Turbulent flow between counter-rotating concentric cylinders: a direct numerical simulation study

2008 ◽  
Vol 615 ◽  
pp. 371-399 ◽  
Author(s):  
S. DONG
Keyword(s):  
Turbulent Flow ◽  
Large Scale ◽  
Outer Cylinder ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Taylor Vortex ◽  
Small Scale ◽  
Mean Flow ◽  
Concentric Cylinders ◽  
High Reynolds

We report three-dimensional direct numerical simulations of the turbulent flow between counter-rotating concentric cylinders with a radius ratio 0.5. The inner- and outer-cylinder Reynolds numbers have the same magnitude, which ranges from 500 to 4000 in the simulations. We show that with the increase of Reynolds number, the prevailing structures in the flow are azimuthal vortices with scales much smaller than the cylinder gap. At high Reynolds numbers, while the instantaneous small-scale vortices permeate the entire domain, the large-scale Taylor vortex motions manifested by the time-averaged field do not penetrate a layer of fluid near the outer cylinder. Comparisons between the standard Taylor–Couette system (rotating inner cylinder, fixed outer cylinder) and the counter-rotating system demonstrate the profound effects of the Coriolis force on the mean flow and other statistical quantities. The dynamical and statistical features of the flow have been investigated in detail.

Direct numerical simulation of spiral turbulence

2010 ◽  
Vol 668 ◽  
pp. 150-173 ◽  
Author(s):  
S. DONG ◽  
X. ZHENG
Keyword(s):  
Outer Cylinder ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Direct Numerical Simulations ◽  
Small Scale ◽  
Cylinder Axis ◽  
Mean Velocity ◽  
Plane Normal ◽  
Concentric Cylinders ◽  
The 1960S

In this paper, we present results of three-dimensional direct numerical simulations of the spiral turbulence phenomenon in a range of moderate Reynolds numbers, in which alternating intertwined helical bands of turbulent and laminar fluids co-exist and propagate between two counter-rotating concentric cylinders. We show that the turbulent spiral is comprised of numerous small-scale azimuthally elongated vortices, which align into and collectively form the barber-pole-like pattern. The domain occupied by such vortices in a plane normal to the cylinder axis resembles a ‘crescent moon’, a shape made well known by Van Atta with his experiments in the 1960s. The time-averaged mean velocity of spiral turbulence is characterized in the radial–axial plane by two layers of axial flows of opposite directions. We also observe that, as the Reynolds number increases, the transition from spiral turbulence to featureless turbulence does not occur simultaneously in the whole domain, but progresses in succession from the inner cylinder towards the outer cylinder. Certain aspects pertaining to the dynamics and statistics of spiral turbulence and issues pertaining to the simulation are discussed.

Coherent structures in coflowing jets and wakes

1978 ◽  
Vol 88 (3) ◽  
pp. 451-463 ◽  
Author(s):  
A. E. Perry ◽  
T. T. Lim
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
Glass Tube ◽  
Reynolds Numbers ◽  
Reynolds Number Flow ◽  
Naturally Occurring ◽  
Number Flow ◽  
High Reynolds ◽  
Scale Motion

By applying small lateral oscillations to a glass tube from which smoke was issuing, perfectly periodic coflowing jets and wake structures were produced at Reynolds numbers of order 300-1000. These structures remained coherent over long streamwise distances and appeared to be perfectly frozen when viewed under stroboscopic light which was synchronized with the disturbing oscillation. By the use of strobing laser beams, longitudinal sections of the structures were photographed and an account of the geometry of these structures is reported.When the tube was unforced, similar structures occurred but they modulated in scale and frequency, and their orientation was random.A classification of structures is presented and examples are demonstrated in naturally occurring situations such as smoke from a cigarette, the wake behind a three-dimensional blunt body, and the high Reynolds number flow in a plume from a chimney. It is suggested that an examination of these structures may give some insight into the large-scale motion in fully turbulent flow.

Three-dimensional conditional structure of a high-Reynolds-number turbulent boundary layer

2011 ◽  
Vol 673 ◽  
pp. 255-285 ◽  
Author(s):  
N. HUTCHINS ◽  
J. P. MONTY ◽  
B. GANAPATHISUBRAMANI ◽  
H. C. H. NG ◽  
I. MARUSIC
Keyword(s):  
Skin Friction ◽  
High Reynolds Number ◽  
Large Scale ◽  
Three Dimensional ◽  
Streamwise Velocity ◽  
Small Scale ◽  
Large Scale Structures ◽  
Local Mean ◽  
Scale Structures ◽  
High Reynolds

An array of surface hot-film shear-stress sensors together with a traversing hot-wire probe is used to identify the conditional structure associated with a large-scale skin-friction event in a high-Reynolds-number turbulent boundary layer. It is found that the large-scale skin-friction events convect at a velocity that is much faster than the local mean in the near-wall region (the convection velocity for large-scale skin-friction fluctuations is found to be close to the local mean at the midpoint of the logarithmic region). Instantaneous shear-stress data indicate the presence of large-scale structures at the wall that are comparable in scale and arrangement to the superstructure events that have been previously observed to populate the logarithmic regions of turbulent boundary layers. Conditional averages of streamwise velocity computed based on a low skin-friction footprint at the wall offer a wider three-dimensional view of the average superstructure event. These events consist of highly elongated forward-leaning low-speed structures, flanked on either side by high-speed events of similar general form. An analysis of small-scale energy associated with these large-scale events reveals that the small-scale velocity fluctuations are attenuated near the wall and upstream of a low skin-friction event, while downstream and above the low skin-friction event, the fluctuations are significantly amplified. In general, it is observed that the attenuation and amplification of the small-scale energy seems to approximately align with large-scale regions of streamwise acceleration and deceleration, respectively. Further conditional averaging based on streamwise skin-friction gradients confirms this observation. A conditioning scheme to detect the presence of meandering large-scale structures is also proposed. The large-scale meandering events are shown to be a possible source of the strong streamwise velocity gradients, and as such play a significant role in modulating the small-scale motions.

scholarly journals Reynolds number trend of hierarchies and scale interactions in turbulent boundary layers

2017 ◽  
Vol 375 (2089) ◽  
pp. 20160077 ◽  
Author(s):  
W. J. Baars ◽  
N. Hutchins ◽  
I. Marusic
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Reynolds Numbers ◽  
Shear Layers ◽  
Wall Turbulence ◽  
Small Scale ◽  
Velocity Fluctuations ◽  
Scale Interaction ◽  
High Reynolds ◽  
Near Wall

Small-scale velocity fluctuations in turbulent boundary layers are often coupled with the larger-scale motions. Studying the nature and extent of this scale interaction allows for a statistically representative description of the small scales over a time scale of the larger, coherent scales. In this study, we consider temporal data from hot-wire anemometry at Reynolds numbers ranging from Re τ ≈2800 to 22 800, in order to reveal how the scale interaction varies with Reynolds number. Large-scale conditional views of the representative amplitude and frequency of the small-scale turbulence, relative to the large-scale features, complement the existing consensus on large-scale modulation of the small-scale dynamics in the near-wall region. Modulation is a type of scale interaction, where the amplitude of the small-scale fluctuations is continuously proportional to the near-wall footprint of the large-scale velocity fluctuations. Aside from this amplitude modulation phenomenon, we reveal the influence of the large-scale motions on the characteristic frequency of the small scales, known as frequency modulation. From the wall-normal trends in the conditional averages of the small-scale properties, it is revealed how the near-wall modulation transitions to an intermittent-type scale arrangement in the log-region. On average, the amplitude of the small-scale velocity fluctuations only deviates from its mean value in a confined temporal domain, the duration of which is fixed in terms of the local Taylor time scale. These concentrated temporal regions are centred on the internal shear layers of the large-scale uniform momentum zones, which exhibit regions of positive and negative streamwise velocity fluctuations. With an increasing scale separation at high Reynolds numbers, this interaction pattern encompasses the features found in studies on internal shear layers and concentrated vorticity fluctuations in high-Reynolds-number wall turbulence. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

Flow Regime Characteristics in Porous Media Flows at High Reynolds Numbers

2012 ◽  
Author(s):  
Vishal A. Patil ◽  
James A. Liburdy
Keyword(s):  
Turbulent Flow ◽  
Flow Characteristics ◽  
Reynolds Numbers ◽  
Small Scale ◽  
Mean Velocity ◽  
Time Resolved ◽  
Vortical Structures ◽  
Large Eddy ◽  
High Reynolds ◽  
Media Flows

An experimental study on the turbulent flow characteristics in a randomly packed porous bed is presented and discussed. Time resolved PIV measurements, taken in specific pore spaces are used to evaluate transitional and developed turbulent flow statistics for pore Reynolds numbers from 54 to 3964. Three different regimes of steady laminar, transitional and turbulent flow are presented. Small scale coherent vortical structures are examined, using large eddy scale (LES) decomposition, for pore Reynolds number of greater than 1000. Integral length scales were found to reach asymptotic values of approximately 0.1 times the hydraulic diameter of the bed. The integral Eulerian time scales are found to reach an asymptotic value of approximately 0.3 times the convective time scale in the bed. Mean velocity vector maps show flattening of the velocity distribution due to increased momentum mixing. Turbulent stresses show increasing level of homogeneity at higher pore Reynolds numbers.

scholarly journals The origin of turbulence in wall-bounded flows

2017 ◽  
Vol 21 (suppl. 3) ◽  
pp. 565-572 ◽  
Author(s):  
Jovan Jovanovic ◽  
Mina Nishi
Keyword(s):  
Three Dimensional ◽  
Reynolds Numbers ◽  
Small Scale ◽  
Deterministic Theory ◽  
Sequence Of Events ◽  
Flow Configurations ◽  
High Reynolds ◽  
Special Circumstances ◽  
Anisotropy Decays ◽  
Universal Mechanism

The motion of liquids and gases can be either laminar, flowing slowly in orderly parallel and continuous layers of fluid that cannot mix, or turbulent in which motion exhibits disorder in time and space with the ability to promote mixing. Breakdown of ordered to disordered motion can follow different scenarios so that no universal mechanism can be identified even in similar flow configurations [1]. Only under very special circumstances can the mechanism associated with the appearance of turbulence be studied within the deterministic theory of hydrodynamic stability [2] or employing direct numerical simulations [3] which themselves cannot provide the necessary understanding [4]. Here we show that the representative mechanism responsible for the origin of turbulence in wallbounded flows is associated with large variations of anisotropy in the disturbances [5]. During the breakdown process, anisotropy decays from a maximum towards its minimum value, inducing the explosive production of the dissipation which logically leads to the appearance of small-scale three-dimensional motions. By projecting the sequence of events leading to turbulence in the space which emphasizes the anisotropic nature in the disturbances [6], we explain why, demonstrate how and present what can be achieved if the process is treated analytically using statistical techniques [7]. It is shown that the statistical approach provides not only predictions of the breakdown phenomena which are in fair agreement with available data but also requirements which ensure persistence of the laminar regime up to very high Reynolds numbers.

Amplitude modulation of all three velocity components in turbulent boundary layers

2014 ◽  
Vol 746 ◽  
Author(s):  
K. M. Talluru ◽  
R. Baidya ◽  
N. Hutchins ◽  
I. Marusic
Keyword(s):  
Amplitude Modulation ◽  
Large Scale ◽  
Reynolds Shear Stress ◽  
Three Dimensional ◽  
Small Scale ◽  
Large Scale Structures ◽  
Scale Structures ◽  
Normal Fluctuations ◽  
High Reynolds ◽  
Cross Wire

AbstractA combination of cross-wire probes with an array of flush-mounted skin-friction sensors are used to study the three-dimensional conditional organisation of large-scale structures in a high-Reynolds-number turbulent boundary layer. Previous studies have documented the amplitude modulation of small-scale motions in response to conditionally averaged large-scale events, but the data are largely restricted to the streamwise component of velocity alone. Here, we report results based on all three components of velocity and find that the small-scale spanwise and wall-normal fluctuations ($v$ and $w$) and the instantaneous Reynolds shear stress ($-{uw}$) are modulated in a very similar manner to that previously noted for the streamwise fluctuations ($u$). The envelope of the small scale fluctuations for all velocity components is well described by the large-scale component of the $u$ fluctuation. These results also confirm the conditional existence of roll modes associated with the very large-scale or ‘superstructure’ motions.

An Experimental Characterization of the Flow Past an Airfoil in the Wake of a Circular Rod

2002 ◽  
Author(s):  
M. Michard ◽  
M. C. Jacob ◽  
N. Grosjean
Keyword(s):  
Source Region ◽  
Three Dimensional ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Small Scale ◽  
Vortex Identification ◽  
Turbulence Structures ◽  
Flow Past ◽  
Scale Turbulence ◽  
High Reynolds

An experimental study of the flow past an airfoil in the wake of a rod shows that, at high Reynolds numbers, the vortices shed by the rod are strongly stretched and split near the leading edge and affected by small scale turbulence structures. These are shown to enhance three-dimensional effects, and to broaden the spectrum around the shedding frequency. The airfoil leading edge is the dominant acoustic source region. Post-processing tools combining Proper Orthogonal Decomposition and new vortex identification algorithms are applied to PIV measurements in order to extract the main vortical structures from snapshots, and study their variability.

scholarly journals On the finite Dean problem: linear theory

1988 ◽  
Vol 30 (2) ◽  
pp. 157-178
Author(s):  
B. J. Kachoyan ◽  
P. J. Blennerhassett
Keyword(s):  
Outer Cylinder ◽  
Taylor Number ◽  
Taylor Vortex ◽  
Mean Flow ◽  
Dean Flow ◽  
Taylor Vortices ◽  
Taylor Vortex Flow ◽  
Concentric Cylinders ◽  
End Conditions ◽  
Pressure Driven Flow

AbstractThe Dean problem of pressure-driven flow between finite-length concentric cylinders is considered. The outer cylinder is at rest and the small-gap approximation is used. In a similar procedure to that of Blennerhassett and Hall [8] in the context of Taylor vortices, special end conditions are imposed in which the ends of the cylinder move with the mean flow, allowing the use of a perturbation analysis from a known basic flow. Difficulties specific to Dean flow (and more generally to non-Taylor-vortex flow) require the use of a parameter α which measures the relative strengths of the velocities due to rotation and the pressure gradient, to trace the solution from Taylor to Dean flow. Asymptotic expansions are derived for axial wavenumbers at a given Taylor number. The calculation of critical Taylor number for a given cylinder height is then carried out. Corresponding stream-function contours clearly show features not evident in infinite flow.

Turbulent flow of a fluid with anisotropic viscosity

2016 ◽  
Vol 792 ◽  
pp. 252-273 ◽  
Author(s):  
Tim Grünberg ◽  
Thomas Rösgen
Keyword(s):  
Turbulent Flow ◽  
Large Scale ◽  
Tracer Particle ◽  
Mean Flow ◽  
Flow Topology ◽  
Velocity Statistics ◽  
The Mean ◽  
High Reynolds ◽  
Ultrasound Velocimetry ◽  
Anisotropic Viscosity

We ask if and how the large-scale structure of a turbulent flow depends on anisotropies introduced at the smallest scales. We generate such anisotropy on the viscous scale in a paramagnetic colloid whose rheology is modified by an external, uniform magnetic field. We report measurements in a high Reynolds number turbulence experiment ($R_{{\it\lambda}}=120$). Ultrasound velocimetry provides records of tracer particle velocity. Distinct changes in the velocity statistics can be observed from the dissipative scales up to the mean flow topology.

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