Frequency selection and asymptotic states in laminar wakes

1989 ◽  
Vol 199 ◽  
pp. 441-469 ◽  
Author(s):  
George Em Karniadakis ◽  
George S. Triantafyllou
Keyword(s):  
Excitation Frequency ◽  
Transition Process ◽  
Reynolds Numbers ◽  
Spectral Element ◽  
Dominant Frequency ◽  
Circular Cylinders ◽  
Natural State ◽  
Periodic State ◽  
Lock In ◽  
Laminar Wakes

A better understanding of the transition process in open flows can be obtained through identification of the possible asymptotic response states in the flow. In the present work, the asymptotic states in laminar wakes behind circular cylinders at low supercritical Reynolds numbers are investigated. Direct numerical simulation of the flow is performed, using spectral-element techniques. Naturally produced wakes, and periodically forced wakes are considered separately.It is shown that, in the absence of external forcing, a periodic state is obtained, the frequency of which is selected by the absolute instability of the time-average flow. The non-dimensional frequency of the vortex street (Strouhal number) is a continuous function of the Reynolds number. In periodically forced wakes, however, non-periodic states are also possible, resulting from the bifurcation of the natural periodic state. The response of forced wakes can be characterized as: (i) lock-in, if the dominant frequency in the wake equals the excitation frequency, or (ii) non-lock-in, when the dominant frequency in the wake equals the Strouhal frequency. Both types of response can be periodic or quasi-periodic, depending on the combination of the amplitude and frequency of the forcing. At the boundary separating the two types of response transitional states develop, which are found to exhibit a low-order chaotic behaviour. Finally, all states resulting from the bifurcation of the natural state can be represented in a two-parameter space inside ‘resonant horn’ type of regions.

STABILITY OF FLOW PAST TWO SIDE-BY-SIDE CIRCULAR CYLINDERS

2009 ◽  
Vol 23 (03) ◽  
pp. 269-272
Author(s):  
KUN LIU ◽  
DONG-JUN MA ◽  
DE-JUN SUN ◽  
XIE-YUAN YIN
Keyword(s):  
Global Stability ◽  
Spectral Element ◽  
Separation Distance ◽  
Circular Cylinders ◽  
Navier Stokes ◽  
Remarkable Feature ◽  
Phase Lock ◽  
Flow Past ◽  
Critical Reynolds Numbers ◽  
Lock In

The global stability of flow past two side-by-side circular cylinders is investigated by a linear global stability analysis method based on a spectral/element Navier-Stokes solver. The special attention is paid to the parameter regime of 1<T/D<3, where T is the spacing between two cylinder centers and D the cylinder diameter. A remarkable feature we found is that there exist two critical Reynolds numbers associated with twice bifurcations, first a pitchfork and second a Hopf one, for about 1.55<T/D<1.65. A new flow pattern namely biased steady pattern is identified. In addition, the transition from in-phase lock-in to anti-phase lock-in pattern for larger separation distance T/D>1.65 is proved to be related to the switch between two leading eigenmodes.

Vortex Shedding Frequencies of the Flow through Two-Row Banks of Tubes

1969 ◽  
Vol 11 (5) ◽  
pp. 498-502 ◽  
Author(s):  
A. R. J. Borges
Keyword(s):  
Vortex Shedding ◽  
Reynolds Numbers ◽  
Dominant Frequency ◽  
Experimental Results ◽  
Circular Cylinders ◽  
Single Row ◽  
Flow Through ◽  
Set Up

This paper deals with the problem of vortex shedding from parallel rows of circular cylinders of equal diameter set normal to an airstream. A single row of cylinders is first discussed. The experimental results show that when the lateral spacing between the axes of two adjacent cylinders is less than two diameters the flow downstream of the row does not exhibit any obvious single dominant frequency of vortex shedding. The flow set up by two rows of cylinders is next considered for both tandem and staggered arrangements of the cylinders. The sets of measured values reported are complete in the sense that they cover the whole range of spacings for which a dominant frequency of vortex shedding could be measured. The Reynolds numbers of these tests correspond to the high subscritical range for a cylinder in isolation.

Cross-Flow Past a Pair of Staggered Cylinders With the Upstream Cylinder Subjected to a Transverse Harmonic Oscillation

2002 ◽  
Author(s):  
Stuart J. Price ◽  
Srikanth Krishnamoorthy ◽  
Michael P. Pai¨doussis
Keyword(s):  
Flow Direction ◽  
Vortex Formation ◽  
Cross Flow ◽  
Harmonic Oscillation ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Flow Past ◽  
The Mean ◽  
Lock In ◽  
Hot Film

An experimental investigation of the cross-flow past a pair of staggered circular cylinders, with the downstream cylinder subject to forced harmonic oscillation transverse to the flow direction, is presented in this paper. In particular, flow-visualization of the wakeformation region and hot-film measurements of the wake spectra are reported. Experiments were conducted in a water tunnel for Reynolds numbers, based on upstream velocity, U, and cylinder diameter, D, in the range 1440 ≤ Re ≤ 1680. The longitudinal separation between cylinder centers is L/D = 2.0, with a transverse separation (for the mean position of the upstream cylinder) of T/D = 0.17. As shown in an earlier study, depending on the actual position of the upstream cylinder in its oscillation cycle, this configuration straddles the shear-layer reattachment and induced separation regimes. The results show that the oscillation of the upstream cylinder causes considerable modification of the flow patterns and regimes compared to what is obtained when the cylinder is fixed. In particular, depending on the frequency of oscillation of the upstream cylinder, sub- and superharmonic resonances are obtained between the vortex formation frequency and oscillation frequency, as well as the usual fundamental lock-in. These resonances and accompanying wake regimes are examined in detail in this paper.

Intermittency in free vibration of a cylinder beyond the laminar regime

2019 ◽  
Vol 870 ◽  
Author(s):  
Navrose ◽  
Sanjay Mittal
Keyword(s):  
Three Dimensional ◽  
Time History ◽  
Reynolds Numbers ◽  
Dominant Frequency ◽  
Laminar Regime ◽  
Mass Ratio ◽  
Aerodynamic Coefficients ◽  
History Of ◽  
Lock In ◽  
Intermittent Switching

Vortex-induced vibration of a circular cylinder that is free to move in the transverse ($Y$) and streamwise ($X$) directions is investigated at subcritical Reynolds numbers ($1500\lesssim Re\lesssim 9000$) via three-dimensional (3-D) numerical simulations. The mass ratio of the system for all the simulations is $m^{\ast }=10$. It is observed that while some of the characteristics associated with the $XY$-oscillation are similar to those of the $Y$-only oscillation (in line with the observations made by Jauvtis & Williamson (J. Fluid Mech., vol. 509, 2004, pp. 23–62)), notable differences exist between the two systems with respect to the transition between the branches of the cylinder response in the lock-in regime. The flow regime between the initial and lower branch is characterized by intermittent switching in the cylinder response, aerodynamic coefficients and modes of vortex shedding. Similar to the regime of laminar flow, the system exhibits a hysteretic response near the lower- and higher-$Re$ end of the lock-in regime. The frequency spectrum of time history of the cylinder response shows that the most dominant frequency in the streamwise oscillation on the initial branch is the same as that of the transverse oscillation.

Cross-Flow Past a Pair of Staggered Cylinders With the Upstream Cylinder Subjected to a Transverse Harmonic Oscillation

2006 ◽  
Author(s):  
Stuart J. Price ◽  
Michael P. Pai¨doussis ◽  
Srikanth Krishnamoorthy
Keyword(s):  
Flow Direction ◽  
Vortex Formation ◽  
Cross Flow ◽  
Harmonic Oscillation ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Vortex Pairing ◽  
Flow Past ◽  
Lock In ◽  
Hot Film

The results of an experimental investigation are presented for the cross-flow past a pair of staggered circular cylinders, with the upstream cylinder being subject to forced harmonic oscillation transverse to the flow direction. Flow-visualization of the wake-formation region and hot-film measurements of the wake spectra are reported. Experiments were conducted in a water tunnel for Reynolds numbers, based on upstream velocity, U, and cylinder diameter, D, in the range 1440 ≤ Re ≤ 1680. Results are presented for the case where the longitudinal separation between cylinder centres (for the mean position of the upstream cylinder) is L/D = 2.0, with the transverse separation being T/D = 1.0. As shown by Sumner et al. [1] this configuration corresponds to either the gap vortex pairing and enveloping or gap vortex pairing, splitting and enveloping regimes. The results show that the oscillation of the upstream cylinder causes considerable modification of the flow patterns and regimes compared to what is obtained when the cylinder is fixed. In particular, depending on the frequency of oscillation of the upstream cylinder, sub- and super-harmonic resonances are obtained between the vortex formation frequency and oscillation frequency, as well as the usual fundamental lock-in. These resonances and accompanying wake regimes are examined in detail in the paper.

scholarly journals Aerodynamics of smooth and rough square-section prisms at incidence in very high Reynolds-number cross-flows

2021 ◽  
Vol 62 (3) ◽  
Author(s):  
Nils Paul van Hinsberg
Keyword(s):  
Reynolds Number ◽  
Cross Sections ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Surface Boundary ◽  
Experimental Proof ◽  
Surface Boundary Layer ◽  
Pitch Moment ◽  
The Mean ◽  
High Reynolds

Abstract The aerodynamics of smooth and slightly rough prisms with square cross-sections and sharp edges is investigated through wind tunnel experiments. Mean and fluctuating forces, the mean pitch moment, Strouhal numbers, the mean surface pressures and the mean wake profiles in the mid-span cross-section of the prism are recorded simultaneously for Reynolds numbers between 1$$\times$$ × 10$$^{5}$$ 5 $$\le$$ ≤ Re$$_{D}$$ D $$\le$$ ≤ 1$$\times$$ × 10$$^{7}$$ 7 . For the smooth prism with $$k_s$$ k s /D = 4$$\times$$ × 10$$^{-5}$$ - 5 , tests were performed at three angles of incidence, i.e. $$\alpha$$ α = 0$$^{\circ }$$ ∘ , −22.5$$^{\circ }$$ ∘ and −45$$^{\circ }$$ ∘ , whereas only both “symmetric” angles were studied for its slightly rough counterpart with $$k_s$$ k s /D = 1$$\times$$ × 10$$^{-3}$$ - 3 . First-time experimental proof is given that, within the accuracy of the data, no significant variation with Reynolds number occurs for all mean and fluctuating aerodynamic coefficients of smooth square prisms up to Reynolds numbers as high as $$\mathcal {O}$$ O (10$$^{7}$$ 7 ). This Reynolds-number independent behaviour applies to the Strouhal number and the wake profile as well. In contrast to what is known from square prisms with rounded edges and circular cylinders, an increase in surface roughness height by a factor 25 on the current sharp-edged square prism does not lead to any notable effects on the surface boundary layer and thus on the prism’s aerodynamics. For both prisms, distinct changes in the aerostatics between the various angles of incidence are seen to take place though. Graphic abstract

scholarly journals On the Scope of Lagrangian Vortex Methods for Two-Dimensional Flow Simulations and the POD Technique Application for Data Storing and Analyzing

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 118
Author(s):  
Kseniia Kuzmina ◽  
Ilia Marchevsky ◽  
Irina Soldatova ◽  
Yulia Izmailova
Keyword(s):  
Flow Simulation ◽  
Internal Flow ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Vortex Methods ◽  
Flow Simulations ◽  
Additional Information ◽  
Two Dimensional Flow ◽  
Different Shapes ◽  
Problem Formulations

The possibilities of applying the pure Lagrangian vortex methods of computational fluid dynamics to viscous incompressible flow simulations are considered in relation to various problem formulations. The modification of vortex methods—the Viscous Vortex Domain method—is used which is implemented in the VM2D code developed by the authors. Problems of flow simulation around airfoils with different shapes at various Reynolds numbers are considered: the Blasius problem, the flow around circular cylinders at different Reynolds numbers, the flow around a wing airfoil at the Reynolds numbers 104 and 105, the flow around two closely spaced circular cylinders and the flow around rectangular airfoils with a different chord to the thickness ratio. In addition, the problem of the internal flow modeling in the channel with a backward-facing step is considered. To store the results of the calculations, the POD technique is used, which, in addition, allows one to investigate the structure of the flow and obtain some additional information about the properties of flow regimes.

scholarly journals Fluid-Structure Energy Transfer of a Tensioned Beam Subject to Vortex-Induced Vibrations in Shear Flow

2011 ◽  
Author(s):  
Remi Bourguet ◽  
Michael S. Triantafyllou ◽  
Michael Tognarelli ◽  
Pierre Beynet
Keyword(s):  
Energy Transfer ◽  
Shear Flow ◽  
Cross Flow ◽  
Reynolds Numbers ◽  
Structural Vibrations ◽  
Fluid Structure ◽  
Vortex Induced Vibrations ◽  
Linear Shear ◽  
Structural Responses ◽  
Lock In

The fluid-structure energy transfer of a tensioned beam of length to diameter ratio 200, subject to vortex-induced vibrations in linear shear flow, is investigated by means of direct numerical simulation at three Reynolds numbers, from 110 to 1,100. In both the in-line and cross-flow directions, the high-wavenumber structural responses are characterized by mixed standing-traveling wave patterns. The spanwise zones where the flow provides energy to excite the structural vibrations are located mainly within the region of high current where the lock-in condition is established, i.e. where vortex shedding and cross-flow vibration frequencies coincide. However, the energy input is not uniform across the entire lock-in region. This can be related to observed changes from counterclockwise to clockwise structural orbits. The energy transfer is also impacted by the possible occurrence of multi-frequency vibrations.

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