scholarly journals A statistical state dynamics-based study of the structure and mechanism of large-scale motions in plane Poiseuille flow

2016 ◽  
Vol 809 ◽  
pp. 290-315 ◽  
Author(s):  
Brian F. Farrell ◽  
Petros J. Ioannou ◽  
Javier Jiménez ◽  
Navid C. Constantinou ◽  
Adrián Lozano-Durán ◽  
...  
Keyword(s):  
Dynamical System ◽  
Poiseuille Flow ◽  
Large Scale ◽  
Dynamic Properties ◽  
Reynolds Numbers ◽  
Wall Turbulence ◽  
Plane Poiseuille Flow ◽  
Statistical State ◽  
The Mean ◽  
High Reynolds

The perspective of statistical state dynamics (SSD) has recently been applied to the study of mechanisms underlying turbulence in a variety of physical systems. An SSD is a dynamical system that evolves a representation of the statistical state of the system. An example of an SSD is the second-order cumulant closure referred to as stochastic structural stability theory (S3T), which has provided insight into the dynamics of wall turbulence, and specifically the emergence and maintenance of the roll/streak structure. S3T comprises a coupled set of equations for the streamwise mean and perturbation covariance, in which nonlinear interactions among the perturbations has been removed, restricting nonlinearity in the dynamics to that of the mean equation and the interaction between the mean and perturbation covariance. In this work, this quasi-linear restriction of the dynamics is used to study the structure and dynamics of turbulence in plane Poiseuille flow at moderately high Reynolds numbers in a closely related dynamical system, referred to as the restricted nonlinear (RNL) system. Simulations using this RNL system reveal that the essential features of wall-turbulence dynamics are retained. Consistent with previous analyses based on the S3T version of SSD, the RNL system spontaneously limits the support of its turbulence to a small set of streamwise Fourier components, giving rise to a naturally minimal representation of its turbulence dynamics. Although greatly simplified, this RNL turbulence exhibits natural-looking structures and statistics, albeit with quantitative differences from those in direct numerical simulations (DNS) of the full equations. Surprisingly, even when further truncation of the perturbation support to a single streamwise component is imposed, the RNL system continues to self-sustain turbulence with qualitatively realistic structure and dynamic properties. RNL turbulence at the Reynolds numbers studied is dominated by the roll/streak structure in the buffer layer and similar very large-scale structure (VLSM) in the outer layer. In this work, diagnostics of the structure, spectrum and energetics of RNL and DNS turbulence are used to demonstrate that the roll/streak dynamics supporting the turbulence in the buffer and logarithmic layer is essentially similar in RNL and DNS.

scholarly journals Natural logarithms

2013 ◽  
Vol 718 ◽  
pp. 1-4 ◽  
Author(s):  
B. J. McKeon
Keyword(s):  
Turbulent Flows ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Wall Turbulence ◽  
Significant Advance ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
Logarithmic Scaling ◽  
The Mean ◽  
High Reynolds

AbstractMarusic et al. (J. Fluid Mech., vol. 716, 2013, R3) show the first clear evidence of universal logarithmic scaling emerging naturally (and simultaneously) in the mean velocity and the intensity of the streamwise velocity fluctuations about that mean in canonical turbulent flows near walls. These observations represent a significant advance in understanding of the behaviour of wall turbulence at high Reynolds number, but perhaps the most exciting implication of the experimental results lies in the agreement with the predictions of such scaling from a model introduced by Townsend (J. Fluid Mech., vol. 11, 1961, pp. 97–120), commonly termed the attached eddy hypothesis. The elegantly simple, yet powerful, study by Marusic et al. should spark further investigation of the behaviour of all fluctuating velocity components at high Reynolds numbers and the outstanding predictions of the attached eddy hypothesis.

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’.

scholarly journals Aerodynamics of smooth and rough square-section prisms at incidence in very high Reynolds-number cross-flows

2021 ◽  
Vol 62 (3) ◽  
Author(s):  
Nils Paul van Hinsberg
Keyword(s):  
Reynolds Number ◽  
Cross Sections ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Surface Boundary ◽  
Experimental Proof ◽  
Surface Boundary Layer ◽  
Pitch Moment ◽  
The Mean ◽  
High Reynolds

Abstract The aerodynamics of smooth and slightly rough prisms with square cross-sections and sharp edges is investigated through wind tunnel experiments. Mean and fluctuating forces, the mean pitch moment, Strouhal numbers, the mean surface pressures and the mean wake profiles in the mid-span cross-section of the prism are recorded simultaneously for Reynolds numbers between 1$$\times$$ × 10$$^{5}$$ 5 $$\le$$ ≤ Re$$_{D}$$ D $$\le$$ ≤ 1$$\times$$ × 10$$^{7}$$ 7 . For the smooth prism with $$k_s$$ k s /D = 4$$\times$$ × 10$$^{-5}$$ - 5 , tests were performed at three angles of incidence, i.e. $$\alpha$$ α = 0$$^{\circ }$$ ∘ , −22.5$$^{\circ }$$ ∘ and −45$$^{\circ }$$ ∘ , whereas only both “symmetric” angles were studied for its slightly rough counterpart with $$k_s$$ k s /D = 1$$\times$$ × 10$$^{-3}$$ - 3 . First-time experimental proof is given that, within the accuracy of the data, no significant variation with Reynolds number occurs for all mean and fluctuating aerodynamic coefficients of smooth square prisms up to Reynolds numbers as high as $$\mathcal {O}$$ O (10$$^{7}$$ 7 ). This Reynolds-number independent behaviour applies to the Strouhal number and the wake profile as well. In contrast to what is known from square prisms with rounded edges and circular cylinders, an increase in surface roughness height by a factor 25 on the current sharp-edged square prism does not lead to any notable effects on the surface boundary layer and thus on the prism’s aerodynamics. For both prisms, distinct changes in the aerostatics between the various angles of incidence are seen to take place though. Graphic abstract

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.

Non-uniqueness in wakes and boundary layers

1984 ◽  
Vol 391 (1800) ◽  
pp. 1-26 ◽  
Keyword(s):  
Boundary Layer ◽  
Large Scale ◽  
Reynolds Numbers ◽  
Near Wake ◽  
Algebraic Decay ◽  
Scale Separation ◽  
Boundary Layer Equations ◽  
Classical Boundary ◽  
Streamlined Flow ◽  
High Reynolds

In streamlined flow past a flat plate aligned with a uniform stream, it is shown that ( a ) the Goldstein near-wake and ( b ) the Blasius boundary layer are non-unique solutions locally for the classical boundary layer equations, whereas ( c ) the Rott-Hakkinen very-near-wake appears to be unique. In each of ( a ) and ( b ) an alternative solution exists, which has reversed flow and which apparently cannot be discounted on immediate grounds. So, depending mainly on how the alternatives for ( a ), ( b ) develop downstream, the symmetric flow at high Reynolds numbers could have two, four or more steady forms. Concerning non-streamlined flow, for example past a bluff obstacle, new similarity forms are described for the pressure-free viscous symmetric closure of a predominantly slender long wake beyond a large-scale separation. Features arising include non-uniqueness, singularities and algebraic behaviour, consistent with non-entraining shear layers with algebraic decay. Non-uniqueness also seems possible in reattachment onto a solid surface and for non-symmetric or pressure-controlled flows including the wake of a symmetric cascade.

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.

Turbulent Annular Pipe Flow in Subcritical Transition Regime: Direct Numerical Simulation of a Large Domain

2015 ◽  
Author(s):  
Takahiro Ishida ◽  
Takahiro Tsukahara
Keyword(s):  
Reynolds Number ◽  
Poiseuille Flow ◽  
Reynolds Numbers ◽  
Radius Ratio ◽  
Transition Regime ◽  
Transitional Regime ◽  
Large Domain ◽  
High Reynolds ◽  
Annular Pipe ◽  
Transition Scenario

We performed direct numerical simulations of annular Poiseuille flow (APF) with a radius ratio of η (= rin/rout) = 0.8, in order to investigate the subcritical transition scenario from the developed turbulent state to the laminar state. In previous studies on annular Poiseuille flow, the flows at high Reynolds numbers were well examined and various turbulence statistics were obtained for several η, because of their dependence on η. Since the transitional APF is still unclear, we investigate annular Poiseuille flows in the transitional regime through the large-domain simulations in a range of the friction Reynolds number from Reτ = 150 down to 56. At a transitional Reynolds number, weak-fluctuation regions occur intermittently and regularly in the flow field, and the localized turbulence appears in the form of banded patterns same as in plane Poiseuille flow (PPF). The flow system of APF with a high radius ratio η ≈ 1 can be regarded as PPF and, hence, the transition regime in high radius-ratio of APF and in PPF should be analogous. However, in APF, the banded structure takes on helical shape around the inner cylinder, since APF is a closed system in the spanwise (azimuthal) direction. In this paper, the (dis-)similarity between APF and PPF is discussed.

LDV and PIV Velocity Results in a Thermosiphon

2003 ◽  
Author(s):  
J. Kulman ◽  
D. Gray ◽  
S. Sivanagere ◽  
S. Guffey
Keyword(s):  
Large Scale ◽  
Single Phase ◽  
Flow Characteristics ◽  
Reynolds Numbers ◽  
Flow Patterns ◽  
Laser Doppler Velocimeter ◽  
Mean Velocity ◽  
Developed Turbulence ◽  
The Mean ◽  
Good Agreement

Heat transfer and flow characteristics have been determined for a single-phase rectangular loop thermosiphon. The plane of the loop was vertical, and tests were performed with in-plane tilt angles ranging from 3.6° CW to 4.2° CCW. Velocity profiles were measured in one vertical leg of the loop using both a single-component Laser Doppler Velocimeter (LDV), and a commercial Particle Image Velocimeter (PIV) system. The LDV data and PIV data were found to be in good agreement. The measured average velocities were approximately 2–2.5 cm/s at an average heating rate of 70 W, and were independent of tilt angle. Significant RMS fluctuations of 10–20% of the mean velocity were observed in the test section, in spite of the laminar or transitional Reynolds numbers (order of 700, based on the hydraulic diameter). These fluctuations have been attributed to vortex shedding from the upstream temperature probes and mitre bends, rather than to fully developed turbulence. Animations of the PIV data clearly show these large scale unsteady flow patterns. Multiple steady state flow patterns were not observed.

Sign in / Sign up

Export Citation Format

Share Document