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 L12: Turbulence: Mixing II |
Hide Abstracts |
Chair: Kenneth Christensen, University of Illinois at Urbana-Champaign Room: 315 |
Monday, November 21, 2011 3:35PM - 3:48PM |
L12.00001: The Eddy-Diffusivity in Turbulent Two-Particle Dispersion Damien Benveniste, Gregory Eyink R. H. Kraichnan (1966) and T. S. Lundgren (1981) derived a formula for the eddy-diffusivity in Richardson's theory of turbulent 2-particle dispersion: $$\eta _{ij}({\bf r}, t)=\int ^{t}_{0} ds \langle(u_{i} ({\bf x} + {\bf r}, t) - u_{i} ({\bf x}, t)) (u_{i}({\bf x} + {\bf r}, t\vert s) - u_{j}({\bf x}, t \vert s)\rangle. $$ This formula involves the Lagrangian velocity field ${\bf u}({\bf x}, t \vert s)$ experienced at time $s < t$ by the fluid particle which is at point ${\bf x}$ at time t. Evaluating this formula requires tracking fluid particles backward in time, a difficult task with standard DNS. We compute the formula using the JHU Turbulence Database,\footnote{http://turbulence.pha.jhu.edu/} which stores the entire spacetime history of a 1024$^{3}$ DNS of homogeneous, isotropic turbulence at $Re_{\lambda }=433$. We average over particle pairs started at many different initial positions ${\bf x}$ with initial separations ${\bf r}$. We obtain a time-dependent eddy-diffusivity $\eta_{ij}({\bf r}, t)$ which has Batchelor scaling $(\varepsilon r)^{2/3}t$ for short time and Richardson scaling $\varepsilon^{1/3 }r^{4/3}$ for long time. Our resulting diffusion model describes both the Batchelor and Richardson regimes and also predicts new phenomena not yet seen in experiment or simulations. [Preview Abstract] |
Monday, November 21, 2011 3:48PM - 4:01PM |
L12.00002: Passive Scalar in 2D Turbulence Rory Cerbus, Walter Goldburg We examined the behavior of a passive scalar in a 2D turbulent flow and confirm the so-called Batchelor scaling. For large r, the second order structure function S$_2$($r$) = $<(\theta(x+r) - \theta(x))^2>$ $\sim$ log($r$). For small r, S$_2$($r$) $\sim$ $r^2$. The logarithmic dependence of S$_2$($r$) is consistent with a power spectrum that goes as the inverse power of $k$, the wavenumber. These experiments are performed using a falling soap film as the 2D turbulent system and various colored dyes for the passive scalar, which is injected at a point. The decaying turbulence is generated using a comb oriented perpendicular to the film. It does not appear to matter whether the dye is injected above or below the comb. The measurements were made in the Eulerian frame at a single point. Time is then replaced by distance using the Taylor frozen turbulence hypothesis. The structure function is determined from the correlation function, which is calculated using a photon correlation scheme. The passive scalar measurements are compared with the behavior of thickness fluctuations in the soap film, which is another random variable. [Preview Abstract] |
Monday, November 21, 2011 4:01PM - 4:14PM |
L12.00003: Encounter rates of Lagrangian particles in homogeneous isotropic turbulence Satoshi Yokojima, Takashi Mashiko, Takahiro Matsuzaka, Takashi Miyahara Contact rates of Lagrangian particles are investigated numerically by direct simulation of homogeneous isotropic turbulence. The flow Reynolds number, the number of particles, and the contact radius are systematically changed, and the effects on the contact rates are discussed. In the talk, results based on a kinematic simulation of turbulence by unsteady random Fourier modes will be also presented. [Preview Abstract] |
Monday, November 21, 2011 4:14PM - 4:27PM |
L12.00004: Bounded Stochastic Shell Mixing Model: Further Development and Application to Inhomogeneous Scalar Mixing T. Vaithianathan, Yanjun Xia, Lance R. Collins \parindent 0pt Xia and Collins [\emph{Physics of Fluids} {\bf 23} (6):065107, 2011] developed the Bounded Stochastic Shell Mixing (BSSM) model that takes into account the multi-scale nature of the turbulent mixing process. They successfully applied the model to mixing of isotropic scalars with an initial double-delta probability density function (PDF). To enforce the scalar bounds, they introduced a novel ``zeroth mode'' that precisely cancels the inherently non-conservative random terms in the formulation. The extension of the model to the mixing of inhomogeneous scalar fields uses notional particles that move with a fluctuating velocity that is chosen to conform with the underlying turbulent energy spectrum. A consistency condition further requires the particle motion in the direction of the mean scalar gradient be carefully connected to the generation of the scalar fluctuation. The appropriate constraint has been derived and is enforced by the numerical algorithm. This new formulation has been applied to turbulent mixing of a scalar slab of specified thickness. (In the limit of zero thickness, this reduces to the classical ``line source'' problem.) We analyze multiple scalars so that differential diffusion can be considered as well as the effect of the thickness of the slab (relative to the turbulence length scales). The predictions of the BSSM model compare well with direct numerical simulations. [Preview Abstract] |
Monday, November 21, 2011 4:27PM - 4:40PM |
L12.00005: Variations in scalar transport characteristics between forwards and backwards turbulent dispersion Chiranth Srinivasan, Dimitrios Papavassiliou Recent studies about backwards dispersion in time have shown differences with forwards turbulent dispersion, and have highlighted the importance of understanding these differences for practical applications. This work used a direct numerical simulation combined with a Lagrangian scalar tracking approach to obtain single particle and relative dispersion statistics for both forwards and backwards dispersion in an infinitely long turbulent channel flow. The computational domain was 4$\pi $h $\times $ 2h $\times $ 2$\pi $h in x, y, z (where h is the half channel height and h = 300 and h = 150). Results showed differences in the rates of forwards and backwards relative scalar dispersion. The variation in the rates of relative scalar dispersion for a variety of Prandtl numbers (Pr) from 0.1 to 50 was also investigated. The primary direction of heat transport was found to be oriented almost close to the direction perpendicular to the channel walls, for all regions of the channel and for Pr up to 1000. Higher and enduring rates of heat transport were observed for the case of backwards turbulent dispersion. In analogy with the physics of optics, a quantity named the ``turbulent dispersive ratio'' was introduced to indicate the differences between backwards and forwards dispersion. [Preview Abstract] |
Monday, November 21, 2011 4:40PM - 4:53PM |
L12.00006: Passive Scalar Mixing in Compressible Isotropic Turbulence Adam J. Wachtor, Fernando F. Grinstein, C. Richard DeVore Turbulent mixing of a passive scalar is studied through use of implicit large-eddy simulation (ILES) in the context of forced compressible, isotropic turbulence with a mean scalar gradient. The under-resolved prediction of mixing by an under-resolved turbulent velocity field is the problem that the ILES framework addresses without using any explicit model. Low wavenumber forcing is done separately for the solenoidal and dilatational components of the velocity in order for the flow field to achieve a statistically stationary state. The efficiency of ILES allows for the creation of large time-volume ensembles at relatively low computational cost. Effects of Mach number, grid resolution, and the forcing ratio of solenoidal to dilatational kinetic energy on the flow and subsequent scalar mixing will be presented. [Preview Abstract] |
Monday, November 21, 2011 4:53PM - 5:06PM |
L12.00007: Stochastic transport models for mixing in variable-density turbulence J. Bakosi, J.R. Ristorcelli In variable-density (VD) turbulent mixing, where very-different- density materials coexist, the density fluctuations can be an order of magnitude larger than their mean. Density fluctuations are non-negligible in the inertia terms of the Navier-Stokes equation which has both quadratic and cubic nonlinearities. Very different mixing rates of different materials give rise to large differential accelerations and some fundamentally new physics that is not seen in constant-density turbulence. In VD flows material mixing is active in a sense far stronger than that applied in the Boussinesq approximation of buoyantly-driven flows: the mass fraction fluctuations are coupled to each other and to the fluid momentum. Statistical modeling of VD mixing requires accounting for basic constraints that are not important in the small-density-fluctuation passive-scalar-mixing approximation: the unit-sum of mass fractions, bounded sample space, and the highly skewed nature of the probability densities become essential. We derive a transport equation for the joint probability of mass fractions, equivalent to a system of stochastic differential equations, that is consistent with VD mixing in multi-component turbulence and consistently reduces to passive scalar mixing in constant-density flows. [Preview Abstract] |
Monday, November 21, 2011 5:06PM - 5:19PM |
L12.00008: Consistency and realizability requirements for stochastic diffusion models for variable-density turbulent mixing J.R. Ristorcelli, J. Bakosi Rational turbulence model development has applied principles that ensure consistency with the physical conservation laws and statistical constraints. Examples are the principles of invariance and realizability (Lumley, Adv.\ Appl.\ Mech., 18, 1979, pp.\ 123--176), and linearity and independence of passive scalars in mixing (Pope, Phys.\ Fluids, 26, 1983, pp.\ 404--408). Models that violate these principles can produce unphysical results. We discuss modeling principles and constraints for variable-density multi-material turbulent mixing. We develop the consequences of the mass conservation law for multi-component mixtures for random-walk methods in variable- density turbulence. In such flows the density fluctuations can be larger than the mean density and several important constraints restrict the functional forms of mixing models. One consequence of the constraints developed is that the coefficient of the Wiener process (if nonzero) must be nonlinear and coupled to the other mass fractions to ensure consistency with mass conservation. Typical Langevin-type models for these processes violate these constraints peculiar to variable-density mixing. [Preview Abstract] |
Monday, November 21, 2011 5:19PM - 5:32PM |
L12.00009: Modeling the subfilter scalar variance for large eddy simulation in forced isotropic turbulence Adam Cheminet, Guillaume Blanquart Static and dynamic model for the subfilter scalar variance in homogeneous isotropic turbulence are investigated using direct numerical simulations (DNS) of a lineary forced passive scalar field. First, we introduce a new scalar forcing technique conditioned only on the scalar field which allows the fluctuating scalar field to reach a statistically stationary state. Statistical properties, including 2nd and 3rd statistical moments, spectra, and probability density functions of the scalar field have been analyzed. Using this technique, we performed constant density and variable density DNS of scalar mixing in isotropic turbulence. The results are used in an a-priori study of scalar variance models. Emphasis is placed on further studying the dynamic model introduced by G. Balarac, H. Pitsch and V. Raman [ Phys. Fluids 20, (2008) ]. Scalar variance models based on Bedford and Yeo's expansion are accurate for small filter width but errors arise in the inertial subrange. Results suggest that a constant coefficient computed from an assumed Kolmogorov spectrum is often sufficient to predict the subfilter scalar variance. [Preview Abstract] |
Monday, November 21, 2011 5:32PM - 5:45PM |
L12.00010: Effect of initial conditions on mixing within a turbulent channel flow Emmanuel Germaine, Laurent Mydlarski, Luca Cortelezzi We analyze the mixing of a passive scalar (temperature) in a turbulent channel flow for different initial conditions by means of numerical simulations. The numerical domain is a channel delimited by two parallel and infinite flat walls, simulated using periodic boundary conditions in the streamwise and spanwise directions. We consider three initial distributions of temperature, where hot and cold fluids are separated by a sharp but continuous interface that subdivides the computational domain into two identical halves. The interface is taken parallel to the walls or perpendicular to them, oriented in the streamwise or spanwise directions. We perform a direct numerical simulation of the temperature field at $Re_{\tau} = 190$ when the flow is fully turbulent. The numerical scheme combines an advection diffusion solver, i.e, a third-order flux integral method based on UTOPIA (Leonard \emph{et al.}, Appl. Math. Modeling, 1995), with a Navier-Stokes solver, i.e, spectral code released by Prof. John Gibson, http://www.channelflow.org). We quantify the time-evolution of the mixing performance of the turbulent flow using different measures of the mixing, including a negative Sobolev norm -- a diagnostic currently used to asses the mixing performance of laminar flows. Finally, we discuss the influence of the initial conditions on the turbulent mixing. Funding was provided by NSERC (grants RGPIN217169 and RGPIN217184). [Preview Abstract] |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2022 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
1 Research Road, Ridge, NY 11961-2701
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700