Lateral vorticity measurements in a turbulent wake

1996 ◽  
Vol 323 ◽  
pp. 173-200 ◽  
Author(s):  
R. A. Antonia ◽  
Y. Zhu ◽  
H. S. Shafi
Keyword(s):  
Velocity Structure ◽  
Streamwise Velocity ◽  
Turbulent Wake ◽  
Lateral Velocity ◽  
Local Isotropy ◽  
Wire Probe ◽  
Spatial Derivatives ◽  
Velocity Derivative ◽  
Derivatives Of ◽  
Flatness Factor

The accurate measurement of vorticity has proven difficult because of the difficulty of estimating spatial derivatives of velocity fluctuations reliably. A method is proposed for correcting the lateral vorticity spectrum measured using a four-wire probe. The attenuation of the measured spectrum increases as the wavenumber increases but does not vanish when the wavenumber is zero. Although the correction procedure assumes local isotropy, the major contributor to the high-wavenumber part of the vorticity spectrum is the streamwise derivative of the lateral velocity fluctuation, and the correction of this latter quantity does not depend on local isotropy. Satisfactory support for local isotropy is provided by the high-wavenumber parts of the velocity, velocity derivative and vorticity spectra measured on the centreline of a turbulent wake. Second- and fourth-order moments of vorticity show departures from local isotropy but the degree of departure seems unaffected by the turbulence Reynolds number Rλ. The vorticity probability density function is approximately exponential and has tails which stretch out to larger amplitudes as Rλ increases. The vorticity flatness factor, which is appreciably larger than the flatness factor of the streamwise velocity derivative, also increases with Rλ. When Rλ is sufficiently large for velocity structure functions to indicate a r2/3 inertial range, two-point longitudinal correlations of lateral vorticity fluctuations give encouraging support for the theoretical r−4/3 behaviour.

Derivative Statistics of Axial Velocity and Passive Scalar in the Jet Diffusion Field of High-Schmidt-Number Matter

2007 ◽  
Author(s):  
Y. Sakai ◽  
K. Uchida ◽  
T. Kubo ◽  
K. Nagata
Keyword(s):  
Axial Velocity ◽  
Schmidt Number ◽  
Water Solution ◽  
Passive Scalar ◽  
Streamwise Velocity ◽  
The Other ◽  
Diffusion Field ◽  
High Schmidt Number ◽  
Velocity Derivative ◽  
Flatness Factor

In this study, a water solution of dye (whose Schmidt number is about 3,800) was issued into the quiescent water as an axisymmetric turbulent jet and the simultaneous measurements of axial velocity and concentration have been performed using the combined probe of I-type hot-film and fiber-optic concentration sensor based on the Lambert-Beer’s law. Then we calculated the PDF (Probability Density Function) for the streamwise velocity derivative ∂u/∂x and streamwise concentration derivative ∂c/∂x. It was confirmed that the PDFs for ∂u/∂x skew negatively, and the values of skewness (S∂u/∂x) and flatness factor (F∂u/∂x) are consistent with the other data (see Sreenivasan and Antonia, 1997). However, with regard to the PDFs for ∂c/∂x, the skewness (S∂c/∂x) show the values very close to zero, unlikely the past other data which show the magnitude of 0.5∼1.0. On the other hand, the flatness factor (F∂c/∂x) show the values of 7.0∼8.0 which are consistent with other data. This result suggests that the fine-scale structure of a high-Schmidt-number diffusion field is almost isotropic although it is intermittent.

Vibration attenuation of a two-link flexible arm carried by a translational stage

2018 ◽  
Vol 24 (23) ◽  
pp. 5650-5664 ◽  
Author(s):  
Shang–Teh Wu ◽  
Shan-Qun Tang ◽  
Kuan–Po Huang
Keyword(s):  
Feedback Loop ◽  
Control Method ◽  
Flexible Manipulator ◽  
Closed Loop System ◽  
Flexible Arm ◽  
Vibration Attenuation ◽  
Shaft Encoder ◽  
High Frequency Vibrations ◽  
Spatial Derivatives ◽  
Derivatives Of

This paper investigates the vibration control of a two-link flexible manipulator carried by a translational stage. The first and the second links are each driven by a stage motor and a joint motor. By treating the joint motor as a virtual spring, the two-link manipulator can be regarded as an integral flexible arm driven by the stage motor. A noncollocated controller is devised based on feedback from the deflection of the virtual spring, which can be measured by a shaft encoder. Stability of the closed-loop system is analyzed by examining the spatial derivatives of the modal functions. By including a bandpass filter in the feedback loop, residual vibrations can be attenuated without exciting high-frequency vibrations. The control method is simple to implement; its effectiveness is confirmed by simulation and experimental results.

The effect of microscale random Alfvén waves on the propagation of large-scale Alfvén waves

1983 ◽  
Vol 29 (2) ◽  
pp. 243-253 ◽  
Author(s):  
Tomikazu Namikawa ◽  
Hiromitsu Hamabata
Keyword(s):  
Large Scale ◽  
Ponderomotive Force ◽  
Collisionless Plasma ◽  
Alfven Waves ◽  
Velocity Fields ◽  
Velocity Shear ◽  
Alfvén Waves ◽  
Spectrum Function ◽  
Spatial Derivatives ◽  
Derivatives Of

The ponderomotive force generated by random Alfvén waves in a collisionless plasma is evaluated taking into account mean magnetic and velocity shear and is expressed as a series involving spatial derivatives of mean magnetic and velocity fields whose coefficients are associated with the helicity spectrum function of random velocity field. The effect of microscale random Alfvén waves through ponderomotive and mean electromotive forces generated by them on the propagation of large-scale Alfvén waves is also investigated.

The structure of internal intermittency in turbulent flows at large Reynolds number: experiments on scale similarity

1973 ◽  
Vol 59 (3) ◽  
pp. 537-559 ◽  
Author(s):  
C. W. Van Atta ◽  
T. T. Yeh
Keyword(s):  
Reynolds Number ◽  
Probability Density ◽  
Streamwise Velocity ◽  
Statistical Characteristics ◽  
Large Reynolds Number ◽  
Higher Moments ◽  
Scale Similarity ◽  
Probability Densities ◽  
Scale Ratio ◽  
Velocity Derivative

Some of the statistical characteristics of the breakdown coefficient, defined as the ratio of averages over different spatial regions of positive variables characterizing the fine structure and internal intermittency in high Reynolds number turbulence, have been investigated using experimental data for the streamwise velocity derivative ∂u/∂tmeasured in an atmospheric boundary layer. The assumptions and predictions of the hypothesis of scale similarity developed by Novikov and by Gurvich & Yaglom do not adequately describe or predict the statistical characteristics of the breakdown coefficientqr,lof the square of the streamwise velocity derivative. Systematic variations in the measured probability densities and consistent variations in the measured moments show that the assumption that the probability density of the breakdown coefficient is a function only of the scale ratio is not satisfied. The small positive correlation between adjoint values ofqr,land measurements of higher moments indicate that the assumption that the probability densities for adjoint values ofqr,lare statistically independent is also not satisfied. The moments ofqr,ldo not have the simple power-law character that is a consequence of scale similarity.As the scale ratiol/rchanges, the probability density ofqr,levolves from a sharply peaked, highly negatively skewed density for large values of the scale ratio to a very symmetrical distribution when the scale ratio is equal to two, and then to a highly positively skewed density as the scale ratio approaches one. There is a considerable effect of heterogeneity on the values of the higher moments, and a small but measurable effect on the mean value. The moments are roughly symmetrical functions of the displacement of the shorter segment from the centre of the larger one, with a minimum value when the shorter segment is centrally located within the larger one.

scholarly journals Hexagonal Grid Computation of the Derivatives of the Solution to the Heat Equation by Using Fourth-Order Accurate Two-Stage Implicit Methods

2021 ◽  
Vol 5 (4) ◽  
pp. 203
Author(s):  
Suzan Cival Buranay ◽  
Nouman Arshad ◽  
Ahmed Hersi Matan
Keyword(s):  
Heat Equation ◽  
Fourth Order ◽  
Boundary Value ◽  
Time Variable ◽  
Implicit Methods ◽  
First Order ◽  
Mixed Derivatives ◽  
Hexagonal Grids ◽  
Spatial Derivatives ◽  
Derivatives Of

We give fourth-order accurate implicit methods for the computation of the first-order spatial derivatives and second-order mixed derivatives involving the time derivative of the solution of first type boundary value problem of two dimensional heat equation. The methods are constructed based on two stages: At the first stage of the methods, the solution and its derivative with respect to time variable are approximated by using the implicit scheme in Buranay and Arshad in 2020. Therefore, Oh4+τ of convergence on constructed hexagonal grids is obtained that the step sizes in the space variables x1, x2 and in time variable are indicated by h, 32h and τ, respectively. Special difference boundary value problems on hexagonal grids are constructed at the second stages to approximate the first order spatial derivatives and the second order mixed derivatives of the solution. Further, Oh4+τ order of uniform convergence of these schemes are shown for r=ωτh2≥116,ω>0. Additionally, the methods are applied on two sample problems.

scholarly journals Comparison between experiments and direct numerical simulations in a channel flow with roughness on one wall

2008 ◽  
Vol 600 ◽  
pp. 403-426 ◽  
Author(s):  
P. BURATTINI ◽  
S. LEONARDI ◽  
P. ORLANDI ◽  
R. A. ANTONIA
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Friction Velocity ◽  
Streamwise Velocity ◽  
Negative Energy ◽  
Direct Numerical Simulations ◽  
Rough Wall ◽  
Local Isotropy ◽  
Taylor’S Hypothesis ◽  
Yielding Support

The turbulent flow in a two-dimensional channel with roughness on one wall is investigated using experiments and direct numerical simulations (DNS). The elements have a square cross-section with height k=0.1H (H is the channel half-width) and a streamwise spacing of 4k. The Reynolds number Reτr, based on the friction velocity at the rough wall and H, is in the range 300–1100. Particular attention is given to the rough-wall side. Measured turbulence intensities, length scales, leading terms in the turbulent kinetic energy budget, and velocity spectra are compared with those obtained from the DNS. Close agreement is found, yielding support for the simplifying assumptions in the experiment (notably local isotropy and Taylor's hypothesis) and the adequacy of the spatial resolution in the simulation. Overall, the profiles of the Reynolds normal stresses on the roughness side are almost independent of Reτr, when normalized by outer variables. Energy spectra at different locations above the rough wall collapse well at high wavenumbers, when normalized by Kolmogorov scales. In contrast to previous studies, a region of negative energy production near the location of the maximum streamwise velocity is not observed. Comparison with a smooth-wall channel, at similar values of the friction-velocity Reynolds number, highlights differences only in the streamwise velocity component near the wall.

An Experimental Study of Artificially-Generated Turbulent Spots Under Strong Favorable Pressure Gradients and Freestream Turbulence

2006 ◽  
Vol 129 (5) ◽  
pp. 563-572 ◽  
Author(s):  
M. I. Yaras
Keyword(s):  
Velocity Structure ◽  
Three Dimensional ◽  
Internal Flow ◽  
Leading Edge ◽  
Streamwise Velocity ◽  
Test Surface ◽  
Freestream Turbulence ◽  
Turbulent Spot ◽  
Turbulent Spots ◽  
Acceleration Rate

This paper presents experimental results on the internal flow structure of turbulent spots, and examines the sensitivity of this structure to streamwise acceleration rate and freestream turbulence. Measurements were performed on a flat plate, with two levels of freestream acceleration rate and three levels of freestream turbulence. The turbulent spots were generated artificially at a fixed distance from the test-surface leading edge, and the development of the spot was documented through hotwire measurements at three streamwise locations. The measurements were performed at multiple spanwise locations to allow observation of the three-dimensional spatial structure of the turbulent spot and the temporal evolution of this structure. Analysis of the perturbation velocity and rms velocity fluctuations provides insight into the variations of the streaky streamwise-velocity structure within the turbulent spot, with a focus on the effects of freestream acceleration rate and turbulence level.

Measurement of the Instantaneous Velocity Gradients in Plane and Axisymmetric Turbulent Wake Flows

2001 ◽  
Vol 124 (1) ◽  
pp. 143-153 ◽  
Author(s):  
T. Schenck ◽  
J. Jovanovic´
Keyword(s):  
Correction Method ◽  
Flow Speed ◽  
Low Flow ◽  
Sphere Diameter ◽  
Hot Wire ◽  
Local Isotropy ◽  
Plane Wake ◽  
Good Spatial Resolution ◽  
Pressure Transport ◽  
Derivatives Of

All first-order spatial derivatives of the turbulent velocity fluctuations were measured using a pair of X hot-wire probes. Measurements were performed in the self-preserving region of a turbulent plane wake downstream of a cylinder and in an axisymmetric wake behind the sphere. Good spatial resolution of the measurements was ensured by choosing small values for the cylinder/sphere diameter and a low flow speed. Errors due to the finite hot-wire length and the wire and probe separation were analyzed using Wyngaard’s correction method. The derived corrections were verified experimentally. The measuring technique and the experimental results were systematically checked and compared with the results available in the literature. The assumptions of local isotropy and local axisymmetry were examined. Both investigated flows deviate only moderately from local isotropy and local axisymmetry. Support for the measured results is provided by plotting the data on an anisotropy invariant map. The budgets of the turbulent kinetic energy were computed from the measured data. In contrast to the results obtained in the plane wake, where the pressure transport is nearly negligible, in the axisymmetric wake it was found to play an important role and closely follows the estimate made by Lumley, uip¯/ρ≈−0.2q2ui¯.

scholarly journals Reynolds number effect on the velocity derivative flatness factor

2018 ◽  
Vol 856 ◽  
pp. 426-443 ◽  
Author(s):  
M. Meldi ◽  
L. Djenidi ◽  
R. Antonia
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Nauk Sssr ◽  
Quantitative Agreement ◽  
Homogeneous Isotropic Turbulence ◽  
Simulation Data ◽  
Akad Nauk Sssr ◽  
Analytic Expression ◽  
Velocity Derivative ◽  
Flatness Factor

This paper investigates the effect of a finite Reynolds number (FRN) on the flatness factor ($F$) of the velocity derivative in decaying homogeneous isotropic turbulence by applying the eddy damped quasi-normal Markovian (EDQNM) method to calculate all terms in an analytic expression for $F$ (Djenidi et al., Phys. Fluids, vol. 29 (5), 2017b, 051702). These terms and hence $F$ become constant when the Taylor microscale Reynolds number, $Re_{\unicode[STIX]{x1D706}}$ exceeds approximately $10^{4}$. For smaller values of $Re_{\unicode[STIX]{x1D706}}$, $F$, like the skewness $-S$, increases with $Re_{\unicode[STIX]{x1D706}}$; this behaviour is in quantitative agreement with experimental and direct numerical simulation data. These results indicate that one must first ensure that $Re_{\unicode[STIX]{x1D706}}$ is large enough for the FRN effect to be negligibly small before the hypotheses of Kolmogorov (Dokl. Akad. Nauk SSSR, vol. 30, 1941a, pp. 301–305; Dokl. Akad. Nauk SSSR, vol. 32, 1941b, pp. 16–18; J. Fluid Mech., vol. 13, 1962, pp. 82–85) can be assessed unambiguously. An obvious implication is that results from experiments and direct numerical simulations for which $Re_{\unicode[STIX]{x1D706}}$ is well below $10^{4}$ may not be immune from the FRN effect. Another implication is that a power-law increase of $F$ with respect to $Re_{\unicode[STIX]{x1D706}}$, as suggested by the Kolmogorov 1962 theory, is not tenable when $Re_{\unicode[STIX]{x1D706}}$ is large enough.

scholarly journals Derivation of Conservation Laws for the Magma Equation Using the Multiplier Method: Power Law and Exponential Law for Permeability and Viscosity

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
N. Mindu ◽  
D. P. Mason
Keyword(s):  
Conservation Laws ◽  
Power Law ◽  
Travelling Waves ◽  
Travelling Wave ◽  
Multiplier Method ◽  
Reduction Theorem ◽  
Double Reduction ◽  
Exponential Law ◽  
Spatial Derivatives ◽  
Derivatives Of

The derivation of conservation laws for the magma equation using the multiplier method for both the power law and exponential law relating the permeability and matrix viscosity to the voidage is considered. It is found that all known conserved vectors for the magma equation and the new conserved vectors for the exponential laws can be derived using multipliers which depend on the voidage and spatial derivatives of the voidage. It is also found that the conserved vectors are associated with the Lie point symmetry of the magma equation which generates travelling wave solutions which may explain by the double reduction theorem for associated Lie point symmetries why many of the known analytical solutions are travelling waves.

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