Topology of three-dimensional steady cellular flow in a two-sided anti-parallel lid-driven cavity

2017 ◽  
Vol 826 ◽  
pp. 302-334 ◽  
Author(s):  
Francesco Romanò ◽  
Stefan Albensoeder ◽  
Hendrik C. Kuhlmann
Keyword(s):  
Reynolds Number ◽  
Limit Cycle ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Convection Cell ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Driven Cavity ◽  
Dimensional Flow ◽  
Wide Range

The structure of the incompressible steady three-dimensional flow in a two-sided anti-symmetrically lid-driven cavity is investigated for an aspect ratio $\unicode[STIX]{x1D6E4}=1.7$ and spanwise-periodic boundary conditions. Flow fields are computed by solving the Navier–Stokes equations with a fully spectral method on $128^{3}$ grid points utilizing second-order asymptotic solutions near the singular corners. The supercritical flow arises in the form of steady rectangular convection cells within which the flow is point symmetric with respect to the cell centre. Global streamline chaos occupying the whole domain is found immediately above the threshold to three-dimensional flow. Beyond a certain Reynolds number the chaotic sea recedes from the interior, giving way to regular islands. The regular Kolmogorov–Arnold–Moser tori grow with increasing Reynolds number before they shrink again to eventually vanish completely. The global chaos at onset is traced back to the existence of one hyperbolic and two elliptic periodic lines in the basic flow. The singular points of the three-dimensional flow which emerge from the periodic lines quickly change such that, for a wide range of supercritical Reynolds number, each periodic convection cell houses a double spiralling-in saddle focus in its centre, a spiralling-out saddle focus on each of the two cell boundaries and two types of saddle limit cycle on the walls. A representative analysis for $\mathit{Re}=500$ shows chaotic streamlines to be due to chaotic tangling of the two-dimensional stable manifold of the central spiralling-in saddle focus and the two-dimensional unstable manifold of the central wall limit cycle. Embedded Kolmogorov–Arnold–Moser tori and the associated closed streamlines are computed for several supercritical Reynolds numbers owing to their importance for particle transport.

A Comparison of Forces in Two- and Three-Dimensional Flow Past an Oscillating Cylinder

2015 ◽  
Author(s):  
Sofia Peppa ◽  
Lambros Kaiktsis ◽  
Christos Frouzakis ◽  
George Triantafyllou
Keyword(s):  
Stokes Equations ◽  
Oscillation Amplitude ◽  
Three Dimensional ◽  
Oscillation Mode ◽  
Transverse Oscillation ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Flow Past ◽  
Two Dimensional Flow

DNS results are presented for three-dimensional flow past a circular cylinder forced to oscillate both in the transverse and in-line direction with respect to a uniform stream, at Reynolds number equal to 400, and are compared against simulation results for two-dimensional flow. The cylinder follows a figure-eight motion, traversed either counter-clockwise or clockwise in the upper half-plane for a flow stream from left to right. The transverse oscillation frequency is equal to the natural frequency of the Kármán vortex street. The Navier-Stokes equations are solved using a spectral element code, and the forces acting on the cylinder are computed for both three- and two-dimensional flow. The results demonstrate that the effect of cylinder oscillation on the flow structure and forces differs substantially between the counter-clockwise and the clockwise oscillation mode. For the counter-clockwise mode, forcing at low amplitude decreases the flow three-dimensionality, with the wake becoming increasingly three-dimensional for transverse oscillation amplitudes higher than 0.25–0.30 cylinder diameters, with corresponding discrepancies in forces with respect to two-dimensional flow. For the case of clockwise mode, a strong stabilizing effect is found: the wake becomes two-dimensional for a transverse oscillation amplitude of 0.20 cylinder diameters, and remains so at higher amplitudes, resulting in nearly equal values of the force coefficients for three- and two-dimensional flow.

Coherent structures in rotating three-dimensional turbulence

1994 ◽  
Vol 273 ◽  
pp. 1-29 ◽  
Author(s):  
Peter Bartello ◽  
Olivier Métais ◽  
Marcel Lesieur
Keyword(s):  
Numerical Simulations ◽  
Velocity Structure ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Maximum Energy ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Hairpin Vortices ◽  
Dimensional Flow

Numerical simulations investigating the formation and stability of quasi-two-dimensional coherent vortices in rotating homogeneous three-dimensional flow are described. In a numerical study of shear flows Lesieur, Yanase & Métais (1991) found that cyclones (respectively anticyclones) with |ω2D| ∼ O(2Ω), where ω2D is the vorticity and Ω is the rotation rate, are stabilized (respectively destabilized) by the rotation. A study of triply periodic pseudo-spectral simulations (643) was undertaken in order to investigate the vorticity asymmetry in homogeneous turbulence. Specifically, we examine (i) the possible three-dimensionalization of initially two-dimensional vortices and (ii) the emergence of quasi-two-dimensional structures in initially-isotropic three-dimensional turbulence. Direct numerical simulations of the Navier—Stokes equations are compared with large-eddy simulations employing a subgridscale model based on the second-order velocity structure function evaluated at the grid separation and with simulations employing hyperviscosity.Isolated coherent two-dimensional vortices, obtained from a two-dimensional decay simulation, were superposed with a low-amplitude three-dimensional perturbation, and used to initialize the first set of simulations. With Ω = 0, a three-dimensionalization of all vortices was observed. This occurred first in the small scales in conjunction with the formation of longitudinal hairpin vortices with vorticity perpendicular to that of the initial quasi-two-dimensional flow. In agreement with centrifugal stability arguments, when 2Ω = [ω2D]rms a rapid destabilization of anticyclones was observed to occur, whereas the initial two-dimensional cyclonic vortices persisted throughout the simulation. At larger Ω, both cyclones and anticyclones remained two-dimensional, consistent with the Taylor—Proudman theorem. A second set of simulations starting from isotropic three-dimensional fields was initialized by allowing a random velocity field to evolve (Ω = 0) until maximum energy dissipation. When the simulations were continued with 2Ω = [ω · Ω]rms/Ω, the three-dimensional flow was observed to organize into two-dimensional cyclonic vortices. At larger Ω, two-dimensional anticyclones also emerged from the initially-isotropic flow. The consequences for a variety of industrial and geophysical applications are clear. For quasi-two-dimensional eddies whose characteristic circulation times are of the order ofder of Ω−1, rotation induces a complete disruption of anticyclonic vortices, while stabilizing cyclonic ones.

Two-dimensional and three-dimensional self-sustained flow oscillations in interrupted fin heat exchangers

2006 ◽  
Vol 220 (3) ◽  
pp. 297-306
Author(s):  
G Croce ◽  
P D'Agaro
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Heat Transfer Enhancement ◽  
Three Dimensional ◽  
Chaotic Regime ◽  
Flow Structures ◽  
Two Dimensional ◽  
Transfer Enhancement ◽  
Three Dimensional Flow ◽  
Dimensional Flow

A numerical analysis of three-dimensional flow structures in a nominally two-dimensional fin geometry is presented. A sinusoidal louvred fin is considered. The heat transfer enhancement is achieved by combining boundary layer interruptions and vortical structures induced by the corrugation of the base fin. The fin shape and pitch, as well as flow conditions, are representative of typical automotive application. A wide ranging values of Reynolds number are investigated, spanning the steady laminar regime, the unsteady periodic laminar flow, and the chaotic transitional flow. Two- and three-dimensional numerical solutions are compared, looking for the onset of three-dimensional instabilities. At low values of the Reynolds number, up to the steady-unsteady flow transition, the flow is two-dimensional. As soon as unsteady oscillation appears, the simulation results show three-dimensional flow structures, even in a nominally two-dimensional geometry. The typical longitudinal vortex size is evaluated. In the periodic unsteady regime, fully three-dimensional computations yield time-averaged Nusselt number and friction factor significantly higher than those predicted by two-dimensional models. Furthermore, these flow structures induce an early transition from the periodic regime to the chaotic regime. In the chaotic regime, however, the heat transfer enhancement due to the three-dimensional flow structures is much lower.

Direct Numerical Simulation of Three-Dimensional Flow and Augmented Heat Transfer in a Grooved Channel

1998 ◽  
Vol 120 (3) ◽  
pp. 717-723 ◽  
Author(s):  
M. Greiner ◽  
G. J. Spencer ◽  
P. F. Fischer
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Friction Factor ◽  
Three Dimensional ◽  
Spectral Element ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Number Range ◽  
Dimensional Flow ◽  
Element Technique

Direct numerical simulations of three-dimensional flow and augmented convective heat transfer in a transversely grooved channel are presented for the Reynolds number range 140 < Re < 2000. These calculations employ the spectral element technique. Multiple flow transitions are documented as the Reynolds number increases, from steady two-dimensional flow through broad-banded unsteady three-dimensional mixing. Three-dimensional simulations correctly predict the Reynolds-number-independent friction factor behavior of this flow and quantify its heat transfer to within 16 percent of measured values. Two-dimensional simulations, however, incorrectly predict laminar-like friction factor and heat transfer behaviors.

Three-dimensional flow in cavities

1963 ◽  
Vol 16 (4) ◽  
pp. 620-632 ◽  
Author(s):  
D. J. Maull ◽  
L. F. East
Keyword(s):  
Static Pressure ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Large Span ◽  
Dimensional Flow ◽  
Pressure Distributions ◽  
Oil Flow ◽  
Two Dimensional Flow

The flow inside rectangular and other cavities in a wall has been investigated at low subsonic velocities using oil flow and surface static-pressure distributions. Evidence has been found of regular three-dimensional flows in cavities with large span-to-chord ratios which would normally be considered to have two-dimensional flow near their centre-lines. The dependence of the steadiness of the flow upon the cavity's span as well as its chord and depth has also been observed.

Cellular flow in a partially filled rotating drum: regular and chaotic advection

2017 ◽  
Vol 825 ◽  
pp. 631-650 ◽  
Author(s):  
Francesco Romanò ◽  
Arash Hajisharifi ◽  
Hendrik C. Kuhlmann
Keyword(s):  
Three Dimensional ◽  
Reynolds Numbers ◽  
Chaotic Advection ◽  
Two Dimensional ◽  
Rotating Drum ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Heteroclinic Connection ◽  
Two Dimensional Flow ◽  
Chaotic Streamlines

The topology of the incompressible steady three-dimensional flow in a partially filled cylindrical rotating drum, infinitely extended along its axis, is investigated numerically for a ratio of pool depth to radius of 0.2. In the limit of vanishing Froude and capillary numbers, the liquid–gas interface remains flat and the two-dimensional flow becomes unstable to steady three-dimensional convection cells. The Lagrangian transport in the cellular flow is organised by periodic spiralling-in and spiralling-out saddle foci, and by saddle limit cycles. Chaotic advection is caused by a breakup of a degenerate heteroclinic connection between the two saddle foci when the flow becomes three-dimensional. On increasing the Reynolds number, chaotic streamlines invade the cells from the cell boundary and from the interior along the broken heteroclinic connection. This trend is made evident by computing the Kolmogorov–Arnold–Moser tori for five supercritical Reynolds numbers.

Reconstruction of three-dimensional flow fields from two-dimensional data

2020 ◽  
Vol 407 ◽  
pp. 109239
Author(s):  
José Miguel Pérez ◽  
Soledad Le Clainche ◽  
José Manuel Vega
Keyword(s):  
Three Dimensional ◽  
Flow Fields ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Dimensional Flow
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