Scaling of longitudinal and transverse velocity increments in a cylinder wake

2005 ◽  
Vol 71 (6) ◽  
Author(s):  
T. Zhou ◽  
Z. Hao ◽  
L. P. Chua ◽  
S. C. M. Yu
Keyword(s):  
Transverse Velocity ◽  
Cylinder Wake ◽  
Velocity Increments

Lock-On Vortex Shedding Patterns and Bifurcation Analysis of the Forced Streamwise Oscillation of the Cylinder Wake

2015 ◽  
Vol 25 (09) ◽  
pp. 1530022
Author(s):  
N. Nabatian ◽  
N. W. Mureithi
Keyword(s):  
Frequency Ratio ◽  
Transverse Velocity ◽  
Lift Coefficient ◽  
Oscillation Amplitude ◽  
Vortex Formation ◽  
Excitation Frequency ◽  
Immersed Boundary ◽  
Cylinder Wake ◽  
Single Vortex ◽  
Frequency Ratios

The two-dimensional numerical simulation of the flow over a cylinder forced to oscillate in the streamwise direction for Re = 200 is performed in CFX ANSYS. The controlled-vibration comprises of prescribed inline vibration from displacement amplitude-to-cylinder diameter A/D = 0.05 up to 0.5 with the excitation frequency ratios of 1, 1.5 and 2 including the harmonic and superharmonic excitation regions. The immersed boundary method is used to model the cylinder oscillation. Modal decomposition of the transverse velocity field via the proper orthogonal decomposition (POD) method is applied to uncover the interaction of symmetric and antisymmetric modes of the near wake. A model using the first two POD modes is developed based on symmetry group equivariance. The model predicts the mode interactions and bifurcated solution branches for all cases, and is shown to be in good agreement with numerical as well as previous experimental results. Lock-on is determined for a range of values of the oscillation amplitudes and frequency ratios. It is shown that the lock-on range widens with increasing nondimensional oscillation amplitude. The asymmetric 2S, P + S and symmetric pattern S with symbol S for a single vortex and P for a vortex pair shed per cycle, as well as a regime in which vortex formation is not synchronized with cylinder motion are observed in the cylinder wake depending on the combination of oscillation amplitude and frequency ratio. The frequency ratio variation from 1 to 2 leads to the switching from asymmetric to symmetric modes. The symmetric flow pattern corresponds to a near zero lift coefficient on the cylinder.

Three-component vorticity measurements in a turbulent grid flow

1998 ◽  
Vol 374 ◽  
pp. 29-57 ◽  
Author(s):  
R. A. ANTONIA ◽  
T. ZHOU ◽  
Y. ZHU
Keyword(s):  
Energy Dissipation ◽  
Dissipation Rate ◽  
Velocity Structure ◽  
Transverse Velocity ◽  
Longitudinal Velocity ◽  
Energy Dissipation Rate ◽  
Grid Turbulence ◽  
Local Isotropy ◽  
Velocity Increments ◽  
The Mean

All components of the fluctuating vorticity vector have been measured in decaying grid turbulence using a vorticity probe of relatively simple geometry (four X-probes, i.e. a total of eight hot wires). The data indicate that local isotropy is more closely satisfied than global isotropy, the r.m.s. vorticities being more nearly equal than the r.m.s. velocities. Two checks indicate that the performance of the probe is satisfactory. Firstly, the fully measured mean energy dissipation rate 〈ε〉 is in good agreement with the value inferred from the rate of decay of the mean turbulent energy 〈q2〉 in the quasi-homogeneous region; the isotropic mean energy dissipation rate 〈εiso〉 agrees closely with this value even though individual elements of 〈ε〉 indicate departures from isotropy. Secondly, the measured decay rate of the mean-square vorticity 〈ω2〉 is consistent with that of 〈q2〉 and in reasonable agreement with the isotropic form of the transport equation for 〈ω2〉. Although 〈ε〉≃〈εiso〉, there are discernible differences between the statistics of ε and εiso; in particular, εiso is poorly correlated with either ε or ω2. The behaviour of velocity increments has been examined over a narrow range of separations for which the third-order longitudinal velocity structure function is approximately linear. In this range, transverse velocity increments show larger departures than longitudinal increments from predictions of Kolmogorov (1941). The data indicate that this discrepancy is only partly associated with differences between statistics of locally averaged ε and ω2, the latter remaining more intermittent than the former across this range. It is more likely caused by a departure from isotropy due to the small value of Rλ, the Taylor microscale Reynolds number, in this experiment.

Reynolds number dependence of the small-scale structure of grid turbulence

2000 ◽  
Vol 406 ◽  
pp. 81-107 ◽  
Author(s):  
T. ZHOU ◽  
R. A. ANTONIA
Keyword(s):  
Reynolds Number ◽  
Power Law ◽  
Fourth Order ◽  
Transverse Velocity ◽  
Scale Structure ◽  
Small Scale ◽  
Grid Turbulence ◽  
Small Scale Structure ◽  
Velocity Increments ◽  
The Difference

The small-scale structure of grid turbulence is studied primarily using data obtained with a transverse vorticity (ω3) probe for values of the Taylor-microscale Reynolds number Rλ in the range 27–100. The measured spectra of the transverse vorticity component agree within ±10% with those calculated using the isotropic relation over nearly all wavenumbers. Scaling-range exponents of transverse velocity increments are appreciably smaller than exponents of longitudinal velocity increments. Only a small fraction of this difference can be attributed to the difference in intermittency between the locally averaged energy dissipation rate and enstrophy fluctuations. The anisotropy of turbulence structures in the scaling range, which reflects the small values of Rλ, is more likely to account for most of the difference. All four fourth-order rotational invariants Iα (α = 1 to 4) proposed by Siggia (1981) were evaluated. For any particular value of α, the magnitude of the ratio Iα / I1 is approximately constant, independently of Rλ. The implication is that the invariants are interdependent, at least in isotropic and quasi-Gaussian turbulence, so that only one power-law exponent may be sufficient to describe the Rλ dependence of all fourth-order velocity derivative moments in this type of flow. This contrasts with previous suggestions that at least two power-law exponents are needed, one for the rate of strain and the other for vorticity.

Bifurcation Analysis and the Role of Normal Form Symmetries on the Harmonic Forced Inline Oscillation of the Cylinder Wake

2016 ◽  
Author(s):  
N. Nabatian ◽  
N. W. Mureithi
Keyword(s):  
Normal Form ◽  
Numerical Computation ◽  
Vortex Shedding ◽  
Transverse Velocity ◽  
Lift Coefficient ◽  
Cylinder Wake ◽  
Order Model ◽  
Periodic State ◽  
Shedding Frequency ◽  
Low Order

Vortex shedding over a cylinder is strongly affected by the cylinder oscillation. The dynamics of the cylinder wake subjected to harmonic forced excitation in the inline direction at Re = 200 is investigated in this work. Two dominant modes of the transverse velocity field are considered to model and predict the nonlinear interaction of 2D vortex shedding. The normal form symmetries have the main role in the pattern formation. The interaction of two steady modes in the presence of O(2) × S1 symmetry is described by equivariant theory. Considering the symmetries, the amplitude equations are developed with the frequency saturation information included by the addition of complex coefficients. The reduced model is expanded up to 7th order, in order to include the spatio-temporal effects. The coefficients of the model are obtained from 2D simulations of the cylinder wake flow. The physical significance of the inline amplitude oscillation on the wake dynamics is captured by the variation of the two linear coefficients of the low order model. Similarly to the numerical results, as the amplitude of oscillation increases, two limit cycles undergo the symmetry-breaking bifurcation leading to a quasi-periodic state. The existence of the second frequency in addition to the natural shedding frequency is manifested as the small amplitude oscillation in the quasi-periodic state. For a forcing amplitude A/D = 0.5, the quasi-periodic state undergoes a torus doubling bifurcation. The dominant frequency of the bifurcated S mode matches the lift coefficient shedding frequency at A/D = 0.5 obtained from the numerical computation. The lift coefficient signal is not absolutely periodic due to the presence of the other peaks in addition to the dominant one at St = 0.1 representing the quasi-periodic flow pattern. The modulated travelling waves bifurcated from the low order model have mode S as the basic v-velocity mode which verifies the symmetric torus-doubled transverse velocity pattern observed in CFD simulation. Thus the proposed low order model can predict, with reasonable accuracy, the bifurcation sequence of the forced cylinder wake dynamic transitions observed in the numerical computation results.

Decay of Temperature Variance in the Presence of Nonhomogeneous Strain

1992 ◽  
Vol 114 (2) ◽  
pp. 155-160
Author(s):  
H. R. Rahai ◽  
J. C. LaRue
Keyword(s):  
Decay Rate ◽  
Transverse Velocity ◽  
Single Point ◽  
Maximum Shear Stress ◽  
Decay Rates ◽  
Cylinder Wake ◽  
Integral Scale ◽  
Time Resolved ◽  
Temperature Variance ◽  
Thin Wires

The effect of nonhomogeneous strain caused by two-dimensional objects on single point statistical properties of the turbulent velocity and turbulent scalar (temperature) and their cross moments are investigated experimentally. The heated turbulent flow is produced by means of a biplane array of round rods and a biplane array of heated, thin wires placed downstream of the turbulence producing grid. The experiments are performed for three different ratios of the integral scale, L0, to the object dimension, D, of 0.38, 1.90 and 3.1. Measurements of time resolved temperature and longitudinal and transverse velocity components are obtained using a triple wire probe consisting of a cold wire and two hot wires. Results indicate that, for L0 =1.9 and 3.1, the decay rate of temperature variance is nearly the same in the region of maximum shear stress (mss) and near the centerline. However, the decay rate in these regions is less than the decay rate of the temperature variance outside the cylinder wake. For L0/D = 0.38, the decay rates of temperature variance are the same in the regions of mss, near the centerline and outside the wake. Transverse growth of the wake is found to be either increased or nearly unchanged depending on, respectively, whether the free stream integral scale is larger or less than that of the wake.

Reynolds-number dependence of turbulent velocity and pressure increments

2001 ◽  
Vol 444 ◽  
pp. 343-382 ◽  
Author(s):  
B. R. PEARSON ◽  
R. A. ANTONIA
Keyword(s):  
Reynolds Number ◽  
Fourth Order ◽  
Transverse Velocity ◽  
Inertial Range ◽  
Integral Length Scale ◽  
Length Scale ◽  
Scaling Exponents ◽  
Velocity Increments ◽  
The Mean ◽  
Reynolds Number Dependence

The main focus is the Reynolds number dependence of Kolmogorov normalized low-order moments of longitudinal and transverse velocity increments. The velocity increments are obtained in a large number of flows and over a wide range (40–4250) of the Taylor microscale Reynolds number Rλ. The Rλ dependence is examined for values of the separation, r, in the dissipative range, inertial range and in excess of the integral length scale. In each range, the Kolmogorov-normalized moments of longitudinal and transverse velocity increments increase with Rλ. The scaling exponents of both longitudinal and transverse velocity increments increase with Rλ, the increase being more significant for the latter than the former. As Rλ increases, the inequality between scaling exponents of longitudinal and transverse velocity increments diminishes, reflecting a reduced influence from the large-scale anisotropy or the mean shear on inertial range scales. At sufficiently large Rλ, inertial range exponents for the second-order moment of the pressure increment follow more closely those for the fourth-order moments of transverse velocity increments than the fourth-order moments of longitudinal velocity increments. Comparison with DNS data indicates that the magnitude and Rλ dependence of the mean square pressure gradient, based on the joint-Gaussian approximation, is incorrect. The validity of this approximation improves as r increases; when r exceeds the integral length scale, the Rλ dependence of the second-order pressure structure functions is in reasonable agreement with the result originally given by Batchelor (1951).

POD ANALYSIS OF THREE-DIMENSIONAL HARMONICALLY FORCED WAKE FLOW OF A CIRCULAR CYLINDER

2015 ◽  
Vol 39 (4) ◽  
pp. 789-803 ◽  
Author(s):  
Negar Nabatian ◽  
Xiaofei Xu ◽  
Njuki Mureithi
Keyword(s):  
Circular Cylinder ◽  
Vortex Shedding ◽  
Transverse Velocity ◽  
Lift Coefficient ◽  
Oscillation Amplitude ◽  
Three Dimensional ◽  
Wake Flow ◽  
Cylinder Wake ◽  
Pod Analysis ◽  
Vortex Shedding Modes

A 3D numerical simulation of a circular cylinder wake is presented in this paper. The cylinder is harmonically forced in the stream-wise direction. The objective of the present work is to investigate the effect of the oscillation amplitude on the secondary transition of the wake. The frequency of the lift force is then linked to the form of the vortex shedding mode. The relation between these vortex shedding modes using POD analysis of the transverse velocity and the unsteady lift coefficient of 3D simulation is in good agreement with the 2D model. Results show that the 3D spanwise effect, which can change the wake structure, is suppressed at Re = 200 by streamwise oscillation of the cylinder. Thus the 2D analysis can effectively model the temporal instability of the wake flow.

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