This article reviews evidence concerning the cornerstone dissipation scaling of turbulence theory: � = CU 3 /L, with C� = const., � the dissipation rate of turbulent kinetic energy U 2 ,a ndL an integral length scale characterizing the energy-containing turbulent eddies. This scaling is intimately linked to the Richardson-Kolmogorov equilibrium cascade. Accumulating evidence shows that a significant nonequilibrium region exists in various turbulent flows in which the energy spectrum has Kolmogorov's −5/3 wave-number scaling over a wide wave-number range, yet C� ∼ Re m /Re n ,w ithm ≈ 1 ≈ n, Re I a global/inlet Reynolds number, and ReL a local turbulence Reynolds number.

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Dissipation in Turbulent Flows

Computational Models for Turbulent Reacting Flows: References

面内振動する粗面近くでの流速測定(Journal of Fluid Mechanics,Vol.73,Part 4,1976 2)

The previously reported non-equilibrium dissipation law is investigated in turbulent flows generated by various regular and fractal square grids. The flows are documented in terms of various turbulent profiles which reveal their differences. In spite of significant inhomogeneity and anisotropy differences, the new non-equilibrium dissipation law is observed in all of these flows. Various transverse and longitudinal integral scales are measured and used to define the dissipation coefficient . It is found that the new non-equilibrium dissipation law is not an artefact of a particular choice of the integral scale and that the usual equilibrium dissipation law can actually coexist with the non-equilibrium law in different regions of the same flow.

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The non-equilibrium region of grid-generated decaying turbulence

We perform particle image velocimetry (PIV) measurements of various terms of the non-homogeneous Karman–Howarth–Monin equation in the most inhomogeneous and anisotropic region of grid-generated turbulence, the production region which lies between the grid and the peak of turbulence intensity. We use a well-documented fractal grid which is known to magnify the streamwise extent of the production region and abate its turbulence activity. On the centreline around the centre of that region the two-point advection and transport terms are dominant and the production is significant too. It is therefore impossible to apply usual Kolmogorov arguments based on the Karman–Howarth–Monin equation and resulting dimensional considerations to deduce interscale flux and spectral properties. The interscale energy transfers at this location turn out to be highly anisotropic and consist of a combined forward and inverse cascade in different directions which, when averaged over directions, gives an interscale energy flux that is negative (hence forward cascade on average) and not too far from linear in , the modulus of the separation vector between two points. The energy spectrum of the streamwise fluctuating component exhibits a well-defined power law over one decade, even though the streamwise direction is at a small angle to the inverse cascading direction.

The energy cascade in near-field non-homogeneous non-isotropic turbulence

The turbulence structure and turbulence kinetic energy transport in multiscale/fractal-generated turbulence in a wind tunnel are investigated. A low-blockage, space-filling square-type (i.e., fractal elements with square shapes) fractal grid is placed at the inlet of the test section. On the basis of the thickness of the biggest grid bar, t0, and the inflow velocity U∞, the Reynolds numbers (Re0) are set to 5900 and 11 400; these values are the same as those considered in previous experiments [D. Hurst and J. C. Vassilicos, “Scalings and decay of fractal-generated turbulence,” Phys. Fluids 19, 035103 (2007)10.1063/1.2676448; N. Mazellier and J. C. Vassilicos, “Turbulence without Richardson-Kolmogorov cascade,” Phys. Fluids 22, 075101 (2010)10.1063/1.3453708]. The turbulence characteristics are measured using hot-wire anemometry with I- and X-type probes. Generally, good agreements are observed despite the difference in the size of the test sections used: The longitudinal integral length-scale Lu and the T...

Turbulence structure and turbulence kinetic energy transport in multiscale/fractal-generated turbulence

The decay characteristics and invariants of grid turbulence were investigated by means of laboratory experiments conducted in a wind tunnel. A turbulence-generating grid was installed at the entrance of the test section for generating nearly isotropic turbulence. Five grids (square bars of mesh sizes , 25 and 50 mm and cylindrical bars of mesh sizes and 25 mm) were used. The solidity of all grids is . The instantaneous streamwise and vertical (cross-stream) velocities were measured by hot-wire anemometry. The mesh Reynolds numbers were adjusted to , 9600, 16 000 and 33 000. The Reynolds numbers based on the Taylor microscale in the decay region ranged from 27 to 112. In each case, the result shows that the decay exponent of turbulence intensity is close to the theoretical value of (for the grid, ) for Saffman turbulence. Here, is the power of the dimensionless energy dissipation coefficient, . Furthermore, each case shows that streamwise variations in the integral length scales, and , and the Taylor microscale grow according to (for the grid, ) and , respectively, at (depending on the experimental conditions, including grid geometry), where is the streamwise distance from the grid and is the virtual origin. We demonstrated that in the decay region of grid turbulence, and , which correspond to Saffman’s integral, are constant for all grids and examined values. However, and , which correspond to Loitsianskii’s integral, and and , which correspond to the complete self-similarity of energy spectrum and , are not constant. Consequently, we conclude that grid turbulence is a type of Saffman turbulence for the examined range of 6700–33 000 ( ) regardless of grid geometry.

On invariants in grid turbulence at moderate Reynolds numbers

Direct numerical simulations were carried out to study the turbulence generated by a fractal square grid at a Reynolds number of ReL0 = 20000 (based on the inlet velocity Uin and length of the largest grid bar L0). We found that in the near-field region, the fractal square grid can generate much higher turbulence levels and has a better mixing performance than the single square grid. However, the current numerical results show that a single square grid can produce a turbulence intensity and turbulent Reynolds number at the end of the simulation region (i.e., X/L0 ≃ 13) comparable to those of a higher-blockage fractal square grid because the two turbulent flows have quite different energy decay rates. We also demonstrated that for the fractal square grid, the length L0 gives a physical description of the inlet Reynolds number. An examination of the characteristic length scale for the fractal square grid reveals that the unusual high energy decay rates in previous experiments [D. Hurst and J. C. Vassilicos,...

Relevance of turbulence behind the single square grid to turbulence generated by regular- and multiscale-grids

In this paper, direct numerical simulations are carried out to study single-square grid-generated turbulence at a Reynolds number ReL0 = 20 000 (based on the inlet velocity Uin and the length of grid bar L0). Different from the regular grid and the multiscale/fractal grid, here only single large square grid is placed at the center near the inlet. First, we investigate the evolutions of turbulence characteristics (e.g., mean streamwise velocity, turbulence intensity, Taylor microscale, etc.) along the centerline. The common characteristics possessed by turbulent flows generated by the single square grid and by the fractal square grid are presented. We confirm the hypothesis proposed by Mazellier and Vassilicos [“Turbulence without Richardson-Kolmogorov cascade,” Phys. Fluids 22, 075101 (2010)] that for the fractal square grid, the location of turbulence intensity peak along the centerline is mainly determined by large-scale wake interactions. Current numerical results show that in turbulence generated by t...

Osamu Terashima

Papers

Turbulence structure and turbulence kinetic energy transport in multiscale/fractal-generated turbulence

On invariants in grid turbulence at moderate Reynolds numbers

Relevance of turbulence behind the single square grid to turbulence generated by regular- and multiscale-grids

Development of turbulence behind the single square grid

Broadband vibration control of a structure by using a magnetorheological elastomer-based tuned dynamic absorber