Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session L29: Turbulence: MixingTurbulence

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Chair: Susan Kurien, Los Alamos National Laboratory Room: 205 
Monday, November 20, 2017 4:05PM  4:18PM 
L29.00001: On the kinematics of scalar isosurfaces in turbulent flow Brandon C. Blakeley, James J. Riley, Duane W. Storti, Weirong Wang The behavior of scalar isosurfaces in turbulent flows is of fundamental interest and importance in a number of problems, e.g., the stoichiometric surface in nonpremixed reactions, and the turbulent/nonturbulent interface in localized turbulent shear flows. Of particular interest here is the behavior of the average surface area per unit volume, $\Sigma$. We report on the use of direct numerical simulations and sophisticated surface tracking techniques to directly compute $\Sigma$ and model its evolution. We consider two different scalar configurations in decaying, isotropic turbulence: first, the isosurface is initially homogenous and isotropic in space, second, the isosurface is initially planar. A novel method of computing integral properties from regularlysampled values of a scalar function is leveraged to provide accurate estimates of $\Sigma$. Guided by simulation results, modeling is introduced from two perspectives. The first approach models the various terms in the evolution equation for $\Sigma$, while the second uses Rice’s theorem to model $\Sigma$ directly. In particular, the two principal effects on the evolution of $\Sigma$, i.e., the growth of the surface area due to local surface stretching, and the ultimate decay due to molecular destruction, are addressed. [Preview Abstract] 
Monday, November 20, 2017 4:18PM  4:31PM 
L29.00002: Reproducing scalar mixing of turbulent jets in a 3D periodic box K. Jeff Rah, Guillaume Blanquart A triply periodic DNS is a convenient framework to analyze the turbulent mixing process, since it can produce statistically stationary turbulence. In addition, the periodic boundary condition makes it easy to compute the spatial spectra of scalars. However, it is difficult to create a realistic turbulent flow with such a geometry. In this current investigation, we aim to develop a method to simulate a realistic turbulent mixing process inside a 3D periodic box. The target real flow is an axisymmetric jet with passive scalars on its centerline. The velocity and scalar information of turbulent jets on the centerline is applied to the momentum equation and scalar transport equation in physical space. The result is the combination of a mean gradient term and a linear forcing term in the scalar equation. These new forcing terms are derived to replicate the scalar mixing properties of jets in a triply periodic DNS. The present analysis differs from other forcing schemes for their derivation process did not involve any use of the velocity or scalar information of a real turbulent flow. A set of DNS has been performed with the new forcing term, and various turbulent parameters and spectral relations are compared against experiments. [Preview Abstract] 
Monday, November 20, 2017 4:31PM  4:44PM 
L29.00003: Ensemblebased data assimilation and optimal sensor placement for scalar source reconstruction Vincent Mons, Qi Wang, Tamer Zaki Reconstructing the characteristics of a scalar source from limited remote measurements in a turbulent flow is a problem of great interest for environmental monitoring, and is challenging due to several aspects. Firstly, the numerical estimation of the scalar dispersion in a turbulent flow requires significant computational resources. Secondly, in actual practice, only a limited number of observations are available, which generally makes the corresponding inverse problem illposed. Ensemblebased variational data assimilation techniques are adopted to solve the problem of scalar source localization in a turbulent channel flow at $Re_{\tau}=180$. This approach combines the components of variational data assimilation and ensemble Kalman filtering, and inherits the robustness from the former and the ease of implementation from the latter. An ensemblebased methodology for optimal sensor placement is also proposed in order to improve the condition of the inverse problem, which enhances the performances of the data assimilation scheme. [Preview Abstract] 
Monday, November 20, 2017 4:44PM  4:57PM 
L29.00004: Optimal initial condition of passive tracers for their maximal mixing in finite time Mohammad Farazmand The efficiency of fluid flow for mixing passive tracers is often limited by fundamental laws and/or design constraints, such that a perfectly homogeneous mixture cannot be obtained in finite time. Here we address the natural corollary question: Given a fluid flow, what is the optimal initial tracer pattern that leads to the most homogeneous mixture after a prescribed finite time? We show that this optimal initial condition coincides with the right singular vector (corresponding to the smallest singular value) of a suitably truncated PerronFrobenius (PF) operator. The truncation of the PF operator is made under the assumption that there is a small lengthscale threshold under which the tracer blobs are considered, for all practical purposes, completely mixed. We demonstrate our results on two examples: a prototypical model known as the sine flow and a direct numerical simulation of twodimensional turbulence. Evaluating the optimal initial condition through this framework requires only the position of a dense grid of fluid particles at the final instance and their preimages at the initial instance of the prescribed time interval. As such, our framework can be readily applied to flows where such data are available through numerical simulations or or experimental measurements. [Preview Abstract] 
Monday, November 20, 2017 4:57PM  5:10PM 
L29.00005: Symmetry Breaking in a random passive scalar Zeliha Kilic, Richard Mclaughlin, Roberto Camassa We consider the evolution of a decaying passive scalar in the presence of a gaussian white noise fluctuating shear flow. We focus on deterministic initial data and establish the short, intermediate, and long time symmetry properties of the evolving point wise probability measure for the random passive scalar. Analytical results are compared directly to Monte Carlo simulations. Time permitting we will compare the predictions to experimental observations. [Preview Abstract] 
Monday, November 20, 2017 5:10PM  5:23PM 
L29.00006: Measurements of multiscalar mixing in a turbulent coaxial jet Alais Hewes, Laurent Mydlarski There are relatively few studies of turbulent multiscalar mixing, despite the occurrence of this phenomenon in common processes (e.g. chemically reacting flows, oceanic mixing). In the present work, we simultaneously measure the evolution of two passive scalars (temperature and helium concentration) \textit{and} velocity in a coaxial jet. Such a flow is particularly relevant, as coaxial jets are regularly employed in applications of turbulent nonpremixed combustion, which relies on multiscalar mixing. The coaxial jet used in the current experiment is based on the work of Cai \textit{et al}. (\textit{J. Fluid Mech.}, 2011), and consists of a vertically oriented central jet of helium and air, surrounded by an annular flow of (unheated) pure air, emanating into a slow coflow of (pure) heated air. The simultaneous twoscalar and velocity measurements are made using a 3wire hotwire anemometry probe. The first two wires of this probe form an interference (or WayLibby) probe, and measure velocity and concentration. The third wire, a hotwire operating at a low overheat ratio, measures temperature. The 3wire probe is used to obtain concurrent velocity, concentration, and temperature statistics to characterize the mixing process by way of single and multivariable/joint statistics. [Preview Abstract] 
Monday, November 20, 2017 5:23PM  5:36PM 
L29.00007: Extracting a mix parameter from 2D radiography of variable density flow Susan Kurien, Forrest Doss, Daniel Livescu A methodology is presented for extracting quantities related to the statistical description of the mixing state from the 2D radiographic image of a flow. Xray attenuation through a target flow is given by the BeerLambert law which exponentially damps the incident beam intensity by a factor proportional to the density, opacity and thickness of the target. By making reasonable assumptions for the mean density, opacity and effective thickness of the target flow, we estimate the contribution of density fluctuations to the attenuation. The fluctuations thus inferred may be used to form the correlation of density and specificvolume, averaged across the thickness of the flow in the direction of the beam. This correlation function, denoted by $b$ in RANS modeling, quantifies turbulent mixing in variable density flows. The scheme is tested using DNS data computed for variabledensity buoyancydriven mixing. We quantify the deficits in the extracted value of $b$ due to target thickness, Atwood number, and modeled noise in the incident beam. This analysis corroborates the proposed scheme to infer the mix parameter from thin targets at moderate to low Atwood numbers. The scheme is then applied to an image of countershear flow obtained from experiments at the National Ignition Facility. [Preview Abstract] 
Monday, November 20, 2017 5:36PM  5:49PM 
L29.00008: Measurement of Turbulent Fluxes of Swirling Flow in a Scaled Up Multi Inlet Vortex Reactor Michael Olsen, Emmanual Hitimana, James Hill, Rodney Fox The multiinlet vortex reactor (MIVR) has been developed for use in the FlashNanoprecipitation (FNP) process. The MIVR has four identical square inlets connected to a central cylindrical mixing chamber with one common outlet creating a highly turbulent swirling flow dominated by a strong vortex in the center. Efficient FNP requires rapid mixing within the MIVR. To investigate the mixing, instantaneous velocity and concentration fields were acquired using simultaneous stereoscopic particle image velocimetry and planar laserinduced fluorescence. The simultaneous velocity and concentration data were used to determine turbulent fluxes and spatial crosscorrelations of velocity and concentration fluctuations. The measurements were performed for four inlet flow Reynolds numbers (3250, 4875, 6500, and 8125) and at three measurement planes within the reactor. A correlation between turbulent fluxes and vortex strength was found. For all Reynolds numbers, turbulent fluxes are maximum in the vortex dominated central region of the reactor and decay away from the vortex. Increasing Reynolds number increased turbulent fluxes and subsequently enhanced mixing. The mixing performance was confirmed by determining coefficients of concentration variance within the reactor. [Preview Abstract] 
Monday, November 20, 2017 5:49PM  6:02PM 
L29.00009: On the selfpreservation of turbulent jet flows with variable viscosity Luminita Danaila, Michael Gauding, Emilien Varea The concept of selfpreservation has played an important role in shaping the understanding of turbulent flows. The assumption of complete selfpreservation imposes certain constrains on the dynamics of the flow, allowing to express onepoint or twopoint statistics by choosing an appropriate unique length scale. Determining this length scale and its scaling is of high relevance for modeling. In this work, we study turbulent jet flows with variable viscosity from the selfpreservation perspective. Turbulent flows encountered in engineering and environmental applications are often characterized by fluctuations of viscosity resulting for instance from variations of temperature or species composition. Starting from the transport equation for the moments of the mixture fraction increment, constraints for selfpreservation are derived. The analysis is based on direct numerical simulations of turbulent jet flows where the viscosity between host and jet fluid differs. It is shown that fluctuations of viscosity do not affect the decay exponents of the turbulent energy or the dissipation but modify the scaling of twopoint statistics in the dissipative range. Moreover, the analysis reveals that complete selfpreservation in turbulent flows with variable viscosity cannot be achieved. [Preview Abstract] 
Monday, November 20, 2017 6:02PM  6:15PM 
L29.00010: The selfpreservation of dissipation elements in homogeneous isotropic decaying turbulence Michael Gauding, Luminita Danaila, Emilien Varea The concept of selfpreservation has played an important role in shaping the understanding of turbulent flows. The assumption of complete selfpreservation imposes certain constrains on the dynamics of the flow, allowing to express statistics by choosing an appropriate unique length scale. Another approach in turbulence research is to study the dynamics of geometrical objects, like dissipation elements (DE). DE appear as coherent spacefilling structures in turbulent scalar fields and can be parameterized by the linear length between their ending points. This distance is a natural length scale that provides information about the local structure of turbulence. In this work, the evolution of DE in decaying turbulence is investigated from a selfpreservation perspective. The analysis is based on data obtained from direct numerical simulations (DNS). The temporal evolution of DE is governed by a complex process, involving cutting and reconnection events, which change the number and consequently also the length of DE. An analysis of the evolution equation for the probability density function of the length of DE is carried out and leads to specific constraints for the selfpreservation of DE, which are justified from DNS. [Preview Abstract] 
Monday, November 20, 2017 6:15PM  6:28PM 
L29.00011: On statistical conservation laws in smooth chaotic velocity fields Siim Ainsaar, Jaan Kalda, Mihkel Kree It is known that at small scales, the separation of Lagrangian tracer particles in a $d$dimensional incompressible isotropic turbulent flow obeys a statistical conservation law $\langle r^{d} \rangle = \mathrm{const}$. We present a novel simple geometric proof of this fact, and generalize it to the case of compressible velocity fields. This law constrains the entropy function and thus the nongaussianity of the probability distribution of the logarithm of particle separation. This suggests an approximate way to minimally generalize the FokkerPlanck equation describing the evolution of this probability distribution, in order to account for the effects of finite correlation time. Numerical simulations verify the validity of this approach. [Preview Abstract] 
Monday, November 20, 2017 6:28PM  6:41PM 
L29.00012: Multiscale statistics of trajectories with applications to fluid particles in turbulence and football players Kai Schneider, Benjamin Kadoch, Wouter Bos The angle between two subsequent particle displacement increments is evaluated as a function of the time lag. The directional change of particles can thus be quantified at different scales and multiscale statistics can be performed. Flow dependent and geometry dependent features can be distinguished. The mean angle satisfies scaling behaviors for short time lags based on the smoothness of the trajectories. For intermediate time lags a power law behavior can be observed for some turbulent flows, which can be related to Kolmogorov scaling. The long time behavior depends on the confinement geometry of the flow. We show that the shape of the probability distribution function of the directional change can be well described by a Fischer distribution. Results for twodimensional (direct and inverse cascade) and threedimensional turbulence with and without confinement, illustrate the properties of the proposed multiscale statistics. The presented MonteCarlo simulations allow disentangling geometry dependent and flow independent features. Finally, we also analyze trajectories of football players, which are, in general, not randomly spaced on a field.\\ B.Kadoch, W.Bos, K.Schneider. Phys. Rev. Fluids, 2, 064604, 2017.\\ W.Bos, B.Kadoch, K.Schneider. Phys. Rev. Lett., 114, 214502, 2015. [Preview Abstract] 
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