Transition to turbulence in two-dimensional wakes

AIAA Journal ◽  
1978 ◽  
Vol 16 (6) ◽  
pp. 587-591 ◽  
Author(s):  
Anthony Demetriades
Keyword(s):  
Transition To Turbulence ◽  
Two Dimensional

scholarly journals Transition to turbulence in quasi-two-dimensional MHD flow driven by lateral walls

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Christopher J. Camobreco ◽  
Alban Pothérat ◽  
Gregory J. Sheard
Keyword(s):  
Mhd Flow ◽  
Transition To Turbulence ◽  
Two Dimensional ◽  
Lateral Walls

scholarly journals On the two-dimensional steady flow of a viscous fluid behind a solid body.-II

1933 ◽  
Vol 142 (847) ◽  
pp. 563-573 ◽  
Keyword(s):  
Experimental Study ◽  
Viscous Fluid ◽  
Pressure Gradient ◽  
Steady Flow ◽  
Solid Body ◽  
Asymptotic Approximation ◽  
Transition To Turbulence ◽  
Two Dimensional ◽  
Prandtl Equations ◽  
Sufficient Distance

One reason for carrying out the calculations of the previous paper was to provide material for an experimental study of the transition to turbulence in the wake behind a plate parallel to the stream. A second reason was to compare the results with certain results due to Filon, who has calculated both the List and second approximations to the velocity at a considerable distance from a fixed cylindrical obstacle in an unlimited stream whose velocity at infinity is constant.* He also uses the notions of the Oseen approximation; that is to say, he assumes that the departures from the undisturbed velocity are small, and neglects terms quadratic in these departures for the first approximations, etc .; but he does not assume that v is small and does not use the Prandtl equations. Thus the formulæ of paper 1, paragraph 2, should be limiting forms, for small v, of Filon's formulæ for a symmetrical wake. This is verified in paragraph 2 below; and the calculations in paper 1, paragraph 2, other than the attempt at a third approximation, may be regarded as a simplified form of Filon's calculations. The direct simplification of Filon's results gives the formulæ 2 (31) (p. 569), for the velocity at a sufficient distance downstream in any symmetrical wake provided that the motion is steady, whether v is small or not. these formulæ differ only in the last terms from the formulæ 2 (27) on p. 553 of paper 1, obtained from the Prandtl equations, and these terms are negligible, compared with the others, when v is small, (For the meaning of the symbols, see paragraph 1.3 of paper 1.) Thus the first asymptotic approximation is exactly the same here as in the previous paper ; in the second approximation the more accurate results of this paper contain extra terms, which it is shown on p. 567 arise entirely from the previous neglect of the pressure gradient in the direction of the stream.

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.

An Experimental and Analytical Investigation of Rectangular Synthetic Jets

2009 ◽  
Vol 131 (12) ◽  
Author(s):  
Gopi Krishnan ◽  
Kamran Mohseni
Keyword(s):  
Flow Field ◽  
Turbulent Jets ◽  
Velocity Profiles ◽  
Synthetic Jet ◽  
Synthetic Jets ◽  
Empirical Modeling ◽  
Transition To Turbulence ◽  
Two Dimensional ◽  
Limited Region ◽  
Velocity Decay

In this paper the flow field of a rectangular synthetic jet driven by a piezoelectric membrane issuing into a quiescent environment is studied. The similarities exhibited by synthetic and continuous turbulent jets lead to the hypothesis that a rectangular synthetic jet within a limited region downstream of the orifice be modeled using similarity analysis just as a continuous planar jet. Accordingly, the jet is modeled using the classic two-dimensional solution to a continuous jet, where the virtual viscosity coefficient of the continuous turbulent jet is replaced with that measured for a synthetic jet. The virtual viscosity of the synthetic jet at a particular axial location is related to the spreading rate and velocity decay rate of the jet. Hot-wire anemometry is used to characterize the flow downstream of the orifice. The flow field of rectangular synthetic jets is thought to consist of four regions as distinguished by the centerline velocity decay. The regions are the developing, the quasi-two-dimensional, the transitional, and the axisymmetric regions. It is in the quasi-two-dimensional region that the planar model applies, and where indeed the jet exhibits self-similar behavior as distinguished by the collapse of the lateral time average velocity profiles when scaled. Furthermore, within this region the spanwise velocity profiles display a saddleback profile that is attributed to the secondary flow generated at the smaller edges of the rectangular orifice. The scaled spreading and decay rates are seen to increase with stroke ratio and be independent of Reynolds number. However, the geometry of the actuator is seen to additionally affect the external characteristics of the jet. The eddy viscosities of the synthetic jets under consideration are shown to be larger than equivalent continuous turbulent jets. This enhanced eddy viscosity is attributed to the additional mixing brought about by the introduction of the periodic vortical structures in synthetic jets and their ensuing break down and transition to turbulence. Further, a semi-empirical modeling approach is proposed, the final objective of which is to obtain a functional relationship between the parameters that describe the external flow field of the synthetic jet and the input operational parameters to the system.

The Suppression of Shear Layer Turbulence in Rotating Systems

1973 ◽  
Vol 95 (2) ◽  
pp. 229-235 ◽  
Author(s):  
J. P. Johnston
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
High Reynolds Number ◽  
Transition To Turbulence ◽  
Two Dimensional ◽  
Simple Method ◽  
Coriolis Forces ◽  
Rotating Systems ◽  
Two Dimensional Flow ◽  
High Reynolds

Stabilization of turbulent boundary layer type flows by the action of Coriolis forces engendered by system rotation is studied. Experiments on fully developed, two-dimensional flow in a long, straight channel that was rotated about an axis perpendicular to the plane of mean shear are reviewed to demonstrate the principal effects of stabilization. In particular, the delay of transition to turbulence on the stabilized side of the channel to high Reynolds number (u¯mh/ν) as the rotation number (|Ω|h/u¯m) is increased is demonstrated. A simple method which utilizes the eddy Reynolds number criterion of Bradshaw, is employed to show that rotation-induced suppression of transition may be predicted for the channel flow case. The applicability of the predictive method to boundary layer type flows is indicated.

scholarly journals Maximum Heat Transfer Rate Density in Two-Dimensional Minichannels and Microchannels

2003 ◽  
Author(s):  
M. Favre-Marinet ◽  
S. Le Person ◽  
A. Bejan
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Transition To Turbulence ◽  
Experimental Investigations ◽  
Two Dimensional ◽  
Parallel Plates ◽  
Maximum Heat ◽  
Maximum Heat Transfer ◽  
Optimal Spacing

Experimental investigations of the flow and the associated heat transfer were conducted in two-dimensional microchannels in order to test possible size effects on the laws of hydrodynamics and heat transfer and to infer optimal conditions of use from the measurements. The test section was designed to modify easily the channel height e between 1 mm and 0.1 mm. Measurements of the overall friction factor and local Nusselt numbers show that the classical laws of hydrodynamics and heat transfer are verified for e > 0.4 mm. For lower values of e, a significant decrease of the Nusselt number is observed, whereas the Poiseuille number continues to have the conventional value of laminar developed flow. The transition to turbulence is not affected by the channel size. For fixed pressure drop across the channel, a maximum of heat transfer rate density is found for a particular value of e. The corresponding dimensionless optimal spacing and heat transfer rate density are in very good agreement with the predictions of Bejan and Sciubba (1992). This paper is the first time that the optimal spacing between parallel plates is determined experimentally.

scholarly journals Transient growth of perturbations in Stokes oscillatory flows

2016 ◽  
Vol 794 ◽  
Author(s):  
Damien Biau
Keyword(s):  
Maximum Energy ◽  
Base Flow ◽  
Low Energy ◽  
Transition To Turbulence ◽  
Two Dimensional ◽  
Oscillatory Flows ◽  
Energy Growth ◽  
Subcritical Regime ◽  
Nonlinear Simulations ◽  
Orr Mechanism

Oscillatory Stokes flows, with zero mean, are subjected to subcritical transition to turbulence. The maximal energy growth of perturbations is computed in the subcritical regime through an optimisation method. The results show strong amplifications during half a period. The energy transfer from the base flow involves an Orr mechanism with two-dimensional vorticity waves, and the maximum energy scales exponentially with the Reynolds number. Nonlinear simulations show that low-energy perturbations are sufficient to trigger turbulent flow.

scholarly journals Transition to turbulence in an elliptic vortex

1996 ◽  
Vol 307 ◽  
pp. 43-62 ◽  
Author(s):  
T. S. Lundgren ◽  
N. N. Mansour
Keyword(s):  
Swirling Flow ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Periodic Wave ◽  
Transition To Turbulence ◽  
Energy Spectra ◽  
Small Scale ◽  
Two Dimensional ◽  
Secondary Instabilities ◽  
Vortex Tubes

Stability and transition to turbulence are studied in a simple incompressible two-dimensional bounded swirling flow with a rectangular planform – a vortex in a box. This flow is unstable to three-dimensional disturbances. The instability takes the form of counter-rotating swirls perpendicular to the axis which bend the vortex into a periodic wave. As these swirls grow in amplitude the primary vorticity is compressed into thin vortex layers. These develop secondary instabilities which roll up into vortex tubes. In this way the flow attains a turbulent state which is populated by intense elongated vortex tubes and weaker vortex layers which spiral around them. The flow was computed at two Reynolds numbers by spectral methods with up to 2563 resolution. At the higher Reynolds number broad three-dimensional shell-averaged energy spectra are found with nearly a decade of Kolmogorov k−5/3 law and small-scale isotropy.

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