Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session FS: Turbulent Scalar Mixing II |
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Chair: Rodney Fox, Iowa State University Room: Hilton Chicago Stevens 4 |
Monday, November 21, 2005 8:00AM - 8:13AM |
FS.00001: Measurements of joint statistics of a passive scalar and its dissipation rate Mohsen Ferchichi, Tony Standbridge, Stavros Tavoularis The pdf formulation of scalar transport in turbulent flows requires modeling of the expectation of the scalar fluctuation destruction rate by molecular motions (``dissipation'' rate), conditional upon the scalar value. In most previous experimental studies, the scalar dissipation rate has been approximated by its streamwise component, under the assumption of local isotropy. In the present study, we have measured simultaneously both the streamwise and transverse components of the dissipation rate and we have determined joint pdf of the scalar and its dissipation rate in uniformly sheared turbulence with a uniform mean scalar gradient. These joint pdf and corresponding co-spectra of the scalar and its dissipation rate suggest that these properties are statistically independent, whether the latter is approximated by its streamwise or transverse component. Further tests of scalar local isotropy in moderately large Reynolds number flow will also be presented. [Preview Abstract] |
Monday, November 21, 2005 8:13AM - 8:26AM |
FS.00002: Universal range scaling of dissipation elements Norbert Peters, Lipo Wang In order to extract statistics from turbulent passive scalars fields obtained from DNS simulations a new method of analysis is introduced. It consists of determining local mininum and maximum points of the fluctuating scalar field via trajectories starting from every grid in direction of ascending and descending scalar gradients. The ensemble of grid points from which the same minimum and maximum points are reached determine a spatial region which is called a ``dissipation element.'' These are parameterized by the linear distance between the minimum and maximum points and the absolute value of the scalar difference at these points. The joint pdf of these parameters is decom-posed into a marginal pdf of the linear distance and a conditional pdf of the scalar difference. A Boltzmann-type evolution equation is presented for the marginal pdf. It is also found that the conditional mean of the fluctuating scalar difference follows the same inertial range scaling as the square root of the structure function. This scaling turns out to be more robust than that of structure functions which show no scale separation in low Reynolds number DNS. The latter is explained by the stronger correlation of the scalar field in the vicinity of extremal points, which tends to contaminate the inertial range scaling in structure function analysis. Finally, the ``Extended Self Similarity'' hypothesis is discussed by recontructing the scalings of higher moments and comparing it to the DNS results. [Preview Abstract] |
Monday, November 21, 2005 8:26AM - 8:39AM |
FS.00003: Asymptotic form of the PDF of scalar dissipation rate in isotropic turbulence Diego Donzis, P.K. Yeung, K.R. Sreenivasan An accurate knowledge of the probability density function (PDF) of scalar dissipation rate fluctuations is important for numerous reasons, such as small-scale intermittency and local flame extinction in turbulent reacting flows. Previous work in the literature suggest the wide tails of the scalar dissipation PDF can be described by stretched exponential fits whose parameters are Reynolds- and Schmidt-number dependent. We consider the asymptotic form of this PDF using direct numerical simulation data in isotropic turbulence at resolution up to $2048^3$ covering Taylor-scale Reynolds numbers from 8 to 700 and Schmidt numbers from 1/8 to 1024. For moderately diffusive scalars ($Sc=O(1)$) the stretched-exponential parameters are consistent with an increase in intermittency with Reynolds number similar to energy dissipation and enstrophy. For weakly-diffusive scalars ($Sc\gg 1$) saturation of intermittency occurs beyond a value of $Sc$ which decreases with increasing Reynolds number. In general, the stretched-exponential form predicts higher-order moments more accurately than the log-normal hypothesis used often in modeling. We also discuss the PDF of scalar dissipation averaged locally over a box of size falling in the classical inertial-convective and viscous-convective ranges. [Preview Abstract] |
Monday, November 21, 2005 8:39AM - 8:52AM |
FS.00004: Multiscale mixing efficiencies for passive scalars Jean-Luc Thiffeault, Tiffany A. Shaw, Charles R. Doering The evolution of a passive scalar $\theta({\bf x},t)$ maintained by a steady spatially mean-zero source $s({\bf x})$ and stirred by a prescribed velocity field $u({\bf x},t)$ is the advection-diffusion equation $\partial_t \theta + {\bf u} \cdot \nabla \theta = \kappa \Delta \theta + s$, where $\kappa$ is the molecular diffusivity. In a finite volume the space-time averaged variances $\left<|\nabla\theta|^2 \right>$, $\left<\theta^2 \right>$ and $\left<|\nabla^{-1} \theta|^2\right>$ are quantitative measures of the mixing due to the combination of advection and diffusion at small, intermediate and large scales respectively: the smaller the variances, the better the mixing. The enhancement of mixing over molecular diffusion due to the stirring is naturally gauged in dimensionless form by the small, intermediate and large scale mixing efficiencies $M_{p}^{2} := \left<|\nabla^{p}\theta_0|^2\right> /\left<|\nabla^{p} \theta|^2\right>$ for $p\in\left\{-1,0,1\right\}$ where $\theta_0$ is the steady solution of the diffusion equation $\partial_t \theta_0 = \kappa \Delta \theta_0 + s$ without stirring. These efficiencies depend on the structure of the source and the stirring as well as the domain and $\kappa$. We report rigorous mathematical limits on $M_p$ in terms of the P\'eclet number $Pe = UL/\kappa$, where $U^2=\left< |{\bf u}|^2 \right>$ and $L$ is a domain length scale. The mathematical estimates are compared to the results of direct numerical simulations for a model problem. [Preview Abstract] |
Monday, November 21, 2005 8:52AM - 9:05AM |
FS.00005: Lagrangian measurements in two-dimensional turbulence Michael Rivera, Michael Twardos, Robert Ecke We present statistical properties of two-dimensional turbulence from the lagrangian perspective. Utilizing experimental measurements from an electromagnetically forced stratified layer, results obtained from classical analysis tools, such as the relative diffusion rate of two particles ({\em i.e.} the $t^3$ Richardson diffusion law), as well as more recent techniques, such as relative position doubling time analysis, are presented and compared. These results will be contrasted with earlier measurements in a similar system to help clarify the interpretation of these earlier results, as well as shed light on mixing properties of two-dimensional turbulence. [Preview Abstract] |
Monday, November 21, 2005 9:05AM - 9:18AM |
FS.00006: Multi-point correlation functions of a passive scalar field in a turbulent boundary layer D.R. Webster, R.J. Miller Multi-point correlation functions are used to analyze a fluctuating passive scalar field that develops downstream of an iso-kinetic point release of a high Schmidt number dye into the inertial layer of a fully developed open channel turbulent boundary layer. Instantaneous images of the field are captured using planar laser-induced fluorescence (PLIF). The spatial structure is fully resolved by ensuring that the laser sheet thickness and camera pixel spacing are on the order of the Batchelor length scale. Data are collected for a range of Reynolds numbers (60 $< \quad R \& e_\lambda \quad <$ 120) and injection length scales (2.2 mm $< \quad d \quad <$ 9.4 mm). The fields are evaluated by determining the scaling properties, extracting geometric relationships, and examining the small-scale structures. Two-point correlation functions are used to quantify the integral length scale, which is subsequently used to scale the spacing of the multi-point correlation functions. Multi-point correlators probe the scalar field for the presence of spatial structures and simultaneously retain scaling property information. The results of this research are expected to aid in predicting the mixing and transport of the turbulent passive scalar field. [Preview Abstract] |
Monday, November 21, 2005 9:18AM - 9:31AM |
FS.00007: The dispersion of microscopic molecular clouds in turbulence Mira Pashtrapanshka, Willem van de Water We write thin lines (width 60 $\mu$m) and small dots (size 100 $\mu$m) in a strongly turbulent jet flow of air. These patterns are written through photosynthesis of NO molecules using focussed light from a UV excimer laser and are followed in time through laser-induced fluorescence. The size of the written objects is a few times the Kolmogorov length. The Lagrangian trajectories of these clouds can be used for velocimetry, but also to study the dispersion of molecular tracers in turbulence. Our molecular tracers have Schmidt number unity and momentum diffuses at the same rate as mass. Ultraviolet images of the clouds offer a unique view on small- scale mixing. The clouds are dispersed by turbulence and by molecular diffusion, resulting in highly intermittent concentration fluctuations after a few small eddy turnover times. Consequently, large-order structure functions of the fluctuation concentration have strongly anomalous inertial-range scaling exponents. [Preview Abstract] |
Monday, November 21, 2005 9:31AM - 9:44AM |
FS.00008: The coarse graining scale in turbulent mixtures Emmanuel Villermaux, J\'er\^ome Duplat What is the physical lengthscale which supports the concentration content in a stirred mixture? Among the lengthscales familiar in stirred mixtures is the dissipation scale which equilibrates substrate deformation and diffusive smearing rates. That scale is a decreasing function of the deformation rate, and is thus a decreasing function of the Reynolds number in turbulent flows. We will show that the mixture concentration content is defined on a support whose elementary brick \begin{equation} \eta=LSc^{-2/5}, \label{etaval} \end{equation} is much larger. It scales like the stirring scale $L$, depends on the Schmidt number $Sc$ and is independent of the Reynolds number. This scale results from the aggregation of bundles of elementary stretched scalar sheets, merging under large scale substrate deformation. The above law is supported by measurements covering two decades in $L$ and three decades in $Sc$. [Preview Abstract] |
Monday, November 21, 2005 9:44AM - 9:57AM |
FS.00009: The Influence of Transport Phenomena on Turbulent Mixing rates Xinfeng Liu New simulations compare Rayleigh-Taylor mixing rates for ideal fluids and for real fluids with experimental values for surface tension and for mass diffusion. The simulated real fluid mixing rates agree with those measured experimentally within 15\%. Comparison to theoretical predictions relating the mixing rate, the bubble width and the bubble height fluctuations based on bubble merger models shows similar agreement with experiment. The ideal fluid mixing rate is some 50\% larger, providing an example of the sensitivity of the mixing rate to physical scale breaking interfacial phenomena; we also observe sensitivity to numerical scale breaking artifacts. [Preview Abstract] |
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