Inertia Effects in Thin Film Flow With a Corrugated Boundary

1991 ◽  
Vol 58 (1) ◽  
pp. 272-277 ◽  
Author(s):  
Ilter Serbetci ◽  
John A. Tichy
Keyword(s):  
Pressure Distribution ◽  
Film Flow ◽  
Stokes Equations ◽  
Lubrication Theory ◽  
Navier Stokes ◽  
Thin Film Flow ◽  
Perturbation Expansions ◽  
Navier Stokes Equations ◽  
Inertia Effects ◽  
Grooved Surface

An analytical solution is presented for two-dimensional, incompressible film flow between a sinusoidally grooved (or rough) surface and a flat surface. The upper grooved surface is stationary whereas the lower, smooth surface moves with a constant speed, The Navier-Stokes equations were solved employing both mapping techniques and perturbation expansions. Due to the inclusion of the inertia effects, a different pressure distribution is obtained than predicted by the classical lubrication theory. In particular, the amplitude of the pressure distribution of the classical lubrication theory is found to be in error by over 100 percent (for modified Reynolds number of 3–4).

Influences of Recess Geometry and Restrictor Dimension on Flow Patterns and Pressure Distribution of Hydrostatic Bearings

2007 ◽  
Author(s):  
Cheng-Hsien Chen ◽  
Yuan Kang ◽  
Yeon-Pun Chang ◽  
De-Xing Peng ◽  
Ding-Wen Yang
Keyword(s):  
Pressure Distribution ◽  
Stokes Equations ◽  
Flow Patterns ◽  
Lubricant Film ◽  
Navier Stokes ◽  
Width Ratio ◽  
Navier Stokes Equations ◽  
Hydrostatic Bearing ◽  
Lubricant Flow ◽  
Land Width

This paper studies the influences of recess geometry and restrictor dimensions on the flow patterns and pressure distribution of lubricant film, which are coupled effects of hybrid characteristics of a hydrostatic bearing. The lubricant flow is described by using the Navier-Stokes equations. The Galerkin weighted residual finite element method is applied to determine the lubricant velocities and pressure in the bearing clearance. The numerical simulations will evaluate the effects of the land-width ratio and restriction parameter as well as the influence of modified Reynolds number and the jet-strength coefficient on the flow patterns in the recess and pressure distribution in lubricant film. On the basis of the simulation drawn from this study, the simulated results are expected to help engineers make better use of the design of hydrostatic bearing and its restrictors.

scholarly journals Effects of Hydrostatic Pocket Shape on the Flow Pattern and Pressure Distribution

1995 ◽  
Vol 1 (3-4) ◽  
pp. 225-235 ◽  
Author(s):  
M. J. Braun ◽  
M. Dzodzo
Keyword(s):  
Numerical Simulation ◽  
Pressure Distribution ◽  
Flow Pattern ◽  
Stokes Equations ◽  
The Other ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Hydrostatic Bearing ◽  
Collocated Grid ◽  
Dimensionless Formulation

The flow in a hydrostatic pocket is numerically simulated using a dimensionless formulation of the 2-D Navier-Stokes equations written in primitive variables, for a body fitted coordinates system, and applied through a collocated grid. In essence, we continue the work of Braun et al. 1993a, 1993b] and extend it to the study of the effects of the pocket geometric format on the flow pattern and pressure distribution. The model includes the coupling between the pocket flow and a finite length feedline flow, on one hand, and the pocket and its adjacent lands on the other hand. In this context we shall present, on a comparative basis, the flow and the pressure patterns at the runner surface for square, ramped-Rayleigh step, and arc of circle pockets. Geometrically all pockets have the same footprint, same lands length, and same capillary feedline. The numerical simulation uses the Reynolds number based on the lid(runner) velocity and the inlet jet strengthFas the dynamic similarity parameters. The study aims at establishing criteria for the optimization of the pocket geometry in the larger context of the performance of a hydrostatic bearing.

scholarly journals Calculating Rotordynamic Coefficients of Seals by Finite-Difference Techniques

1987 ◽  
Vol 109 (3) ◽  
pp. 388-394 ◽  
Author(s):  
F. J. Dietzen ◽  
R. Nordmann
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Flow Field ◽  
Pressure Distribution ◽  
Difference Method ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Rotordynamic Coefficients ◽  
Finite Difference Techniques

For modelling the turbulent flow in a seal the Navier-Stokes equations in connection with a turbulence model (k-ε-model) are solved by a finite-difference method. A motion of the shaft around the centered position is assumed. After calculating the corresponding flow field and the pressure distribution, the rotordynamic coefficients of the seal can be determined. These coefficients are compared with results obtained by using the bulk flow theory of Childs [1] and with experimental results.

Determination of Dynamic Coefficients in a Hydrodynamic Journal Bearing Based on the 3-D Navier-Stokes Equations and Considering Cavitation Effects

2012 ◽  
Author(s):  
Changhu Xing ◽  
Minel J. Braun
Keyword(s):  
Pressure Distribution ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Maximum Magnitude ◽  
Navier Stokes Equations ◽  
Dynamic Coefficients ◽  
Finite Perturbation ◽  
Hydrodynamic Journal Bearing

Dynamic coefficients are very important for the stability of a hydrodynamic journal bearing and therefore for its design. In order to determine the stiffness, damping and added mass coefficients of the hydrodynamic bearing, the finite perturbation method around its stabilization position was employed. Based on the Reynolds equation with Gumbel cavitation algorithm, the maximum magnitude of the perturbation was judged by comparing results from finite perturbation (numerical way) to those from infinitesimal perturbation (additional analytical equations need to be derived based on order analysis), as well as theoretical analysis. Using the determined perturbation amplitude, the full three-dimensional Navier-Stokes equations in CFD-ACE+ were used to evaluate coefficients from an actual lubricant and compare to those obtained with Reynolds equation. Finally, a homogeneous gaseous cavitation algorithm is coupled with the Navier-Stokes equation to establish the pressure distribution in the bearing. When gas concentration was varied, the pressure distribution as well as the dynamic coefficients changed significantly.

A Multiscale Method Modeling Surface Texture Effects

2006 ◽  
Vol 129 (2) ◽  
pp. 221-230 ◽  
Author(s):  
Alex de Kraker ◽  
Ron A. J. van Ostayen ◽  
A. van Beek ◽  
Daniel J. Rixen
Keyword(s):  
Surface Texture ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Stokes Equations ◽  
Multiscale Method ◽  
Operating Conditions ◽  
Contact Load ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Inertia Effects

In this paper a multiscale method is presented that includes surface texture in a mixed lubrication journal bearing model. Recent publications have shown that the pressure generating effect of surface texture in bearings that operate in full film conditions may be the result of micro-cavitation and/or convective inertia. To include inertia effects, the Navier–Stokes equations have to be used instead of the Reynolds equation. It has been shown in earlier work (de Kraker et al., 2006, Tribol. Trans., in press) that the coupled two-dimensional (2D) Reynolds and 3D structure deformation problem with partial contact resulting from the soft EHL journal bearing model is not easy to solve due to the strong nonlinear coupling, especially for soft surfaces. Therefore, replacing the 2D Reynolds equation by the 3D Navier–Stokes equations in this coupled problem will need an enormous amount of computing power that is not readily available nowadays. In this paper, the development of a micro–macro multiscale method is described. The local (micro) flow effects for a single surface pocket are analyzed using the Navier–Stokes equations and compared to the Reynolds solution for a similar smooth piece of surface. It is shown how flow factors can be derived and added to the macroscopic smooth flow problem, that is modeled by the 2D Reynolds equation. The flow factors are a function of the operating conditions such as the ratio between the film height and the pocket dimensions, the surface velocity, and the pressure gradient over a surface texture unit cell. To account for an additional pressure buildup in the texture cell due to inertia effects, a pressure gain is introduced at macroscopic level. The method also allows for microcavitation. Microcavitation occurs when the pressure variation due to surface texture is larger than the average pressure level at that particular bearing location. In contrast with the work of Patir and Cheng (1978, J. Lubrication Technol., 78, pp. 1–10), where the microlevel is solved by the Reynolds equation, and the Navier–Stokes equations are used at the microlevel. Depending on the texture geometry and film height, the Reynolds equation may become invalid. A second pocket effect occurs when the pocket is located in the moving surface. In mixed lubrication, fluid can become trapped inside a pocket and squeezed out when the pocket is running into an area with higher contact load. To include this effect, an additional source term that represents the average fluid inflow due to the deformation of the surface around the pocket is added to the Reynolds equation at macrolevel. The additional inflow is computed at microlevel by numerical solution of the surface deformation for a single pocket that is subject to a contact load. The pocket volume is a function of the contact pressure. It must be emphasized that before ready-to-use results can be presented, a large number of simulations to determine the flow factors and pressure gain as a function of the texture parameters and operating conditions have yet to be done. Before conclusions can be drawn, regarding the dominanant mechanism(s), the flow factors and pressure gain have to be added to the macrobearing model. In this paper, only a limited number of preliminary illustrative simulation results, calculating the flow factors for a single 2D texture geometry, are shown to give insight into the method.

Asymptotic Model of the 3D Flow in a Progressing-Cavity Pump

SPE Journal ◽  
2011 ◽  
Vol 16 (02) ◽  
pp. 451-462 ◽  
Author(s):  
S.F.A.. F.A. Andrade ◽  
J.V.. V. Valério ◽  
M.S.. S. Carvalho
Keyword(s):  
Stokes Equations ◽  
Computing Time ◽  
Petroleum Industry ◽  
Lubrication Theory ◽  
Moving Boundaries ◽  
Navier Stokes ◽  
Channel Height ◽  
Asymptotic Model ◽  
Navier Stokes Equations ◽  
The Difference

Summary Fundamental understanding of the flow inside progressing-cavity pumps (PCPs) represents an important step in the optimization of the efficiency of these pumps, which are largely used in artificial-lift processes in the petroleum industry. The computation of the flow inside a PCP is extremely complex because of the transient character of the flow, the moving boundaries, and the difference in length scale of the channel height between the stator and rotor. This complexity makes the use of computational fluid dynamics (CFD) as an engineering tool almost impossible. This work presents an asymptotic model to describe the single-phase flow inside PCPs using lubrication theory. The model was developed for Newtonian fluid, and lubrication theory was used to reduce the 3D Navier-Stokes equations in cylindrical coordinates to a 2D Poisson's equation for the pressure field at each timestep, which is solved numerically by a second-order finite-difference method. The predictions are close to the experimental data and the results obtained by solving the complete 3D, transient Navier-Stokes equations with moving boundaries, available in the literature. Although the accuracy is similar to the complete 3D model, the computing time of the presented model is orders of magnitude smaller. The model was used to study the effect of geometry, fluid properties, and operating parameters in the pump-performance curves and can be used in the design of new pumping processes.

Laminar film flow on a cylindrical surface

1976 ◽  
Vol 74 (2) ◽  
pp. 297-315 ◽  
Author(s):  
Ernst Becker
Keyword(s):  
Stagnation Point ◽  
Cylindrical Surface ◽  
Film Flow ◽  
Stokes Equations ◽  
Inviscid Flow ◽  
Navier Stokes ◽  
Point Problem ◽  
Navier Stokes Equations ◽  
Laminar Film ◽  
Particular Solution

The paper deals with steady laminar film flow which is set up at the cylindrical surface of an idealized horizontal ‘road’ when homogeneous ‘rain’ is falling onto the road in a vertical downward direction. It is shown that a particular solution of the Navier-Stokes equations is possible for which the depth of the liquid film is constant. In that case the Navier-Stokes equations reduce to the equations governing plane stagnation-point flow. However, the boundary conditions differ from those for the classical stagnation-point problem. Solutions for nearly inviscid flow and predominantly viscous flow are derived analytically. In particular, simple formulae for the depth of the film are found in both cases. Finally, the importance of the particular solution as a member of a whole class of solutions is discussed on the basis of a momentum integral approximation.

Investigation on Propeller Slipstream by Using an Unstructured Rans Solver Based on Overlapping Grids

2017 ◽  
Vol 34 (2) ◽  
pp. 89-101 ◽  
Author(s):  
X. Q. Gong ◽  
M. S. Ma ◽  
J. Zhang ◽  
J. Tang
Keyword(s):  
Pressure Distribution ◽  
Stokes Equations ◽  
Lift Coefficient ◽  
Linear Interpolation ◽  
Aerodynamic Characteristics ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Overlapping Grids ◽  
Moment Coefficient ◽  
Grid Technique

AbstractBased on unstructured hybrid grid and dynamic overlapping grid technique, numerical simulations of Unsteady Reynolds Averaged Navier-Stokes equations were performed and investigation on isolated propeller aerodynamic characteristics and effects of propeller slipstream on turboprops were undertaken. The computational grid consisted of rotational subzone of propeller and stationary major-zone of aircraft, and walls criterion was used in the automatic hole-cutting procedure. Distance weight interpolation and tri-linear interpolation were developed to transfer information between the rotational and stationary subzones. The boundaries of overlapping grids were optimized for fixed axis rotation. The governing equations were solved by dual-time method and Lower Upper-Symmetric Gauss-Seidel method. The method and grid technique were verified by isolated propeller configuration and the computational results were in well agreement with the experimental data. The grid independence was studied to establish the numerical results. Finally, the flow around a turboprop case was simulated and the influence of propeller slipstream was presented by analyzing the surface pressure contours, profile pressure distribution, vorticity contours and profile streamline. It's indicated that the slipstream accelerates and rotates the free stream flow, changing the local angle of attack, enhancing the downwash effects, affecting the pressure distribution on wing and horizontal tail, as well as increasing the drag coefficient, pitching moment coefficient and the slope of lift coefficient.

A Numerical Solution of the Thermal Elastohydrodynamic Lubrication in an Elliptical Contact

1982 ◽  
Vol 104 (3) ◽  
pp. 392-400 ◽  
Author(s):  
H. Bru¨ggemann ◽  
F. G. Kollmann
Keyword(s):  
Numerical Solution ◽  
Pressure Distribution ◽  
Energy Equation ◽  
Stokes Equations ◽  
Elastohydrodynamic Lubrication ◽  
Navier Stokes ◽  
Time Dependency ◽  
Navier Stokes Equations ◽  
Elliptical Contact ◽  
The Finite Difference Method

A numerical solution for the calculation of thickness and temperature of film and traction coefficients between heavily loaded elliptical contact is developed. To start the calculation a Hertzian pressure distribution modified at the inlet and outlet regions is assumed and the surface deformations are calculated. The Navier-Stokes equations and the energy equation are simultaneously solved by the finite difference method. The pressure distribution introduced is verified with the help of the condition of continuity and, if necessary, corrected. The dependence of the viscosity and the density of the lubricant on pressure and temperature is determined by empirical equations which are derived from experimental data. A time dependency of the viscosity is allowed for high viscosities. The distribution of temperature in the film is obtained for a selected example. The thicknesses of the oil film and the traction coefficients are compared with experimental results.

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