Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session S6: Turbulence: Mixing III |
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Chair: P.K. Yeung, Georgia Institute of Technology Room: 309 |
Tuesday, November 22, 2011 3:05PM - 3:18PM |
S6.00001: Schmidt-number dependence in turbulent mixing: very low Schmidt numbers and spectral transfer P.K. Yeung, K.R. Sreenivasan, K.P. Iyer, D. Buaria The physics of turbulent mixing depends on both the Reynolds number and Schmidt number ($Sc$), which varies widely in applications and leads to different scaling regimes. The case of $Sc\ll 1$, which is relevant in liquid metals and astrophysics, is perhaps the least understood since laboratory data are difficult to obtain. We have performed direct numerical simulations of passive scalars of $Sc$ from 1/32 to 1/512, on a periodic domain of larger size than usual to accommodate the growth of large scales in the scalar fields, and with a very small time step to resolve the time scales of molecular diffusion. For $Sc=1/128$ and 1/512 the spectrum obtained appears to support $k^{-17/3}$ inertial-diffusive behavior proposed by Batchelor, Howells \& Townsend (1959) although results at higher Reynolds numbers are required. Calculations of spectral transfer, including the transfer flux, indicate that the spectral cascade is greatly suppressed, which implies a number of classical notions such as dissipative anomaly and local isotropy become inapplicable in this regime. Together with other recently published data the new results also enable progress towards a unified view of Schmidt number dependence for small-scale turbulent mixing. [Preview Abstract] |
Tuesday, November 22, 2011 3:18PM - 3:31PM |
S6.00002: A conditional sampling-based method for noise and resolution corrections for scalar dissipation rate measurements Chenning Tong, Jian Cai A conditional sampling-based method for correcting noise and resolution effects for scalar dissipation rate measurements is developed. Noise and resolution effects on the measured dissipation rate have opposite trends, making their separation and accurate corrections difficult. A major task in dissipation rate correction, therefore, is to isolate each effect. The method presented in this work uses instantaneous local scalar mean and variance as conditioning variables, and is based in part on Kolmogorov's refined similarity hypotheses. It ensures selection of instantaneous fully resolved local scalar fields, which are analyzed to determine the measurement noise. Noise correction is applied to potentially under-resolved local scalar fields, also selected using the conditional-sampling procedure, effectively separating the effects of noise from those of resolution. The error function is used as a model for the potentially under-resolved local scalar fields to evaluate their dissipation length scales and to make corrections for the dissipation rate. The present method uses local instead of spectral analyses; therefore, can be applied to the mean scalar dissipation rate conditional on the scalar values. An application of the method to temperature dissipation rate in a slightly heated turbulent jet shows excellent results, validating the method. The method has also been applied to turbulent flames. [Preview Abstract] |
Tuesday, November 22, 2011 3:31PM - 3:44PM |
S6.00003: Can fractal objects operate as efficient inline mixers? Sylvain Laizet, John Christos Vassilicos Recently, Hurst {\&} Vassilicos, PoF 2007, Seoud {\&} Vassilicos, PoF 2007, Mazellier {\&} Vassilicos, PoF, 2010 used different multiscale grids to generate turbulence in a wind tunnel and have shown that complex multiscale boundary/initial conditions can drastically influence the behaviour of a turbulent flow, but that the detailled specific nature of the multiscale geometry matters too. Multiscale (fractal) objects can be designed to be immersed in any fluid flow where there is a need to control and design the turbulence generated by the object. Different types of multiscale objects can be designed as different types of energy-efficient mixers with varying degrees of high turbulent intensities, small pressure drop and downstream distance from the grid where the turbulence is most vigorous. Here, we present a 3D DNS study of the stirring and mixing of a passive scalar by turbulence generated with either a fractal square grid or a regular grid in the presence of a mean scalar gradient. The results show that: (1) there is a linear increase for the passive scalar variance for both grids, (2) the passive scalar variance is ten times bigger for the fractal grid, (3) the passive scalar flux is constant after the production region for both grids, (4) the passive scalar flux is enhanced by an order of magnitude for the fractal grid. [Preview Abstract] |
Tuesday, November 22, 2011 3:44PM - 3:57PM |
S6.00004: Instabilities and mixing in a quasi-2D Lorentz-force driven flow Radford Mitchell, Roman Grigoriev In this talk we describe the transition to weak turbulence in a Kolmogorov flow inside a thin layer of electrolyte driven by a steady current in experiment and a computational model. We find the mixing efficiency of the flow to be a non-monotonic function of the driving current, mirroring the temporal complexity of the flow pattern. We also illustrate the generic mechanism of mixing by time-periodic two-dimensional flows near a supercritical Hopf bifurcation and provide a perturbative description of the mixing process. [Preview Abstract] |
Tuesday, November 22, 2011 3:57PM - 4:10PM |
S6.00005: Toward topology-based characterization of small-scale mixing in compressible turbulence Sawan Suman, Sharath Girimaji Turbulent mixing rate at small scales of motion (molecular mixing) is governed by the steepness of the scalar-gradient field which in turn is dependent upon the prevailing velocity gradients. Thus motivated, we propose a velocity-gradient topology-based approach for characterizing small-scale mixing in compressible turbulence. We define a mixing efficiency metric that is dependent upon the topology of the solenoidal and dilatational deformation rates of a fluid element. The mixing characteristics of solenoidal and dilatational velocity fluctuations are clearly delineated. We validate this new approach by employing mixing data from direct numerical simulations (DNS) of compressible decaying turbulence with passive scalar. For each velocity-gradient topology, we compare the mixing efficiency predicted by the topology-based model with the corresponding conditional scalar variance obtained from DNS. The new mixing metric accurately distinguishes good and poor mixing topologies and indeed reasonably captures the numerical values. The results clearly demonstrate the viability of the proposed approach for characterizing and predicting mixing in compressible flows. [Preview Abstract] |
Tuesday, November 22, 2011 4:10PM - 4:23PM |
S6.00006: Influence of Forcing Structure on Two-Dimensional Weak Turbulence Yang Liao, Douglas Kelley, Nicholas Ouellette The dependence of the dynamics of two-dimensional turbulence on its forcing topology is an interesting and practical question for experiments. We generate quasi-two-dimensional flows in thin layers of salt water with a forcing geometry that is either a lattice of alternating vortices or an array of alternating shear bands. We observe that the vortex flow has more fluctuating energy, but that the shear flow has larger spatial gradients. We attribute these differences to the fact that shear forcing imposes fewer constraints on the flow and allows the production of smaller length scales. [Preview Abstract] |
Tuesday, November 22, 2011 4:23PM - 4:36PM |
S6.00007: Cloud microphysical effects of turbulent mixing and entrainment Raymond Shaw, Bipin Kumar, Joerg Schumacher Turbulent mixing and entrainment at the boundary of a cloud is studied by means of direct numerical simulations that couple the Eulerian description of the turbulent velocity and water vapor fields with a Lagrangian ensemble of cloud water droplets that can grow and shrink by condensation and evaporation. The focus is on detailed analysis of the relaxation process of the droplet ensemble during the entrainment of subsaturated air, in particular the dependence on turbulence time scales, droplet number density, initial droplet radius and particle inertia. We find that the droplet evolution during the entrainment process is captured best by a phase relaxation time that is based on the droplet number density with respect to the entire simulation domain and the initial droplet radius. Even under conditions favoring homogeneous mixing, the probability density function of supersaturation at droplet locations exhibits strong negative skewness, consistent with droplets near the cloud boundary being suddenly mixed into clear air, but rapidly approaches a narrower, bimodal shape. The droplet size distribution, which is initialized as perfectly monodisperse, broadens and also becomes somewhat negatively skewed. However, particle inertia and gravitational settling impose a sharp cutoff in both tails of the droplet size distribution during later stages of the mixing. [Preview Abstract] |
Tuesday, November 22, 2011 4:36PM - 4:49PM |
S6.00008: Rapid growth of cloud droplets by turbulence John Christos Vassilicos, Vassilis Dallas Assuming perfect collision efficiency, we demonstrate that turbulence can initiate and sustain rapid growth of very small water droplets in air even when these droplets are too small to cluster, and even without having to take gravity and small-scale intermittency into account. This is because the range of local Stokes numbers of identical droplets in the turbulent flow field is broad enough even when small-scale intermittency is neglected. This demonstration is given for turbulence which is one order of magnitude less intense than typically in warm clouds but with a volume fraction which, even though small, is nevertheless large enough for an estimated a priori frequency of collisions to be ten times larger than in warm clouds. However, the time of growth in these conditions turns out to be one order of magnitude smaller than in warm clouds. [Preview Abstract] |
Tuesday, November 22, 2011 4:49PM - 5:02PM |
S6.00009: The emergence of correlations from distant sources in turbulent flows Mihkel Kree, J\'er\^ome Duplat, Emmanuel Villermaux A scalar field injected from a point source in a turbulent flow resolves into a set of elongated sheet-like structures whose concentration probability distribution $P(C)$ is well understood in terms of the interplay between stretching histories of fluid particles, and molecular diffusion. Additionally, neighboring sheets may diffusively merge and evolve further in an undistinguishable fashion. We report here on experiments using two distinct dyes (Fluorescein and Rhodamine in water) injected form sources separated by a variable distance $s$ in a turbulent jet. This method allows to separate the total concentration field $C$ into its subparts $C_1$ and $C_2$ originating from each sources. Joint probability distributions $Q(C_1,C_2)$ and correlations between the fields can thus be measured. We evidence this way the crossover scale above which the fields are and remain independent in the flow. [Preview Abstract] |
Tuesday, November 22, 2011 5:02PM - 5:15PM |
S6.00010: Spatiotemporal persistence of spectral fluxes in two-dimensional weak turbulence Douglas H. Kelley, Nicholas T. Ouellette Nonlinearity in a dynamical system necessarily leads to coupling between different spatial and temporal frequencies. Using a recently developed filtering technique, we study the spatiotemporal properties of the scale-to-scale fluxes of energy and enstrophy in a weakly turbulent experimental quasi-two-dimensional flow. Although these spectral properties vary in time and space, we show that they persist along the Lagrangian trajectories of fluid elements for times that can be nearly as long as the correlation time of the velocity field itself. Additionally, we show that at small scales, the spectral energy flux persists longest for fluid elements in strongly hyperbolic regions of the flow, whereas at large scales it persists in strongly elliptic regions. [Preview Abstract] |
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