scholarly journals Axisymmetric vortex breakdown Part 1. Confined swirling flow

1990 ◽  
Vol 221 ◽  
pp. 533-552 ◽  
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.

scholarly journals Axisymmetric vortex breakdown Part 2. Physical mechanisms

1990 ◽  
Vol 221 ◽  
pp. 553-576 ◽  
Author(s):  
G. L. Brown ◽  
J. M. Lopez
Keyword(s):  
Stream Function ◽  
Stokes Equations ◽  
Vortex Breakdown ◽  
Equation Of Motion ◽  
Navier Stokes ◽  
Azimuthal Component ◽  
Navier Stokes Equations ◽  
Physical Mechanisms ◽  
Axisymmetric Vortex ◽  
Starting Point

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.

scholarly journals PARALLEL COMPUTATIONS IN STUDIES OF DEPENDENCE OF GAS DYNAMIC PARAMETERS OF UPWARD SWIRLING FLOW OF GAS ON BLOWING VELOCITY

2016 ◽  
pp. 92-97
Author(s):  
R. E. Volkov ◽  
A. G. Obukhov
Keyword(s):  
Stokes Equations ◽  
Swirling Flow ◽  
Initial Conditions ◽  
Exact Analytical Solution ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Computational Domain ◽  
Navier Stokes Equations ◽  
Gas Dynamic

The rectangular parallelepiped explicit difference schemes for the numerical solution of the complete built system of Navier-Stokes equations. These solutions describe the three-dimensional flow of a compressible viscous heat-conducting gas in a rising swirling flows, provided the forces of gravity and Coriolis. This assumes constancy of the coefficient of viscosity and thermal conductivity. The initial conditions are the features that are the exact analytical solution of the complete Navier-Stokes equations. Propose specific boundary conditions under which the upward flow of gas is modeled by blowing through the square hole in the upper surface of the computational domain. A variant of parallelization algorithm for calculating gas dynamic and energy characteristics. The results of calculations of gasdynamic parameters dependency on the speed of the vertical blowing by the time the flow of a steady state flow.

Simulation of Acoustic Streaming in a Resonator

2004 ◽  
Author(s):  
Bakhtier Farouk ◽  
Murat K. Aktas
Keyword(s):  
Flow Field ◽  
Standing Wave ◽  
Oscillatory Flow ◽  
Stokes Equations ◽  
Acoustic Streaming ◽  
Flow Patterns ◽  
Vortical Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Streaming Flow

Formation of vortical flow structures in a rectangular enclosure due to acoustic streaming is investigated numerically. The oscillatory flow field in the enclosure is created by the vibration of a vertical side wall of the enclosure. The frequency of the wall vibration is chosen such that a standing wave forms in the enclosure. The interaction of this standing wave with the horizontal solid walls leads to the production of Rayleigh type acoustic streaming flow patterns in the enclosure. All four walls of the enclosure considered are thermally insulated. The fully compressible form of the Navier-Stokes equations is considered and an explicit time-marching algorithm is used to explicitly track the acoustic waves. Numerical solutions are obtained by employing a highly accurate flux corrected transport (FCT) algorithm for the convection terms. A time-splitting technique is used to couple the viscous and diffusion terms of the full Navier-Stokes equations. Non-uniform grid structure is employed in the computations. The simulation of the primary oscillatory flow and the secondary (steady) streaming flows in the enclosure is performed. Streaming flow patterns are obtained by time averaging the primary oscillatory flow velocity distributions. The effect of the amount of wall displacement on the formation of the oscillatory flow field and the streaming structures are studied. Computations indicate that the nonlinearity of the acoustic field increases with increasing amount of the vibration amplitude. The form and the strength of the secondary flow associated with the oscillatory flow field and viscous effects are found to be strongly correlated to the maximum displacement of the vibrating wall. Total number of acoustic streaming cells per wavelength is also determined by the strength and the level of the nonlinearity of the sound field in the resonator.

The evolution of a perturbed vortex in a pipe to axisymmetric vortex breakdown

1998 ◽  
Vol 366 ◽  
pp. 211-237 ◽  
Author(s):  
Z. RUSAK ◽  
S. WANG ◽  
C. H. WHITING
Keyword(s):  
Vortex Breakdown ◽  
Swirling Flow ◽  
Nonlinear Ordinary Differential Equation ◽  
Swirling Flows ◽  
Axisymmetric Vortex ◽  
Burgers Vortex ◽  
Theoretical Predictions ◽  
Necessary And Sufficient Criteria ◽  
High Reynolds ◽  
Necessary And Sufficient

The evolution of a perturbed vortex in a pipe to axisymmetric vortex breakdown is studied through numerical computations. These unique simulations are guided by a recent rigorous theory on this subject presented by Wang & Rusak (1997a). Using the unsteady and axisymmetric Euler equations, the nonlinear dynamics of both small- and large-amplitude disturbances in a swirling flow are described and the transition to axisymmetric breakdown is demonstrated. The simulations clarify the relation between our linear stability analyses of swirling flows (Wang & Rusak 1996a, b) and the time-asymptotic behaviour of the flow as described by steady-state solutions of the problem presented in Wang & Rusak (1997a). The numerical calculations support the theoretical predictions and shed light on the mechanism leading to the breakdown process in swirling flows. It has also been demonstrated that the fundamental characteristics which lead to vortex instability and breakdown in high-Reynolds-number flows may be calculated from considerations of a single, reduced-order, nonlinear ordinary differential equation, representing a columnar flow problem. Necessary and sufficient criteria for the onset of vortex breakdown in a Burgers vortex are presented.

scholarly journals Numerical and Analytical Study of Fluid Dynamic Forces in Seals and Bearings

1988 ◽  
Vol 110 (3) ◽  
pp. 315-325 ◽  
Author(s):  
L. T. Tam ◽  
A. J. Przekwas ◽  
A. Muszynska ◽  
R. C. Hendricks ◽  
M. J. Braun ◽  
...  
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Fluid Dynamic ◽  
Three Dimensional ◽  
Circumferential Velocity ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Lumped Model ◽  
Destabilizing Factors ◽  
Recirculation Zones

A numerical model based on a transformed, conservative form of the three-dimensional Navier-Stokes equations and an analytical model based on “lumped” fluid parameters are presented and compared with studies of modeled rotor/bearing/seal systems. The rotor destabilizing factors are related to the rotative character of the flow field. It is shown that these destabilizing factors can be reduced through a descrease in the fluid average circumferential velocity. However, the rotative character of the flow field is a complex three-dimensional system with bifurcated secondary flow patterns that significantly alter the fluid circumferential velocity. By transforming the Navier-Stokes equations to those for a rotating observer and using the numerical code PHOENICS-84 with a nonorthogonal body fitted grid, several numerical experiments were carried out to demonstrate the character of this complex flow field. In general, fluid injection and/or preswirl of the flow field opposing the shaft rotation significantly intensified these secondary recirculation zones and thus reduced the average circumferential velocity, while injection or preswirl in the direction of rotation significantly weakened these zones. A decrease in average circumferential velocity was related to an increase in the strength of the recirculation zones and thereby promoted stability. The influence of the axial flow was analyzed. The lumped model of fluid dynamic force based on the average circumferential velocity ratio (as opposed to the bearing/seal coefficient model) well described the obtained results for relatively large but limited ranges of parameters. This lumped model is extremely useful in rotor/bearing/seal system dynamic analysis and should be widely recommended. Fluid dynamic forces and leakage rates were calculated and compared with seal data where the working fluid was bromotrifluoromethane (CBrF3). The radial and tangential force predictions were in reasonable agreement with selected experimental data. Nonsynchronous perturbation provided meaningful information for system lumped parameter identification from numerical experiment data.

Simulations of the formation of an axisymmetric vortex ring

1997 ◽  
Vol 339 ◽  
pp. 199-211 ◽  
Author(s):  
R. S. HEEG ◽  
N. RILEY
Keyword(s):  
Vortex Ring ◽  
Reasonable Agreement ◽  
Stokes Equations ◽  
Circular Tube ◽  
Inviscid Flow ◽  
High Rate ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Axisymmetric Vortex ◽  
High Reynolds

In this paper we present the results from numerical calculations, based upon the Navier–Stokes equations at relatively high Reynolds number, of the formation of a vortex ring when fluid is ejected from a circular tube. Our results are compared with the experiments of Didden (1979), and the inviscid flow calculations of Nitsche & Krasny (1994). Reasonable agreement is achieved except for the rate of shedding of circulation during the initial stages of ring formation. The theoretically predicted rate of shedding is substantially higher than that predicted by Didden. By contrast the inviscid theory predicts an anomalously high rate of initial shedding. We offer explanations for both of these apparent discrepancies.

scholarly journals Direct numerical simulation of the oscillatory flow around a sphere resting on a rough bottom

2017 ◽  
Vol 822 ◽  
pp. 235-266 ◽  
Author(s):  
Marco Mazzuoli ◽  
Paolo Blondeaux ◽  
Julian Simeonov ◽  
Joseph Calantoni
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Oscillatory Flow ◽  
Stokes Equations ◽  
Coarse Sand ◽  
Spherical Particles ◽  
Navier Stokes ◽  
Sea Waves ◽  
Spherical Object ◽  
Navier Stokes Equations

The oscillatory flow around a spherical object lying on a rough bottom is investigated by means of direct numerical simulations of the continuity and Navier–Stokes equations. The rough bottom is simulated by a layer/multiple layers of spherical particles, the size of which is much smaller that the size of the object. The period and amplitude of the velocity oscillations of the free stream are chosen to mimic the flow at the bottom of sea waves and the size of the small spherical particles falls in the range of coarse sand/very fine gravel. Even though the computational costs allow only the simulation of moderate values of the Reynolds number characterizing the bottom boundary layer, the results show that the coherent vortex structures, shed by the spherical object, can break up and generate turbulence, if the Reynolds number of the object is sufficiently large. The knowledge of the velocity field allows the dynamics of the large-scale coherent vortices shed by the object to be determined and turbulence characteristics to be evaluated. Moreover, the forces and torques acting on both the large spherical object and the small particles, simulating sediment grains, can be determined and analysed, thus laying the groundwork for the investigation of sediment dynamics and scour developments.

Numerical Simulation Study on the Concentration Field in an Oscillatory Flow Reactor with Conic Ring Baffles

2013 ◽  
Vol 378 ◽  
pp. 418-423
Author(s):  
Gang Liu ◽  
Jia Wu ◽  
Wei Li
Keyword(s):  
Numerical Simulation ◽  
Oscillatory Flow ◽  
Flow Reactor ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Concentration Field ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Turbulent Diffusion Coefficient ◽  
Simulation Results

The three-dimensional construct of concentration field in an oscillatory flow reactor (OFR) containing periodically spaced conic ring baffles was investigated by numerical simulation employing Reynolds-averaged Navier-Stokes equations. The computation covered a range of Oscillatory Reynolds number (Reo) from 623.32 to 3116.58 at Strouhal number (St) 0.995 and 1.99. The contour of concentration field showed that the concentration in the most part of the channel is relative uniform and a small retention area is found below the conic ring baffles, which means a region of relative poor mixing. In addition, the turbulent diffusion coefficient calculated from the simulation results implied the greater oscillatory amplitude and oscillatory frequency superimposed to the fluid, the stronger is the turbulence intensity.

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