The development of asymmetry and period doubling for oscillatory flow in baffled channels

1996 ◽  
Vol 328 ◽  
pp. 19-48 ◽  
Author(s):  
E. P. L. Roberts ◽  
M. R. Mackley
Keyword(s):  
Reynolds Number ◽  
Oscillatory Flow ◽  
Three Dimensional ◽  
Period Doubling ◽  
Progressive Increase ◽  
Newtonian Flow ◽  
Chaotic Flow ◽  
Spatially Periodic ◽  
Dimensional Simulation ◽  
Time Periodic

We report experimental and numerical observations on the way initially symmetric and time-periodic fluid oscillations in baffled channels develop in complexity. Experiments are carried out in a spatially periodic baffled channel with a sinusoidal oscillatory flow. At modest Reynolds number the observed vortex structure is symmetric and time periodic. At higher values the flow progressively becomes three-dimensional, asymmetric and aperiodic. A two-dimensional simulation of incompressible Newtonian flow is able to follow the flow pattern at modest oscillatory Reynolds number. At higher values we report the development of both asymmetry and a period-doubling cascade leading to a chaotic flow regime. A bifurcation diagram is constructed that can describe the progressive increase in complexity of the flow.

Three-dimensional dynamics and transition to turbulence in the wake of bluff objects

1992 ◽  
Vol 238 ◽  
pp. 1-30 ◽  
Author(s):  
George Em Karniadakis ◽  
George S. Triantafyllou
Keyword(s):  
Reynolds Number ◽  
Three Dimensional ◽  
Period Doubling ◽  
Reynolds Numbers ◽  
Transition To Turbulence ◽  
Two Dimensional ◽  
Near Wake ◽  
Vortex Filaments ◽  
Average Flow ◽  
Time Average

The wakes of bluff objects and in particular of circular cylinders are known to undergo a ‘fast’ transition, from a laminar two-dimensional state at Reynolds number 200 to a turbulent state at Reynolds number 400. The process has been documented in several experimental investigations, but the underlying physical mechanisms have remained largely unknown so far. In this paper, the transition process is investigated numerically, through direct simulation of the Navier—Stokes equations at representative Reynolds numbers, up to 500. A high-order time-accurate, mixed spectral/spectral element technique is used. It is shown that the wake first becomes three-dimensional, as a result of a secondary instability of the two-dimensional vortex street. This secondary instability appears at a Reynolds number close to 200. For slightly supercritical Reynolds numbers, a harmonic state develops, in which the flow oscillates at its fundamental frequency (Strouhal number) around a spanwise modulated time-average flow. In the near wake the modulation wavelength of the time-average flow is half of the spanwise wavelength of the perturbation flow, consistently with linear instability theory. The vortex filaments have a spanwise wavy shape in the near wake, and form rib-like structures further downstream. At higher Reynolds numbers the three-dimensional flow oscillation undergoes a period-doubling bifurcation, in which the flow alternates between two different states. Phase-space analysis of the flow shows that the basic limit cycle has branched into two connected limit cycles. In physical space the period doubling appears as the shedding of two distinct types of vortex filaments.Further increases of the Reynolds number result in a cascade of period-doubling bifurcations, which create a chaotic state in the flow at a Reynolds number of about 500. The flow is characterized by broadband power spectra, and the appearance of intermittent phenomena. It is concluded that the wake undergoes transition to turbulence following the period-doubling route.

Three-Dimensional Simulation of Micro Air Vehicles with Low-Aspect-Ratio Wings

2007 ◽  
Vol 339 ◽  
pp. 377-381
Author(s):  
Xiao Quan Zhang ◽  
L. Tian
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Wind Tunnel ◽  
Aspect Ratio ◽  
Low Reynolds Number ◽  
Three Dimensional ◽  
Micro Air Vehicles ◽  
Wind Tunnel Experiments ◽  
Low Aspect Ratio ◽  
Dimensional Simulation

Micro Air Vehicles (MAVs) are catching more and more attentions for their broad application in civilian and military fields. Since the theories on the aerodynamics of low Reynolds number are not maturely presented and the wind-tunnel experiments cost long periods and great expenses. The numerical simulation based on computational fluid dynamics (CFD) is a good method to choose. Through three-dimensional simulation of the wings, the aerodynamic characteristics of the flows around MAVs can be easily obtained. The tip vortices produced around low-Reynolds-number and low-aspect-ratio wings can increase the lift and stall angles. The result of numerical simulation can be used as references of theory analysis and wind-tunnel experiments.

The dynamics of breaking internal solitary waves on slopes

2014 ◽  
Vol 761 ◽  
pp. 360-398 ◽  
Author(s):  
Robert S. Arthur ◽  
Oliver B. Fringer
Keyword(s):  
Reynolds Number ◽  
Velocity Structure ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Mixing Efficiency ◽  
Streamwise Vorticity ◽  
Initial Wave ◽  
Reynolds Number Effects ◽  
Dimensional Simulation ◽  
Dimensional Domain

AbstractUsing direct numerical simulations (DNS), we investigate the structure and energetics of breaking internal waves on slopes. We employ a Navier–Stokes code in an idealized three-dimensional domain where an internal solitary wave of depression impinges upon a sloping bottom. Seven cases with varying initial wave amplitude and bathymetric slope, but constant wave Reynolds number $\mathit{Re}_{w}$ are considered. Volume-integrated values of dissipation and irreversible mixing are related to the density and velocity structure of the wave throughout the breaking process. The majority of dissipation (63 %) occurs along the no-slip bottom boundary. Most of the remaining dissipation (35 %) and nearly all irreversible mixing occurs in the interior after breaking, when density overturns are present at the interface. Breaking introduces three-dimensionality to the flow field that is driven by the lateral breakdown of density overturns and the lobe–cleft instability typical of gravity currents. The resulting longitudinal rolls (streamwise vorticity) increase dissipation by roughly 8 % and decrease irreversible mixing by roughly 20 % when compared with a similar two-dimensional simulation. The bulk mixing efficiency is shown to increase for larger and smaller values of the internal Iribarren number ${\it\xi}$, with a minimum for intermediate values of ${\it\xi}$ and a peak near ${\it\xi}=0.8$ for plunging breakers. This trend is explained by the degree of two-dimensionality in the flow, and agrees with previous results in the literature after accounting for Reynolds number effects. Local turbulence quantities are also calculated at ‘virtual moorings’, and a location upslope of the breakpoint but downslope of the intersection of the pycnocline and the bottom is shown to provide a signal that is most representative of the volume-integrated dissipation and mixing results.

The onset of chaos in a class of Navier–Stokes solutions

1999 ◽  
Vol 393 ◽  
pp. 59-87 ◽  
Author(s):  
PHILIP HALL ◽  
DEMETRIOS T. PAPAGEORGIOU
Keyword(s):  
Reynolds Number ◽  
Practical Importance ◽  
Periodic Oscillation ◽  
Navier Stokes ◽  
Chaotic Flows ◽  
Steady Streaming ◽  
Chaotic Flow ◽  
High Reynolds ◽  
Time Periodic ◽  
Point Form

The flow between parallel walls driven by the time-periodic oscillation of one of the walls is investigated. The flow is characterized by a non-dimensional amplitude Δ and a Reynolds number R. At small values of the Reynolds number the flow is synchronous with the wall motion and is stable. If the amplitude of oscillation is held fixed and the Reynolds number is increased there is a symmetry-breaking bifurcation at a finite value of R. When R is further increased, additional bifurcations take place, but the structure which develops, essentially chaotic flow resulting from a Feigenbaum cascade or a quasi-periodic flow, depends on the amplitude of oscillation. The flow in the different regimes is investigated by a combination of asymptotic and numerical methods. In the small-amplitude high-Reynolds-number limit we show that the flow structure develops on two time scales with chaos occurring on the longer time scale. The chaos in that case is shown to be associated with the unsteady breakdown of a steady streaming flow. The chaotic flows which we describe are of particular interest because they correspond to Navier–Stokes solutions of stagnation-point form. These flows are relevant to a wide variety of flows of practical importance.

Analysis and direct numerical simulation of the flow at a gravity-current head. Part 1. Flow topology and front speed for slip and no-slip boundaries

2000 ◽  
Vol 418 ◽  
pp. 189-212 ◽  
Author(s):  
CARLOS HÄRTEL ◽  
ECKART MEIBURG ◽  
FRIEDER NECKER
Keyword(s):  
Reynolds Number ◽  
Stagnation Point ◽  
Flow Structure ◽  
Gravity Current ◽  
Three Dimensional ◽  
Head Part ◽  
Two Dimensional ◽  
Flow Topology ◽  
Reynolds Number Effects ◽  
Dimensional Simulation

Direct numerical simulations are performed of gravity-current fronts in the lock-exchange configuration. The case of small density differences is considered, where the Boussinesq approximations can be adopted. The key objective of the investigation is a detailed analysis of the flow structure at the foremost part of the front, where no previous high-resolution data were available. For the simulations, high-order numerical methods are used, based on spectral and spectral-element discretizations and compact finite differences. A three-dimensional simulation is conducted of a front spreading along a no-slip boundary at a Reynolds number of about 750. The simulation exhibits all features typically observed in experimental flows near the gravity-current head, including the lobe-and-cleft structure at the leading edge. The results reveal that the flow topology at the head differs from what has been assumed previously, in that the foremost point is not a stagnation point in a translating system. Rather, the stagnation point is located below and slightly behind the foremost point in the vicinity of the wall. The relevance of this finding for the mechanism behind the lobe-and-cleft instability is discussed. In order to explore the high-Reynolds-number regime, and to assess potential Reynolds-number effects, two-dimensional simulations are conducted for Reynolds numbers up to about 30 000, for both no-slip and slip (i.e. shear-stress free) boundaries. It is shown that although quantitative Reynolds-number effects persist over the whole range examined, no qualitative changes in the flow structure at the head can be observed. A comparison of the two-dimensional results with laboratory data and the three-dimensional simulation provides evidence that a two-dimensional model is able to capture essential features of the flow at the head. The simulations also show that for the free-slip case the shape of the head agrees closely with the classical inviscid theory of Benjamin.

Simulations of Flow and Mass Transfer in a Passive Micromixer

2011 ◽  
Author(s):  
Hamid Farangis Zadeh ◽  
Arash Marahel
Keyword(s):  
Reynolds Number ◽  
Three Dimensional ◽  
Main Idea ◽  
Contact Layer ◽  
Reynolds Numbers ◽  
Secondary Flows ◽  
Low Reynolds Numbers ◽  
Passive Micromixer ◽  
Simulation Results ◽  
Dimensional Simulation

We present three-dimensional simulation results regarding performance of a novel planar passive micromixer functioning at low Reynolds numbers. A combination of folding and contracting of microchannels is the main idea for designing of an effective, easy-to-produce, and non-expensive micromixer. The simulation results show that, depend on Reynolds number, centrifugal forces can generate different secondary flows and Dean vortices after each bend. Consequently, the thickness and the form of the contact layer between fluids become strongly affected. The simulation process is repeated for different Reynolds numbers from 10 to 100, and we observe that the maximum and minimum mixing efficiencies at the output channel are related to Reynolds number 60 and 80, respectively.

A Simple Chaotic Flow with a Continuously Adjustable Attractor Dimension

2015 ◽  
Vol 25 (12) ◽  
pp. 1530036 ◽  
Author(s):  
Buncha Munmuangsaen ◽  
Julien Clinton Sprott ◽  
Wesley Joo-Chen Thio ◽  
Arturo Buscarino ◽  
Luigi Fortuna
Keyword(s):  
Jacobian Matrix ◽  
Three Dimensional ◽  
Period Doubling ◽  
Electronic Version ◽  
Largest Lyapunov Exponent ◽  
Coexisting Attractors ◽  
Attractor Dimension ◽  
Chaotic Flows ◽  
Absolute Value ◽  
Chaotic Flow

This paper describes two simple three-dimensional autonomous chaotic flows whose attractor dimensions can be adjusted continuously from [Formula: see text] to [Formula: see text] by a single control parameter. Such a parameter provides a means to explore the route through limit cycles, period-doubling, dissipative chaos, and eventually conservative chaos. With an absolute-value nonlinearity and certain choices of parameters, the systems have a vast and smooth continual transition path from dissipative chaos to conservative chaos. One system is analyzed in detail by means of the largest Lyapunov exponent, Kaplan–Yorke dimension, bifurcations, coexisting attractors and eigenvalues of the Jacobian matrix. An electronic version of the system has been constructed and shown to perform in accordance with expectations.

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