scholarly journals Statistics of turbulence in the energy-containing range of Taylor–Couette compared to canonical wall-bounded flows

2017 ◽  
Vol 830 ◽  
pp. 797-819 ◽  
Author(s):  
Dominik Krug ◽  
Xiang I. A. Yang ◽  
Charitha M. de Silva ◽  
Rodolfo Ostilla-Mónico ◽  
Roberto Verzicco ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Velocity Component ◽  
Large Scale ◽  
Streamwise Velocity ◽  
Structure Functions ◽  
Self Similarity ◽  
Moderate Reynolds Number ◽  
Taylor Couette ◽  
Wall Bounded Flows ◽  
Universal Behaviour

Considering structure functions of the streamwise velocity component in a framework akin to the extended self-similarity hypothesis (ESS), de Silva et al. (J. Fluid Mech., vol. 823, 2017, pp. 498–510) observed that remarkably the large-scale (energy-containing range) statistics in canonical wall-bounded flows exhibit universal behaviour. In the present study, we extend this universality, which was seen to encompass also flows at moderate Reynolds number, to Taylor–Couette flow. In doing so, we find that also the transversal structure function of the spanwise velocity component exhibits the same universal behaviour across all flow types considered. We further demonstrate that these observations are consistent with predictions developed based on an attached-eddy hypothesis. These considerations also yield a possible explanation for the efficacy of the ESS framework by showing that it relaxes the self-similarity assumption for the attached-eddy contributions. By taking the effect of streamwise alignment into account, the attached-eddy model predicts different behaviour for structure functions in the streamwise and in the spanwise directions and that this effect cancels in the ESS framework – both consistent with the data. Moreover, it is demonstrated here that also the additive constants, which were previously believed to be flow dependent, are indeed universal at least in turbulent boundary layers and pipe flow where high Reynolds number data are currently available.

Experiments on the flow and acoustic properties of a moderate-Reynolds-number supersonic jet

1982 ◽  
Vol 116 ◽  
pp. 123-156 ◽  
Author(s):  
T. R. Troutt ◽  
D. K. Mclaughlin
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Near Field ◽  
Acoustic Properties ◽  
Generation Model ◽  
Initial Growth ◽  
Noise Generation ◽  
Mean Flow ◽  
Potential Core ◽  
Moderate Reynolds Number

An experimental investigation of the flow and acoustic properties of a moderate-Reynolds-number (Re = 70000), Mach number M = 2·1, axisymmetric jet has been performed. These measurements extended the experimental studies conducted previously in this laboratory to a higher-Reynolds-number regime where the flow and acoustic processes are considerably more complex. In fact, mean-flow and acoustic properties of this jet were determined to be closely comparable to published properties of high-Reynolds-number jets.The major results of the flow-field measurements demonstrate that the jet shear annulus is unstable over a broad frequency range. The initial growth rates and wavelengths of these instabilities as measured by a hot wire were found to be in reasonable agreement with linear stability theory predictions. Also, in agreement with subsonic-jet results, the potential core of the jet was found to be most responsive to excitation at frequencies near a Strouhal number of S = 0·3. The overall development of organized disturbances around S = 0·2 seems to agree in general with calculations performed using the instability theory originally developed by Morris and Tam.The acoustic near field was characterized in terms of sound-pressure level and directivity for both natural and excited (pure-tone) jets. In addition, propagation direction and azimuthal character of dominant spectral components were also measured. It was determined that the large-scale flow disturbances radiate noise in a directional pattern centred about 30° from the jet axis. The noise from these disturbances appears from simple ray tracing to be generated primarily near the region of the jet where the coherent fluctuations saturate in amplitude and begin to decay. It was also determined that the large-scale components of the near-field sound are made up predominately of axisymmetric (n = 0) and helical (n = ±1) modes. The dominant noise-generation mechanism appears to be a combination of Mach-wave generation and a process associated with the saturation and disintegration of the large-scale instability. Finally, the further development of a noise-generation model of the instability type appears to hold considerable promise.

A resonance mechanism in plane Couette flow

1980 ◽  
Vol 98 (1) ◽  
pp. 149-159 ◽  
Author(s):  
L. HÅKan Gustavsson ◽  
Lennart S. Hultgren
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
Velocity Component ◽  
Three Dimensional ◽  
Phase Speed ◽  
Maximum Amplitude ◽  
Streamwise Velocity ◽  
Plane Couette Flow ◽  
Mean Velocity ◽  
Streamwise Velocity Component

The temporal evolution of small three-dimensional disturbances on viscous flows between parallel walls is studied. The initial-value problem is formally solved by using Fourier–Laplace transform techniques. The streamwise velocity component is obtained as the solution of a forced problem. As a consequence of the three-dimensionality, a resonant response is possible, leading to algebraic growth for small times. It occurs when the eigenvalues of the Orr–Sommerfeld equation coincide with the eigenvalues of the homogeneous operator for the streamwise velocity component. The resonance has been investigated numerically for plane Couette flow. The phase speed of the resonant waves equals the average mean velocity. The wavenumber combination that leads to the largest amplitude corresponds to structures highly elongated in the streamwise direction. The maximum amplitude, and the time to reach this maximum, scale with the Reynolds number. The aspect ratio of the most rapidly growing wave increases with the Reynolds number, with its spanwise wavelength approaching a constant value of about 3 channel heights.

Wall shear stress and velocity in a turbulent axisymmetric boundary layer

1994 ◽  
Vol 259 ◽  
pp. 191-218 ◽  
Author(s):  
Anthony Wietrzak ◽  
Richard M. Lueptow
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Large Scale ◽  
Low Frequency ◽  
Streamwise Velocity ◽  
Outer Flow ◽  
Planar Wall ◽  
Wall Bounded Flows ◽  
Wall Shear

Instantaneous streamwise fluctuations of the wall shear stress have been measured using a hot-element probe in a thick axisymmetric turbulent boundary layer on a cylinder aligned parallel to the flow. The measurements were made at a momentum-thickness Reynolds number Rθ = 3050 and a ratio of boundary-layer thickness to cylinder radius of δ/a = 5.7. The ratio of the r.m.s. of the fluctuation to the mean value of the wall shear stress, $\tau_{rms}/\bar{\tau}$, is about 0.32, a value slightly lower than that for recent measurements for flow over a flat plate. The probability density function of the wall shear stress is similar to that for planar wall-bounded flows within experimental error. The power spectral density of the wall shear stress shows that a cylindrical boundary layer contains less energy at lower frequencies and more energy at higher frequencies than other wall-bounded flows. Analysis of simultaneous measurement of the streamwise wall shear stress and the streamwise velocity using VITA and peak detection suggests that transverse curvature has little effect on the near-wall burst–sweep cycle compared to planar wall-bounded flows. The angle of inclination of the structures is similar to that measured for large-scale structures in planar wall-bounded flows. However, measurements of the cross-correlation between the shear stress and the velocity suggest the existence of smaller structures yawed to the axis of the cylinder. The coherence between shear stress and velocity shows a low frequency associated with the inclined structures and a higher frequency associated with the yawed structures. The yawed structures could have an arrowhead or half-arrowhead shape and may be associated with fluid from the outer flow washing over the cylinder.

scholarly journals Turbulent fluctuations above the buffer layer of wall-bounded flows

2008 ◽  
Vol 611 ◽  
pp. 215-236 ◽  
Author(s):  
JAVIER JIMÉNEZ ◽  
SERGIO HOYAS
Keyword(s):  
Reynolds Number ◽  
Buffer Layer ◽  
Turbulent Flows ◽  
Large Scale ◽  
Pressure Fluctuations ◽  
Strong Support ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Normal Velocity ◽  
Channel Statistics

The behaviour of the velocity and pressure fluctuations in the logarithmic and outer layers of turbulent flows is analysed using spectral information and probability density functions from channel simulations at Reτ≤2000. Comparisons are made with experimental data at higher Reynolds numbers. It is found, in agreement with previous investigations, that the intensity profiles of the streamwise and spanwise velocity components have logarithmic ranges that are traced to the widening spectral range of scales as the wall is approached. The same is true for the pressure, both theoretically and observationally, but not for the normal velocity or for the tangential stress cospectrum, although even those two quantities have structures with lengths of the order of several hundred times the wall distance. Because the logarithmic range grows longer as the Reynolds number increases, variables which are ‘attached’ in this sense scale in the buffer layer in mixed units. These results give strong support to the attached-eddy scenario proposed by Townsend (1976), but they are not linked to any particular eddy model. The scaling of the outer modes is also examined. The intensity of the streamwise velocity at fixed y/h increases with the Reynolds number. This is traced to the large-scale modes, and to an increased intensity of the ejections but not of the sweeps. Several differences are found between the outer structures of different flows. The outer modes of the spanwise and wall-normal velocities in boundary layers are stronger than in internal flows, and their streamwise velocities penetrate closer to the wall. As a consequence, their logarithmic layers are thinner, and some of their logarithmic slopes are different. The channel statistics are available electronically at http://torroja.dmt.upm.es/ftp/channels/.

Partially filled pipes: experiments in laminar and turbulent flow

2018 ◽  
Vol 848 ◽  
pp. 467-507 ◽  
Author(s):  
Henry C.-H. Ng ◽  
Hope L. F. Cregan ◽  
Jonathan M. Dodds ◽  
Robert J. Poole ◽  
David J. C. Dennis
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Turbulent Flow ◽  
Pipe Flow ◽  
Large Scale ◽  
Open Channel ◽  
Streamwise Velocity ◽  
Flow Depth ◽  
Secondary Motion ◽  
Laminar And Turbulent Flow

Pressure-driven laminar and turbulent flow in a horizontal partially filled pipe was investigated using stereoscopic particle imaging velocimetry (S-PIV) in the cross-stream plane. Laminar flow velocity measurements are in excellent agreement with a recent theoretical solution in the literature. For turbulent flow, the flow depth was varied independently of a nominally constant Reynolds number (based on hydraulic diameter, $D_{H}$; bulk velocity, $U_{b}$ and kinematic viscosity $\unicode[STIX]{x1D708}$) of $Re_{H}=U_{b}D_{H}/\unicode[STIX]{x1D708}\approx 30\,000\pm 5\,\%$. When running partially full, the inferred friction factor is no longer a simple function of Reynolds number, but also depends on the Froude number $Fr=U_{b}/\sqrt{gD_{m}}$ where $g$ is gravitational acceleration and $D_{m}$ is hydraulic mean depth. S-PIV measurements in turbulent flow reveal the presence of secondary currents which causes the maximum streamwise velocity to occur below the free surface consistent with results reported in the literature for rectangular cross-section open channel flows. Unlike square duct and rectangular open channel flow the mean secondary motion observed here manifests only as a single pair of vortices mirrored about the vertical bisector and these rollers, which fill the half-width of the pipe, remain at a constant distance from the free surface even with decreasing flow depth for the range of depths tested. Spatial distributions of streamwise Reynolds normal stress and turbulent kinetic energy exhibit preferential arrangement rather than having the same profile around the azimuth of the pipe as in a full pipe flow. Instantaneous fields reveal the signatures of elements of canonical wall-bounded turbulent flows near the pipe wall such as large-scale and very-large-scale motions and associated hairpin packets whilst near the free surface, the signatures of free surface turbulence in the absence of imposed mean shear such as ‘upwellings’, ‘downdrafts’ and ‘whirlpools’ are present. Two-point spatio-temporal correlations of streamwise velocity fluctuation suggest that the large-scale coherent motions present in full pipe flow persist in partially filled pipes but are compressed and distorted by the presence of the free surface and mean secondary motion.

scholarly journals Self-similarity of time-evolving plane wakes

1998 ◽  
Vol 367 ◽  
pp. 255-289 ◽  
Author(s):  
ROBERT D. MOSER ◽  
MICHAEL M. ROGERS ◽  
DANIEL W. EWING
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Initial Conditions ◽  
Spreading Rate ◽  
Momentum Thickness ◽  
Two Dimensional ◽  
Self Similarity ◽  
Order Of Magnitude ◽  
The Difference ◽  
Velocity Spectra

Direct numerical simulations of three time-developing turbulent plane wakes have been performed. Initial conditions for the simulations were obtained using two realizations of a direct simulation from a turbulent boundary layer at momentum-thickness Reynolds number 670. In addition, extra two-dimensional disturbances were added in two of the cases to mimic two-dimensional forcing. The wakes are allowed to evolve long enough to attain approximate self-similarity, although in the strongly forced case this self-similarity is of short duration. For all three flows, the mass-flux Reynolds number (equivalent to the momentum-thickness Reynolds number in spatially developing wakes) is 2000, which is high enough for a short k−5/3 range to be evident in the streamwise one-dimensional velocity spectra.The spreading rate, turbulence Reynolds number, and turbulence intensities all increase with forcing (by nearly an order of magnitude for the strongly forced case), with experimental data falling between the unforced and weakly forced cases. The simulation results are used in conjunction with a self-similar analysis of the Reynolds stress equations to develop scalings that approximately collapse the profiles from different wakes. Factors containing the wake spreading rate are required to bring profiles from different wakes into agreement. Part of the difference between the various cases is due to the increased level of spanwise-coherent (roughly two-dimensional) energy in the forced cases. Forcing also has a significant impact on flow structure, with the forced flows exhibiting more organized large-scale structures similar to those observed in transitional wakes.

Flow Structure Above Stationary and Oscillating Low-Aspect-Ratio Wing

2012 ◽  
Author(s):  
Miguel R. Visbal ◽  
Daniel J. Garmann
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Flow Structure ◽  
Large Scale ◽  
Lift Coefficient ◽  
Pressure Fluctuations ◽  
Leading Edge ◽  
Tip Vortex ◽  
Eddy Simulation ◽  
Moderate Reynolds Number

Computations have been carried out in order to describe the complex unsteady flow structure over a stationary and plunging aspect-ratio-two wing under low Reynolds number conditions (Rec = 104). The flow fields are computed employing a high-fidelity implicit large-eddy simulation (ILES) approach found to be effective for moderate Reynolds number flows exhibiting mixed laminar, transitional and turbulent regions. The evolution of the flow structure and aerodynamic loading as a function of increasing angle of attack is presented. Lift and pressure fluctuations are found to be primarily dominated by the large scale circulatory pattern established above the wing due to separation from the leading edge, and by the inherent three dimensionality of the flow induced by the finite aspect ratio. The spanwise distribution of the sectional lift coefficient revealed only a minor direct contribution to the loading exherted by the tip vortex. High-frequency, small-amplitude oscillations are shown to have a significant effect on the separation process and accompanying loads suggesting potential flow control through either suitable actuation or aero-elastic tailoring.

Numerical Analysis of Sub-Millimeter-Scale Microturbomachinery Aerothermodynamics

2008 ◽  
Author(s):  
Philippe B. Martel ◽  
Luc G. Fre´chette
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Microelectromechanical Systems ◽  
Numerical Study ◽  
Reynolds Numbers ◽  
Viscous Effects ◽  
Analysis And Design ◽  
Moderate Reynolds Number ◽  
Throat Width ◽  
Solid Foundation

This paper presents a complete numerical study of the aerothermodynamics of subsonic moderate Reynolds number microturbomachinery using 2D computational fluid dynamics (CFD) on 24 cascade geometries and covering over 2000 conditions. Profile and mixing losses, as well as deviation and heat transfer correlations are developed for use in mean-line analysis and design. Both losses and thermal transfer tend to increase with decreasing Reynolds number, Mach number, and throat width. Deviation follows large scale turbomachinery behavior but tends to increase with viscous effects. A slender cascade geometry using a modified profile is suggested, potentially increasing isentropic efficiency by as much as 15%. This work defines a solid foundation for the design of microturbines used in power microelectromechanical systems (MEMS), such as gas and steam microturbines with sub-millimeter-scale blade chords operating at moderate Reynolds numbers (100 < Rec < 2000).

Large scales in the developing mixing layer

1976 ◽  
Vol 76 (1) ◽  
pp. 127-144 ◽  
Author(s):  
F. K. Browand ◽  
P. D. Weidman
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Vortical Structure ◽  
Mixing Layer ◽  
Two Dimensional ◽  
Conditional Sampling ◽  
Pairing Interaction ◽  
Vortical Structures ◽  
Developing Flow ◽  
Moderate Reynolds Number

A new experimental technique is described for the study of the interactions between the large-scale vortical features in the two-dimensional mixing layer. Detector probes above and below the mixing layer are used to monitor the large-scale structure. Conditional sampling is performed in a moderate Reynolds number developing flow, by using phase and amplitude information from these detector probes. It is shown that significant Reynolds-stress production is associated with the pairing interaction in which two vortical structures combine to form a single, larger vortical structure.

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