128 ◽  
Author(s):  
Y Yue ◽  
T. A. Stolarski
Keyword(s):  
Control Volume ◽  
Numerical Procedure ◽  
Operating Conditions ◽  
Hydrodynamic Bearings ◽  
Thrust Bearings ◽  
Flow Balance ◽  
Control Volumes ◽  
Volume Method ◽  
Spiral Angle ◽  
Spiral Grooves

The objective of this paper is to develop an accurate numerical procedure for the analysis of nominally flat contacts with spiral grooves lubricated by gases. The numerical procedure, which is based on the control-volume method, enables the solutions of the non-linear Reynolds equation to be obtained without limitation in geometry and operating conditions. Satisfactory flow balance was achieved on the control volumes as well as on the whole boundary and the method was proved to be very accurate. Convergence of the method was quick for any compressibility number. Three types of contact with spiral grooves were analysed. They were hydrodynamic bearings without interior chambers, hydrodynamic bearings with interior chambers and hybrid bearings. The effects of spiral angle, groove geometry (length, depth and width) and compressibility on performances were investigated for all possible designs.

Contact force analysis on two-fingered robot grasping

2020 ◽  
pp. 146441932096402
Author(s):  
Jiun-Ru Chen ◽  
Wei-En Chen ◽  
CH Liu ◽  
Yin-Tien Wang ◽  
CB Lin ◽  
...  
Keyword(s):  
Kinetic Analysis ◽  
Contact Force ◽  
Numerical Procedure ◽  
Spherical Body ◽  
Solution Procedure ◽  
The Body ◽  
Contact Forces ◽  
Grasping Forces ◽  
Robot Grasping ◽  
Force Displacement

A procedure for inverse kinetic analysis on two hard fingers grasping a hard sphere is proposed in this study. Contact forces may be found for given linear and angular accelerations of a spherical body. Elastic force-displacement relations predicted by Hertz contact theory are used to remove the indeterminancy produced by rigid body modelling. Two types of inverse kinetic analysis may be dealt with. Firstly, as the fingers impose a given tightening displacement on the body, and carry it to move with known accelerations, corresponding grasping forces may be determined by a numerical procedure. In this procedure one contact force may be chosen as the principal unknown, and all other contact forces are expressed in terms of this force. The numerical procedure is hence very efficient since it deals with a problem with only one unknown. The solution procedure eliminates slipping thus only nonslip solutions, if they exist, are found. Secondly, when the body is moving with known accelerations, if the grasping direction of the two fingers is also known, then the minimum tightening displacement required for non-sliding grasping may be obtained in closed form. In short, the proposed technique deals with a grasping system that has accelerations, and in this study the authors show that indeterminancy may be used to reduce the complexity of the problem.

LDA Measurements and Numerical Prediction of Pulsatile Laminar Flow in a Plane 90-Degree Bifurcation

1988 ◽  
Vol 110 (2) ◽  
pp. 129-136 ◽  
Author(s):  
J. M. Khodadadi ◽  
N. S. Vlachos ◽  
D. Liepsch ◽  
S. Moravec
Keyword(s):  
Laminar Flow ◽  
Numerical Study ◽  
Numerical Procedure ◽  
Stokes Number ◽  
Flow Rate Ratio ◽  
Velocity Measurements ◽  
Numerical Predictions ◽  
Dependent Variables ◽  
Separation Zones ◽  
Good Agreement

An experimental and numerical study of pulsatile laminar flow in a plane 90-degree bifurcation is presented. Detailed LDA velocity measurements of the oscillatory flow field have been carried out. The numerical predictions, which are based on an iterative, finite-difference numerical procedure using primitive dependent variables, are in good agreement with the measurements. The results show that one separation zone is established near the bottom wall of the main duct and another near the upstream wall of the branch. The location and size of the separation zones vary within the cycle and are influenced by the Reynolds number, the flow rate ratio, and the Stokes number.

Mathematical Modelling and Field Measurements of Nitrogen Oxides in Metropolitan Areas

1992 ◽  
Vol 3 (2) ◽  
pp. 133-147
Author(s):  
M.M. Elkotb ◽  
O.M.F. Elbahar ◽  
T.A. Abdou Ahmed ◽  
T.W. Abou-Arab
Keyword(s):  
Mathematical Model ◽  
Wind Speed ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Field Measurements ◽  
Mass Conservation ◽  
Eddy Diffusivity ◽  
Solution Procedure ◽  
Pollutant Emissions ◽  
Motor Vehicles

A mathematical model for the prediction of pollutant emissions from motor vehicles is presented. The model is based on the numerical solution of the three-dimensional equation representing the mass conservation of dilute diffusing species. The variation of wind speed and eddy diffusivity with height is taken into consideration. The three-dimensional diffusion equation is solved numerically. The numerical procedure involves the discretization of the partial differential equation using the finite volume approach. The resulting set of discretization equation is solved iteratively using a fully implicit solution procedure. Furthermore, field measurements of the concentrations of nitrogen oxide in the downtown area of Cairo were conducted. For this purpose, a mobile air pollution laboratory fitted with gas analyzers, particulate matter sampler and equipment for the measurement of wind speed and direction has been used. This laboratory is also fitted with data recording and monitoring facility. The mathematical model is tested by comparing the computed pollutant concentrations with the experimental data obtained from the field measurements in the Cairo Metropolitan Area.

An Analytical/Numerical Procedure for Structural Analysis of Hybrid Riser Systems

2005 ◽  
Author(s):  
G. J. O. Rodrigues ◽  
Daniel C. T. Cardoso ◽  
Beatriz S. L. P. de Lima ◽  
Breno P. Jacob ◽  
Antonio C. Fernandes
Keyword(s):  
Finite Element ◽  
Dynamic Simulation ◽  
Production Systems ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Solution Procedure ◽  
Analysis Tool ◽  
Full Time ◽  
Transient Effects ◽  
Dimensional Solution

In deep and ultra-deep water petroleum exploitation activities, floating production systems such as semi submersible platforms and FPSO (Floating Production, Storage and Offloading) units have been commonly employed. However, the utilization of flexible risers in ultra-deep waters has been hindered by technical and economical reasons. On the other hand, first order motions from the floating unit due to environmental loads are not favorable to the use of Steel Catenary Risers (SCR) in a free-hanging configuration. This fact has motivated several studies on hybrid riser systems, including the system studied in this work, which is based on a sub-surface buoy with large dimensions, moored to the seabed by tethers. This system employs flexible lines connecting the floating unit to the buoy, in the region where dynamic effects are more relevant due to the floating unit motions, and also SCRs that extend from the buoy to the seabed, in the region where dynamic motions are not so significant. The objective of this work is to describe a solution procedure for the analysis of such a hybrid riser system. This procedure is based on an analytical formulation that is solved numerically. One of the main features of this procedure is the fact that it takes into account the effects of current loads acting on the lines. Current profiles can be considered, with direction and velocities varying with depth, therefore configuring a full three-dimensional solution. This procedure can be employed either as a preliminary static analysis tool, to be used in parametric studies in order to assess the feasibility of candidate configurations of hybrid riser systems, or else for the generation of finite-element meshes for a full time-domain nonlinear dynamic simulation. It is important to start the dynamic simulation from a statically balanced configuration, since the transient effects can be dramatically shortened and the total simulation time can be reduced. The results obtained from this procedure are compared with a discrete solution obtained using a nonlinear finite-element based solver. The strategy considered here is intended to be an approach that will speed up the tasks involved in the design of hybrid risers systems based on the subsurface buoy concept.

Numerical simulation of the evolution of Tollmien–Schlichting waves over finite compliant panels

1997 ◽  
Vol 335 ◽  
pp. 361-392 ◽  
Author(s):  
CHRISTOPHER DAVIES ◽  
PETER W. CARPENTER
Keyword(s):  
Numerical Simulation ◽  
Laminar Flow ◽  
Stokes Equations ◽  
Plane Channel ◽  
Solution Procedure ◽  
Good Prospect ◽  
Flow Perturbation ◽  
Compliant Wall ◽  
Compliant Walls ◽  
Tollmien Schlichting

The evolution of two-dimensional Tollmien–Schlichting waves propagating along a wall shear layer as it passes over a compliant panel of finite length is investigated by means of numerical simulation. It is shown that the interaction of such waves with the edges of the panel can lead to complex patterns of behaviour. The behaviour of the Tollmien–Schlichting waves in this situation, particularly the effect on their growth rate, is pertinent to the practical application of compliant walls for the delay of laminar–turbulent transition. If compliant panels could be made sufficiently short whilst retaining the capability to stabilize Tollmien–Schlichting waves, there is a good prospect that multiple-panel compliant walls could be used to maintain laminar flow at indefinitely high Reynolds numbers.We consider a model problem whereby a section of a plane channel is replaced with a compliant panel. A growing Tollmien–Schlichting wave is then introduced into the plane, rigid-walled, channel flow upstream of the compliant panel. The results obtained are very encouraging from the viewpoint of laminar-flow control. They indicate that compliant panels as short as a single Tollmien–Schlichting wavelength can have a strong stabilizing effect. In some cases the passage of the Tollmien–Schlichting wave over the panel edges leads to the excitation of stable flow-induced surface waves. The presence of these additional waves does not appear to be associated with any adverse effect on the stability of the Tollmien–Schlichting waves. Except very near the panel edges the panel response and flow perturbation can be represented by a superposition of the Tollmien–Schlichting wave and two other eigenmodes of the coupled Orr–Sommerfeld/compliant-wall eigensystem.The numerical scheme employed for the simulations is derived from a novel vorticity–velocity formulation of the linearized Navier–Stokes equations and uses a mixed finite-difference/spectral spatial discretization. This approach facilitated the development of a highly efficient solution procedure. Problems with numerical stability were overcome by combining the inertias of the compliant wall and fluid when imposing the boundary conditions. This allowed the interactively coupled fluid and wall motions to be computed without any prior restriction on the form taken by the disturbances.

The Effects of Geometry and Inertia on Face Seal Performance—Turbulent Flow

1968 ◽  
Vol 90 (2) ◽  
pp. 342-350 ◽  
Author(s):  
H. J. Sneck
Keyword(s):  
Laminar Flow ◽  
Turbulent Flow ◽  
Velocity Distribution ◽  
Power Law ◽  
Apparent Viscosity ◽  
Lubrication Theory ◽  
Inertial Effects ◽  
Face Seal ◽  
Geometric Deviations ◽  
The Ideal

The “short bearing” equation of lubrication theory, modified to include the inertial effects, is used to study the influence of geometric deviations from the ideal. The turbulent nature of the flow is described by an isotropic apparent viscosity and a power-law velocity distribution. It is found that geometric deviations from the ideal are less influential than in laminar flow.

Transient and Steady State Vibration Analysis of a Wavy Thrust Bearing

2005 ◽  
Vol 128 (1) ◽  
pp. 139-145 ◽  
Author(s):  
H. Zhao ◽  
F. K. Choy ◽  
M. J. Braun
Keyword(s):  
Steady State ◽  
Vibration Analysis ◽  
Thrust Bearing ◽  
Numerical Procedure ◽  
Operating Conditions ◽  
System Stability ◽  
Thrust Bearings ◽  
External Perturbations ◽  
Vibration Signature ◽  
Transient And Steady State

This paper describes a numerical procedure for analyzing the dynamics of transient and steady state vibrations in a wavy thrust bearing. The major effects of the wavy geometry and the operating parameters on the dynamic characteristics of the bearing had been discussed in a previous paper; the present paper thus concentrates on examining the relationships between the development of the transient and steady state vibrations when operating conditions are parametrically varied. Special attention is given to the development of steady state vibrations from initial transients with comparisons and consequences to the overall system stability. Numerical based vibration signature analysis procedures are then used to identify and quantify the transient vibrations. The conclusions provide general indicators for designing wavy thrust bearings that are less susceptible to transients induced by external perturbations.

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