Centrifugal Effects in Thrust Bearings and Seals Under Laminar Conditions

1981 ◽  
Vol 103 (1) ◽  
pp. 126-136 ◽  
Author(s):  
Oscar Pinkus ◽  
J. W. Lund
Keyword(s):  
High Speed ◽  
Stokes Equations ◽  
Load Capacity ◽  
Finite Difference Methods ◽  
Navier Stokes ◽  
Negative Consequences ◽  
Centrifugal Forces ◽  
Thrust Bearings ◽  
Dominant Component ◽  
The Individual

An analysis is conducted and solutions are provided for the effect of centrifugal forces on the hydrodynamics of high-speed thrust bearings and seals. First, a scrutiny of the individual inertia terms of the Navier-Stokes equations delineates the circumstances under which the centrifugal term (u2/r) becomes the dominant component. A Reynolds equation incorporating centrifugal forces is then derived for finite sectorial configurations operating under incompressible laminar conditions. Thermal effects are included. The equation is solved by finite difference methods. The results show that at the upper limits of laminar operation centrifugal forces reduce considerably the load capacity and alter the pattern of lubricant flow. As a result, at sufficiently high velocities the inflow of lubricant at the inner radius of a sectorial configuration may bring about the scavenging of lubricant from wide portions of the bearing surface, producing a form of thrust bearing cavitation. Design features which would reduce the negative consequences of centrifugal action are outlined, including the introduction of radial tapers.

Theory Versus Experiment for the Effects of Pressure Ratio on the Performance of an Orifice-Compensated Hybrid Bearing

1998 ◽  
Vol 120 (4) ◽  
pp. 930-936 ◽  
Author(s):  
P. Mosher ◽  
D. W. Childs
Keyword(s):  
High Speed ◽  
Stokes Equations ◽  
Load Capacity ◽  
Dynamic Stiffness ◽  
Pressure Ratio ◽  
Navier Stokes ◽  
Rotordynamic Coefficients ◽  
Wide Range ◽  
Bearing Load ◽  
Hybrid Bearing

This research investigates the effect of varying the concentric recess pressure ratio of hybrid (combination hydrostatic and hydrodynamic) bearings to be used in high-speed, high-pressure applications. Bearing flowrate, load capacity, torque, rotordynamic coefficients, and whirl frequency ratio are examined to determine the concentric, recess-pressure ratio which yields optimum bearing load capacity and dynamic stiffness. An analytical model, using two-dimensional bulk-flow Navier-Stokes equations and anchored by experimental test results, is used to examine bearing performance over a wide range of concentric recess pressure ratios. Typically, a concentric recess pressure ratio of 0.50 is used to obtain maximum bearing load capacity. This analysis reveals that theoretical optimum bearing performance occurs for a pressure ratio near 0.40, while experimental results indicate the optimum value to he somewhat higher than 0.45. This research demonstrates the ability to analytically investigate hybrid bearings and shows the need for more hybrid-bearing experimental data.

Quantitative Analysis of Reynolds and Navier–Stokes Based Modeling Approaches for Isothermal Newtonian Elastohydrodynamic Lubrication

2021 ◽  
Vol 143 (12) ◽  
Author(s):  
Leoluca Scurria ◽  
Tommaso Tamarozzi ◽  
Oleg Voronkov ◽  
Dieter Fauconnier
Keyword(s):  
High Speed ◽  
Stokes Equations ◽  
Thickness Distribution ◽  
Elastohydrodynamic Lubrication ◽  
Lubricant Film ◽  
Secondary Flows ◽  
Navier Stokes ◽  
Shear Stresses ◽  
Low Viscosity ◽  
Fluid Film Thickness

Abstract When simulating elastohydrodynamic lubrication, two main approaches are usually followed to predict the pressure and fluid film thickness distribution throughout the contact. The conventional approach relies on the Reynolds equation to describe the thin lubricant film, which is coupled to a Boussinesq description of the linear elastic deformation of the solids. A more accurate, yet a time-consuming method is the use of computational fluid dynamics in which the Navier–Stokes equations describe the flow of the thin lubricant film, coupled to a finite element solver for the description of the local contact deformation. This investigation aims at assessing both methods for different lubrication conditions in different elastohydrodynamic lubrication (EHL) regimes and quantify their differences to understand advantages and limitations of both methods. This investigation shows how the results from both approaches deviate for three scenarios: (1) inertial contributions (Re > 1), i.e., thick films, high speed, and low viscosity; (2) high shear stresses leading to secondary flows; and (3) large deformations of the solids leading to inaccuracies of the Boussinesq equation.

The numerical analysis of bifurcation problems with application to fluid mechanics

Acta Numerica ◽  
2000 ◽  
Vol 9 ◽  
pp. 39-131 ◽  
Author(s):  
K. A. Cliffe ◽  
A. Spence ◽  
S. J. Tavener
Keyword(s):  
Numerical Analysis ◽  
Fluid Mechanics ◽  
Stokes Equations ◽  
Mixed Finite Element ◽  
Finite Difference Methods ◽  
Singularity Theory ◽  
Mixed Finite Element Method ◽  
Convergence Theory ◽  
Navier Stokes ◽  
Bifurcation Problems

In this review we discuss bifurcation theory in a Banach space setting using the singularity theory developed by Golubitsky and Schaeffer to classify bifurcation points. The numerical analysis of bifurcation problems is discussed and the convergence theory for several important bifurcations is described for both projection and finite difference methods. These results are used to provide a convergence theory for the mixed finite element method applied to the steady incompressible Navier–Stokes equations. Numerical methods for the calculation of several common bifurcations are described and the performance of these methods is illustrated by application to several problems in fluid mechanics. A detailed description of the Taylor–Couette problem is given, and extensive numerical and experimental results are provided for comparison and discussion.

Analytical and Semi-empirical Models of Tornadoes and Downbursts

2021 ◽  
Author(s):  
Djordje Romanic ◽  
Horia Hangan
Keyword(s):  
Numerical Simulations ◽  
Stokes Equations ◽  
Empirical Models ◽  
Navier Stokes ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Boundary Layer Equations ◽  
Simplifying Assumptions ◽  
The Individual ◽  
Semi Empirical

Analytical and semi-empirical models are inexpensive to run and can complement experimental and numerical simulations for risk analysis-related applications. Some models are developed by employing simplifying assumptions in the Navier-Stokes equations and searching for exact, but many times inviscid solutions occasionally complemented by boundary layer equations to take surface effects into account. Other use simple superposition of generic, canonical flows for which the individual solutions are known. These solutions are then ensembled together by empirical or semi-empirical fitting procedures. Few models address turbulent or fluctuating flow fields, and all models have a series of constants that are fitted against experiments or numerical simulations. This chapter presents the main models used to provide primarily mean flow solutions for tornadoes and downbursts. The models are organized based on the adopted solution techniques, with an emphasis on their assumptions and validity.

scholarly journals Flow Pressure Behavior Downstream of Ski Jumps

Fluids ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 168 ◽  
Author(s):  
Agostino Lauria ◽  
Giancarlo Alfonsi ◽  
Ali Tafarojnoruz
Keyword(s):  
High Speed ◽  
Stokes Equations ◽  
Dynamic Pressure ◽  
Pressure Head ◽  
Navier Stokes ◽  
Maximum Pressure ◽  
Navier Stokes Equations ◽  
Free Jet ◽  
Jet Characteristics ◽  
The Impact

Ski jump spillways are frequently implemented to dissipate energy from high-speed flows. The general feature of this structure is to transform the spillway flow into a free jet up to a location where the impact of the jet creates a plunge pool, representing an area for potential erosion phenomena. In the present investigation, several tests with different ski jump bucket angles are executed numerically by means of the OpenFOAM® digital library, taking advantage of the Reynolds-averaged Navier–Stokes equations (RANS) approach. The results are compared to those obtained experimentally by other authors as related to the jet length and shape, obtaining physical insights into the jet characteristics. Particular attention is given to the maximum pressure head at the tailwater. Simple equations are proposed to predict the maximum dynamic pressure head acting on the tailwater, as dependent upon the Froude number, and the maximum pressure head on the bucket. Results of this study provide useful suggestions for the design of ski jump spillways in dam construction.

Analysis of Three-Lobe Bearings Having Non-Newtonian Lubricants by a Finite Element Method

1983 ◽  
Vol 7 (1) ◽  
pp. 7-11 ◽  
Author(s):  
D.V. Singh ◽  
R. Sinhasan ◽  
S.P. Tayal
Keyword(s):  
Shear Stress ◽  
Stokes Equations ◽  
Load Capacity ◽  
Navier Stokes ◽  
Shear Strain Rate ◽  
Navier Stokes Equations ◽  
Viscosity Term ◽  
Static Performance ◽  
Iteration Technique ◽  
Element Method

Additives are extensively used in the commercial lubricants to improve their specific qualities. These lubricants are therefore non-Newtonian and their nonlinear relations between shear stress and shear strain rate are generally represented by cubic shear stress laws. The Navier-Stokes equations and the continuity equation in clindrical coordinates, representing the flow-field in the clearance space of each lobe of the three-lobe hydrodynamic journal bearings having Newtonian fluids, are solved by the finie element method using Galerkin’s technique. The solution for non-Newtonian lubricants is obtained by an iteration technique modifying the viscosity term in each iteration. The static performance characteristics have been obtained for both Newtonian and the non-Newtonian lubricants. The load capacity and friction of the bearing decrease with increase in the nonlinearity of the lubricant whereas the end flow is relatively unaffected.

Development of Foil Thrust Bearings with Simple Structure for Micro Turbines

2011 ◽  
Vol 368-373 ◽  
pp. 1392-1395 ◽  
Author(s):  
Quan Zhou ◽  
Yu Hou ◽  
Ru Gang Chen
Keyword(s):  
High Speed ◽  
Simple Structure ◽  
Thrust Bearing ◽  
Load Capacity ◽  
Complicated Structure ◽  
Thrust Bearings ◽  
Foil Bearings ◽  
Rotational Systems ◽  
Micro Turbine ◽  
Foil Thrust Bearing

Because of the low power loss and high stability, foil bearings are suitable lubrication components for high speed rotational systems. At present, the foil bearings used in actual applications almost have complicated structure and are hard to manufacture. In this paper, two kinds of foil thrust bearings with simple structure are presented. Configurations of these two foil thrust bearings are introduced; meanwhile, the load capacity and running stability are also tested in a high speed micro turbine. It is shown that viscoelastic supported foil thrust bearing has higher load capacity and hemisphere convex dots supported foil thrust bearing is more stable in high speed operational condition.

Numerical simulation of the stalled flow within a vaned centrifugal pump

2004 ◽  
Vol 218 (4) ◽  
pp. 425-435 ◽  
Author(s):  
K M Guleren ◽  
A Pinarbasi
Keyword(s):  
Numerical Simulation ◽  
Centrifugal Pump ◽  
High Speed ◽  
Stokes Equations ◽  
Reverse Flow ◽  
Flow Characteristics ◽  
Navier Stokes ◽  
Leakage Flow ◽  
Navier Stokes Equations ◽  
Low Pass

The main goal of the present work is to analyse the numerical simulation of a centrifugal pump by solving Navier-Stokes equations, coupled with the ‘standard k-∊’ turbulence model. The pump consists of an impeller having five curved blades with nine diffuser vanes. The shaft rotates at 890r/min. Flow characteristics are assumed to be stalled in the appropriate region of flowrate levels of 1.31-2.861/s. Numerical analysis techniques are performed on a commercial FLUENT package program assuming steady, incompressible flow conditions with decreasing flowrate. Under stall conditions the flow in the diffuser passage alternates between outward jetting when the low-pass-filtered pressure is high to a reverse flow when the filtered pressure is low. Being below design conditions, there is a consistent high-speed leakage flow in the gap between the impeller and the diffuser from the exit side of the diffuser to the beginning of the volute. Separation of this leakage flow from the diffuser vane causes the onset of stall. As the flowrate decreases both the magnitude of the leakage within the vaneless part of the pump and reverse flow within a stalled diffuser passage increase. As this occurs, the stall-cell size extends from one to two diffuser passages. Comparisons are made with experimental data and show good agreement.

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