Axisymmetric vortex breakdown Part 2. Physical mechanisms

The physical mechanisms for vortex breakdown which, it is proposed here, rely on the production of a negative azimuthal component of vorticity, are elucidated with the aid of a simple, steady, inviscid, axisymmetric equation of motion. Most studies of vortex breakdown use as a starting point an equation for the azimuthal vorticity (Squire 1960), but a departure in the present study is that it is explored directly and not through perturbations of an initial stream function. The inviscid equation of motion that is derived leads to a criterion for vortex breakdown based on the generation of negative azimuthal vorticity on some stream surfaces. Inviscid predictions are tested against results from numerical calculations of the Navier-Stokes equations for which breakdown occurs.

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Axisymmetric vortex breakdown Part 1. Confined swirling flow

Journal of Fluid Mechanics ◽

10.1017/s0022112090003664 ◽

1990 ◽

Vol 221 ◽

pp. 533-552 ◽

Cited By ~ 213

Author(s):

J. M. Lopez

Keyword(s):

Oscillatory Flow ◽

Stokes Equations ◽

Vortex Breakdown ◽

Swirling Flow ◽

Swirling Flows ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Axisymmetric Vortex ◽

Recirculation Zones ◽

Visualization Experiments

A comparison between the experimental visualization and numerical simulations of the occurrence of vortex breakdown in laminar swirling flows produced by a rotating endwall is presented. The experimental visualizations of Escudier (1984) were the first to detect the presence of multiple recirculation zones and the numerical model presented here, consisting of a numerical solution of the unsteady axisymmetric Navier-Stokes equations, faithfully reproduces these phenomena and all other observed characteristics of the flow. Further, the numerical calculations elucidate the onset of oscillatory flow, an aspect of the flow that was not clearly resolved by the flow visualization experiments. Part 2 of the paper examines the underlying physics of these vortex flows.

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Growing process and structure of axisymmetric vortex breakdown. 2nd Report. Numerical analysis based on the Navier-Stokes equations.

TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series B ◽

10.1299/kikaib.52.2819 ◽

1986 ◽

Vol 52 (480) ◽

pp. 2819-2827

Author(s):

Yoshikazu SUEMATSU ◽

Tadaya ITO ◽

Norihiko KATO

Keyword(s):

Numerical Analysis ◽

Stokes Equations ◽

Vortex Breakdown ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Axisymmetric Vortex

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On the compactness of a nonlinear operator related to stream function-vorticity formulation for the Navier-Stokes equations

JSIAM Letters ◽

10.14495/jsiaml.9.77 ◽

2017 ◽

Vol 9 (0) ◽

pp. 77-80 ◽

Cited By ~ 1

Author(s):

Yoshitaka Watanabe ◽

Mitsuhiro T. Nakao ◽

Kaori Nagatou

Keyword(s):

Stream Function ◽

Nonlinear Operator ◽

Stokes Equations ◽

Navier Stokes ◽

Navier Stokes Equations

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FIRST PROJECTION OF THE EQUATION OF MOTION IN THE CYLINDRICAL COORDINATE SYSTEM

Oil and Gas Studies ◽

10.31660/0445-0108-2016-4-90-92 ◽

2016 ◽

pp. 90-92

Author(s):

A. G. Obukhov ◽

R. E. Volkov

Keyword(s):

Coordinate System ◽

Stokes Equations ◽

Equation Of Motion ◽

Cylindrical Coordinate System ◽

Navier Stokes ◽

Gas Flows ◽

Heat Conducting ◽

Complex Flows ◽

Navier Stokes Equations ◽

Cylindrical Coordinate

It is proved that complex flows of the viscous compressible heat-conducting gas, arising during heating the vertical field, have a pronounced axial symmetry. Therefore, for the numerical solution of the full Navier-Stokes equations for description of such gas flows it are advisable to use a cylindrical coordinate system. This paper describes the transformation of the first projection of the equation of motion of the full Navier-Stokes equations system. The result of the transformation is a record of the first projection of the equation of a continuous medium motion in the cylindrical coordinate system.

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Numerical Simulation of Slip effect on Lid-Driven Cavity Flow Problem for High Reynolds Number: Vorticity – Stream Function Approach

Mathematical Modelling and Engineering Problems ◽

10.18280/mmep.080311 ◽

2021 ◽

Vol 8 (3) ◽

pp. 418-424

Author(s):

Syed Fazuruddin ◽

Seelam Sreekanth ◽

G. Sankara Sekhar Raju

Keyword(s):

Reynolds Number ◽

Stream Function ◽

Stokes Equations ◽

Cavity Flow ◽

Partial Slip ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Driven Cavity ◽

Slip Conditions ◽

Driven Cavity Flow

Incompressible 2-D Navier-stokes equations for various values of Reynolds number with and without partial slip conditions are studied numerically. The Lid-Driven cavity (LDC) with uniform driven lid problem is employed with vorticity - Stream function (VSF) approach. The uniform mesh grid is used in finite difference approximation for solving the governing Navier-stokes equations and developed MATLAB code. The numerical method is validated with benchmark results. The present work is focused on the analysis of lid driven cavity flow of incompressible fluid with partial slip conditions (imposed on side walls of the cavity). The fluid flow patterns are studied with wide range of Reynolds number and slip parameters.

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