Global frequency selection in the observed time-mean wakes of circular cylinders

2008 ◽  
Vol 601 ◽  
pp. 425-441 ◽  
Author(s):  
MOSES KHOR ◽  
JOHN SHERIDAN ◽  
MARK C. THOMPSON ◽  
KERRY HOURIGAN
Keyword(s):  
Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Linear Instability ◽  
Circular Cylinders ◽  
Near Wake ◽  
Mean Velocity ◽  
Number Range ◽  
Wake Instability ◽  
Karman Vortex

Observations have been made of the time-mean velocity profile at midspan in the near-wake of circular cylinders at moderate Reynolds numbers between 600 and 4600, well beyond the Reynolds number of approximately 200 at which the wake becomes three-dimensional. The measured profiles are found to be represented quite accurately by a family of function profiles with known linear instability characteristics. The complex instability frequency is then determined as a function of wake position, using the function profiles. In general, the near wake undergoes a transition from convective to absolute instability; the distance downstream to the point of transition is found to increase over the Reynolds number range investigated. The emergence of a significant region of convective instability is consistent with the known appearance of Bloor–Gerrard vortices. The selected frequency of the wake instability is determined by the saddle-point criterion; the Strouhal numbers for Bénard–von Kármán vortex shedding are found to compare well with the values in the literature.

Simulations of Droplet Collisions in Shear Flow

2012 ◽  
Author(s):  
Orest Shardt ◽  
J. J. Derksen ◽  
Sushanta K. Mitra
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Capillary Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Simple Shear Flow ◽  
Number Range ◽  
Droplet Collisions ◽  
Critical Capillary Number ◽  
Boltzmann Method

When droplets collide in a shear flow, they may coalesce or remain separate after the collision. At low Reynolds numbers, droplets coalesce when the capillary number does not exceed a critical value. We present three-dimensional simulations of droplet coalescence in a simple shear flow. We use a free-energy lattice Boltzmann method (LBM) and study the collision outcome as a function of the Reynolds and capillary numbers. We study the Reynolds number range from 0.2 to 1.4 and capillary numbers between 0.1 and 0.5. We determine the critical capillary number for the simulations (0.19) and find that it is does not depend on the Reynolds number. The simulations are compared with experiments on collisions between confined droplets in shear flow. The critical capillary number in the simulations is about a factor of 25 higher than the experimental value.

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.

Turbulent flow in smooth and rough pipes

2007 ◽  
Vol 365 (1852) ◽  
pp. 699-714 ◽  
Author(s):  
J.J Allen ◽  
M.A Shockling ◽  
G.J Kunkel ◽  
A.J Smits
Keyword(s):  
Reynolds Number ◽  
Friction Factor ◽  
Outer Layer ◽  
Strong Support ◽  
Reynolds Numbers ◽  
Mean Velocity ◽  
Number Range ◽  
Princeton University ◽  
Smooth Pipe ◽  
Logarithmic Region

Recent experiments at Princeton University have revealed aspects of smooth pipe flow behaviour that suggest a more complex scaling than previously noted. In particular, the pressure gradient results yield a new friction factor relationship for smooth pipes, and the velocity profiles indicate the presence of a power-law region near the wall and, for Reynolds numbers greater than about 400×10 3 ( R + >9×10 3 ), a logarithmic region further out. New experiments on a rough pipe with a honed surface finish with k rms / D =19.4×10 −6 , over a Reynolds number range of 57×10 3 –21×10 6 , show that in the transitionally rough regime this surface follows an inflectional friction factor relationship rather than the monotonic relationship given in the Moody diagram. Outer-layer scaling of the mean velocity data and streamwise turbulence intensities for the rough pipe show excellent collapse and provide strong support for Townsend's outer-layer similarity hypothesis for rough-walled flows. The streamwise rough-wall spectra also agree well with the corresponding smooth-wall data. The pipe exhibited smooth behaviour for , which supports the suggestion that the original smooth pipe was indeed hydraulically smooth for Re D ≤24×10 6 . The relationship between the velocity shift, Δ U / u τ , and the roughness Reynolds number, , has been used to generalize the form of the transition from smooth to fully rough flow for an arbitrary relative roughness k rms / D . These predictions apply for honed pipes when the separation of pipe diameter to roughness height is large, and they differ significantly from the traditional Moody curves.

Round Sudden-Expansion Flows

1986 ◽  
Vol 200 (6) ◽  
pp. 447-455 ◽  
Author(s):  
L Khezzar ◽  
J H Whitelaw ◽  
M Yianneskis
Keyword(s):  
Three Dimensional ◽  
Reynolds Numbers ◽  
Sudden Expansion ◽  
Vortex Rings ◽  
Mean Flow ◽  
Mean Velocity ◽  
Number Range ◽  
Laser Anemometry ◽  
Diameter Pipe ◽  
Inlet Geometry

This paper describes an experimental investigation of the water flows through one axisymmetric and two asymmetric round sudden expansions from a 48 mm to an 84 mm diameter pipe and eccentricities of the pipe axes of 0, 5 and 15 mm respectively. Flow visualization revealed the presence of vortex rings downstream of the plane of expansion for transitional Reynolds numbers (Re, based on the upstream pipe diameter and bulk flow velocity) and reattachment lengths were determined in the Reynolds number range 120–40 000 for all three cases. Detailed measurements of the three mean velocity components and corresponding fluctuations were obtained by laser anemometry for Re = 40000. Wall static pressure measurements are also presented. The results show that asymmetry of the inlet geometry strongly influences the distribution of mean and turbulence quantities downstream of the expansion and results in three-dimensional reattachment. In all three flows, the mean flow was nearly uniform and the turbulence nearly homogeneous at distances of seven diameters of the large pipe downstream of the expansion. Higher levels of turbulence were found in the asymmetric ducts with maxima twice those in the axisymmetric duct.

Particle capture by a circular cylinder in the vortex-shedding regime

2013 ◽  
Vol 733 ◽  
pp. 171-188 ◽  
Author(s):  
Alexis Espinosa-Gayosso ◽  
Marco Ghisalberti ◽  
Gregory N. Ivey ◽  
Nicole L. Jones
Keyword(s):  
Reynolds Number ◽  
Vortex Shedding ◽  
Aquatic Vegetation ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Capture Efficiency ◽  
Particle Capture ◽  
Number Range ◽  
Rapid Changes ◽  
High Reynolds

AbstractParticle capture, whereby suspended particles contact and adhere to a solid surface (a ‘collector’), is an important mechanism for a range of environmental processes including suspension feeding by corals and ‘filtering’ by aquatic vegetation. In this paper, we use two- and three-dimensional direct numerical simulations to quantify the capture efficiency ($\eta $) of low-inertia particles by a circular cylindrical collector at intermediate Reynolds numbers in the vortex-shedding regime (i.e. for $47\lt \mathit{Re}\leq 1000$, where $\mathit{Re}$ is the collector Reynolds number). We demonstrate that vortex shedding induces oscillations near the leading face of the collector which greatly affect the quantity and distribution of captured particles. Unlike in steady, low-$\mathit{Re}$ flow, particles directly upstream of the collector are not the most likely to be captured. Our results demonstrate the dependence of the time-averaged capture efficiency on $\mathit{Re}$ and particle size, improving the predictive capability for the capture of particles by aquatic collectors. The transition to theoretical high-Reynolds-number behaviour (i.e. $\eta \sim {\mathit{Re}}^{1/ 2} $) is complex due to comparatively rapid changes in wake conditions in this Reynolds number range.

A note on vortex streets behind circular cylinders at low Reynolds numbers

1971 ◽  
Vol 45 (1) ◽  
pp. 203-208 ◽  
Author(s):  
D. J. Tritton
Keyword(s):  
Reynolds Number ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Number Range ◽  
Low Reynolds Numbers ◽  
Current State ◽  
Reynolds Number Range ◽  
Vortex Streets ◽  
Low Reynolds

A discussion is given of the current state of knowledge of vortex streets behind circular cylinders in the Reynolds number range 50 to 160. This was prompted by Gaster's (1969) report that he could not find the transition at a Reynolds number of about 90 observed by Tritton (1959) and Berger (1964a). A further brief experiment confirming the existence of the transition is described Reasons for rejecting Gaster's interpretation are advanced. Possible (mutually alternative) explanations of the discrepant observations are suggested.

scholarly journals Influence of initial turbulence level on the flow and sound fields of a subsonic jet at a diameter-based Reynolds number of 105

2012 ◽  
Vol 701 ◽  
pp. 352-385 ◽  
Author(s):  
C. Bogey ◽  
O. Marsden ◽  
C. Bailly
Keyword(s):  
Reynolds Number ◽  
Nozzle Exit ◽  
Structural Characteristics ◽  
Three Dimensional ◽  
Shear Layers ◽  
Linear Instability ◽  
Mean Velocity ◽  
Sound Fields ◽  
First Case ◽  
Initial Turbulence

AbstractFive isothermal round jets at Mach number $M= 0. 9$ and Reynolds number ${\mathit{Re}}_{D} = 1{0}^{5} $ originating from a pipe nozzle are computed by large-eddy simulations to investigate the effects of initial turbulence on flow development and noise generation. In the pipe, the boundary layers are untripped in the first case and tripped numerically in the four others in order to obtain, at the exit, mean velocity profiles similar to a Blasius laminar profile of momentum thickness equal to 1.8 % of the jet radius, yielding Reynolds number ${\mathit{Re}}_{\theta } = 900$, and peak turbulence levels ${ u}_{e}^{\ensuremath{\prime} } $ around 0, 3 %, 6 %, 9 % or 12 % of the jet velocity ${u}_{j} $. As the initial turbulence intensity increases, the shear layers develop more slowly with much lower root-mean-square (r.m.s.) fluctuating velocities, and the jet potential cores are longer. Velocity disturbances downstream of the nozzle exit also exhibit different structural characteristics. For low ${ u}_{e}^{\ensuremath{\prime} } / {u}_{j} $, they are dominated by the first azimuthal modes ${n}_{\theta } = 0$, 1 and 2, and show significant skewness and intermittency. The growth of linear instability waves and a first stage of vortex pairings occur in the shear layers for ${ u}_{e}^{\ensuremath{\prime} } / {u}_{j} \leq 6\hspace{0.167em} \% $. For higher ${ u}_{e}^{\ensuremath{\prime} } / {u}_{j} $, three-dimensional features and high azimuthal modes prevail, in particular close to the nozzle exit where the wavenumbers naturally found in turbulent wall-bounded flows clearly appear. Concerning the sound fields, strong broadband components mainly associated with mode ${n}_{\theta } = 1$ are noticed around the pairing frequency for the untripped jet. With rising ${ u}_{e}^{\ensuremath{\prime} } / {u}_{j} $, however, they become weaker, and the noise levels decrease asymptotically down to those measured for jets at ${\mathit{Re}}_{D} \geq 5\ensuremath{\times} 1{0}^{5} $, which are likely to be initially turbulent and to emit negligible vortex-pairing noise. These results correspond well to experimental observations, made separately for either mixing layers, jet flow or sound fields.

Investigation of effects of compressibility, geometric and flow parameters on the simulation of a synthetic jet behaviour

2016 ◽  
Vol 120 (1225) ◽  
pp. 521-546 ◽  
Author(s):  
F. Bazdidi-Tehrani ◽  
A. Abouata ◽  
M. Hatami ◽  
N. Bohlooli
Keyword(s):  
Reynolds Number ◽  
Turbulence Model ◽  
Mass Flow ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Synthetic Jet ◽  
Instantaneous Velocity ◽  
Mean Velocity ◽  
Velocity Magnitude ◽  
Flow Parameters

ABSTRACTThe present paper focuses on a three-dimensional unsteady turbulent synthetic jet to assess the accuracy of a compressible simulation and some important parameters including the simulations of the actuator, cavity height and Reynolds number. The two-equationSST/k− ω turbulence model is used to predict the flow behaviour. Results show that the compressible simulation case is more accurate than the incompressible one and the dynamic mesh exhibits more reliable results than the mass flow inlet boundary in the compressible simulation. The compressible case displays a delay in the phase of instantaneous velocity for all three Reynolds numbers. Also, the maximum of mean velocity is less than the incompressible case. Moreover, an increase in the Reynolds number leads to an amplification of the peak of mean velocity magnitude. Finally, results demonstrate that a reduction in the cavity height regarding the compressible simulation case causes a reduction in the phase delay and rise in peak of instantaneous velocity magnitude.

The wake behind a cylinder rolling on a wall at varying rotation rates

2010 ◽  
Vol 648 ◽  
pp. 225-256 ◽  
Author(s):  
B. E. STEWART ◽  
M. C. THOMPSON ◽  
T. LEWEKE ◽  
K. HOURIGAN
Keyword(s):  
Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Wake Flow ◽  
Recirculation Region ◽  
Two Dimensional ◽  
Number Range ◽  
Rotation Rates ◽  
Transition Mechanism ◽  
Three Dimensional Simulations

A study investigating the flow around a cylinder rolling or sliding on a wall has been undertaken in two and three dimensions. The cylinder motion is specified from a set of five discrete rotation rates, ranging from prograde through to retrograde rolling. A Reynolds number range of 20–500 is considered. The effects of the nearby wall and the imposed body motion on the wake structure and dominant wake transitions have been determined. Prograde rolling is shown to destabilize the wake flow, while retrograde rotation delays the onset of unsteady flow to Reynolds numbers well above those observed for a cylinder in an unbounded flow.Two-dimensional simulations show the presence of two recirculation zones in the steady wake, the lengths of which increase approximately linearly with the Reynolds number. Values of the lift and drag coefficient are also reported for the steady flow regime. Results from a linear stability analysis show that the wake initially undergoes a regular bifurcation from a steady two-dimensional flow to a steady three-dimensional wake for all rotation rates. The critical Reynolds number Rec of transition and the spanwise wavelength of the dominant mode are shown to be highly dependent on, but smoothly varying with, the rotation rate of the cylinder. Varying the rotation from prograde to retrograde rolling acts to increase the value of Rec and decrease the preferred wavelength. The structure of the fully evolved wake mode is then established through three-dimensional simulations. In fact it is found that at Reynolds numbers only marginally (~5%) above critical, the three-dimensional simulations indicate that the saturated state becomes time dependent, although at least initially, this does not result in a significant change to the mode structure. It is only at higher Reynolds numbers that the wake undergoes a transition to vortex shedding.An analysis of the three-dimensional transition indicates that it is unlikely to be due to a centrifugal instability despite the superficial similarity to the flow over a backward-facing step, for which the transition mechanism has been speculated to be centrifugal. However, the attached elongated recirculation region and distribution of the spanwise perturbation vorticity field, and the similarity of these features with those of the flow through a partially blocked channel, suggest the possibility that the mechanism is elliptic in nature. Some analysis which supports this conjecture is undertaken.

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