Solution for the Pressure and Temperature in an Infinite Slider Bearing of Arbitrary Profile

1967 ◽  
Vol 89 (4) ◽  
pp. 445-452 ◽  
Author(s):  
E. J. Hahn ◽  
C. F. Kettleborough
Keyword(s):  
Energy Equation ◽  
Fluid Film ◽  
Navier Stokes ◽  
Subsequent Paper ◽  
Slider Bearing ◽  
Navier Stokes Equation ◽  
Temperature Distributions ◽  
Elastic Distortion ◽  
Temperature And Pressure ◽  
State Pressure

An iterative method of calculating the steady-state pressure and temperature distributions in the fluid film for infinitely wide slider bearings is presented. The bearing profile is assumed to be quite general, rendering the method particularly applicable to problems involving thermal or elastic distortion. The viscosity of the lubricant is regarded as a function of temperature and pressure; the density as a function of temperature only. The inertia terms are retained in the simplified Navier-Stokes equation and the energy equation includes the compression work term. Heat transfer between the bearing surfaces and the fluid film are accounted for. Several numerical examples are evaluated and compared with existing solutions. The solution presented is believed to be the most complete to date. A subsequent paper will deal with the effect of thermal distortions of similar geometrical arrangements described herein.

A Study of Thermohydrodynamic Squeeze Films

1974 ◽  
Vol 96 (2) ◽  
pp. 198-205 ◽  
Author(s):  
S. M. Rohde ◽  
H. A. Ezzat
Keyword(s):  
Heat Conduction Equation ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Time Dependent ◽  
Fluid Film ◽  
Squeeze Film ◽  
3 Dimensional ◽  
Temperature Distributions ◽  
Film Parameter ◽  
The Mathematical Model

This paper presents an analysis of the thermohydrodynamic performance of squeeze films. The mathematical model consists of a 3-dimensional Reynolds equation, a 3-dimensional time dependent energy equation, and a 3-dimensional time dependent heat conduction equation. The system of equations is solved numerically. Fluid film pressure and temperature distributions and the temperature distribution in the solids are presented. Fluid film velocity profiles as a function of time are also shown. The load-time characteristics for different operative conditions are studied. It is shown that a thermohydrodynamic squeeze-film parameter can give rise to a phenomenon which radically changes the fluid film performance.

scholarly journals Recirculation Flow and Pressure Distributions in a Rayleigh Step Bearing

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Feng Shen ◽  
Cheng-Jin Yan ◽  
Jian-Feng Dai ◽  
Zhao-Miao Liu
Keyword(s):  
Flow Field ◽  
Flow Characteristics ◽  
Lower Surface ◽  
Navier Stokes ◽  
Maximum Pressure ◽  
Slider Bearing ◽  
Navier Stokes Equation ◽  
Recirculation Flow ◽  
Lubrication Equation ◽  
Pressure Distributions

Flow characteristics in the Rayleigh step slider bearing with infinite width have been studied using both analytical and numerical methods. The conservation equations of mass and momentum were solved utilizing a finite volume approach and the whole flow field was simulated. More detailed information about the flow patterns and pressure distributions neglected by the Reynolds lubrication equation has been obtained, such as jumping phenomenon around a Rayleigh step, vortex structure, and shear stress distribution. The pressure distribution of the Rayleigh step bearing with optimum geometry has been numerically simulated and the results obtained agreed with the analytical solution of the classical Reynolds lubrication equation. The simulation results show that the maximum pressure of the flow field is at the step tip not on the lower surface and the increment of the strain rate from Navier-Stokes equation is approximately 49 percent greater than that from Reynolds theory at the step tip. It is also shown that the position of the maximum pressure of the lower surface is a little less than the length of the first region. These results neglected by the Reynolds lubrication equation are important for designing a bearing.

Prediction of Flow Behavior on Diffuser Angle in an Enclosure

2005 ◽  
Author(s):  
B. Tripathi ◽  
R. C. Arora ◽  
S. G. Moulic
Keyword(s):  
Laminar Flow ◽  
Energy Equation ◽  
Stokes Equations ◽  
Flow Behavior ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Specific Location ◽  
Temperature Distributions ◽  
Diffuser Angle

The present investigation deals with numerical prediction of airflow pattern in a room (enclosure) with a specific location of inlet and outlet with different values of Gr/Re2. Two-dimensional, steady, incompressible, laminar flow under Boussinesq’s approximation has been considered. The velocity and temperature distributions in a room have been found by solving Navier Stokes equations and energy equation numerically by SIMPLE and SIMPLEC algorithms.

Influence of bearing surface irregularities on hybrid slot-entry journal bearing with electrically conducting lubricant

2019 ◽  
Vol 234 (8) ◽  
pp. 1185-1207
Author(s):  
Krishnkant Sahu ◽  
Satish C Sharma
Keyword(s):  
Journal Bearing ◽  
Equations Of Motion ◽  
Fluid Film ◽  
Navier Stokes ◽  
Bearing Surface ◽  
Navier Stokes Equation ◽  
Electrically Conducting ◽  
Surface Irregularities ◽  
Fluid Film Thickness ◽  
Effect Of Surface

This study concerns with the numerical simulation of a hybrid slot entry journal bearing lubricated with electrically conducting lubricant under the influence of magnetic field for both thermal and isothermal conditions. The Navier–Stokes equation has been used to formulate the flow of electrically conducting lubricant through slot restrictor and combining the Lorentz force in the equations of motion, together with the Ohm’s law and Maxwell equations. Further, the effect of surface irregularities on bearing surface is considered to analyse the performance of the slot-entry bearing. The surface irregularities asperity profile has been modelled in both axial as well as circumferential directions. Finite element method is used to solve the Modified MHD Reynolds equation. To compute the bearing performance characteristic parameters, a MATLAB source code based on Gauss–Seidel iteration method has been developed. A comparative numerical analysis has been carried out for an electrically conducting lubricant, Newtonian lubricant, bearing surface having irregularities and bearing with smooth surface. The numerically simulated results indicate that considering the bearing surface irregularities and MHD effects enhances the value of fluid film damping coefficients [Formula: see text] and the value of minimum fluid film thickness [Formula: see text].

Thermohydrodynamic Lubrication Analysis of Slider Bearings With Steps on Bearing Surface

2009 ◽  
Author(s):  
Hideki Ogata
Keyword(s):  
Reynolds Equation ◽  
Energy Equation ◽  
Fluid Velocity ◽  
Differential Method ◽  
Fluid Film ◽  
Bearing Surface ◽  
Fluid Film Bearings ◽  
Temperature Distributions ◽  
Finite Differential Method ◽  
Good Agreement

This study focuses on the thermohydrodynamic lubrication analysis of fluid film bearings with step on the surface such as a Rayleigh step bearing. In general, the Reynolds equation does not satisfy the continuity of the fluid velocity components at steps. This discontinuity results in the difficulty to solve the energy equation for the lubricants, because the energy equation needs the velocity components explicitly. The author has solved this problem by introducing the equivalent clearance height and the equivalent gradient of clearance height at steps. These parameters remove the discontinuity of velocity components and the energy equation as well, so that one can solve these equations on all of the bearing surfaces including the step region by finite differential method (FDM). The numerical results of pressure and temperature distributions by the proposed method for a Rayleigh step bearing were compared with the results obtained by a commercial CFD package. These results showed good agreement with each other. This method is extended to 2D unequal grid problems.

Oil-Film Temperature Distribution in an Infinitely wide Slider Bearing: An Application of the Finite-Element Method

1973 ◽  
Vol 15 (4) ◽  
pp. 311-320 ◽  
Author(s):  
A. K. Tieu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Energy Equation ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Slider Bearing ◽  
Oil Film ◽  
Temperature Distributions ◽  
Oil Films ◽  
Element Method

From the Glansdorff–Prigogine local potential in non-equilibrium thermodynamics (1)† (2), a variational principle for a thin film incompressible flow with viscous dissipation is formulated as the basis of a finite-element method, which is applied to solve the energy equation. Temperature distributions in tapered land and parallel oil films for infinitely wide bearings are obtained by digital computer. The application of the finite-element method in a three-dimensional oil film with side leakage is also discussed.

Investigation of Geometry Effect on Heat and Mass Transfer in Buoyancy Assisting with the Vertical Backward and Forward Facing Steps

2019 ◽  
Vol 20 (3-4) ◽  
pp. 407-431
Author(s):  
Alibek Issakhov ◽  
Yeldos Zhandaulet
Keyword(s):  
Buoyancy Force ◽  
Numerical Solutions ◽  
Temperature Fluctuations ◽  
Bottom Wall ◽  
Navier Stokes ◽  
Heat Transfer Characteristics ◽  
Navier Stokes Equation ◽  
Temperature Distributions ◽  
Buoyancy Forces ◽  
Incompressible Navier Stokes Equation

AbstractThis paper is a Direct Numerical Simulation (DNS) of the temperature distribution in the flow with the forward and backward facing steps with buoyancy forces for different lengths of the bottom walls and flow regimes. The different lengths of the bottom walls effect were studied with buoyancy forces. A two-dimensional incompressible Navier–Stokes equation and equations for temperature transfer were used to describe this process. The obtained numerical solutions for the test problem, laminar flow with the backward facing step with buoyancy force, are compared with the numerical results of other authors. A verified numerical algorithm is applied to the problem with the forward and backward facing steps with buoyancy forces. The influence of changes in the bottom wall length on temperature distributions and velocity components is revealed. It was also revealed that the heat transfer characteristics of the bottom wall have strong changes in different lengths. In cases for the lengths of the bottom walls (${X_e} = 12, \,16$) atRe=1,000, the rotational movement of the vortices along the channel wall revealed an increase in the exchange of cold and hot fluids, which leads to temperature fluctuations from the lower wall to the upper wall of the channel.

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