Inertia Effects in Fully Developed Axisymmetric Laminar Flow

1971 ◽  
Vol 93 (3) ◽  
pp. 408-414 ◽  
Author(s):  
E. Makay ◽  
P. R. Trumpler
Keyword(s):  
Integral Equations ◽  
High Speed ◽  
Equations Of Motion ◽  
Rotating Disk ◽  
Navier Stokes ◽  
Centrifugal Impeller ◽  
Navier Stokes Equation ◽  
Inertia Effects ◽  
Nonlinear Form ◽  
Clearance Face

The three components of the Navier-Stokes equation are solved here simultaneously in their nonlinear form for axisymmetric radial inward and outward flow cases between two parallel rotating walls. Examples of application in rotating machinery are close clearance face seals, thrust bearings, high speed thrust device, rotating disk, narrow gap between centrifugal impeller and housing, etc. The differential equations of motion with the proper boundary conditions were converted into integral equations of the “Fredholm second kind” type and solutions have been obtained for the nonlinear cases. The use of integral equations greatly enhanced the advantage of the numerical solution developed here. The results are compared to simplified solutions and to solutions considering some of the nonlinear members. The effects of the inertia forces are especially emphasized and discussed in detail. The inclusion of these terms significantly affected the velocity field in the area discussed here. It is shown here that for low inward or outward flows the centrifugal force, and for high flows the convective acceleration terms have the main controlling influence on the radical velocity component.

Analytical Solution of Hydrostatic Pocket Tilting

2016 ◽  
Vol 821 ◽  
pp. 113-119 ◽  
Author(s):  
Eduard Stach ◽  
Jiří Falta ◽  
Matěj Sulitka
Keyword(s):  
Computational Models ◽  
Load Capacity ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Detailed Model ◽  
Limit Values ◽  
Inertia Effects ◽  
Proposed Model ◽  
Machine Tool Structure

Tilting (parallelism error) of guiding surfaces may cause reduction of load capacity of hydrostatic (HS) guideways and bearings in machine tools (MT). Using coupled finite element (FE) computational models of MT structures, it is nowadays possible to determine the extent of guiding surfaces deformation caused by thermal effects, gravitational force, cutting forces and inertia effects. Assessment of maximum allowable tilt has so far been based merely on experience. The paper presents a detailed model developed for description of the effect of HS bearing tilt on the load capacity characteristics of HS guideways. The model allows an evaluation of the tilt influence on the change of the characteristics as well as determination of the limit values of allowable tilt in interaction with compliant machine tool structure. The proposed model is based on the model of flow over the land of the HS pocket under extended Navier-Stokes equation. The model is verified using an experimental test rig.

Learning the Dynamics of Objects by Optimal Functional Interpolation

2012 ◽  
Vol 24 (9) ◽  
pp. 2457-2472
Author(s):  
Jong-Hoon Ahn ◽  
In Young Kim
Keyword(s):  
Functional Data ◽  
Continuity Equation ◽  
Particle Concentration ◽  
Equations Of Motion ◽  
Navier Stokes ◽  
Conserved Quantities ◽  
Time Varying ◽  
Science And Engineering ◽  
Navier Stokes Equation ◽  
Over Time

Many areas of science and engineering rely on functional data and their numerical analysis. The need to analyze time-varying functional data raises the general problem of interpolation, that is, how to learn a smooth time evolution from a finite number of observations. Here, we introduce optimal functional interpolation (OFI), a numerical algorithm that interpolates functional data over time. Unlike the usual interpolation or learning algorithms, the OFI algorithm obeys the continuity equation, which describes the transport of some types of conserved quantities, and its implementation shows smooth, continuous flows of quantities. Without the need to take into account equations of motion such as the Navier-Stokes equation or the diffusion equation, OFI is capable of learning the dynamics of objects such as those represented by mass, image intensity, particle concentration, heat, spectral density, and probability density.

Axial Leakage Flow-Induced Vibration of Thin Cylindrical Shell With Respect to Circumferential Vibration

2002 ◽  
Author(s):  
Katsuhisa Fujita ◽  
Atsuhiko Shintani ◽  
Masakazu Ono
Keyword(s):  
Cylindrical Shell ◽  
Equations Of Motion ◽  
Fluid Pressure ◽  
Navier Stokes ◽  
Leakage Flow ◽  
Thin Cylindrical Shell ◽  
Flow Induced Vibration ◽  
Navier Stokes Equation ◽  
Coupled Equations ◽  
Unstable Vibration

In this paper, the dynamic stability of a thin cylindrical shell subjected to axial leakage flow is discussed. In this paper, the third part of a study of the axial leakage flow-induced vibration of a thin cylindrical shell, we focus on circumferential vibration, that is, the ovaling vibration of a shell. The coupled equations of motion between shell and liquid are obtained by using Donnell’s shell theory and the Navier-Stokes equation. The added mass, added damping and added stiffness in the coupled equations of motion are described by utilizing the unsteady fluid pressure acting on the shell. The relations between axial velocity and the unstable vibration phenomena are clarified concerning the circumferential vibration of a shell. Numerical parametric studies are done for various dimensions of a shell and an axial leakage flow.

Simulation of the subsonic flow in a high-speed centrifugal compressor impeller by the pressure-based method

1998 ◽  
Vol 212 (4) ◽  
pp. 269-287 ◽  
Author(s):  
Y Wang ◽  
S Komori
Keyword(s):  
High Speed ◽  
Compressible Flows ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Centrifugal Impeller ◽  
Navier Stokes Equations ◽  
Compressor Impeller ◽  
Collocated Grid

A pressure-based finite volume procedure developed previously for incompressible flows is extended to predict the three-dimensional compressible flow within a centrifugal impeller. In this procedure, the general curvilinear coordinate system is used and the collocated grid arrangement is adopted. Mass-averaging is used to close the instantaneous Navier-Stokes equations. The covariant velocity components are used as the main variables for the momentum equations, making the pressure-velocity coupling easier. The procedure is successfully applied to predict various compressible flows from subsonic to supersonic. With the aid of the k-ɛ turbulence model, the flow details within a centrifugal impeller are obtained using the present procedure. Predicted distributions of the meridional velocity and the static pressure are reasonable. Calculated radial velocities and flow angles are favourably compared with the measurements at the exit of the impeller.

scholarly journals Thermo-Elastohydrodynamic Study on Textured Journal Bearing with High-Speed and High-Specific-Pressure

2019 ◽  
Vol 37 (4) ◽  
pp. 751-756 ◽  
Author(s):  
Lin Wang ◽  
Yu Zhang ◽  
Guoding Chen
Keyword(s):  
Elastic Deformation ◽  
High Speed ◽  
Journal Bearing ◽  
Hydrodynamic Performance ◽  
Navier Stokes ◽  
Specific Pressure ◽  
Analysis Model ◽  
Navier Stokes Equation ◽  
Gear Transmission System ◽  
Load Carrying

The performance of supporting journal bearing of the star gear transmission system in the geared turbo fan engine (GTF) is analyzed. A thermal-elastohydrodynamic analysis model was developed for textured journal bearing used in high-speed and high-specific-pressure conditions. The Navier-Stokes equation, energy equation, and viscosity-temperature equation were calculated by the computational fluid dynamics method. The influence of elastic deformation on bearing thermal hydrodynamic performance was studied in detail. The results indicate that the elastic deformation has an influence on the distribution of oil temperature and oil pressure. Besides, a comparative thermo-elastohydrodynamic analysis was conducted between the textured bearing and the un-textured bearing, and the discrepancies of maximum oil pressure, load carrying capacity and the maximum oil temperature are few. However, the textured bearing has a lower elastic deformation than the un-textured bearing.

A Transient CFD Simulation of the Flow in a Test Rig of an Aeroengine Bearing Chamber

2014 ◽  
Author(s):  
Akinola A. Adeniyi ◽  
Hervé P. Morvan ◽  
Kathy A. Simmons
Keyword(s):  
High Speed ◽  
Cfd Simulation ◽  
Film Formation ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Oil Film ◽  
Sheared Flow ◽  
Fine Mesh ◽  
Computational Overhead ◽  
Formation Pattern

In this paper, we present results for the application of an Eulerian-Lagrangian technique to the transient simulation of an oil film formation on the walls of an aeroengine bearing chamber. The flow of oil in an aeroengine bearing chamber consists of high speed oil droplets interacting with the bearing structures and flowing oil film. The situation in the chamber is highly rotational and consisting of sheared flow of air over oil. The bearing chamber may also be located in the vicinity of the combustion chamber. The oil provides lubrication and cooling of the hot structures. Modelling the flow in the bearing chamber is therefore complex. The Volume of Fluid (VoF) technique offers a potential platform to model droplet-film interaction; however, it requires fine mesh details to capture the flow to the droplet level. Such detailed resolution would not be practical for the complete chamber geometry because of the prohibitively expensive computational overhead requirements. A Lagrangian formulation is therefore proposed to represent the droplets as source terms in the Navier-Stokes equation while the film is represented using VoF. This effectively reduces the need to resolve the droplets explicitly. The predicted film formation pattern compares with experimental results.

PARTICLE DYNAMICS SIMULATIONS OF THE NAVIER–STOKES FLOW WITH HARD DISKS

2004 ◽  
Vol 15 (10) ◽  
pp. 1413-1424 ◽  
Author(s):  
TATSUYA ISHIWATA ◽  
TERUYOSHI MURAKAMI ◽  
SATOSHI YUKAWA ◽  
NOBUYASU ITO
Keyword(s):  
Equations Of Motion ◽  
Local Equilibrium ◽  
Flow Simulation ◽  
Quantitative Agreement ◽  
Particle Dynamics ◽  
Navier Stokes ◽  
Hard Disks ◽  
Navier Stokes Equation ◽  
Dynamics Simulations ◽  
Energy And Momentum

Flow simulation with a particle dynamics method is studied. The fluid is made of hard particles which obey the Newtonian equations of motion and the collisions between particles are elastic, that is, energy and momentum are conserved. The viscosity appears autonomously together with the local equilibrium state. When a particle collides with a nonslip boundary, a new velocity is given randomly from the thermal distribution if the wall is isothermal, or a random reflection angle is selected if the wall is adiabatic. Shear viscosity is estimated from simulations of plane Poiseuille flow together with the confirmation that the system obeys the Navier–Stokes equation. Flows past a cylinder are also simulated. Depending on the Reynolds number up to 106, flow patterns are properly reproduced, and Kármán vortex shedding is observed. The estimated values of drag coefficient show quantitative agreement with experiments.

Development of a 3D Navier Stokes Solver for Application to all Types of Turbomachinery

1988 ◽  
Author(s):  
W. N. Dawes
Keyword(s):  
High Speed ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Navier Stokes ◽  
Compressor Cascade ◽  
Basic Algorithm ◽  
Navier Stokes Equations ◽  
Transonic Compressor ◽  
Stage Of Development ◽  
Code Performance

This paper describes the current stage of development of a code aimed at solving the 3D Navier-Stokes equations in any type of turbomachinery geometry. The basic algorithm time marches the fully 3D unsteady equations of motion expressed in finite volume form with a two step explicit / one step implicit method. Full multigrid acceleration is used to reduce solution time and maintain code performance on fine meshes. Turbulence modelling is via mixing-length closure and the widely used Baldwin-Lomax model. The generality and robustness of the code is demonstrated by application to five different test cases, three axial and two radial configurations. Also included is a grid independence study which demonstrates near grid independent solutions for transonic compressor cascade flow (albeit with the actual result subject to transition modelling constraints). For two of the axial cases (transonic compressor in cascade, secondary flow in a high speed compressor) and one radial case (Eckardt high speed impellor) sufficient mesh is employed for the predictions to be essentially quantitative. The other two cases (radial inflow turbine with clearance and compressor stator with hub clearance) are really simulations rather than predictions, but are included as the flows are novel and provide much physical insight.

Stability Analysis of a 2” Floppy Disk Drive System and the Optimum Design of the Disk Stabilizer

1992 ◽  
Vol 114 (2) ◽  
pp. 283-286 ◽  
Author(s):  
S. Chonan ◽  
Z. W. Jiang ◽  
Y. J. Shyu
Keyword(s):  
Design Method ◽  
Floppy Disk ◽  
Rotating Disk ◽  
Disk Drive ◽  
Drive System ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Modal Expansion ◽  
Floppy Disk Drive ◽  
The Stability

This paper presents a study on the stability of a 2″ floppy disk drive system. A design method of the disk stabilizer that makes the rotating disk stable is presented. The stabilizer and the read/write head are both modeled by springs with high axial stiffnesses. The stiffness of the air film surrounding the disk is determined from the Navier-Stokes equation as a function of the flow rate of the air within the disk jacket. The solution is obtained by using the multi-modal expansion approximation and applying the Galerkin method to the resulting equations. Numerical results show that the 2″ floppy disk rotating at 3600 rpm is unstable without the stabilizer. Further, it is shown that the stability of the disk is much affected by the geometrical configuration of the stabilizer attached to the rotating disk. A stabilizer that contacts the disk at four points was found quite effective in stabilizing the 2″ disk working at 3600 rpm.

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