Study of Flow and Thrust in Nozzle-Flapper Valves

1975 ◽  
Vol 97 (1) ◽  
pp. 39-50 ◽  
Author(s):  
S. Hayashi ◽  
T. Matsui ◽  
T. Ito
Keyword(s):  
Approximate Formula ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Relaxation Method ◽  
Experimental Results ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Vena Contracta ◽  
Radial Gap ◽  
Good Agreement

The Navier-Stokes equations and the equation of continuity describing the flow in the flat-faced nozzle-flapper valve are numerically solved by the iterative relaxation method and the effect of the flow contraction (vena contracta) occurring in the radial gap in the valve is investigated. Furthermore, an approximate formula for the flow force acting on the flapper is derived on the basis of the numerical solutions. The formula for the flow force is in good agreement with experimental results.

On the Flow Fields of Inertial Impactors

1974 ◽  
Vol 96 (4) ◽  
pp. 394-400 ◽  
Author(s):  
V. A. Marple ◽  
B. Y. H. Liu ◽  
K. T. Whitby
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Relaxation Method ◽  
Water Model ◽  
Navier Stokes ◽  
Visualization Technique ◽  
Navier Stokes Equations ◽  
Theoretical Results ◽  
Plate Distance ◽  
Good Agreement

The flow field in an inertial impactor was studied experimentally with a water model by means of a flow visualization technique. The influence of such parameters as Reynolds number and jet-to-plate distance on the flow field was determined. The Navier-Stokes equations describing the laminar flow field in the impactor were solved numerically by means of a finite difference relaxation method. The theoretical results were found to be in good agreement with the empirical observations made with the water model.

Optimized Accelerating Parameters of Convergence for the Navier-Stokes Equations

1992 ◽  
Author(s):  
Bashar S. AbdulNour
Keyword(s):  
Stream Function ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Relaxation Method ◽  
Reynolds Numbers ◽  
Computer Time ◽  
Navier Stokes ◽  
Computational Time ◽  
Navier Stokes Equations ◽  
Successive Over Relaxation

Abstract An over-relaxation procedure, that includes weighing factors, is applied to the steady, two-dimensional Navier-Stokes equations in order to reduce the computational time. The benefits obtained from this strategy are illustrated by the problem of viscous flow in the entrance region of an unconstricted and a constricted channel. The describing equations are expressed in terms of the stream function and vorticity. The convergence domain for the Successive Over-Relaxation method and the optimum values of the accelerating parameters, which consist of the over-relaxation and weighting factors for both the stream function and vorticity, are discussed. Numerical solutions are obtained for Reynolds numbers ranging from 20 to 2000. The computer time is reduced by as much as a factor of six using the optimum values of the accelerating parameters.

Numerical Solutions of Viscous Flow through a Pipe Orifice at Low Reynolds Numbers

1968 ◽  
Vol 10 (2) ◽  
pp. 133-140 ◽  
Author(s):  
R. D. Mills
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Viscous Incompressible Fluid ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Axially Symmetric ◽  
Navier Stokes Equations ◽  
Low Reynolds Numbers ◽  
Flow Through ◽  
Good Agreement

Numerical solutions of the Navier-Stokes equations have been obtained in the low range of Reynolds numbers for steady, axially symmetric, viscous, incompressible fluid flow through an orifice in a circular pipe with a fixed orifice/pipe diameter ratio. Streamline patterns and vorticity contours are presented as functions of Reynolds number. The theoretically determined discharge coefficients are in good agreement with experimental results of Johansen (2).

Inertially driven inhomogeneities in violently collapsing bubbles: the validity of the Rayleigh–Plesset equation

2002 ◽  
Vol 452 ◽  
pp. 145-162 ◽  
Author(s):  
HAO LIN ◽  
BRIAN D. STOREY ◽  
ANDREW J. SZERI
Keyword(s):  
Wave Motion ◽  
Bubble Dynamics ◽  
Pressure Field ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Spatial Inhomogeneity ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Self Consistency ◽  
Good Agreement

When a bubble collapses mildly the interior pressure field is spatially uniform; this is an assumption often made to close the Rayleigh–Plesset equation of bubble dynamics. The present work is a study of the self-consistency of this assumption, particularly in the case of violent collapses. To begin, an approximation is developed for a spatially non-uniform pressure field, which in a violent collapse is inertially driven. Comparisons of this approximation show good agreement with direct numerical solutions of the compressible Navier–Stokes equations with heat and mass transfer. With knowledge of the departures from pressure uniformity in strongly forced bubbles, one is in a position to develop criteria to assess when pressure uniformity is a physically valid assumption, as well as the significance of wave motion in the gas. An examination of the Rayleigh–Plesset equation reveals that its solutions are quite accurate even in the case of significant inertially driven spatial inhomogeneity in the pressure field, and even when wave-like motions in the gas are present. This extends the range of utility of the Rayleigh–Plesset equation well into the regime where the Mach number is no longer small; at the same time the theory sheds light on the interior of a strongly forced bubble.

Steady flow through a channel with a symmetrical constriction in the form of a step

1980 ◽  
Vol 372 (1750) ◽  
pp. 393-414 ◽  
Keyword(s):  
Asymptotic Theory ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Volumetric Flow Rate ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Uniform Grids ◽  
Flow Through ◽  
Good Agreement

Numerical solutions of the Navier-Stokes equations are given for the steady, two-dimensional, laminar flow of an incompressible fluid through a channel with a symmetric constriction in the form of a semi-infinite step change in width. The flow proceeds from a steady Poiseuille velocity distribution far enough upstream of the step in the wider part of the channel to a corresponding distribution downstream in the narrower part and is assumed to remain symmetrical about the centre line of the channel. The numerical scheme involves an accurate and efficient centred difference treatment developed by Dennis & Hudson (1978) and results are obtained for Reynolds numbers, based on half the volumetric flow rate, up to 2000. For a step that halves the width of the channel it is found that very fine uniform grids, with 80 intervals spaced across half of the wider channel upstream, are necessary for resolution of the solution for the flow downstream of the onset of the step. Slightly less refined grids are adequate to resolve the flow upstream. The calculated flow ahead of the step exhibits very good agreement with the asymptotic theory of Smith (1979 b)for Reynolds numbers greater than about 100; indeed, comparisons of the upstream separation position and of the wall vorticity nearby are believed to yield the best agreement between numerical and asymptotic solutions yet found. Downstream there is also qualitative agreement regarding separation and reattachment as the grid size is refined in the numerical results.

scholarly journals Homotopy analysis method for the solution of lubrication of a long porous slider

2016 ◽  
Vol 1 (2) ◽  
pp. 507-516 ◽  
Author(s):  
Vishwanath B. Awati ◽  
Manjunath Jyoti
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Convergent Series ◽  
Navier Stokes ◽  
Analysis Method ◽  
Navier Stokes Equations ◽  
Similarity Transformations ◽  
Convergence Of Series ◽  
Homotopy Analysis ◽  
Good Agreement

AbstractIn this article, the lubrication of a long porous slider in which the fluid is injected into the porous bottom is considered. The similarity transformations reduce the governing problem of Navier-Stokes equations to coupled nonlinear ordinary differential equations which are solved by HAM. Solutions are obtained for much larger values of Reynolds number compared to analytical and numerical methods. The results comprise good agreement between approximate and numerical solutions. HAM gives rapid convergent series solutions which show that this method is efficient, accurate and has advantages over other methods. Further, homotopy-pade’ technique is used to accelerate the convergence of series solution.

Data-parallel line relaxation method for the Navier-Stokes equations

AIAA Journal ◽  
1998 ◽  
Vol 36 ◽  
pp. 1603-1609 ◽  
Author(s):  
Michael J. Wright ◽  
Graham V. Candler ◽  
Deepak Bose
Keyword(s):  
Stokes Equations ◽  
Relaxation Method ◽  
Parallel Line ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Data Parallel

Simulation of Unsteady Flow Around a Cylinder

2015 ◽  
Vol 3 (2) ◽  
pp. 28-49
Author(s):  
Ridha Alwan Ahmed
Keyword(s):  
Stokes Equations ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Mean Value ◽  
Navier Stokes ◽  
Cylinder Surface ◽  
Navier Stokes Equations ◽  
Flow Around A Cylinder ◽  
Numerical Grid ◽  
Good Agreement

       In this paper, the phenomena of vortex shedding from the circular cylinder surface has been studied at several Reynolds Numbers (40≤Re≤ 300).The 2D, unsteady, incompressible, Laminar flow, continuity and Navier Stokes equations have been solved numerically by using CFD Package FLUENT. In this package PISO algorithm is used in the pressure-velocity coupling.        The numerical grid is generated by using Gambit program. The velocity and pressure fields are obtained upstream and downstream of the cylinder at each time and it is also calculated the mean value of drag coefficient and value of lift coefficient .The results showed that the flow is strongly unsteady and unsymmetrical at Re>60. The results have been compared with the available experiments and a good agreement has been found between them

Numerical Modeling of Evolution of Boundary Between Incompressible Gas and Liquid in Two-Dimensional Region

2006 ◽  
Vol 4 ◽  
pp. 224-236
Author(s):  
A.S. Topolnikov
Keyword(s):  
Numerical Modeling ◽  
Interphase Boundary ◽  
Incompressible Liquid ◽  
Stokes Equations ◽  
Numerical Code ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Incompressible Media ◽  
Good Agreement

The paper is devoted to numerical modeling of Navier–Stokes equations for incompressible media in the case, when there exist gas and liquid inside the rectangular calculation region, which are separated by interphase boundary. The set of equations for incompressible liquid accounting for viscous, gravitational and surface (capillary) forces is solved by finite-difference scheme on the spaced grid, for description of interphase boundary the ideology of Level Set Method is used. By developed numerical code the set of hydrodynamic problems is solved, which describe the motion of two-phase incompressible media with interphase boundary. As a result of numerical simulation the solutions are obtained, which are in good agreement with existing analytical and experimental solutions.

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