Experimental assessment of fractal scale similarity in turbulent flows. Part 4. Effects of Reynolds and Schmidt numbers

1998 ◽  
Vol 377 ◽  
pp. 169-187 ◽  
Author(s):  
RICHARD D. FREDERIKSEN ◽  
WERNER J. A. DAHM ◽  
DAVID R. DOWLING
Keyword(s):  
Turbulent Flows ◽  
Dissipation Rate ◽  
Single Point ◽  
Energy Dissipation Rate ◽  
Scalar Dissipation ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Outer Scale ◽  
Scale Invariant ◽  
Scale Similarity

Experimental results are presented for the influence of Reynolds number on multifractal scale similarity in turbulent flows. These are obtained from single-point measurements of a dynamically passive Sc≈1 conserved scalar quantity ζ(t) in a turbulent shear flow at outer-scale Reynolds numbers of 14000[les ]Reδ[les ]110000. Statistical criteria based on the maximum allowable scale-to-scale variation L1(ε) in multiplier distributions P(Mε) from multifractal gauge sets allow accurate discrimination between multifractal and non-multifractal scaling. Results show that the surrogate scalar energy dissipation rate χs(t)≡(dζ/dt)2is found to display a scale-invariant similarity consistent with a random multiplicative cascade characterized by a bilinear multiplier distribution P(Mε) over a range of scales extending downward from the outer scaleTδ. For a range of scales extending upward from the inner (diffusive) scale TD, the dissipation rate displays a different scale-invariant similarity characterized by a uniform multiplier distribution. The former scale-invariance becomes evident in the present Sc≈1 data only when Reδ is sufficiently large. Comparisons with results from Sc 1 data indicate that this scale-invariant similarity applies when the outer-to-inner scale ratio Tδ/TD≈0.09 Re3/4δSc1/2 is greater than about 400. In contrast to the scalar dissipation rate field, the scalar field is found to lack any multifractal scale similarity.

Experimental assessment of fractal scale-similarity in turbulent flows. Part 1. One-dimensional intersections

1996 ◽  
Vol 327 ◽  
pp. 35-72 ◽  
Author(s):  
Richard D. Frederiksen ◽  
Werner J. A. Dahm ◽  
David R. Dowling
Keyword(s):  
Turbulent Flows ◽  
Temporal Structure ◽  
Three Dimensional ◽  
Scalar Fields ◽  
Energy Dissipation Rate ◽  
Random Sets ◽  
Scalar Dissipation ◽  
Temporal Scales ◽  
Scale Similarity ◽  
Spatio Temporal

Results are presented from an assessment of the applicability of fractal scale-similarity in the spatio–temporal structure of Sc [Gt ] 1 conserved scalar fields ζ(x, t) and scalar energy dissipation rate fields ∇(x, t) in turbulent flows. Over 2 million spatial and temporal intersections were analysed from fully resolved three-dimensional (256) spatial measurements as well as fully resolved four-dimensional spatio–temporal measurements containing up to 3 million points. Statistical criteria were used to assess both deterministic and stochastic fractal scale-similarity and to differentiate between fractal and random sets. Results span the range of spatio–temporal scales from the scalar diffusion scales (ΛD, TD) to the viscous diffusion scales (Λv, Tv) and to the outer scales (δ, Tδ). Over this entire range of scales, slightly over 99.0% of all intersections with the scalar dissipation support geometry showed scale-similarity as fractal as stochastically self-similar fBm sets having the same record length. Dissipation values above the mean were found to have support dimension D = 0.66. The dissipation support dimension decreased sharply with increasing dissipation values. Virtually no intersections showed scaling as random as a random set with the same relative cover. In contrast, intersections with scalar isosurfaces showed scaling only approximately as fractal as a corresponding fBm set and only over the range of spatio–temporal scales between (ΛD, TD) and (Λv, Tv). On these inner scales the isosurface dimension was D = 0.48 and was largely independent of the isoscalar value. At larger scales, scalar isosurfaces showed no fractal scale-similarity. In contrast, isoscalar level crossing sets showed no fractal scale-similarity over any range of scales, even though the scalar dissipation support geometry for the same data is clearly fractal. These results were found to be unaffected by noise.

Experimental assessment of fractal scale similarity in turbulent flows. Part 3. Multifractal scaling

1997 ◽  
Vol 338 ◽  
pp. 127-155 ◽  
Author(s):  
RICHARD D. FREDERIKSEN ◽  
WERNER J. A. DAHM ◽  
DAVID R. DOWLING
Keyword(s):  
Scalar Field ◽  
Turbulent Flows ◽  
Finite Length ◽  
Scalar Dissipation ◽  
Statistical Criterion ◽  
Cascade Process ◽  
Scale Invariant ◽  
Scale Similarity ◽  
Multifractal Scaling ◽  
Multiplicative Cascade

Earlier experimental assessments of fractal scale similarity in geometric properties of turbulent flows are extended to assess the applicability of multifractal scale-similarity in the conserved scalar field ζ(x, t) and in the true scalar energy dissipation rate field ∇ζ·∇ζ(x, t). Fully resolved four-dimensional spatio-temporal measurements from a turbulent flow at Reλ≈41 and Reδ≈3000 are analysed. The utility of various classical constructs for identifying multifractal scale similarity in data records of finite length is examined. An objective statistical criterion based on the maximum allowable scale-to-scale variation L1(ε) in multiplier distributions 〈P(Mε)〉 obtained from multifractal gauge fields is developed to allow accurate discrimination between multifractal and non-multifractal scaling in finite-length experimental data records. Results from analyses of temporal intersections show that for scales greater than 0.03 λν/u, corresponding to 1.4 λD/u, the scalar dissipation field clearly demonstrates a scale-invariant similarity consistent with a multiplicative cascade process that can be modelled with a bilinear multiplier distribution. However, the conserved scalar field from precisely the same data does not follow any scale similarity consistent with a multiplicative cascade at scales below 0.5 λν/u. At larger scales, there are indications of a possible scale-invariant similarity in the scalar field, but with a fundamentally different multiplier distribution.

Experimental study of the fine-scale structure of conserved scalar mixing in turbulent shear flows. Part 1. Sc [Gt ] 1

1996 ◽  
Vol 317 ◽  
pp. 21-71 ◽  
Author(s):  
Kenneth A. Buch ◽  
Werner J. A. Dahm
Keyword(s):  
Strain Rate ◽  
Dissipation Rate ◽  
Shear Flows ◽  
Scale Structure ◽  
Scalar Dissipation ◽  
Turbulent Shear ◽  
Fine Scale ◽  
Scalar Dissipation Rate ◽  
Principal Axes ◽  
Turbulent Shear Flows

We present results from an experimental investigation into the fine-scale structure associated with the mixing of a dynamically passive conserved scalar quantity on the inner scales of turbulent shear flows. The present study was based on highly resolved two- and three-dimensional spatio-temporal imaging measurements. For the conditions studied, the Schmidt number (Sc ≡ v/D) was approximately 2000 and the local outerscale Reynolds number (Reσ≡ uσ/v) ranged from 2000 to 10000. The resolution and signal quality allow direct differentiation of the measured scalar field ζ(x, t) to give the instantaneous scalar energy dissipation rate field (Re Sc)−1 ∇ζċ∇ζ(x, t). The results show that the fine-scale structure of the scalar dissipation field, when viewed on the inner-flow scales for Sc ≡ 1, consists entirely of thin strained laminar sheet-like diffusion layers. The internal structure of these scalar dissipation sheets agrees with the one-dimensional self-similar solution for the local strain–diffusion competition in the presence of a spatially uniform but time-varying strain rate field. This similarity solution also shows that line-like structures in the scalar dissipation field decay exponentially in time, while in the vorticity field both line-like and sheet-like structures can be sustained. This sheet-like structure produces a high level of intermittency in the scalar dissipation field – at these conditions approximately 4% of the flow volume accounts for nearly 25% of the total mixing achieved. The scalar gradient vector field ∇ζ(x, t) for large Sc is found to be nearly isotropic, with a weak tendency for the dissipation sheets to align with the principal axes of the mean flow strain rate tensor. Joint probability densities of the conserved scalar and scalar dissipation rate have a shape consistent with this canonical layer-like fine-scale structure. Statistics of the conserved scalar and scalar dissipation rate fields are found to demonstrate similarity on inner-scale variables even at the relatively low Reynolds numbers investigated.

Compressibility effects on the growth and structure of homogeneous turbulent shear flow

1993 ◽  
Vol 256 ◽  
pp. 443-485 ◽  
Author(s):  
G. A. Blaisdell ◽  
N. N. Mansour ◽  
W. C. Reynolds
Keyword(s):  
Growth Rate ◽  
Shear Flow ◽  
Dissipation Rate ◽  
Isotropic Turbulence ◽  
Compressible Turbulence ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Homogeneous Shear ◽  
Homogeneous Shear Flow ◽  
Compressibility Effects

Compressibility effects within decaying isotropic turbulence and homogeneous turbulent shear flow have been studied using direct numerical simulation. The objective of this work is to increase our understanding of compressible turbulence and to aid the development of turbulence models for compressible flows. The numerical simulations of compressible isotropic turbulence show that compressibility effects are highly dependent on the initial conditions. The shear flow simulations, on the other hand, show that measures of compressibility evolve to become independent of their initial values and are parameterized by the root mean square Mach number. The growth rate of the turbulence in compressible homogeneous shear flow is reduced compared to that in the incompressible case. The reduced growth rate is the result of an increase in the dissipation rate and energy transfer to internal energy by the pressure–dilatation correlation. Examination of the structure of compressible homogeneous shear flow reveals the presence of eddy shocklets, which are important for the increased dissipation rate of compressible turbulence.

Experimental study of the fine-scale structure of conserved scalar mixing in turbulent shear flows. Part 2. Sc≈1

1998 ◽  
Vol 364 ◽  
pp. 1-29 ◽  
Author(s):  
KENNETH A. BUCH ◽  
WERNER J. A. DAHM
Keyword(s):  
Experimental Study ◽  
Layer Thickness ◽  
Dissipation Rate ◽  
Shear Flows ◽  
Scale Structure ◽  
The Self ◽  
Turbulent Shear ◽  
Fine Scale ◽  
Outer Scale ◽  
Self Similar

Results are presented from an experimental study into the fine-scale structure of generic, Sc≈1, dynamically passive, conserved scalar fields in turbulent shear flows. The investigation was based on highly resolved, two-dimensional imaging of laser Rayleigh scattering, with measurements obtained in the self-similar far field of an axisymmetric coflowing turbulent jet of propane issuing into air at local outer-scale Reynolds numbers Reδ≡uδ/v of 11000 and 14000. The resolution and signal quality of these measurements allowed direct differentiation of the scalar field data ζ(x, t) to determine the instantaneous scalar energy dissipation rate field (Re Sc)−1∇ζ·∇ζ(x, t). Results show that, as for large-Sc scalars (Buch & Dahm 1996), the scalar dissipation rate field consists entirely of strained, laminar, sheet-like diffusion layers, despite the fact that at Sc≈1 the scale on which these layers are folded by vorticity gradients is comparable to the layer thickness. Good agreement is found between the measured internal structure of these layers and the self-similar local solution of the scalar transport equation for a spatially uniform but time-varying strain field. The self-similar distribution of dissipation layer thicknesses shows that the ratio of maximum to minimum thicknesses is only 3 at these conditions. The local dissipation layer thickness is related to the local outer scale as λD/δ ≡ΛRe−3/4δSc−1/2, with the average thickness found to be 〈Λ〉=11.2, with both the largest and smallest layer thicknesses following Kolmogorov Re−3/4δ) scaling.

Experimental assessment of fractal scale similarity in turbulent flows. Part 2. Higher-dimensional intersections and non-fractal inclusions

1997 ◽  
Vol 338 ◽  
pp. 89-126 ◽  
Author(s):  
RICHARD D. FREDERIKSEN ◽  
WERNER J. A. DAHM ◽  
DAVID R. DOWLING
Keyword(s):  
Turbulent Flows ◽  
Three Dimensional ◽  
Local Scale ◽  
Scalar Dissipation ◽  
Experimental Assessment ◽  
One Dimensional ◽  
Higher Dimensional ◽  
Scale Similarity ◽  
Data Points ◽  
Simple Average

Results from an earlier experimental assessment of fractal scale similarity in one-dimensional spatial and temporal intersections in turbulent flows are here extended to two- and three-dimensional spatial intersections. Over 25000 two-dimensional (2562) intersections and nearly 40 three-dimensional (2563) intersections, collectively representing more than 2.3 billion data points, were analysed using objective statistical methods to determine which intersections were as fractal as stochastically scale-similar fractal gauge sets having the same record length. Results for the geometry of Sc [Gt ]1 scalar isosurfaces and the scalar dissipation support span the range of lengthscales between the scalar and viscous diffusion scales λD and λν. The present study finds clear evidence for stochastic fractal scale similarity in the dissipation support. With increasing intersection dimension n, the data show a decrease in the fraction of intersections satisfying the criteria for fractal scale similarity, consistent with the presence of localized non-fractal inclusions. Local scale similarity analyses on three-dimensional (643) intersections directly show such intermittent non-fractal inclusions with characteristic lengthscale comparable to λν. These inclusions lead to failure of the relation among codimensions Dn≡D−(3−n) when applied to simple average dimensions, which has formed the basis for most previous assessments of fractal scale-similarity. Unlike the dissipation support geometry, scalar isosurface geometries from the same data were found not to be as fractal as fractional Brownian motion gauge sets over the range of scales examined.

Direct Numerical Simulation of Homogeneous Turbulent Shear Flow Containing Bubbles

2006 ◽  
Author(s):  
T. Kawamura ◽  
T. Nakatani
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Production Rate ◽  
Turbulent Flows ◽  
Reynolds Numbers ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Hypothetical Model ◽  
Turbulent Reynolds Number

Direct numerical simulations of homogeneous shear turbulent flows containing deformable bubbles were carried out for clarifying the mechanism of drag reduction by microbubbles. The results show that presence of bubbles can suppress or enhance the development of turbulence depending on condition. The dissipation rate of turbulent kinetic energy is always increased by bubbles, while the production rate can be either increased or decreased depending on the turbulent and shear Reynolds numbers. As a result, the growth rate of turbulent kinetic energy can be either increased or decreased by bubbles depending on conditions. It was shown that the production rate tends to decrease at smaller shear Reynolds number, at larger turbulent Reynolds number, and at larger Weber number. Based on the results, a hypothetical model to explain the dependency on the Reynolds numbers has been proposed.

TURBULENT SHEAR FLOW: A PARADIGMATIC MULTISCALE PHENOMENON

2009 ◽  
Vol 01 (02) ◽  
pp. 197-222 ◽  
Author(s):  
M. A. LESCHZINER ◽  
G. M. FISHPOOL ◽  
S. LARDEAU
Keyword(s):  
Shear Flow ◽  
Computational Modeling ◽  
Modeling And Simulation ◽  
Turbulent Flows ◽  
Structural Features ◽  
Turbulent Shear ◽  
Characteristic Scale ◽  
External Forcing ◽  
Turbulent Shear Flow ◽  
Computational Modeling And Simulation

The paper provides a broad discussion of multiscale and structural features of sheared turbulent flows. Basic phenomenological aspects of turbulence are first introduced, largely in descriptive terms with particular emphasis placed on the range of scales encountered in turbulent flows and in the identification of characteristic scale ranges. There follows a discussion of essential aspects of computational modeling and simulation of turbulence. Finally, the results of simulations for two groups of flows are discussed. These combine shear, separation, and periodicity, the last feature provoked by either a natural instability or by unsteady external forcing. The particular choice of examples is intended to illustrate the capabilities of such simulations to resolve the multiscale nature of complex turbulent flows, as well as the challenges encountered.

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