Axisymmetric Turbulent Wakes with New Nonequilibrium Similarity Scalings

Nedic, Jovan; Vassilicos, J. C.; Ganapathisubramani, Bharathram

doi:10.1103/physrevlett.111.144503

Cited by 91 publications

(93 citation statements)

References 14 publications

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“…Nedić et al [9] confirmed predictions (1) and (2) experimentally using hot wire anemometry (HWA) in the range 5L b < x 50L b on mean flow profiles of axisymmetric and self-preserving turbulent wakes of thin plates with irregular edges placed normal to the incoming free stream (in which case L b is the square root of the plate's frontal area A). Irregular edges increase the velocity deficit without increasing A, hence one can better measure velocity deficits without reducing the streamwise range of measurements in the wind tunnel's test section.…”

supporting

confidence: 66%

“…Both sets of exponents return acceptable linearizations of the data. This explains why previous studies (e.g., [9] and references therein) have concluded that the mean velocity deficit and wake width of axisymmetric turbulent wakes of regular objects scale in the classical equilibrium 044409-5…”

supporting

confidence: 62%

“…However, it remains a key open question whether the nonequilibrium scalings reported in Ref. [9] are specific to plates with irregular edges or are universal and therefore also valid for regular plates.…”

mentioning

confidence: 99%

“…Nedić et al [9] used this nonequilibrium dissipation law in conjunction with the self-preservation hypothesis to derive mean flow profile scalings for nonequilibrium axisymmetric turbulent wakes. Specifically, their nonequilibrium predictions for the streamwise evolution (along x) of the centerline mean velocity deficit u 0 and the wake width δ are…”

mentioning

confidence: 99%

“…[9]. The plate has square peripheries and has a reference length L b = 64 mm with thickness 1.25 mm.…”

mentioning

confidence: 99%

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Nonequilibrium scalings of turbulent wakes

2016

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Nonequilibrium turbulent wake scalings are not the preserve of irregular (fractal-like/ multiscale) plates but appear to be universal, as they also hold for regular plates over a very substantial downstream distance. DOI: 10.1103/PhysRevFluids.1.044409The most basic and arguably most important property that any theory or model of turbulence must predict is the mean flow profile. A model or theory of turbulence which can do this for a wide range of turbulent flows on the basis of only few fundamental and robust assumptions is still lacking. However, in the case of canonical boundary-free turbulent shear flows such as turbulent jets, wakes, and mixing layers, one can predict how the mean velocity difference and the size of the mean flow profile evolve with streamwise distance on the basis of two cornerstone assumptions [1]. These two assumptions may not be sufficient for a complete mean flow profile prediction, but they do lead to some of its most important aspects. The first assumptions is self-preservation of one-point turbulence statistics and the second is the scaling of the turbulence dissipation rate (see [1][2][3]).The high Reynolds number scaling of the turbulence dissipation rate traditionally used is the one consistent with the Richardson-Kolmogorov equilibrium cascade. The resulting streamwise developments (power laws of streamwise distance) of the mean velocity difference and the size of the mean flow profile are in many classical textbooks (e.g., [1,2,4]) for many canonical boundary-free turbulent shear flows. Recently, however, a new high Reynolds number dissipation law has been found in decaying and in forced periodic turbulence [5] and in near-field grid-generated decaying turbulence for many different types of grids (see [6]). The region where this nonequilibrium dissipation law holds can be long, depending on the turbulence-generating grid.Before proceeding to the implications of this nonequilibrium dissipation law for mean flow profiles, we recall the reasons (see [6]) why this dissipation law is termed "nonequilibrium." In a Richardson-Kolmogorov equilibrium cascade of turbulent kinetic energy the turbulent dissipation rate instantaneously equals the rate with which energy is fed into the cascade at the large energycontaining scales. This rate scales with the kinetic energy and size of these large scales at the instant considered and is independent of viscosity. Hence the turbulence dissipation must scale in the same way. Any different scaling of the turbulence dissipation must therefore characterize an instantaneous imbalance between dissipation and the rate with which energy is fed into the cascade at the large scales and it must therefore be a nonequilibrium scaling. This argument has a mathematical analog in terms of the generalized Karman-Howarth equation which can be found in Ref. [6] and which is based on setting the unsteady term in this equation to zero (for equilibrium). Of course, there are also spatial inhomogeneity terms in this equation which are negligible if small enough scales ...

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supporting

confidence: 66%

supporting

confidence: 62%

mentioning

confidence: 99%

mentioning

confidence: 99%

“…[9]. The plate has square peripheries and has a reference length L b = 64 mm with thickness 1.25 mm.…”

mentioning

confidence: 99%

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Nonequilibrium scalings of turbulent wakes

2016

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Power consumption and form drag of regular and fractal‐shaped turbines in a stirred tank

et al. 2016

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Previous wind-tunnel measurements have shown that fractal shaped plates have increased drag compared to square plates of the same area. In this study we measure the power consumption and drag of turbines with fractal and rectangular blades in a stirred tank. Power number decreases from rectangular to fractal impellers by over 10%, increasingly so with fractal iteration number. Our results suggest that this decrease is not caused by the wake interaction of the blades, nor solely by the wake interaction with the walls either.Pressure measurements on the blades' surface show that fractal blades have lower drag than the rectangular ones, opposite to the wind tunnel experiment results. All tested blades' centre of pressure radius increases with Re, while their drag coefficient decreases, a possible effect of the solid body rotation increase with Re. Spectral analysis of the pressure signal reveals two peaks possibly connected to the blades' roll vortices.

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An entrainment‐based model for annular wakes, with applications to airborne wind energy

et al. 2021

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Several novel wind energy systems produce wakes with annular cross‐sections, which are qualitatively different from the wakes with circular cross‐sections commonly generated by conventional horizontal‐axis wind turbines and by compact obstacles. Since wind farms use arrays of hundreds of turbines, good analytical wake models are essential for efficient wind farm planning. Several models already exist for circular wakes; however, none have yet been proposed for annular wakes, making it impossible to estimate their array performance. We use the entrainment hypothesis to develop a reduced‐order model for the shape and flow velocity of an annular wake from a generic annular obstacle. Our model consists of a set of three ordinary differential equations, which we solve numerically. In addition, by assuming that the annular wake does not drift radially, we further reduce the problem to a model comprising only two differential equations, which we solve analytically. Both of our models are in good agreement with previously published large eddy simulation results.

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Axisymmetric Turbulent Wakes with New Nonequilibrium Similarity Scalings

Cited by 91 publications

References 14 publications

Nonequilibrium scalings of turbulent wakes

Nonequilibrium scalings of turbulent wakes

Power consumption and form drag of regular and fractal‐shaped turbines in a stirred tank

An entrainment‐based model for annular wakes, with applications to airborne wind energy

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