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Wednesday, July 8, 2020 | History

3 edition of Fast methods to numerically integrate the Reynolds equation for gas fluid films found in the catalog.

Fast methods to numerically integrate the Reynolds equation for gas fluid films

# Fast methods to numerically integrate the Reynolds equation for gas fluid films

Published by National Aeronautics and Space Administration, National Technical Information Service, distributor in [Washington, DC], [Springfield, Va.? .
Written in English

Subjects:
• Thin films.,
• Reynolds number.

• Edition Notes

The Physical Object ID Numbers Statement Florin Dimofte. Series NASA technical memorandum -- 105415., NASA technical memorandum -- 105415. Contributions United States. National Aeronautics and Space Administration. Format Microform Pagination 1 v. Open Library OL15366202M

Reynolds Numbers Fluid flow in a pipe encounters frictional resistance due to the internal roughness (e) of the pipe wall, which can create local eddy currents within the fluid. Calculation of the Reynolds Number helps to determine if the flow in the pipe is Laminar Flow or Turbulent Flow. solving Reynolds’ equation are shown only for the case L = The predictions are in good agreement, though the Reynolds’ equation over-predicts the bearing load capacity at high eccen-tricity ratio compared to the CFD results. The Reynolds’ equation results are virtually identical to those taken from . Water BearingFile Size: 1MB.

Reynolds equation is used to analyze fluid flow through small gaps. As such, the solution of Reynolds equation provides critical information for a wide range of tribological problems. In any case where a lubricant resides between two moving surfaces, the Reynolds equation can be used to solve for the flow. 5 Equation 10 is the general form of the Reynolds Transport Theorem and can be used to solve many important problems in fluid mechanics.1 Although the theorem looks mathematically complex, it is relatively easy to understand conceptually (i.e., in terms of the word expressions.

There is one way to do that, which ends up being the Reynolds number. The interpretation of inertial to viscous forces comes from looking at the non-dimensional equation. If you inspect the magnitude of the terms, namely the convective (or inertial term) and the viscous term, . Reynolds Number calculator solving for Reynolds Number given density, Equations Calculator Engineering Fluid Mechanics Design Formulas. Reynolds Number assists in the analysis of the type of fluid flow: laminar, turbulent and transitional. It describes the relationship between viscous force and inertial force. Change Equation Select to.

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### Fast methods to numerically integrate the Reynolds equation for gas fluid films Download PDF EPUB FB2

FAST METHODS TO NUMERICALLY INTEGRATE THE REYNOLDS EQUATION FOR GAS FLUID FILMS Jt Florin Dimofte National Aeronautics and Space Administration Lewis Research Center Cleveland, Ohio SUMMARY The alternating direction implicit (ADI) method is adopted, modified, and applied to the Reynolds equation for thin, gas fluid Size: KB.

Get this from a library. Fast methods to numerically integrate the Reynolds equation for gas fluid films. [Florin Dimofte; United States. National Aeronautics and Space Administration.]. Reynolds equation describes behavior of hydrodynamic lubrication caused by a fluid sheared and possibly compressed between surfaces.

The surfaces must be in relative tangential sliding motion, with a gap between surfaces that generally converges along the direction of sliding (Fig. 1).Shearing of the film along the convergent gap tends to compress the film, which generates pressures in the.

The first termon the right-handsidis nothingbute thevariationin theflow rateof fluid integrateacross theslice(“fast”direction)tofind anintegratedquantity suchasthelocalflowrat eperunitdepth, The General Form of Reynolds Equation Author:File Size: KB.

Equation (13) represents a generalized form of Reynolds equation for com- pressible fluid film lubrication considering slip velocities at the bearing sur- faces. The two sets of functions F and G depend upon the variation of fluid properties both along and across the film and on the slip conditions at the Size: KB.

The Reynolds Equation is a partial differential equation governing the pressure distribution of thin viscous fluid films in Lubrication should not be confused with Osborne Reynolds' other namesakes, Reynolds number and Reynolds-averaged Navier–Stokes was first derived by Osborne Reynolds in The classical Reynolds Equation can be used to describe the pressure.

x - Lect 16 - Electromagnetic Induction, Faraday's Law, Lenz Law, SUPER DEMO - Duration: Lectures by Walter Lewin. They will make you ♥ Physics. Recommended for you. Dimofte F. Fast methods to numerically integrate the Reynolds equation for gas fluid films. STLE-ASME Joint Tribology Conference Oct ; flexible rotor supported by externally pressurized.

Abstract. The modified Reynolds equation for ultra-thin gas films between magnetic head and disk assembly is difficult to solve with conventional numerical methods, since the bearing number is very large and there exist boundary layers where pressure changes by: 7. The solution methods of the Reynolds equation and of the evaluation of the bearing characteristics have been also reported in previous works that the author has co-authored [30, 31].

The results. A unified Reynolds equation of the general non-Newtonian fluid is put forward in the present paper by treating the total flow as the sum of the Couette flow and Poiseuille flow.

An extensive set of the full EHL line contact simulations have been presented to investigate the by: 5. Int J Non Linear Mrrhanna Vol 16 No I pp 'Y)=0 sl x\$ Printed m Great Britain 19MI Pergamon Press Ltd GENERALIZED REYNOLDS AND INTEGRATED ENERGY EQUATIONS FOR FLUID-FILM LUBRICATION R L VERMA Department of Mathematics, Indian Institute of Technology KanpurIndia (Received 23 October ) Abstract-A generalized form of Cited by: 1.

Focusing the interest on the flow-rate to pressure-gradient relationship over a representative element of the fracture, an upscaling procedure is applied to the local Reynolds equation using the method of volume averaging, providing a macroscopic model for which the momentum conservation equation has a Reynolds-like by: 8.

Reynolds () presented the basic equation governing the analysis of fluid film lubrication. This equation in fact, arose from the combination of equation of motion and equation of continuity. While deriving this equation Reynolds neglected fluid inertia and gravitationalFile Size: KB.

Abstract: Reynolds equation is used to analyze fluid flow through small gaps. As such, the solution of Reynolds equation provides critical information for a wide range of tribological problems.

In any case where a lubricant resides between two moving surfaces (e.g., thrust and journal bearings), the Reynolds equation can be used to solve for. Fast Marching Methods are numerical schemes for computing solutions to the nonlinear Eikonal equation and related static Hamilton--Jacobi equations.

Based on entropy-satisfying upwind schemes and fast sorting techniques, they yield consistent, accurate, and highly efficient by: Governing equations of fluid flow such as continuity equation, heat transfer equation, momentum equation and Reynolds equation for a turbulent fluid flow of a compressible fluid has been adopted to solve the CFD analysis .

Definition. The simplest form of a 2-dimensional thin film equation reads ∂ ∂ = − ∇ ⋅ (∇ (∇)) where μ is the viscosity of the liquid, h(x,y,t) is the x- y- and t-dependent film thickness and γ is the interfacial tension between the liquid and the gas phase above it.

The parameter γ can also be a function of x and y, which is why it has been left inside the differentiation and. Started from a widely used FK model of Reynolds equation, a new simplified model, called continuous FK (CFK) model, is proposed to simulate the ultra-thin air bearing film in hard disk drives (HDDs).

The new model of Reynolds equation possesses simpler mathematical form than that of FK model. The new model is solved by using a least square finite difference (LSFD) method and the resultant Author: Jia Dong Ji, Bao Jun Shi, Ting Yi Yang, Shi Jun Song.

A fluid flow simulation with different Reynolds numbers by the LBSim software using the Lattice Boltzmann method. The inlet velocity is increased during the simulation while the viscosity is. For steady low-Reynolds-number (laminar) flow through a long tube (see Prob. 1.l2), the axial velocity distribution is given by u = C (R 2 – r 2) where R is the tube radius and r ≤ R.

Integrate u (r) to find the total volume flow Q through the tube%(26).L = length or diameter of the fluid. Reynolds number formula can be used in the problems to calculate the Velocity (V), density (ρ), Viscosity (μ) and diameter (L) of the liquid.

The Kind of flow is based on the value of Re. If Rethe flow is called turbulent.Implementation of Reynolds Equation Solver on GPGPU for Gas Film Lubrication Problem Ji-Hoon Kang, Hun Joo Myung, Kwang Jin Oh, Chan Yeol Park, Supercomputing Center, KISTI Figure of linear compressor H.

Lee, et al., ICSV15 () Gas supply pocket Diameter, D Gas film bearing length, L Gas film thickness, c Reservoir Piston Supply port Gas film.