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14:00   Transport and Mixing 3 14:00 15 mins #148 Self-similarity of scalar spectra in a point-source plume released in a turbulent boundary layer Kapil Chauhan, Krishna M Talluru Abstract: PDF file uploaded 14:15 15 mins #251 Multi-Scalar Mixing in a Coaxial Jet at Different Velocity Ratios Alais HEWES, Laurent MYDLARSKI Abstract: Although turbulent scalar mixing has been the subject of many studies, few of these have focused on the more complex case in which two scalars are mixed, given the difficulty in simultaneously measuring more than one scalar. (This case is sometimes referred to as three-scalar mixing \cite{cai2011}, because the two scalars are mixed with a third scalar-free fluid.) The present work uses a novel 3-wire themal-anemometry-based probe to make concurrent measurements of two scalars \emph{and} velocity with the high levels of temporal and spatial resolution typical of thermal anemometry techniques. The 3-wire probe is used to measure the evolution of two passive scalars (helium concentration and temperature) and the longitudinal velocity in a turbulent coaxial jet similar to the one studied in \cite{cai2011, li_yuan_carter_tong_2017}. One particularly unique aspect of the present work is that joint velocity/multi-scalar statististics are obtained, unlike \cite{cai2011, li_yuan_carter_tong_2017} and most other work on multi-scalar mixing, yielding additional insight into the multi-scalar mixing process. \par The coaxial jet investigated herein consists of a vertically-oriented central jet of a helium/air mixture (scalar $\phi_1$), surrounded by an annular flow of (unheated) pure air, emanating into a slow co-flow of (pure) heated air (scalar $\phi_2$). Thus, the two scalars ($\phi_1$ and $\phi_2$), which have been normalized to be equal to 1 at their respective jet exits, are initially separated by the annular flow. Measurements are made along the centerline and at various cross-stream profiles in the developing region of the coaxial jet. The evolution of the velocity and scalar fields is characterized by means and variances, correlation coefficients, spectra, and joint probability distribution functions (JPDFs). \par The specific objective of the present work is to investigate multi-scalar mixing in a coaxial jet for different velocity ratios, as the near-field flow and mixing are dependent on this quantity. To this end, we present results for three different velocity ratios ($U_{j,a}/U_{j,c} = 0.5, 1, \textrm{and } 2$, where $U_{j,a}$ and $U_{j,c}$ are the average exit velocities of the annular and center jets, respectively). Figure 1 depicts measurements of the correlation coefficients for $U_{j,a}/U_{j,c} =1$ along a) the centerline, and b) a cross-stream profile at $x/d_c=6$. Along the centerline, the two scalars are intially uncorrelated, and become progressively more anti-correlated farther downstream, as incursions from the outer co-flow, which contains $\phi_2$ (temperature), reach the centerline. In the radial direction, the correlation coefficient of $\phi_1$ and $\phi_2$ has a minimum at the center of the annular jet ($r/d_c=0.75$), where it is probable to measure $\phi_1$ or $\phi_2$, but not both simultaneously (at $x/d_c=6$). Similar results are also observed for other cross-stream profiles in the near-field, and are complemented by data from the JPDFs. Such measurements, along with those at other velocity ratios, are used to characterize scalar mixing in coaxial jets, extending our understanding of multi-scalar mixing and providing valuable data for testing mixing models and validating numerical simulations, with ultimate future applications to reacting and combusting flows. 14:30 15 mins #423 NON-RICHARDSON TURBULENT PARTICLE PAIR DIFFUSION Syed Usama, Nadeem Malik Abstract: Richardson’s 1926 theory of turbulent pair diffusion in the inertial subrange has been widely accepted in the community. However, the principle of locality on which he based his theory is an ad hoc assumption which has never been confirmed. Furthermore, it has recently been shown that some of the data that he relied upon was flawed, and an estimate for the diffusion coefficient scaling using the revised data yields the power law scaling of 1.564 for the pair separation against diffusivity. A new theory based on the idea that both local and non-local diffusional processes are important has been proposed. The new theory predicts two non-Richardson regimes, for large and for small inertial subranges. The non-local theory has been extended to inertial particle pair diffusion, in the limit of Stokes drag and it is shown that for large inertial subranges, inertial pair diffusion initially displays ballistic motion, when the particle inertia dominates over the small scale fluid turbulent motions; this is followed by a long transition period as the pair asymptotes towards the non-local fluid pair diffusion regimes, if the subrange is big enough. 14:45 15 mins #453 Direct Numerical Simulations of Combined Rayleigh-Taylor/Shear Flow to Late Times Jon Baltzer, Daniel Livescu Abstract: Rayleigh-Taylor instability between two fluids of differing densities occurs when the density gradient is misaligned with the pressure gradient. In applications, background shear may also be present. Olson et. al., Phys. Fluids 23 (2011) simulated combined Rayleigh-Taylor instability and found that shear produced complex and non-monotonic changes to the growth rate in the early nonlinear regime. Our new simulations explore the turbulence properties at later times after the early nonlinear growth in domains of 1024 x 1024 x 4096 grid points to accommodate interfaces growing to significant thicknesses. The density ratio of 7 corresponds to an Atwood number of A=0.75. Shear visibly alters the structure of the Rayleigh-Taylor turbulence and also significantly changes the statistics of density fluctuations and Reynolds stresses. 15:00 15 mins #479 Small Peclet-small Mach number approximation and its implications on statistical turbulence models Jean-Cedric CHKAIR, Olivier SOULARD, Jerome Griffond, Xavier Blanc Abstract: Turbulence in stars arises in a wide variety of regimes involving stable and unstable stratifications, mixing, shear, radiation losses... Turbulence models used in stellar evolution codes should therefore account explicitly for these different situations. However, as pointed out by Canuto [1], most of these models are based on heuristic considerations. They are actually cast in the form of diffusion coefficients involving a mixing length, as in Prandtl's theory. By contrast, Reynolds stress models (RSM) stand as good candidates for modelling turbulence in stars, because of their simplicity, versatility and predictive abilities. Yet, only Canuto [1] has proposed a complete RSM for stellar applications. Some of these models already account for most of the physics which is required for stellar applications. This is notably the case for the class of models used to predict variable density flows with mixing arising in shock tube facilities, such as the GSG model [2]. Indeed, an important element is missing for extending the mentioned model to stellar applications: radiation losses. The issue is the following: in stellar radiative zones, the Prandtl number is so small (Pr ~ 10^(-8) in the sun) that heat transport by conduction/radiation becomes more efficient than heat transport by turbulence. Then, the flow enters a regime characterized by a high turbulent Reynolds number Ret >> 1 and a small turbulent Peclet number Pec = Pr Ret << 1. While small Prandtl numbers are encountered in numerous applications, as in liquid metals (Pr ~ 10^(-3)-10^(-2)), their value is usually not small enough to allow for both conditions Ret >> 1 and Pec << 1. Hence, most existing RSMs, including the GSG class considered in [2], are designed for large turbulent Reynolds and Peclet numbers. They consequently need to be modified to account for small turbulent Peclet numbers. Thus, the purpose of our work is to examine how the GSG class of RSMs ([2]) can be adapted to flows with small turbulent Peclet numbers. The GSG [2] model follows the evolutions of the correlations of the velocity and density fields, including the mass flux $\rey{\rho' u'_i}/\rey{\rho}$ and the density variance {rhobar'^2. The main unknowns appearing in the evolutions of {\rho' u'_i}bar/{\rhobar}$ and {\rho'^2}bar/{\rho{^2}}bar are respectively the correlations {u'_i \text{div}{u'}}bar and {\rho' {div}{u'}}bar in which the expression of the fluctuating divergence of velocity div{u'} needs to be determined. For this purpose, we perform an asymptotic analysis of the hydro-radiative equations, in the limit of a small Mach number and a small P\'eclet number, which gives an expression of the fluctuating divergence of velocity in this regime. The closures obtained for the two previous correlations {u'_i div{u'}}bar and {rho' div{{u'}}bar are then different from the ones retained in the large Peclet limit for the GSG [2] model when applied to stellar flows. In order to validate those closures, we perform two implicit large eddy simulations (ILES) of a Rayleigh-Taylor turbulent mixing zone (a fundamental instability at work in stellar interiors): one with a small Peclet number and the other one with a large Peclet. Along with these two ILES, we perform two simulations with the GSG model modified with the previous derived closures. It can be seen (see .pdf) that the model reproduces the main trends observed in the simulations and allows to distinguish between small and high Peclet numbers. References: [1] V.M. Canuto. Stellar mixing I. Formalism. A&A, 528:A76, 2011. [2] O. Gregoire, D. Souffland, and S. Gauthier. A second-order turbulence model for gaseous mixtures induced by Richtmyer-Meshkov instabilities. J. of Turbulence, 6(29), 2005. 15:15 15 mins #546 The Role of Turbulence on the Development and Entrainment of a Turbulent Jet in Cross-flow Graham Freedland, Grace Eliason, Stephen Solovitz, Raúl Bayoán Cal Abstract: Development of a computationally efficient model for volcanic eruptions has focused on evaluating the changing mass flux through the length of a plume. Measuring the entrainment and the development the jet is commonly evaluated at the turbulent/non-turbulent interface, where the jet and ambient air can be isolated due to the lack of turbulence. Defining the TNTI is primarily done one of two ways, evaluating the large scale ``engulfment'' or focusing on the small scale ``viscous nibbling''. While entrainment is independent of scale, measuring a coefficient is more difficult as the entrainment velocity is dependent on scale. Experiments to quantify an accurate coefficient primarily focused on evaluating them in a constant cross-flow, ignoring the role of turbulence on the mixing and growth of the jet. Using the closed-loop wind tunnel and Portland State University and utilizing an active grid system, three different protocols were used to create three different turbulence intensities in the cross-flow. A jet of air was placed into the wind tunnel normal to the cross flow and PIV collected velocity data within the bending region. Several jet-to-cross-flow velocity ratios, $R_v$, were used to examine different stages of a bending jet. Evaluation of the mean flow statistics and Reynolds stresses provided allowed for direct measurement of the location of the TNTI using the Reynolds stresses on the leading edge and lee-side of the jet. The inertial and Reynolds stress contributions to the transport of momentum and energy were directionally measured to highlight the regions of greatest entrainment. Additionally, a single entrainment coefficient is evaluated at each shear layer highlighting the role of turbulence on the interaction and growth of a jet in cross-flow. 15:30 15 mins #35 Fragmentation of large aggregates in turbulence Patrice Le Gal, Hector De La Rosa Zambrano, Christophe Brouzet, Gautier Verhille Abstract: Particle aggregates are frequently encountered in many natural and industrial flows. Here we describe the process of fragmentation by turbulence of particle aggregates when these particles and the aggregates they form, have a size belonging to the inertial range of turbulence, so larger than the Kolmogorov scale contrary to numerous analyzes of flocs having sub-Kolmogorov sizes [1]. In a first experiment, we place millimetric magnetic particles initially aggregated by their magnetic fields in a turbulent von Kármán flow with a high Reynolds number (ReT ~ 600-1000, Kolmogorov scale η ~ 28-65 mm). The turbulent fluctuations impose stresses that fragment the aggregates while the cohesion is ensured by the magnetic forces and torques between the dipoles as can be seen on figure 1– a) and b). Through video image analysis, we performed the three-dimensional reconstruction of the aggregates and measured their characteristic sizes. The average number of particles within each aggregate can then be deduced as a function of the intensity of the turbulence. Assuming a Kolmogorov scaling law for increments of velocity fluctuations, we theoretically predict the average size of aggregates as a function of the dissipation rate of turbulence. The experimental results are in very good agreement with our fragmentation model [2]. In a second step, we replaced the magnetic particles with flexible silicone fibers having a length of 5 cm long and a diameter of 0.8 mm. Unlike the previous case of magnetic particles, the cohesive force of fibers aggregates is not precisely characterized here: it depends on the elasticity of the fibers, on the friction between fibers and on their concentration. By analyzing the video images, the average of the void surfaces is measured for each turbulence rate and for different fiber concentrations. At high turbulence rates, the flow with the fibers remains homogeneous while at weaker turbulence, aggregates of fibers appear as it can be observed on figure 1– c) and d). A theoretical analysis based on the balance between aggregation and fragmentation shows the existence of a transition threshold between the dispersed and clustered regimes. This threshold is a function of the intensity of turbulence and of the fiber concentration. Our experiments validate our models of aggregation / fragmentation [3]. References [1] B. Oyegbile, P. Ay, and S. Narra, Flocculation kinetics and hydrodynamic interactions in natural and engineered flow systems: A review, Env. Eng. Res. 21, 1 (2016). [2] H. M. De La Rosa Zambrano, G. Verhille, P. Le Gal, Fragmentation of magnetic particle aggregates in turbulence, Phys. Rev. Fluids 3, 084605 (2018). [3] H. M. De La Rosa Zambrano, Fragmentation des agrégats dans le domaine inertiel de la turbulence, Thèse, Aix Marseille Université (2019).