A Mass-Conserving Complementarity Formulation to Study Fluid Film Lubrication in the Presence of Cavitation for Non-Newtonian and Compressible Fluids

2012 ◽  
Author(s):  
Luca Bertocchi ◽  
Matteo Giacopini ◽  
Antonio Strozzi ◽  
Mark T. Fowell ◽  
Daniele Dini
Keyword(s):  
Reynolds Equation ◽  
Incompressible Fluids ◽  
Compressible Fluids ◽  
Contact Pressure Distribution ◽  
One Dimensional ◽  
The Stability ◽  
Mathematical Derivation ◽  
Dimensional Domain ◽  
Film Lubrication ◽  
Fluid Film Lubrication

A mass-conserving formulation of the Reynolds equation has been recently developed using the concept of complementarity [1]. The mathematical derivation of the Linear Complementarity Problem (LCP) implemented in the solver favoured in [1] overcomes the drawbacks previously associated with the use of such complementarity formulations for the solution of cavitation problems in which reformation of the liquid film occurs. In the present paper, the proposed methodology, already successfully applied to solve textured bearing and squeeze problems in the presence of cavitation in a one dimensional domain and for incompressible fluids [1], has been extend to a two dimensional domain and the fluid compressibility has been included in the formulation. The evolution of the cavitated region and the contact pressure distribution are studied for a number of different configurations. Some of the results obtained with the proposed scheme are critically analysed and compared with the predictions obtained using alternative formulations (including full CFD calculations). The stability of the proposed algorithm and its flexibility in terms of the implementation of different compressibility laws is highlighted.

scholarly journals About the Accuracy and the Grid Convergence of the Numerical Solution of the Energy Equation in Fluid Film Lubrication

2018 ◽  
Author(s):  
Silun Zhang ◽  
Mohamed-Amine Hassini ◽  
Mihai Arghir
Keyword(s):  
Numerical Solution ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Computation Time ◽  
Fluid Film ◽  
Hydrodynamic Analysis ◽  
One Dimensional ◽  
Grid Convergence ◽  
Film Lubrication ◽  
Fluid Film Lubrication

The present work is focused on the numerical solution of the complete energy equation used in fluid film lubrication. The work was motivated by the fact the complete energy equation has no analytic solution that could be used for validations. Its accuracy and computation time are related to the employed numerical method and to the grid resolution. The natural discretization method (NDM) applied on different grids is systematically compared with the spectral method (the Lobatto Point Colocation Method or LPCM) with different polynomial degrees. A one dimensional inclined slider is used for the numerical tests and the energy equation is artificially decoupled from Reynolds. This approach enables to focus all the attention on the numerical solution of the energy equation. The results show that the LPCM is one or two orders of magnitudes more efficient than the NDM in terms of computation time. The energy equation is then coupled with Reynolds equation in a thermo-hydrodynamic analysis of the same 1D slider; the numerical results confirm again the efficiency of the LPCM. A thermo-hydrodynamic analysis of a two-lobe journal bearing is then presented as a practical application.

scholarly journals Accuracy and Grid Convergence of the Numerical Solution of the Energy Equation in Fluid Film Lubrication: Application to the 1D Slider

Lubricants ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 95
Author(s):  
Silun Zhang ◽  
Mohamed-Amine Hassini ◽  
Mihai Arghir
Keyword(s):  
Numerical Solution ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Computation Time ◽  
Fluid Film ◽  
Hydrodynamic Analysis ◽  
One Dimensional ◽  
Grid Convergence ◽  
Film Lubrication ◽  
Fluid Film Lubrication

The present work is focused on the numerical solution of the complete energy equation used in fluid film lubrication. The work was motivated by the fact that the complete energy equation has no analytical solution that can be used for validations. Its accuracy and computation time are related to the employed numerical method and to the grid resolution. The natural discretization method (NDM) applied on different grids is systematically compared with the spectral method (the Lobatto Point Colocation Method or LPCM) with different polynomial degrees. A one dimensional inclined slider is used for the numerical tests, and the energy equation is artificially decoupled from the Reynolds equation. This approach enables us to focus all the attention on the numerical solution of the energy equation. The results show that the LPCM is one or two orders of magnitude more efficient than the NDM in terms of computation time. The energy equation is then coupled with the Reynolds equation in a thermo-hydrodynamic analysis of the same 1D slider; the numerical results confirm again the efficiency of the LPCM. A thermo-hydrodynamic analysis of a two-lobe journal bearing is then presented as a practical application.

An Extended Variational Formulation for Isothermal Gas-Dynamic Lubrication

1970 ◽  
Vol 92 (2) ◽  
pp. 314-317 ◽  
Author(s):  
D. F. Hays
Keyword(s):  
Compressible Flow ◽  
Variational Formulation ◽  
Reynolds Equation ◽  
Lagrange Equation ◽  
Nonlinear Problems ◽  
Perfect Gas ◽  
Gas Dynamic ◽  
Isothermal Gas ◽  
Film Lubrication ◽  
Fluid Film Lubrication

An extended variational formulation is derived which can be applied to problems in isothermal compressible flow where the medium obeys the perfect gas law. The Reynold’s approximations for fluid film lubrication have been applied to this variational formulation to obtain an expression that is applicable to the field of gas-dynamic lubrication. This variational formulation for gas-dynamic lubrication has as its Euler-Lagrange equation, the Reynolds’ equation of lubrication for a perfect gas. The extended variational formulation is shown to differ from the classical Lagrangian expression with respect to its form and to its applicability to nonlinear problems.

A Simultaneous Numerical Solution for the Lubrication and Dynamic Stability of Noncontacting Gas Face Seals

2000 ◽  
Vol 123 (2) ◽  
pp. 388-394 ◽  
Author(s):  
Itzhak Green ◽  
Roger M. Barnsby
Keyword(s):  
Numerical Solution ◽  
Equations Of Motion ◽  
Critical Value ◽  
Pressure Drops ◽  
Mode 2 ◽  
Face Seals ◽  
Natural Response ◽  
The Stability ◽  
Film Lubrication ◽  
Fluid Film Lubrication

A numerical solution is presented for the dynamic analysis of gas lubricated noncontacting mechanical face seals having a single grounded flexibly mounted stator. Seal dynamics is solved in axial and angular modes of motion. Both the Reynolds equation and the equations of motion are arranged into a single state space form, allowing the fluid film lubrication and the dynamics to be solved simultaneously. The resulting set of equations is solved using a high-order multistep ordinary differential equation solver, yielding a complete simulation for the seal dynamic behavior. Examples of seal motion are given in detailed transient responses. The stability threshold is investigated to gauge the influence of seal parameters such as inertia, speed, coning, and the direction of sealed pressure drops. The results show two modes of instability: (1) When the inertia effect is larger than a critical value, the natural response of the seal grows monotonically in a half-frequency-whirl mode. (2) When the seal coning is less than some critical value in an outside pressurized seal, the minimum film thickness diminishes because of hydrostatic instability, and face contact occurs. Conversely, an inside pressurized seal is shown to be hydrostatically stable and have a superior dynamic response at any coning.

Improved Method for Numerical Solutions of the General Incompressible Fluid Film Lubrication Problem

1967 ◽  
Vol 89 (2) ◽  
pp. 211-218 ◽  
Author(s):  
V. Castelli ◽  
W. Shapiro
Keyword(s):  
Numerical Analysis ◽  
Numerical Solutions ◽  
Iterative Scheme ◽  
Incompressible Fluids ◽  
Supply System ◽  
The Other ◽  
Improved Method ◽  
Lubrication Equation ◽  
Film Lubrication ◽  
Fluid Film Lubrication

A numerical analysis for determining performance characteristics of hydrodynamic, hydrostatic, or hybrid bearings with arbitrary clearance distribution is presented. Solution of the Reynolds lubrication equation for incompressible fluids is achieved by formation of coefficient matrices that act upon column vectors of the pressures progressively from one boundary to the other without requiring an iterative scheme. Multiple recesses are handled by component solutions. The external supply system is included and solved for an arbitrary type of individual recess compensation and supply circuit network. Sample results are indicated.

Thermohydrodynamic Phenomena in Fluid Film Lubrication

1973 ◽  
Vol 95 (2) ◽  
pp. 187-194 ◽  
Author(s):  
A. Seireg ◽  
H. Ezzat
Keyword(s):  
Reynolds Equation ◽  
Fluid Film ◽  
Hydrodynamic Theory ◽  
Load Carrying Capacity ◽  
Isothermal Conditions ◽  
Empirical Procedure ◽  
Load Carrying ◽  
Film Lubrication ◽  
Classical Hydrodynamic ◽  
Fluid Film Lubrication

The classical hydrodynamic theory of fluid film lubrication as described by Reynolds’ equation assumes isothermal conditions in the film. Such conditions may never exist in many engineering applications. A common practice is to calculate bearing performance with isothermal conditions at an average film temperature. This paper presents results on the load-carrying capacity of the film when thermal homogeneity does not exist. An empirical procedure is proposed for the prediction of the thermohydrodynamic behavior of the film. A hysteresis-type phenomenon in the pressure-temperature relationship is also observed.

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