Experimental investigation of dissipation-element statistics in scalar fields of a jet flow

2013 ◽  
Vol 724 ◽  
pp. 337-366 ◽  
Author(s):  
Markus Gampert ◽  
Philip Schaefer ◽  
Norbert Peters
Keyword(s):  
Experimental Investigation ◽  
Scalar Field ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Dissipation Rate ◽  
Scalar Dissipation ◽  
Streamwise Direction ◽  
Scalar Dissipation Rate ◽  
Dissipation Elements

AbstractWe present a detailed experimental investigation of conditional statistics obtained from dissipation elements based on the passive scalar field$\theta $and its instantaneous scalar dissipation rate$\chi $. Using high-frequency planar Rayleigh scattering measurements of propane discharging as a round turbulent jet into coflowing carbon dioxide, we acquire with Taylor’s hypothesis a highly resolved three-dimensional field of the propane mass fraction$\theta $. The Reynolds number (based on nozzle diameter and jet exit velocity) varies between 3000 and 8600. The experimental results for the joint probability density of the scalar difference$ \mathrm{\Delta} \theta $and the length$l$of dissipation elements resembles those previously obtained from direct numerical simulations of Wang & Peters (J. Fluid Mech., vol. 554, 2006, pp. 457–475). In addition, the normalized marginal probability density function$\tilde {P} (\tilde {l} )$of the length of dissipation elements follows closely the theoretical model derived by Wang & Peters (J. Fluid Mech., vol. 608, 2008, pp. 113–138). We also find that the mean linear distance${l}_{m} $between two extreme points of an element is of the order of the scalar Taylor microscale${\lambda }_{u} $. Furthermore, the conditional mean$\langle \mathrm{\Delta} \theta \vert l\rangle $scales with Kolmogorov’s$1/ 3$power law. The investigation of the orientation of long dissipation elements in the jet flow reveals a preferential alignment, perpendicular to the streamwise direction for long elements, while the orientation of short elements is close to isotropic. Following an approach proposed by Kholmyansky & Tsinober (Phys. Lett. A, vol. 373, 2009, pp. 2364–2367), we finally investigate the probability density function of the scalar increment$\delta \theta $in the streamwise direction, when strong dissipative events are either retained in or excluded from the measurement volume. In the present study, however, these events are related to maximum points of the scalar dissipation rate$\chi $together with their local extent. When these regions are excluded from the scalar field, we observe a tendency of the probability density function$P(\delta \theta (r))$towards a Gaussian bell-shaped curve.

Multiscale Aspects and Resolution Robustness of Turbulent Scalar Fields and Interfaces

2007 ◽  
Author(s):  
Siarhei Piatrovich ◽  
Haris J. Catrakis
Keyword(s):  
Reynolds Number ◽  
Scalar Field ◽  
High Resolution ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Scalar Fields ◽  
Experimental Database ◽  
Geometrical Properties ◽  
Interfacial Surface

This study focuses on fundamental issues regarding multiscale and multiresolution geometrical properties of turbulent scalar fields and interfaces. The probability density function of the scalar field is examined in terms of geometrical properties of the turbulent interfaces using a high-resolution experimental database of fully-developed turbulent scalar fields in jets at a Reynolds number of Re = 20,000. The pdf is found to exhibit significant robustness to resolution scale. The multiscale properties of the volume of fluid regions enclosed by outer turbulent interfaces are also investigated. The enclosed interfacial volume appears to be significantly robust to the resolution scale as well. An explanation for this behavior is proposed in terms of the opposite effects of protrusions of the scalar interface compared to indentations, which provide positive and negative contributions to the volume respectively. This is in contrast to the interfacial surface area for which protrusions and indentations both have additive contributions.

scholarly journals Gradient trajectory analysis of a scalar field with external intermittency

2009 ◽  
Vol 626 ◽  
pp. 333-365 ◽  
Author(s):  
JUAN PEDRO MELLADO ◽  
LIPO WANG ◽  
NORBERT PETERS
Keyword(s):  
Scalar Field ◽  
Turbulent Combustion ◽  
Dissipation Rate ◽  
Strong Dependence ◽  
Passive Scalar ◽  
Lateral Position ◽  
Scalar Dissipation ◽  
Scalar Dissipation Rate ◽  
Relative Contribution ◽  
Diffusion Layers

The passive scalar field of a temporally evolving shear layer is investigated using gradient trajectories as a means to analyse the scalar probability density function and the conditional scalar dissipation rate in the presence of external intermittency. These results are of significance for turbulent combustion, where improved predictions of the statistics of the conditional dissipation rate are needed in several models. First, the variation of the conventional first and second moments of the conditional dissipation rate across the layer is quantitatively documented in detail. A strong dependence of the conditional dissipation rate on the lateral position and on the conditioning value of the scalar is observed. The dependence on the transverse distance to the centre-plane partially explains the double-hump profile usually reported when this dependence is ignored. The variation with the scalar observed in the ratio between the second and first moments would invalidate certain assumptions commonly done in turbulent combustion. It is also seen that conditioning on the scalar does not reduce the fluctuation of the dissipation rate with respect to unconditional values. Next, the role of external intermittency in these results is investigated. For that purpose, the flow is partitioned into different zones based on different types of gradient trajectories passing through each point, thereby introducing non-local information in comparison with the standard turbulent/non-turbulent separation based on the conventional intermittency function. In addition to the homogeneous outer regions, three zones are identified: a turbulent zone, a turbulence interface and quasi-laminar diffusion layers. The relative contribution from each of these zones to the conventional intermittency factor is reported. The statistics are then conditioned on each of these zones, and the spatial variation of the scalar distribution and of the conditional scalar dissipation rate is explained in terms of the observed zonal statistics. For the Reynolds numbers of the present simulation, between 1500 and 3000 based on the vorticity thickness and the velocity difference, and a Schmidt number equal to 1, it results that the major contribution to both statistics is due to the turbulence interfaces. At the same time, the turbulent zone shows a distinct behaviour, being approximately homogeneous but anisotropic.

scholarly journals Fine-scale statistics of temperature and its derivatives in convective turbulence

2008 ◽  
Vol 611 ◽  
pp. 13-34 ◽  
Author(s):  
M. S. EMRAN ◽  
J. SCHUMACHER
Keyword(s):  
Boundary Layer ◽  
Probability Density Function ◽  
Rayleigh Number ◽  
Probability Density ◽  
Density Function ◽  
Dissipation Rate ◽  
Thermal Boundary Layer ◽  
Temperature Fluctuations ◽  
Thermal Dissipation ◽  
Fine Scale

We study the fine-scale statistics of temperature and its derivatives in turbulent Rayleigh–Bénard convection. Direct numerical simulations are carried out in a cylindrical cell with unit aspect ratio filled with a fluid with Prandtl number equal to 0.7 for Rayleigh numbers between 107 and 109. The probability density function of the temperature or its fluctuations is found to be always non-Gaussian. The asymmetry and strength of deviations from the Gaussian distribution are quantified as a function of the cell height. The deviations of the temperature fluctuations from the local isotropy, as measured by the skewness of the vertical derivative of the temperature fluctuations, decrease in the bulk, but increase in the thermal boundary layer for growing Rayleigh number, respectively. Similarly to the passive scalar mixing, the probability density function of the thermal dissipation rate deviates significantly from a log-normal distribution. The distribution is fitted well by a stretched exponential form. The tails become more extended with increasing Rayleigh number which displays an increasing degree of small-scale intermittency of the thermal dissipation field for both the bulk and the thermal boundary layer. We find that the thermal dissipation rate due to the temperature fluctuations is not only dominant in the bulk of the convection cell, but also yields a significant contribution to the total thermal dissipation in the thermal boundary layer. This is in contrast to the ansatz used in scaling theories and can explain the differences in the scaling of the total thermal dissipation rate with respect to the Rayleigh number.

A Skewed Two-Dimensional Probability Density Function for Methane-Air Turbulent Diffusion Flames

2010 ◽  
Author(s):  
Mohsen Abou-Ellail ◽  
Ryo S. Amano ◽  
Samer Elhaw ◽  
Karam Beshay ◽  
Hatem Kayed
Keyword(s):  
Mathematical Model ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Dissipation Rate ◽  
Diffusion Flames ◽  
Mixture Fraction ◽  
Two Dimensional ◽  
Flamelet Model ◽  
The Mean

The present paper describes a mathematical model for turbulent methane-air jet diffusion flames. The mathematical model solves density-weighted governing equations for momentum, mass continuity, turbulent kinetic energy and its dissipation rate. The combustion model solves density-weighted transport equations for the mixture fraction “f”, its variance “g” and its skewness “s”. These variables are used to compute one part of the probability density function (PDF) in mixture fraction domain. The second part of the PDF is computed from the numerical solutions of the mixture fraction dissipation rate “χ” and its variance χ˜″2. The resulting two-dimensional PDF is defined in the mixture-fraction-scalar-dissipation-rate 2D space. The flamelet combustion sub-model is used to compute the mean flame temperature, density and species mass fractions. The flamelet model provides instantaneous state relationships for the stretched flamelets up to the extinction limit. The mean flame properties are computed through the integration of the stretched flamelet state relationships over the two-dimensional PDF. The present 2D probability density function model can predict rim-attached flames as well as unstable lifted flames. This is because the flamelet model provides information on the flame instability arising from the stretching effects of highspeed flowing gases. The new two-dimensional probability density function is used to predict the flame properties of a free jet methane-air flame for which experimental data exists.

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