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.

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.

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.

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.

scholarly journals Machine-aided turbulence theory

2018 ◽  
Vol 854 ◽  
Author(s):  
Javier Jiménez
Keyword(s):  
Turbulent Flow ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
A Priori ◽  
Turbulence Theory ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Future Evolution ◽  
Decaying Turbulence

The question of whether significant subvolumes of a turbulent flow can be identified by automatic means, independently of a priori assumptions, is addressed using the example of two-dimensional decaying turbulence. Significance is defined as influence on the future evolution of the flow, and the problem is cast as an unsupervised machine ‘game’ in which the rules are the Navier–Stokes equations. It is shown that significance is an intermittent quantity in this particular flow, and that, in accordance with previous intuition, its most significant features are vortices, while the least significant ones are dominated by strain. Subject to cost considerations, the method should be applicable to more general turbulent flows.

Lattice Boltzmann Method Based on Large-Eddy Simulation (LES) Used to Investigate the Unsteady Turbulent Flow on Series of Cavities

2020 ◽  
Author(s):  
Insaf Mehrez ◽  
Ramla Gheith ◽  
Fethi Aloui
Keyword(s):  
Boltzmann Equation ◽  
Turbulent Flow ◽  
Turbulent Flows ◽  
Lattice Boltzmann ◽  
Turbulence Modeling ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Eddy Simulation ◽  
Large Eddy

Abstract A numerical study is proposed to analyze the turbulent flow structures. This paper aims to determine the effect of the series of the cavities. The configuration is similar to that represented by two walls with infinite width, one of which is mobile and the other is fixed. The series of cavity are placed on the fixed wall. The objectives are to study the aero acoustic capabilities of LBM and to build and to assess the efficiency of the Lattice Boltzmann Equation (LBE) as a new computational tool to perform the Large-Eddy Simulations (LES) for turbulent flows. In the first part, the background of LBM is presented and the construction of Navier-Stokes equations from Boltzmann equation is discussed. The LBM-LES model for solving transition is developed and turbulence modeling is implemented. In the second part, the dynamics of the flows in the vicinity of cavities with symmetric or asymmetric edges are considered, to then discuss the oscillation phenomenon. The effect of the geometric of the cavity and the Reynolds numbers were studied to investigate the fluid flow dynamics. We were focusing on the dynamics of asymmetric deep cavity flows, to put forward the topology of the cavity flow and to highlight the effects of dissymmetry and aspect ratio.

A Numerical Study of Unsteady Natural Convection in a Rectangular Enclosure: The Effect of Compressibility

2004 ◽  
Author(s):  
K. M. Akyuzlu ◽  
Y. Pavri ◽  
A. Antoniou
Keyword(s):  
Mathematical Model ◽  
Stokes Equations ◽  
Numerical Study ◽  
Vertical Wall ◽  
Ideal Gas ◽  
Working Fluid ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Rectangular Enclosure ◽  
Circulation Patterns

A two-dimensional, mathematical model is adopted to investigate the development of buoyancy driven circulation patterns and temperature contours inside a rectangular enclosure filled with a compressible fluid (Pr=1.0). One of the vertical walls of the enclosure is kept at a higher temperature then the opposing vertical wall. The top and the bottom of the enclosure are assumed insulated. The physics based mathematical model for this problem consists of conservation of mass, momentum (two-dimensional Navier-Stokes equations) and energy equations for the enclosed fluid subjected to appropriate boundary conditions. The working fluid is assumed to be compressible through a simple ideal gas relation. The governing equations are discretized using second order accurate central differencing for spatial derivatives and first order forward finite differencing for time derivatives where the computation domain is represented by a uniform orthogonal mesh. The resulting nonlinear equations are then linearized using Newton’s linearization method. The set of algebraic equations that result from this process are then put into a matrix form and solved using a Coupled Modified Strongly Implicit Procedure (CMSIP) for the unknowns (primitive variables) of the problem. A numerical experiment is carried out for a benchmark case (driven cavity flow) to verify the accuracy of the proposed solution procedure. Numerical experiments are then carried out using the proposed compressible flow model to simulate the development of the buoyancy driven circulation patterns for Rayleigh numbers between 103 and 105. Finally, an attempt is made to determine the effect of compressibility of the working fluid by comparing the results of the proposed model to that of models that use incompressible flow assumptions together with Boussinesq approximation.

Numerical Study on Heat Transfer Characteristics From Parallel Plates With Cavities Swept by a Visco-Elastic Fluid

2010 ◽  
Author(s):  
Hiroshi Suzuki ◽  
Shinpei Maeda ◽  
Yoshiyuki Komoda
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Thermal Field ◽  
Numerical Study ◽  
Geometric Parameters ◽  
Two Dimensional ◽  
Parallel Plates ◽  
Heat Transfer Characteristics ◽  
Elastic Fluid ◽  
Heat Transfer Augmentation

Two-dimensional numerical computations have been performed in order to investigate the development characteristics of flow and thermal field in a flow between parallel plates swept by a visco-elastic fluid. In the present study, the effect of the cavity number in the domain and of Reynolds number was focused on when the geometric parameters were set constant. From the results, it is found that the flow penetration into the cavities effectively causes the heat transfer augmentation in the cavities in any cavity region compared with that of water case. It is also found that the development of thermal field in cases of the present visco-elastic fluid is quicker compared with that of water cases. The present heat transfer augmentation technique using Barus effect of a visco-elastic fluid is effective in the range of low Reynolds number.

Effect of wall-mounted V-baffle position in a turbulent flow through a channel

2019 ◽  
Vol 29 (10) ◽  
pp. 3908-3937 ◽  
Author(s):  
Younes Menni ◽  
Ahmed Azzi ◽  
Ali J. Chamkha ◽  
Souad Harmand
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Stokes Equations ◽  
Numerical Study ◽  
Rectangular Channel ◽  
Simple Algorithm ◽  
Two Dimensions ◽  
Large Reynolds Number ◽  
Constant Property ◽  
Content Type

Purpose The purpose of this paper is to carry out a numerical study on the dynamic and thermal behavior of a fluid with a constant property and flowing turbulently through a two-dimensional horizontal rectangular channel. The upper surface was put in a constant temperature condition, while the lower one was thermally insulated. Two transverse, solid-type obstacles, having different shapes, i.e. flat rectangular and V-shaped, were inserted into the channel and fixed to the top and bottom walls of the channel, in a periodically staggered manner to force vortices to improve the mixing, and consequently the heat transfer. The flat rectangular obstacle was put in the first position and was placed on the hot top wall of the channel. However, the second V-shaped obstacle was placed on the insulated bottom wall, at an attack angle of 45°; its position was varied to find the optimum configuration for optimal heat transfer. Design/methodology/approach The fluid is considered Newtonian, incompressible with constant properties. The Reynolds averaged Navier–Stokes equations, along with the standard k-epsilon turbulence model and the energy equation, are used to control the channel flow model. The finite volume method is used to integrate all the equations in two-dimensions; the commercial CFD software FLUENT along with the SIMPLE-algorithm is used for pressure-velocity coupling. Various values of the Reynolds number and obstacle spacing were selected to perform the numerical runs, using air as the working medium. Findings The channel containing the flat fin and the 45° V-shaped baffle with a large Reynolds number gave higher heat transfer and friction loss than the one with a smaller Reynolds number. Also, short separation distances between obstacles provided higher values of the ratios Nu/Nu0 and f/f0 and a larger thermal enhancement factor (TEF) than do larger distances. Originality/value This is an original work, as it uses a novel method for the improvement of heat transfer in completely new flow geometry.

Two-dimensional global low-frequency oscillations in a separating boundary-layer flow

2008 ◽  
Vol 614 ◽  
pp. 315-327 ◽  
Author(s):  
UWE EHRENSTEIN ◽  
FRANÇOIS GALLAIRE
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Perturbation Analysis ◽  
Boundary Layer Flow ◽  
Stokes Equations ◽  
Low Frequency ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Optimal Perturbation ◽  
Layer Flow

A separated boundary-layer flow at the rear of a bump is considered. Two-dimensional equilibrium stationary states of the Navier–Stokes equations are determined using a nonlinear continuation procedure varying the bump height as well as the Reynolds number. A global instability analysis of the steady states is performed by computing two-dimensional temporal modes. The onset of instability is shown to be characterized by a family of modes with localized structures around the reattachment point becoming almost simultaneously unstable. The optimal perturbation analysis, by projecting the initial disturbance on the set of temporal eigenmodes, reveals that the non-normal modes are able to describe localized initial perturbations associated with the large transient energy growth. At larger time a global low-frequency oscillation is found, accompanied by a periodic regeneration of the flow perturbation inside the bubble, as the consequence of non-normal cancellation of modes. The initial condition provided by the optimal perturbation analysis is applied to Navier–Stokes time integration and is shown to trigger the nonlinear ‘flapping’ typical of separation bubbles. It is possible to follow the stationary equilibrium state on increasing the Reynolds number far beyond instability, ruling out for the present flow case the hypothesis of some authors that topological flow changes are responsible for the ‘flapping’.

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