Temporal and Convective Inertia Effects in Plain Journal Bearings With Eccentricity, Velocity and Acceleration

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Saeid Dousti ◽  
Jianming Cao ◽  
Amir Younan ◽  
Paul Allaire ◽  
Tim Dimond
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Reynolds Equation ◽  
Stokes Equations ◽  
Hydrodynamic Lubrication ◽  
Operating Conditions ◽  
Inertia Effects ◽  
Pressure Profiles ◽  
Impulsive Loads ◽  
Developed Pressure

This paper extends the theory originally developed by Tichy (Tichy and Bou-Said, 1991, Hydrodynamic Lubrication and Bearing Behavior With Impulsive Loads,” STLE Tribol. Trans. 34, pp. 505–512) for impulsive loads to high reduced Reynolds number lubrication. The incompressible continuity equation and Navier-Stokes equations, including inertia terms, are simplified using an averaged velocity approach to obtain an extended form of short bearing Reynolds equation which applies to both laminar and turbulent flows. A full kinematic analysis of the short journal bearing is developed. Pressure profiles and linearized stiffness, damping and mass coefficients are calculated for different operating conditions. A time transient solution is developed. The change in the rotor displacements when subjected to unbalance forces is explored. Several comparisons between conventional Reynolds equation solutions and the extended Reynolds number form with temporal inertia effects are presented and discussed. In the specific cases considered in this paper, the primary conclusion is that the turbulence effects are significantly more important than inertia effects.

Numerical Study of the Pressure Pattern in a Two-Dimensional Hybrid Journal Bearing Recess, Laminar, and Turbulent Flow Results

2003 ◽  
Vol 125 (2) ◽  
pp. 283-290 ◽  
Author(s):  
Mathieu Helene ◽  
Mihai Arghir ◽  
Jean Frene
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Turbulent Flows ◽  
Journal Bearing ◽  
Stokes Equations ◽  
Numerical Study ◽  
Operating Conditions ◽  
Two Dimensional ◽  
Pressure Pattern ◽  
Inertia Effects

The present work is a parametric study of the pressure pattern in a two-dimensional recess of a hybrid journal bearing (HJB). It is known that theoretical models of HJB are largely dependent on the recess pressure pattern especially for severe working conditions (high rotation speeds, shallow pockets, etc.). The difficulty is that the recess flow is dominated by the interaction of viscous and inertia forces and cannot be analyzed using a thin film model. The present analysis is based on the numerical resolution of the two-dimensional Navier-Stokes equations where only one recess is modeled (with the film lands and the supply region), the fluid being regarded as incompressible and isothermal. Both the laminar and the turbulent flow regimes are considered. The study is governed by two parameters, one related to the HJB operating conditions and the other related to the recess geometric characteristics. The first parameter is the ratio of the runner versus the supply Reynolds number, Rer/Res∈{0,1/4,1/2,1,4,8}. The supply Reynolds number is fixed at 100 for the laminar regime and at 5000 for the turbulent one. The second parameter is the ratio of the recess depth versus the film thickness. Six values of this ratio are considered, ranging from 4 (shallow recess) to 152 (deep recess). Detailed pressure patterns on the runner wall are presented in a systematic manner giving a clear insight of the flow effects intervening in the recess and of their mutual interaction. Some effects are explained by analyzing the recirculation zones inside the recess. It is also shown that for certain parameters turbulent flows have qualitatively similar effects as laminar ones but they can also have specific trends. In order to sustain this remark, the pressure variation at the recess downstream end is analyzed in the paper. Finally, the present results and specially the turbulent ones are intended to contribute to the understanding of viscous and inertia effects interactions in a recess flow and to represent a database in view of HJB theoretical modeling.

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.

The Validity of the Compressible Reynolds Equation for Gas Lubricated Textured Parallel Slider Bearings

2012 ◽  
Author(s):  
Mingfeng Qiu ◽  
Brian Bailey ◽  
Rob Stoll ◽  
Bart Raeymaekers
Keyword(s):  
Gas Flow ◽  
Reynolds Equation ◽  
Stokes Equations ◽  
Hydrodynamic Lubrication ◽  
Operating Conditions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Slider Bearings ◽  
Simplifying Assumptions ◽  
Simulation Results

The Navier-Stokes and compressible Reynolds equations are solved for gas lubricated textured parallel slider bearings under hydrodynamic lubrication for a range of realistic texture geometry parameters and operating conditions. The simplifying assumptions inherent in the Reynolds equation are validated by comparing simulation results to the solution of the Navier-Stokes equations. Using the Reynolds equation to describe shear driven gas flow in textured parallel slider bearings is justified for the range of parameters considered.

Parameter Extension Simulation of Turbulent Flows in a Compressor Cascade With a High Reynolds Number

2020 ◽  
Author(s):  
Yan Jin
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Simulation Method ◽  
Potential Method ◽  
Navier Stokes ◽  
Reference Solution ◽  
Compressor Cascade ◽  
High Reynolds

Abstract The turbulent flow in a compressor cascade is calculated by using a new simulation method, i.e., parameter extension simulation (PES). It is defined as the calculation of a turbulent flow with the help of a reference solution. A special large-eddy simulation (LES) method is developed to calculate the reference solution for PES. Then, the reference solution is extended to approximate the exact solution for the Navier-Stokes equations. The Richardson extrapolation is used to estimate the model error. The compressor cascade is made of NACA0065-009 airfoils. The Reynolds number 3.82 × 105 and the attack angles −2° to 7° are accounted for in the study. The effects of the end-walls, attack angle, and tripping bands on the flow are analyzed. The PES results are compared with the experimental data as well as the LES results using the Smagorinsky, k-equation and WALE subgrid models. The numerical results show that the PES requires a lower mesh resolution than the other LES methods. The details of the flow field including the laminar-turbulence transition can be directly captured from the PES results without introducing any additional model. These characteristics make the PES a potential method for simulating flows in turbomachinery with high Reynolds numbers.

Numerical Three-Dimensional Pressure Patterns in a Recess of a Turbulent and Compressible Hybrid Journal Bearing

2003 ◽  
Vol 125 (2) ◽  
pp. 301-308 ◽  
Author(s):  
Mathieu Helene ◽  
Mihai Arghir ◽  
Jean Frene
Keyword(s):  
Reynolds Number ◽  
Mach Number ◽  
Journal Bearing ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Operating Conditions ◽  
Wire Mesh ◽  
Primary Concern ◽  
Reference Parameters ◽  
Exit Mach Number

The present work investigates the flow in the feeding recess of a hybrid journal bearing. Numerical integration of the complete Navier-Stokes equations was performed with an appropriate turbulence model. Of primary concern is the pressure field on the rotating journal surface that is commonly known as the recess pressure pattern. The goal of the work is to determine the influences of fluid compressibility, operating conditions and recess geometry. Reference parameters selected for this study comprise feeding Reynolds number Rea of 2.105, sliding Reynolds number Rec of 5.103 and recess depth over film thickness ratio e/H of 2.2. Compressibility was considered first. Three values of the axial exit Mach number were selected for computation, namely 0.2, 0.45, and 0.7. As no significant variation was found, the Mach number was fixed at 0.45 in subsequent studies concerning other parameters:     Feeding Reynolds number, Rea       2.104,2.105,4.105     Recess depth, e/H           0, 2.2, 8     Feedhole axis inclination        90°, 135°, 165°     Feedhole location (Figs. 1(a) and 13)   centered, downstream offset. As each parameter is varied, wire mesh plot of pressure and its sectional profiles are examined and effects of varying various parameters are discussed in reference to flow processes as they may affect the support characteristics of the hybrid journal bearing.

scholarly journals SPH modelling of hydrodynamic lubrication: laminar fluid flow–structure interaction with no-slip conditions for slider bearings

2020 ◽  
Author(s):  
Marco Paggi ◽  
Andrea Amicarelli ◽  
Pietro Lenarda
Keyword(s):  
Reynolds Equation ◽  
Stokes Equations ◽  
Hydrodynamic Lubrication ◽  
Flow Direction ◽  
Navier Stokes ◽  
Slider Bearing ◽  
Fluid Films ◽  
Slip Conditions ◽  
Application Fields ◽  
New Research

Abstract The FOSS CFD-SPH code SPHERA v.9.0.0 (RSE SpA) is improved to deal with “fluid–solid body” interactions under no-slip conditions and laminar regimes for the simulation of hydrodynamic lubrication. The code is herein validated in relation to a uniform slider bearing (i.e. for a constant lubricant film depth) and a linear slider bearing (i.e. for a film depth with a linear profile variation along the main flow direction). Validations refer to comparisons with analytical solutions, herein generalized to consider any Dirichlet boundary condition. Further, this study allows a first code validation of the “fluid–fixed frontier” interactions under no-slip conditions. With respect to the most state-of-the-art models (2D codes based on Reynolds’ equation for fluid films), the following distinctive features are highlighted: (1) 3D formulation on all the terms of the Navier–Stokes equations for incompressible fluids with uniform viscosity; (2) validations on both local and global quantities (pressure and velocity profiles; load-bearing capacity); (3) possibility to simulate any 3D topology. This study also shows the advantages of using a CFD-SPH code in simulating the inertia and 3D effects close to the slider edges, and it opens new research directions overcoming the limitations of the codes for hydrodynamic lubrication based on the Reynolds’ equation for fluid films. This study finally allows SPHERA to deal with hydrodynamic lubrication and improves the code for other relevant application fields involving fluid–structure interactions (e.g. transport of solid bodies by floods and earth landslides; rock landslides). SPHERA is developed and distributed on a GitHub public repository.

scholarly journals The emergence of localized vortex–wave interaction states in plane Couette flow

2013 ◽  
Vol 721 ◽  
pp. 58-85 ◽  
Author(s):  
Kengo Deguchi ◽  
Philip Hall ◽  
Andrew Walton
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
High Reynolds Number ◽  
Stokes Equations ◽  
Wave Interaction ◽  
Critical Layer ◽  
Navier Stokes ◽  
Turbulent Spots ◽  
Navier Stokes Equations ◽  
High Reynolds

AbstractThe recently understood relationship between high-Reynolds-number vortex–wave interaction theory and computationally generated self-sustaining processes provides a possible route to an understanding of some of the underlying structures of fully turbulent flows. Here vortex–wave interaction (VWI) theory is used in the long streamwise wavelength limit to continue the development found at order-one wavelengths by Hall & Sherwin (J. Fluid Mech., vol. 661, 2010, pp. 178–205). The asymptotic description given reduces the Navier–Stokes equations to the so-called boundary-region equations, for which we find equilibrium states describing the change in the VWI as the wavelength of the wave increases from $O(h)$ to $O(Rh)$, where $R$ is the Reynolds number and $2h$ is the depth of the channel. The reduced equations do not include the streamwise pressure gradient of the perturbation or the effect of streamwise diffusion of the wave–vortex states. The solutions we calculate have an asymptotic error proportional to ${R}^{- 2} $ when compared to the full Navier–Stokes equations. The results found correspond to the minimum drag configuration for VWI states and might therefore be of relevance to the control of turbulent flows. The key feature of the new states discussed here is the thickening of the critical layer structure associated with the wave part of the flow to completely fill the channel, so that the roll part of the flow is driven throughout the flow rather than as in Hall & Sherwin as a stress discontinuity across the critical layer. We identify a critical streamwise wavenumber scaling, which, when approached, causes the flow to localize and take on similarities with computationally generated or experimentally observed turbulent spots. In effect, the identification of this critical wavenumber for a given value of the assumed high Reynolds number fixes a minimum box length necessary for the emergence of localized structures. Whereas nonlinear equilibrium states of the Navier–Stokes equations are thought to form a backbone on which turbulent flows hang, our results suggest that the localized states found here might play a related role for turbulent spots.

Direct simulations of low-Reynolds-number turbulent flow in a rotating channel

1993 ◽  
Vol 256 ◽  
pp. 163-197 ◽  
Author(s):  
Reidar Kristoffersen ◽  
Helge I. Andersson
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Complete Suppression ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Computational Mesh ◽  
Developed Pressure ◽  
Rotating Channel

Direct numerical simulations of fully developed pressure-driven turbulent flow in a rotating channel have been performed. The unsteady Navier–Stokes equations were written for flow in a constantly rotating frame of reference and solved numerically by means of a finite-difference technique on a 128 × 128 × 128 computational mesh. The Reynolds number, based on the bulk mean velocity Um and the channel half-width h, was about 2900, while the rotation number Ro = 2|Ω|h/Um varied from 0 to 0.5. Without system rotation, results of the simulation were in good agreement with the accurate reference simulation of Kim, Moin & Moser (1987) and available experimental data. The simulated flow fields subject to rotation revealed fascinating effects exerted by the Coriolis force on channel flow turbulence. With weak rotation (Ro = 0.01) the turbulence statistics across the channel varied only slightly compared with the nonrotating case, and opposite effects were observed near the pressure and suction sides of the channel. With increasing rotation the augmentation and damping of the turbulence along the pressure and suction sides, respectively, became more significant, resulting in highly asymmetric profiles of mean velocity and turbulent Reynolds stresses. In accordance with the experimental observations of Johnston, Halleen & Lezius (1972), the mean velocity profile exhibited an appreciable region with slope 2Ω. At Ro = 0.50 the Reynolds stresses vanished in the vicinity of the stabilized side, and the nearly complete suppression of the turbulent agitation was confirmed by marker particle trackings and two-point velocity correlations. Rotational-induced Taylor-Görtler-like counter-rotating streamwise vortices have been identified, and the simulations suggest that the vortices are shifted slightly towards the pressure side with increasing rotation rates, and the number of vortex pairs therefore tend to increase with Ro.

scholarly journals Numerical Investigation of Pressure Profile in Hydrodynamic Lubrication Thrust Bearing

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Farooq Ahmad Najar ◽  
G. A. Harmain
Keyword(s):  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Pressure Profile ◽  
Grid Refinement ◽  
Average Value ◽  
Lubricant Oil ◽  
Pressure Profiles ◽  
Tilting Pad ◽  
Minimum Film Thickness ◽  
Grid Independence

Reynolds equation is solved using finite difference method (FDM) on the surface of the tilting pad to find the pressure distribution in the lubricant oil film. Different pressure profiles with grid independence are described. The present work evaluates pressure at various locations after performing a thorough grid refinement. In recent similar works, this aspect has not been addressed. However, present study shows that it can have significant effect on the pressure profile. Results of a sector shaped pad are presented and it is shown that the maximum average value of pressure is 12% (approximately) greater than the previous results. Grid independence occurs after 24 × 24 grids. A parameter “ψ” has been proposed to provide convenient indicator of obtaining grid independent results. ψ=|(Prefinedgrid-PRefrence-grid)/Prefinedgrid|, ψ≤ε, where “ε” can be fixed to a convenient value and a constant minimum film thickness value of 75 μm is used in present study. This important parameter is highlighted in the present work; the location of the peak pressure zone in terms of (r,θ) coordinates is getting shifted by changing the grid size which will help the designer and experimentalist to conveniently determine the position of pressure measurement probe.

Hydrodynamic Lubrication of Partial Porous Metal Bearings

1966 ◽  
Vol 88 (1) ◽  
pp. 53-60 ◽  
Author(s):  
C. A. Rhodes ◽  
W. T. Rouleau
Keyword(s):  
Series Solution ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Load Capacity ◽  
Porous Metal ◽  
Operating Conditions ◽  
Two Dimensional ◽  
Bearing Material ◽  
Porous Bearing ◽  
The Galerkin Method

Partial porous metal bearings are analyzed to determine their performance during steady-state operating conditions with a full film of lubricant. The pressure distribution is determined by a simultaneous solution of the two-dimensional Reynolds equation in the film region and the Laplace equation within the porous bearing material. An infinite-series solution is obtained for pressure utilizing the Galerkin method to determine coefficients. Numerical values of load capacity and coefficient of friction are presented for bearing arcs of 180, 150, and 120 deg.

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