Lognormality of the scalar dissipation pdf in turbulent flows

Dahm, Werner J. A.; Buch, Kenneth A.

doi:10.1063/1.857356

Cited by 38 publications

(20 citation statements)

References 6 publications

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“…And, PDFs of the SGS growth rate, conditioned on the scalar dissipation, are unimodal with a strong bias toward reducing particle growth. This is useful to know as it suggests that presumed PDF methods may be useful in capturing or representing the unresolved, small-scale particle-particle interactions when performing LES or RANS (Givi 1989;Dahm and Buch 1989;Frankel et al 1993;Piomelli 1993;Garrick 1995;McGraw 1997;Wu and Menon 2001;Marchisio and Fox 2005;Loeffler et al 2011). And, finally, the results show that the effect of the unresolved, small-scale, SGS particle-particle interactions increases with coagulation Damköhler number.…”

Section: Effects Of Turbulence On Nanoparticle Coagulationmentioning

confidence: 79%

Effects of Turbulent Fluctuations on Nanoparticle Coagulation in Shear Flows

Garrick

2011

Aerosol Science and Technology

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The effects of fluid turbulence on the coagulation of aerosols are studied quantitatively and qualitatively. Direct numerical simulation data is used to isolate the effect of the small or subgrid-scale (SGS) particle-particle interactions on nanoparticle coagulation in three-dimensional flows. The rate of particle growth is decomposed into the contribution of the large-scales and small-scales interactions. The contribution of the small-scale interactions is presented as a function of time, space, flow dynamics, and coagulation Damköhler number. Results show that small-scale interactions act to both increase and decrease particle growth. The probability density functions (PDFs) of the SGS growth rate exhibit a negative bias, which increases with time and coagulation Damköhler number. Additionally, PDFs conditioned on the Q-criterion suggest that the contribution of the small-scale interactions primarily act to reduce particle growth in regions characterized by fluid rotation.

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Section: Effects Of Turbulence On Nanoparticle Coagulationmentioning

confidence: 79%

Effects of Turbulent Fluctuations on Nanoparticle Coagulation in Shear Flows

Garrick

2011

Aerosol Science and Technology

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“…Since then, the statistical distribution of χ has been examined with experiments in non-reacting round [9][10][11][12] and planar [13] jets, boundary layers [14,15] and both two- [16] and three-dimensional [17,18] numerical simulations of passive scalar mixing in stationary (forced), homogeneous, isotropic turbulence. These studies have provided some evidence to support the approximately lognormal nature of P(χ ), with deviations from the theorized lognormality that are attached with great theoretical importance because they are seen as indicators of the smallscale behaviour in turbulent flows.…”

Section: Introductionmentioning

confidence: 99%

Measurements of the Statistical Distribution of the Scalar Dissipation Rate in Turbulent Axisymmetric Plumes

Markides

Mastorakos

2007

Flow Turbulence Combust

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In this paper we reconsider the high resolution Planar Laser-Induced Fluorescence (PLIF) mixing measurements that were presented in Markides and Mastorakos (Chem. Eng. Sci. 61:2835-2842, 2006. The PLIF experiments were performed in flows created by the continuous injection, with various velocity ratios, of a passive scalar (acetone) from a finite sized round nozzle, into uniform turbulent co-flows confined within a cylindrical tube with a range of turbulent Reynolds numbers. Here, we extend our study of these flows to include an investigation of the Probability Density Functions (PDFs) of the scalar dissipation rate (χ ), as well as of the scalar dissipation rate conditional on mixture fraction (χ |ξ ). To this effect, we have further processed the resulting data from the earlier work, including an additional correction for density variations in the flow. The results were then reprocessed for the accurate recovery of the spatial gradients of the normalized scalar concentration (ξ ), which resulted in direct measurements of χ . All results that are presented in this paper involve the two-dimensional scalar dissipation rate (χ 2D ) evaluated in the plane of imaging, and furthermore, results are only shown and discussed along the centreline of our axisymmetric configuration. The PDFs of χ were calculated and found to deviate slightly from a lognormal distribution, consistent with other published work. Moreover, the PDFs of χ |ξ followed a similar distribution, and showed a similar deviation. This deviation was more pronounced closer to the source and decayed downstream. The ratio of the standard deviation over the mean of χ and χ |ξ increased with streamwise distance and reached values of 2.8 and 1.2 respectively.

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“…Corrections to reconstruct the pdf that would be measured using all three components of the scalar gradient, assuming isotropy, point to a better fit to a lognormal. 33 In the present measurements, using one or two components of the gradient to calculate the dissipation rate, resulted in pdfs that are largely indistinguishable from each other; whether the full scalar gradient would alter this image is unclear. This is not only of theoretical importance, however, because in certain situations the low dissipation rate values are important in controlling a physical process (e.g., in auto-ignition).…”

Section: Statistical Measures Of the Scalar Dissipation Ratementioning

confidence: 94%

“…Whether this effect depends on the dimensionality of the measurements, the spatial resolution, the measurement noise, or it is an inherent feature of the dissipation pdf is not entirely clear. For example, by assuming an isotropic small scale field, lower dimensional measurements of the dissipation can be reconstructed to provide the pdf of a full 3D measurement, 33 which is shown to follow closely a lognormal distribution.…”

Section: Introductionmentioning

confidence: 99%

Mixing and scalar dissipation rate statistics in a starting gas jet

2015

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We quantify the temporal development of the mixing field of a starting jet by measuring the mixture fraction and the scalar dissipation rate and their statistics in an isothermal, impulsively started, gaseous jet. The scalar measurements are performed using planar laser induced fluorescence and, with appropriate processing of the resulting images, allow scalar dissipation rate measurements within 20%. The probability density functions of the mixture fraction, measured within a region of the order of 3 times the Batchelor length scale of the flow, are bimodal and skewed around a well-mixed radial location, which depends on the downstream distance and the time after the start of injection. The instantaneous distributions of the scalar dissipation rate reveal regions of high mixing at the jet periphery and at the developing vortex ring. The normalised probability density function (pdf) of the scalar dissipation rate at various flow positions and times after the start of injection has the same characteristic shape but differs from the usually suggested lognormal distribution at both low and high dissipation values; the same, also, holds true for the pdf conditioned on different values of the mixture fraction. The mean of the scalar dissipation rate conditional on mixture fraction shows a variation across the mixture fraction range, which differs between flow locations and times after the start of injection; however, at later times and for larger downstream distances the conditional mean between flow locations has similar distributions. Implications of the measurements for the auto-ignition of gaseous jets are examined and demonstrate that near the nozzle exit or at earlier times conditions are un-favourable for auto-ignition.

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Lognormality of the scalar dissipation pdf in turbulent flows

Cited by 38 publications

References 6 publications

Effects of Turbulent Fluctuations on Nanoparticle Coagulation in Shear Flows

Effects of Turbulent Fluctuations on Nanoparticle Coagulation in Shear Flows

Measurements of the Statistical Distribution of the Scalar Dissipation Rate in Turbulent Axisymmetric Plumes

Mixing and scalar dissipation rate statistics in a starting gas jet

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