scholarly journals Towards Reconstruction of Complex Flow Fields Using Unit Flows

Fluids ◽  
2021 ◽  
Vol 6 (7) ◽  
pp. 255
Author(s):  
Paul J. Kristo ◽  
Mark L. Kimber ◽  
Sharath S. Girimaji
Keyword(s):  
Kinetic Energy ◽  
Turbulent Flows ◽  
Coherent Structures ◽  
Large Scale ◽  
Energy Content ◽  
Temporal Frequency ◽  
Flow Structures ◽  
Complex Flow ◽  
Complex Flows ◽  
Single Jet

Many complex turbulent flows in nature and engineering can be qualitatively regarded as being constituted of multiple simpler unit flows. The objective of this work is to characterize the coherent structures in such complex flows as a combination of constituent unitary flow structures for the purpose of reduced-order representation. While turbulence is clearly a non-linear phenomenon, we aim to establish the degree to which the optimally weighted superposition of unitary flow structures can represent the complex flow structures. The rationale for investigating such superposition stems from the fact that the large-scale coherent structures are generated by underlying flow instabilities that may be reasonably described using linear analysis. Clearly, the degree of validity of superposition will depend on the flow under consideration. In this work, we take the first step toward establishing a procedure for investigating superposition. Experimental data of single and triple tandem jets in crossflow are used to demonstrate the procedure. A composite triple tandem jet flow field is generated from optimal superposition of single jet data and compared against ‘true’ triple jet data. Direct comparisons between the true and composite fields are made for spatial, temporal, and kinetic energy content. The large-scale features (obtained from proper orthogonal decomposition or POD) of true and composite tandem jet wakes exhibit nearly 70% agreement in terms of modal eigenvector correlation. Corresponding eigenvalues reveal that the kinetic energy of the flow is also emulated with only a slight overprediction. Temporal frequency features are also examined in an effort to completely characterize POD modes. The proposed method serves as a foundation for more rigorous and robust dimensional reduction in complex flows based on unit flow modes.

Characterization of Geometrical and Temporal Properties of Large-scale Motions in Turbulent Flows

2021 ◽  
Author(s):  
Christina Tsai ◽  
Kuang-Ting Wu
Keyword(s):  
Turbulent Flow ◽  
Turbulent Flows ◽  
Coherent Structures ◽  
Large Scale ◽  
Streamwise Velocity ◽  
Turbulent Structures ◽  
Temporal Properties ◽  
Turbulent Statistics ◽  
Spatial Locations

<p>It is demonstrated that turbulent boundary layers are populated by a hierarchy of recurrent structures, normally referred to as the coherent structures. Thus, it is desirable to gain a better understanding of the spatial-temporal characteristics of coherent structures and their impact on fluid particles. Furthermore, the ejection and sweep events play an important role in turbulent statistics. Therefore, this study focuses on the characterizations of flow particles under the influence of the above-mentioned two structures.</p><div><span>With regard to the geometry of turbulent structures, </span><span>Meinhart & Adrian (1995) </span>first highlighted the existence of large and irregularly shaped regions of uniform streamwise momentum zone (hereafter referred to as a uniform momentum zone, or UMZs), regions of relatively similar streamwise velocity with coherence in the streamwise and wall-normal directions.  <span>Subsequently, </span><span>de Silva et al. (2017) </span><span>provided a detection criterion that had previously been utilized to locate the uniform momentum zones (UMZ) and demonstrated the application of this criterion to estimate the spatial locations of the edges that demarcates UMZs.</span></div><div> </div><div>In this study, detection of the existence of UMZs is a pre-process of identifying the coherent structures. After the edges of UMZs are determined, the identification procedure of ejection and sweep events from turbulent flow DNS data should be defined. As such, an integrated criterion of distinguishing ejection and sweep events is proposed. Based on the integrated criterion, the statistical characterizations of coherent structures from available turbulent flow data such as event durations, event maximum heights, and wall-normal and streamwise lengths can be presented.</div>

Turbulent kinetic energy production and flow structures in flows past smooth and rough walls

2019 ◽  
Vol 866 ◽  
pp. 897-928 ◽  
Author(s):  
P. Orlandi
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulent Flows ◽  
Energy Production ◽  
Compressive Strain ◽  
Turnover Time ◽  
Flow Structures ◽  
Wall Region ◽  
Rate Of Dissipation

Data available in the literature from direct numerical simulations of two-dimensional turbulent channels by Lee & Moser (J. Fluid Mech., vol. 774, 2015, pp. 395–415), Bernardini et al. (J. Fluid Mech., 742, 2014, pp. 171–191), Yamamoto & Tsuji (Phys. Rev. Fluids, vol. 3, 2018, 012062) and Orlandi et al. (J. Fluid Mech., 770, 2015, pp. 424–441) in a large range of Reynolds number have been used to find that $S^{\ast }$ the ratio between the eddy turnover time ($q^{2}/\unicode[STIX]{x1D716}$, with $q^{2}$ being twice the turbulent kinetic energy and $\unicode[STIX]{x1D716}$ the isotropic rate of dissipation) and the time scale of the mean deformation ($1/S$), scales very well with the Reynolds number in the wall region. The good scaling is due to the eddy turnover time, although the turbulent kinetic energy and the rate of isotropic dissipation show a Reynolds dependence near the wall; $S^{\ast }$, as well as $-\langle Q\rangle =\langle s_{ij}s_{ji}\rangle -\langle \unicode[STIX]{x1D714}_{i}\unicode[STIX]{x1D714}_{i}/2\rangle$ are linked to the flow structures, and also the latter quantity presents a good scaling near the wall. It has been found that the maximum of turbulent kinetic energy production $P_{k}$ occurs in the layer with $-\langle Q\rangle \approx 0$, that is, where the unstable sheet-like structures roll-up to become rods. The decomposition of $P_{k}$ in the contribution of elongational and compressive strain demonstrates that the two contributions present a good scaling. However, the good scaling holds when the wall and the outer structures are separated. The same statistics have been evaluated by direct simulations of turbulent flows in the presence of different types of corrugations on both walls. The flow physics in the layer near the plane of the crests is strongly linked to the shape of the surface and it has been demonstrated that the $u_{2}$ (normal to the wall) fluctuations are responsible for the modification of the flow structures, for the increase of the resistance and of the turbulent kinetic energy production.

scholarly journals Flowtrace: simple visualization of coherent structures in biological fluid flows

2016 ◽  
Author(s):  
William Gilpin ◽  
Vivek N. Prakash ◽  
Manu Prakash
Keyword(s):  
Coherent Structures ◽  
Collective Motion ◽  
Biological Fluid ◽  
Source Code ◽  
Fluid Flows ◽  
Flow Structures ◽  
Time Varying ◽  
Middle Ground ◽  
Complex Flow ◽  
User Intervention

1AbstractWe present a simple, intuitive algorithm for visualizing time-varying flow fields that can reveal complex flow structures with minimal user intervention. We apply this technique to a variety of biological systems, including the swimming currents of invertebrates and the collective motion of swarms of insects. We compare our results to more experimentally-diffcult and mathematically-sophisticated techniques for identifying patterns in fluid flows, and suggest that our tool represents an essential “middle ground” allowing experimentalists to easily determine whether a system exhibits interesting flow patterns and coherent structures without the need to resort to more intensive techniques. In addition to being informative, the visualizations generated by our tool are often striking and elegant, illustrating coherent structures directly from videos without the need for computational overlays. Our tool is available as fully-documented open-source code available for MATLAB, Python, or ImageJ at www.flowtrace.org.

scholarly journals Dynamics of Convectively Driven Banded Jets in the Laboratory

2007 ◽  
Vol 64 (11) ◽  
pp. 4031-4052 ◽  
Author(s):  
Peter L. Read ◽  
Yasuhiro H. Yamazaki ◽  
Stephen R. Lewis ◽  
Paul D. Williams ◽  
Robin Wordsworth ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Turbulent Flows ◽  
Large Scale ◽  
Zonal Flow ◽  
Inertial Range ◽  
Instability Criterion ◽  
Rossby Wave Breaking ◽  
Outer Planets ◽  
Zonal Jets ◽  
Geostrophic Turbulence

Abstract The banded organization of clouds and zonal winds in the atmospheres of the outer planets has long fascinated observers. Several recent studies in the theory and idealized modeling of geostrophic turbulence have suggested possible explanations for the emergence of such organized patterns, typically involving highly anisotropic exchanges of kinetic energy and vorticity within the dissipationless inertial ranges of turbulent flows dominated (at least at large scales) by ensembles of propagating Rossby waves. The results from an attempt to reproduce such conditions in the laboratory are presented here. Achievement of a distinct inertial range turns out to require an experiment on the largest feasible scale. Deep, rotating convection on small horizontal scales was induced by gently and continuously spraying dense, salty water onto the free surface of the 13-m-diameter cylindrical tank on the Coriolis platform in Grenoble, France. A “planetary vorticity gradient” or “β effect” was obtained by use of a conically sloping bottom and the whole tank rotated at angular speeds up to 0.15 rad s−1. Over a period of several hours, a highly barotropic, zonally banded large-scale flow pattern was seen to emerge with up to 5–6 narrow, alternating, zonally aligned jets across the tank, indicating the development of an anisotropic field of geostrophic turbulence. Using particle image velocimetry (PIV) techniques, zonal jets are shown to have arisen from nonlinear interactions between barotropic eddies on a scale comparable to either a Rhines or “frictional” wavelength, which scales roughly as (β/Urms)−1/2. This resulted in an anisotropic kinetic energy spectrum with a significantly steeper slope with wavenumber k for the zonal flow than for the nonzonal eddies, which largely follows the classical Kolmogorov k−5/3 inertial range. Potential vorticity fields show evidence of Rossby wave breaking and the presence of a “hyperstaircase” with radius, indicating instantaneous flows that are supercritical with respect to the Rayleigh–Kuo instability criterion and in a state of “barotropic adjustment.” The implications of these results are discussed in light of zonal jets observed in planetary atmospheres and, most recently, in the terrestrial oceans.

Exact Coherent States and the Nonlinear Dynamics of Wall-Bounded Turbulent Flows

2021 ◽  
Vol 53 (1) ◽  
pp. 227-253 ◽  
Author(s):  
Michael D. Graham ◽  
Daniel Floryan
Keyword(s):  
State Space ◽  
Turbulent Flows ◽  
Coherent Structures ◽  
Coherent States ◽  
Large Scale ◽  
Stokes Equations ◽  
Saddle Points ◽  
Transport Processes ◽  
Hairpin Vortices ◽  
Theoretical Approaches

Wall-bounded turbulence exhibits patterns that persist in time and space: coherent structures. These are important for transport processes and form a conceptual framework for important theoretical approaches. Key observed structures include quasi-streamwise and hairpin vortices, as well as the localized spots and puffs of turbulence observed during transition. This review describes recent research on so-called exact coherent states (ECS) in wall-bounded parallel flows at Reynolds numbers Re [Formula: see text] 104; these are nonturbulent, nonlinear solutions to the Navier–Stokes equations that in many cases resemble coherent structures in turbulence. That is, idealized versions of many of these structures exist as distinct, self-sustaining entities. ECS are saddle points in state space and form, at least in part, the state space skeleton of the turbulent dynamics. While most work on ECS focuses on Newtonian flow, some advances have been made on the role of ECS in turbulent drag reduction in polymer solutions. Emerging directions include applications to control and connections to large-scale structures and the attached eddy model.

Asymptotic Effect of Initial and Upstream Conditions on Turbulence

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
William K. George
Keyword(s):  
New York ◽  
Turbulent Flows ◽  
Coherent Structures ◽  
Large Scale ◽  
Initial Conditions ◽  
Single Point ◽  
Building Blocks ◽  
The Self ◽  
Asymptotic Independence ◽  
Small Scale

More than two decades ago the first strong experimental results appeared suggesting that turbulent flows might not be asymptotically independent of their initial (or upstream) conditions (Wygnanski et al., 1986, “On the Large-Scale Structures in Two-Dimensional Smalldeficit, Turbulent Wakes,” J. Fluid Mech., 168, pp. 31–71). And shortly thereafter the first theoretical explanations were offered as to why we came to believe something about turbulence that might not be true (George, 1989, “The Self-Preservation of Turbulent Flows and its Relation to Initial Conditions and Coherent Structures,” Advances in Turbulence, W. George and R. Arndt, eds., Hemisphere, New York, pp. 1–41). These were contrary to popular belief. It was recognized immediately that if turbulence was indeed asymptotically independent of its initial conditions, it meant that there could be no universal single point model for turbulence (George, 1989, “The Self-Preservation of Turbulent Flows and its Relation to Initial Conditions and Coherent Structures,” Advances in Turbulence, W. George and R. Arndt, eds., Hemisphere, New York, pp. 1–41; Taulbee, 1989, “Reynolds Stress Models Applied to Turbulent Jets,” Advances in Turbulence, W. George and R. Arndt, eds., Hemisphere, New York, pp. 29–73) certainly consistent with experience, but even so not easy to accept for the turbulence community. Even now the ideas of asymptotic independence still dominate most texts and teaching of turbulence. This paper reviews the substantial additional evidence - experimental, numerical and theoretical - for the asymptotic effect of initial and upstream conditions that has accumulated over the past 25 years. Also reviewed is evidence that the Kolmogorov theory for small scale turbulence is not as general as previously believed. Emphasis has been placed on the canonical turbulent flows (especially wakes, jets, and homogeneous decaying turbulence), which have been the traditional building blocks for our understanding. Some of the important outstanding issues are discussed; and implications for the future of turbulence modeling and research, especially LES and turbulence control, are also considered.

scholarly journals Assessing Spacing Impact on Coherent Features in a Wind Turbine Array Boundary Layer

2017 ◽  
Author(s):  
Naseem Ali ◽  
Nicholas Hamilton ◽  
Raul Cal
Keyword(s):  
Kinetic Energy ◽  
Turbulent Flow ◽  
Wind Turbine ◽  
Reynolds Stress ◽  
Flow Structure ◽  
Energy Content ◽  
Turbulence Kinetic Energy ◽  
Flow Structures ◽  
Spanwise Direction ◽  
The Impact

Abstract. As wind farms become larger, the spacing between turbines becomes a significant design element that imposes serious economic constraints. Effects of turbine spacing on the power produced and flow structure are crucial for future development of wind energy. To investigate the turbulent flow structures in a 4 × 3 Cartesian wind turbine array, a wind tunnel experiment was carried out parameterizing the streamwise and spanwise wind turbine spacing. Four cases were chosen spacing turbines by 6 diameters (D) or 3D in the streamwise, and 3D or 1.5D in the spanwise direction. Data were obtained experimentally using stereo particle-image velocimetry. Mean streamwise velocity showed maximum values upstream of the turbine with the spacing of 6D and 3D, in the streamwise and spanwise direction, respectively. Fixing the spanwise turbine spacing to 3D, variations in the streamwise spacing influence the turbulent flow structure and the power available to following wind turbines. Quantitative comparisons were made through spatial averaging, shifting measurement data and interpolating to account for the full range between devices to obtain data independent of array spacing. The largest averaged Reynolds stress is seen in cases with spacing of 3D and 3D, in the streamwise and spanwise direction, respectively. Snapshot proper orthogonal decomposition was employed to identify the flow structures based on the turbulence kinetic energy content. The maximum turbulence kinetic energy content in the first POD mode compared with other cases is seen for turbine spacing of 6D × 1.5D. The flow upstream of each wind turbine converges faster than the flow downstream according to accumulation of turbulence kinetic energy by POD modes, regardless of spacing. The streamwise-averaged profile of the Reynolds stress is reconstructed using a specific number of modes for each case; the case of 6D × 1.5D spacing shows the fastest reconstruction. Intermediate modes are also used to reconstruct the averaged profile and show that the intermediate scales are responsible for features seen in the original profile. The variation in streamwise and spanwis spacing leads to changing the background structure of the turbulence, where the color map based on barycentric map and anisotropy stress tensor provides a new perspective on the nature of the perturbations within the wind turbine array. The impact of the streamwise and spanwise spacings on power produced is quantified, where the maximum production corresponds with the case of greatest turbine spacing.

scholarly journals Assessing spacing impact on coherent features in a wind turbine array boundary layer

2018 ◽  
Vol 3 (1) ◽  
pp. 43-56 ◽  
Author(s):  
Naseem Ali ◽  
Nicholas Hamilton ◽  
Dominic DeLucia ◽  
Raúl Bayoán Cal
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Flow ◽  
Wind Turbine ◽  
Reynolds Stress ◽  
Energy Content ◽  
Turbulence Kinetic Energy ◽  
Flow Structures ◽  
Spanwise Direction ◽  
The Impact

Abstract. As wind farms become larger, the spacing between turbines becomes a significant design consideration that can impose serious economic constraints. To investigate the turbulent flow structures in a 4 × 3 Cartesian wind turbine array boundary layer (WTABL), a wind tunnel experiment was carried out parameterizing the streamwise and spanwise wind turbine spacing. Four cases are chosen spacing turbines by 6 or 3D in the streamwise direction, and 3 or 1.5D in the spanwise direction, where D = 12 cm is the rotor diameter. Data are obtained experimentally using stereo particle image velocimetry. Mean streamwise velocity showed maximum values upstream of the turbine with the spacing of 6 and 3D in the streamwise and spanwise direction, respectively. Fixing the spanwise turbine spacing to 3D, variations in the streamwise spacing influence the turbulent flow structure and the power available to following wind turbines. Quantitative comparisons are made through spatial averaging, shifting measurement data and interpolating to account for the full range between devices to obtain data independent of array spacing. The largest averaged Reynolds stress is seen in cases with spacing of 3D × 3D. Snapshot proper orthogonal decomposition (POD) was employed to identify the flow structures based on the turbulence kinetic energy content. The maximum turbulence kinetic energy content in the first POD mode is seen for turbine spacing of 6D × 1.5D. The flow upstream of each wind turbine converges faster than the flow downstream according to accumulation of turbulence kinetic energy by POD modes, regardless of spacing. The streamwise-averaged profile of the Reynolds stress is reconstructed using a specific number of modes for each case; the case of 6D × 1.5D spacing shows the fastest reconstruction to compare the rate of reconstruction of statistical profiles. Intermediate modes are also used to reconstruct the averaged profile and show that the intermediate scales are responsible for features seen in the original profile. The variation in streamwise and spanwise spacing leads to changes in the background structure of the turbulence, where the color map based on barycentric map and Reynolds stress anisotropy tensor provides an alternate perspective on the nature of the perturbations within the wind turbine array. The impact of the streamwise and spanwise spacings on power produced is quantified, where the maximum production corresponds with the case of greatest turbine spacing.

scholarly journals Statistical Analysis of Dynamic Subgrid Modeling Approaches in Large Eddy Simulation

2021 ◽  
Author(s):  
Mohammad Khalid Hossen ◽  
Asokan Mulayath Variyath ◽  
Jahrul M Alam
Keyword(s):  
Kinetic Energy ◽  
Large Eddy Simulation ◽  
Turbulent Flows ◽  
Large Scale ◽  
Physical Space ◽  
Statistical Characteristics ◽  
Small Scale ◽  
Eddy Simulation ◽  
Wide Range ◽  
Large Eddy

In large eddy simulation (LES) of turbulent flows, the most critical dynamical processes to be considered by dynamic subgrid models to account for an average cascade of kinetic energy from the largest to the smallest scales of the flow is not fully clear. Furthermore, evidence of vortex stretching being the primary mechanism of the cascade is not out of the question. In this article, we study some essential statistical characteristics of vortex stretching and its role in dynamic approaches of modeling subgrid-scale turbulence. We have compared the interaction of subgrid stresses with the filtered quantities among four models using invariants of the velocity gradient tensor. This technique is a single unified approach to studying a wide range of length scales in the turbulent flow. In addition, it also provides a rational basis for the statistical characteristics a subgrid model must serve in physical space to ensure an appropriate cascade of kinetic energy. Results indicate that the stretching mechanism extracts energy from the large-scale straining motion and passes it onto small-scale stretched vortices.

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