A Nonlinear-PH Method of Solution for Journal Gas Bearings

1976 ◽  
Vol 98 (4) ◽  
pp. 613-619 ◽  
Author(s):  
M. J. Cohen
Keyword(s):  
Linear Form ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Journal Bearings ◽  
Small Perturbations ◽  
First Order ◽  
Order Solution ◽  
Method Of Solution ◽  
In Series ◽  
Gas Bearing

This paper describes a method of solving the Reynolds equations governing the fluid motion in an infinite journal gas bearing. The method derives from an exact transformation of the classical equations to a quasi-linear form. The only assumption made is the isothermal one which in practice closely describes the changes in the state of the gas within the bearing. The solution to the transformed equation for ph is sought in series and there are no difficulties in taking more terms into considerations, apart from algebraic ones. A first order solution is immediately obtained and corresponds as an approximation to any of the following methods: small perturbations (Ausman [1]) Katto and Soda [2], linear-ph (Ausman [3]) Harrison [4]. A higher order solution is also presented which requires little more algebra for its derivation. The extension of the method to three-dimensional gas journal bearings is also outlined.

Higher-Order Solutions for Unsteady Hypersonic and Supersonic Flow

1974 ◽  
Vol 25 (1) ◽  
pp. 59-68 ◽  
Author(s):  
W H Hui ◽  
J Hamilton
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Supersonic Flow ◽  
Power Series ◽  
Unsteady Flow ◽  
The Body ◽  
Wedge Flow ◽  
First Order ◽  
Order Solution ◽  
Method Of Solution

SummaryThe problem of unsteady hypersonic and supersonic flow with attached shock wave past wedge-like bodies is studied, using as a basis the assumption that the unsteady flow is a small perturbation from a steady uniform wedge flow. It is formulated in the most general case and applicable for any motion or deformation of the body. A method of solution to the perturbation equations is given by expanding the flow quantities in power series in M−2, M being the Mach number of the steady wedge flow. It is shown how solutions of successive orders in the series may be calculated. In particular, the second-order solution is given and shown to give improvements uniformly over the first-order solution.

scholarly journals WAVE SCATTERING BY PERMEABLE AND IMPERMEABLE BREAKWATER OF ARBITRARY SHAPE

1974 ◽  
Vol 1 (14) ◽  
pp. 110
Author(s):  
Takeshi Ijima ◽  
Chung Ren Chou ◽  
Yasu Yumura
Keyword(s):  
Arbitrary Shape ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Theoretical Method ◽  
Floating Body ◽  
Wave Forces ◽  
Method Of Calculation ◽  
Wave Channel ◽  
Method Of Solution ◽  
Special Case

This paper deals with a theoretical method of calculation of the fluid motion, when a sinusoidal plane wave incidents to a permeable breakwater of arbitrary shape at constant water depth and shows that the problem for impermeable breakwater is solved as a special case of this method. The method described here is the extension of the author's method of solution for two-dimensional permeable breakwater by the method of continuation of velocity potentials for two different fluid regions into three-dimensional problems by means of Green functions. Here, the analytical process of calculation is presented and as representative examples, wave height distributions and wave forces around an isolated elliptic- and rectangular breakwater are calculated and compared with experiments in wave channel. The principle of this method is also applied to the analysis of submerged and semi-immersed fixed cylinder and the motions of floating body of arbitrary.

scholarly journals On a Modified Form of Navier-Stokes Equations for Three-Dimensional Flows

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
J. Venetis
Keyword(s):  
Stokes Equations ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Vector Form ◽  
Navier Stokes Equations ◽  
First Order ◽  
Modified Equations ◽  
Cartesian Coordinate ◽  
Fundamental Equations

A rephrased form of Navier-Stokes equations is performed for incompressible, three-dimensional, unsteady flows according to Eulerian formalism for the fluid motion. In particular, we propose a geometrical method for the elimination of the nonlinear terms of these fundamental equations, which are expressed in true vector form, and finally arrive at an equivalent system of three semilinear first order PDEs, which hold for a three-dimensional rectangular Cartesian coordinate system. Next, we present the related variational formulation of these modified equations as well as a general type of weak solutions which mainly concern Sobolev spaces.

Steady three-dimensional vortex flow

1966 ◽  
Vol 25 (3) ◽  
pp. 557-576 ◽  
Author(s):  
Robert Granger
Keyword(s):  
High Speed ◽  
Vortex Flow ◽  
Three Dimensional ◽  
Rotational Flow ◽  
Zeroth Order ◽  
Small Perturbations ◽  
First Order ◽  
Vorticity Distribution ◽  
The Core ◽  
Axis Of Rotation

A theory is developed for an incompressible fluid in a steady three-dimensional rotational flow. Solutions are obtained subject to the restriction of small perturbations and are determinant provided that the vorticity distribution along the axis of rotation is known. Effects of viscosity are included. Closed-form expressions for the zeroth-order circulation and stream function and first-order circulation are given, with other higher-order expressions requiring high-speed computers. Experimental results of radial variation of axial velocity in the core show a distribution more elaborate than Gaussian.

scholarly journals Superconformal boundaries in 4 − ϵ dimensions

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Aleix Gimenez-Grau ◽  
Pedro Liendo ◽  
Philine van Vliet
Keyword(s):  
Three Dimensional ◽  
Spacetime Dimension ◽  
Perfect Agreement ◽  
Bootstrap Analysis ◽  
First Order ◽  
Free Theory ◽  
First Order Correction ◽  
Free Parameters ◽  
Superconformal Theories ◽  
Zumino Model

Abstract Boundaries in three-dimensional $$ \mathcal{N} $$ N = 2 superconformal theories may preserve one half of the original bulk supersymmetry. There are two possibilities which are characterized by the chirality of the leftover supercharges. Depending on the choice, the remaining 2d boundary algebra exhibits $$ \mathcal{N} $$ N = (0, 2) or $$ \mathcal{N} $$ N = (1) supersymmetry. In this work we focus on correlation functions of chiral fields for both types of supersymmetric boundaries. We study a host of correlators using superspace techniques and calculate superconformal blocks for two- and three-point functions. For $$ \mathcal{N} $$ N = (1) supersymmetry, some of our results can be analytically continued in the spacetime dimension while keeping the codimension fixed. This opens the door for a bootstrap analysis of the ϵ-expansion in supersymmetric BCFTs. Armed with our analytically-continued superblocks, we prove that in the free theory limit two-point functions of chiral (and antichiral) fields are unique. The first order correction, which already describes interactions, is universal up to two free parameters. As a check of our analysis, we study the Wess-Zumino model with a super-symmetric boundary using Feynman diagrams, and find perfect agreement between the perturbative and bootstrap results.

On the Boundary Value Problem in A Dihedral Angle for Normally Hyperbolic Systems of First Order

1998 ◽  
Vol 5 (2) ◽  
pp. 121-138
Author(s):  
O. Jokhadze
Keyword(s):  
Partial Differential Equations ◽  
Boundary Value Problem ◽  
Principal Part ◽  
Hyperbolic Systems ◽  
Boundary Value ◽  
Three Dimensional ◽  
Order System ◽  
First Order ◽  
Dimensional Boundary ◽  
Class Of Functions

Abstract Some structural properties as well as a general three-dimensional boundary value problem for normally hyperbolic systems of partial differential equations of first order are studied. A condition is given which enables one to reduce the system under consideration to a first-order system with the spliced principal part. It is shown that the initial problem is correct in a certain class of functions if some conditions are fulfilled.

scholarly journals Experimental and Numerical Investigation about Small Clearance Journal Bearings under Static Load Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Carlo Alberto Niccolini Marmont Du Haut Champ ◽  
Fabrizio Stefani ◽  
Paolo Silvestri
Keyword(s):  
Three Dimensional ◽  
Journal Bearings ◽  
Radial Clearance ◽  
Small Scale ◽  
Test Rig ◽  
Small Clearance ◽  
Dimensional Simulation ◽  
Dynamic Loading Conditions ◽  
Static And Dynamic Loading ◽  
Good Agreement

The aim of the present research is to characterize both experimentally and numerically journal bearings with low radial clearances for rotors in small-scale applications (e.g., microgas turbines); their diameter is in the order of ten millimetres, leading to very small dimensional clearances when the typical relative ones (order of 1/1000) are employed; investigating this particular class of journal bearings under static and dynamic loading conditions represents something unexplored. To this goal, a suitable test rig was designed and the performance of its bearings was investigated under steady load. For the sake of comparison, numerical simulations of the lubrication were also performed by means of a simplified model. The original test rig adopted is a commercial rotor kit (RK), but substantial modifications were carried out in order to allow significant measurements. Indeed, the relative radial clearance of RK4 RK bearings is about 2/100, while it is around 1/1000 in industrial bearings. Therefore, the same original RK bearings are employed in this new test rig, but a new shaft was designed to reduce their original clearance. The new custom shaft allows to study bearing behaviour for different clearances, since it is equipped with interchangeable journals. Experimental data obtained by this test rig are then compared with further results of more sophisticated simulations. They were carried out by means of an in-house developed finite element (FEM) code, suitable for thermoelasto-hydrodynamic (TEHD) analysis of journal bearings both in static and dynamic conditions. In this paper, bearing static performances are studied to assess the reliability of the experimental journal location predictions by comparing them with the ones coming from already validated numerical codes. Such comparisons are presented both for large and small clearance bearings of original and modified RKs, respectively. Good agreement is found only for the modified RK equipped with small clearance bearings (relative radial clearance 8/1000), as expected. In comparison with two-dimensional lubrication analysis, three-dimensional simulation improves prediction of journal location and correlation with experimental results.

Development and Validation of a Three-Dimensional Multiphase Flow CFD Analysis for Journal Bearings in Steam and Heavy Duty Gas Turbines

2012 ◽  
Author(s):  
Stephan Uhkoetter ◽  
Stefan aus der Wiesche ◽  
Michael Kursch ◽  
Christian Beck
Keyword(s):  
Experimental Data ◽  
Multiphase Flow ◽  
Gas Turbines ◽  
High Speed ◽  
Three Dimensional ◽  
Air Entrainment ◽  
Journal Bearings ◽  
Heavy Duty ◽  
Present Contribution ◽  
Two Phase

The traditional method for hydrodynamic journal bearing analysis usually applies the lubrication theory based on the Reynolds equation and suitable empirical modifications to cover turbulence, heat transfer, and cavitation. In cases of complex bearing geometries for steam and heavy-duty gas turbines this approach has its obvious restrictions in regard to detail flow recirculation, mixing, mass balance, and filling level phenomena. These limitations could be circumvented by applying a computational fluid dynamics (CFD) approach resting closer to the fundamental physical laws. The present contribution reports about the state of the art of such a fully three-dimensional multiphase-flow CFD approach including cavitation and air entrainment for high-speed turbo-machinery journal bearings. It has been developed and validated using experimental data. Due to the high ambient shear rates in bearings, the multiphase-flow model for journal bearings requires substantial modifications in comparison to common two-phase flow simulations. Based on experimental data, it is found, that particular cavitation phenomena are essential for the understanding of steam and heavy-duty type gas turbine journal bearings.

Radiant Heat Transfer From Isothermal Dispersions With Isotropic Scattering

1967 ◽  
Vol 89 (4) ◽  
pp. 300-308 ◽  
Author(s):  
R. H. Edwards ◽  
R. P. Bobco
Keyword(s):  
Heat Transfer ◽  
Approximate Solutions ◽  
Radiant Heat ◽  
Second Order ◽  
Isotropic Scattering ◽  
Radiant Heat Transfer ◽  
Approximate Methods ◽  
First Order ◽  
Order Solution ◽  
Radiant Transfer

Two approximate methods are presented for making radiant heat-transfer computations from gray, isothermal dispersions which absorb, emit, and scatter isotropically. The integrodifferential equation of radiant transfer is solved using moment techniques to obtain a first-order solution. A second-order solution is found by iteration. The approximate solutions are compared to exact solutions found in the literature of astrophysics for the case of a plane-parallel geometry. The exact and approximate solutions are both expressed in terms of directional and hemispherical emissivities at a boundary. The comparison for a slab, which is neither optically thin nor thick (τ = 1), indicates that the second-order solution is accurate to within 10 percent for both directional and hemispherical properties. These results suggest that relatively simple techniques may be used to make design computations for more complex geometries and boundary conditions.

Diesel Droplet Diffusion in Isotropic Turbulence With Digital Holographic Cinematography

2005 ◽  
Author(s):  
Balaji Gopalan ◽  
Edwin Malkiel ◽  
Jian Sheng ◽  
Joseph Katz
Keyword(s):  
Time Series ◽  
High Speed ◽  
Isotropic Turbulence ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Time History ◽  
Sample Volume ◽  
Velocity Autocorrelation Function ◽  
Digital Cameras ◽  
Velocity Autocorrelation

High-speed in-line digital holographic cinematography was used to investigate the diffusion of droplets in locally isotropic turbulence. Droplets of diesel fuel (0.3–0.9mm diameter, specific gravity of 0.85) were injected into a 37×37×37mm3 sample volume located in the center of a 160-liter tank. The turbulence was generated by 4 spinning grids, located symmetrically in the corners of the tank, and was characterized prior to the experiments. The sample volume was back illuminated with two perpendicular collimated beams of coherent laser light and time series of in-line holograms were recorded with two high-speed digital cameras at 500 frames/sec. Numerical reconstruction generated a time series of high-resolution images of the droplets throughout the sample volume. We developed an algorithm for automatically detecting the droplet trajectories from each view, for matching the two views to obtain the three-dimensional tracks, and for calculating the time history of velocity. We also measured the mean fluid motion using 2-D PIV. The data enabled us to calculate the Lagrangian velocity autocorrelation function.

Sign in / Sign up

Export Citation Format

Share Document