Bulletin of the American Physical Society
74th Annual Meeting of the APS Division of Fluid Dynamics
Volume 66, Number 17
Sunday–Tuesday, November 21–23, 2021; Phoenix Convention Center, Phoenix, Arizona
Session P22: Turbulence: Mixing |
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Chair: Gokul Pathikonda, Arizona State University Room: North 222 AB |
Monday, November 22, 2021 4:05PM - 4:18PM |
P22.00001: An alternative to gradient diffusion models for material transport in Reynolds-averaged methods Noah O Braun, Rob A Gore Reynolds-Averaged Navier-Stokes (RANS) models often utilize gradient diffusion approximations for terms representing the transport of various quantities by turbulent velocity fluctuations, and thus model material mixing as a diffusion process with some turbulent viscosity. While reasonable in many canonical flows, this approach cannot capture shrinking mixing layers that may be observed in more complex situations such as when a strongly Rayleigh-Taylor stable pressure gradient is introduced onto an already developed mixing layer. We extend the Besnard-Harlow- Rauenzahn (BHR) family of variable density turbulence model to track transport equations associated with the turbulent transport and fluctuations in species mass fraction for each material, and show that the inclusion of these terms improves its ability to model certain phenomena associated with stabilized mixing layers. Although additional equations are introduced, they do not require new empirically tuned coefficients or closure models because the added equations may be derived directly from existing closures in the model. The approach employed here should be straightforward to extend to other variable density RANS models, so long as they track an equation for the turbulent mass flux. |
Monday, November 22, 2021 4:18PM - 4:31PM |
P22.00002: Characterization of entrainment through turbulent diffusion in a self-similar jet Thomas Basset, Bianca Viggiano, Thomas Barois, Mathieu Gibert, Nicolas Mordant, Raúl Bayoán B Cal, Romain Volk, Mickaël Bourgoin A large-scale experimental Lagrangian study based on particle tracking velocimetry has been completed in an incompressible self-similar water jet. The jet is seeded with tracers only through the nozzle: inhomogeneous seeding called nozzle seeding. The Lagrangian flow of tracers therefore does not contain any contribution from particles entrained into the jet from the surrounding fluid. The mean velocity field based on tracer trajectories〈Uφ〉is essentially indistinguishable from the mean velocity field of the jet〈U〉for the axial velocity while important discrepancies are experimentally found for the radial velocity. Even if ▽ ·〈U〉= 0, we have ▽ ·〈Uφ〉≠ 0 due to the absence of entrained particles. By considering the mean tracer concentration field〈φ〉, a new mass conservation equation is proposed: ▽ · (〈φ〉〈Uφ〉) = 0, which leads to a correct description of the experimental radial velocity field and gives new analytical results about entrainment. Finally, to connect entrainment to turbulent diffusion, a classical advection-diffusion equation with a turbulent diffusivity KT is proposed: ▽ · (〈φ〉〈U〉- KT ▽〈φ〉) = 0. We theoretically and experimentally determine KT, which can be linked to turbulent viscosity νT through turbulent Prandtl number σT determined as well. |
Monday, November 22, 2021 4:31PM - 4:44PM |
P22.00003: Self-similarity of scalar iso-surface area density in a temporal mixing layer Brandon Blakeley, James J Riley In many turbulent flows, distinct regions of the flow are separated by sharp interfaces that can be described by iso-surfaces of a scalar field. Examples include the stoichiometric value of the mixture fraction in non-premixed combustion, and a small threshold value of the vorticity magnitude for the turbulent/non-turbulent interface. Recent developments in computer hardware and software now allow for in-depth analysis of the characteristics of these interfaces. This talk discusses the direct numerical simulation of a turbulent, temporally developing mixing layer using GPU resources on the Lassen supercomputer at Lawrence Livermore National Laboratory. A novel software approach has been used to calculate the mean surface area density, Σ, as a function of the cross-stream position. We find that, in addition to the velocity field statistics, the cross-stream profiles of Σ and related quantities also become self-similar. Preliminary results suggest that the self-similarity variable for Σ scales with the Taylor microscale. We also investigate the transport equation for Σ as a function of the cross-stream position, and analyze the resulting terms related to area production, destruction, advection/diffusion and their effects on iso-surface growth within the self-similar period. |
Monday, November 22, 2021 4:44PM - 4:57PM |
P22.00004: Differential diffusion of helium concentration and temperature in a turbulent jet Alais M Hewes, Christian Ivanov, Laurent B Mydlarski When scalars have unequal molecular diffusivities, differential diffusion can occur. However, the consequences of differential diffusion are commonly neglected – an assumption that is typically justified by the argument that the effects of molecular properties are small at high Reynolds numbers. Yet, this assumption has proven to be questionable, especially at moderate Reynolds numbers (e.g. Lavertu et al., J. Fluid Mech., 2008). The present work investigates differential diffusion of two scalars (helium concentration and temperature) in a turbulent jet of air, measured by way of a thermal-anemometry-based interference probe (Hewes and Mydlarski, Meas. Sci. Technol., 2021) combined with a cold-wire thermometer. Statistics of the instantaneous differences of the non-dimensionalized scalar concentrations are investigated. Of particular interest are the effects of the Schmidt number(s) on the differential diffusion. These are inferred by comparing the present results (in which the Schmidt / Prandtl are 0.2 and 0.7, respectively) with those of Lavertu et al. (J. Fluid Mech., 2008), who studied the same flow, but using liquid-phase jets in which the Schmidt numbers of the scalars were 2000 and 5000. |
Monday, November 22, 2021 4:57PM - 5:10PM Not Participating |
P22.00005: Go with the flow: Lagrangian structures of a turbulent jet Willem Van De Water, Jesse Reytenbagh, Jerry Westerweel We have linked the dispersion of dye in a turbulent jet to Lagrangian coherent structures in the velocity field. Two cameras move with the mean flow, one measures concentration through laser-induced fluorescence, and the other one a twodimensional projection of the velocity field using particle image velocimetry. Since we go with the flow, structures remain in view long enough to observe the fine structure of the finite-time Lyapunov field that gauges the exponentially spreading of two fluid parcels that are close initially, either in forward or backward time. The scalar field is tesselated into uniform concentration zones using the fuzzy cluster method. The edges of these zones correlate with the backward-time Lyapunov field, that represents the convergence of fluid parcels. Moving the detection along two axes simultaneously provides a unique Langrangian view of the edge of the jet, and brings structures in focus that shape the turbulent-non turbulent interface. |
Monday, November 22, 2021 5:10PM - 5:23PM |
P22.00006: The physics of mixing and relaminarization characteristics of a co-axial jet with disparate viscosity Mustafa Usta, Cameron Ahmad, Gokul Pathikonda, Bo Zhang, Irfan Khan, Devesh Ranjan, Cyrus K Aidun The mixing of fluids in a coaxial jet is studied under various viscosity ratios using Large-Eddy simulations (LES), Reynolds-Averaged Navier Stokes (RANS), particle image velocimetry (PIV), and planar laser-induced fluorescence (PLIF). In the simulations, the state-of-the-art RANS and LES models are employed, and the accuracy of predictions is tested against data obtained by the simultaneous experimental measurements of velocity and concentration fields. We show that the standard RANS approach without including models for viscosity variations is not applicable whereas dynamic LES models provide high-quality agreement with the measurements. To identify the underlying sources of discrepancy in RANS predictions, two distinct mixing modes are defined based on the viscosity ratio. Then, for each mode, the evolution of mixing structures, analysis of the turbulent activity, and decay of turbulence are investigated using LES results. Overall, the interfacial dynamics and flow relaminarization characteristics are found to be quite distinct in each mixing mode. The scaling of the energy spectrum cascade suggests that, rather than the turbulence, the unsteady laminar shedding is responsible for the eddies observed that explain the reduced mixing in the pipe downstream. |
Monday, November 22, 2021 5:23PM - 5:36PM |
P22.00007: Nonuniform mixing Jean-Luc Thiffeault Fluid mixing usually involves the interplay between advection and diffusion, which together cause any initial distribution of passive scalar to homogenize and ultimately reach a uniform state. However, this scenario only holds when the velocity field is non-divergent and has no normal component to the boundary. If either condition is unmet, such as for active particles in a bounded region, floating particles, or for filters, the ultimate state after a long time is not uniform, and may be time dependent. We show that in those cases of nonuniform mixing it is preferable to characterize the degree of mixing in terms of an f-divergence, which is a generalization of relative entropy, or to use the L1 norm. Unlike concentration variance (L2 norm), the f-divergence and L1 norm always decay monotonically, even for nonuniform mixing, which facilitates measuring the rate of mixing. We show by an example that flows that mix well for the nonuniform case can be drastically different from efficient uniformly mixing flows. |
Monday, November 22, 2021 5:36PM - 5:49PM |
P22.00008: Self-consistent, high-order spatial profiles in a model for two-fluid turbulent mixing Brandon E Morgan A Reynolds-averaged Navier-Stokes model is presented with the property that it admits self-consistent, high-order spatial profiles in simulations of two-fluid turbulent mixing layers. Whereas previous models have been limited by the assumption of a linear mixing profile, the present work relaxes this assumption and, as a result, is shown to achieve much better agreement with experimental profiles. Similarity analysis is presented to derive constraints on model coefficients to enforce desired self-similar growth rates that are fully consistent with the high-order spatial profiles. Through this similarity analysis, it is shown that care must be taken in model construction, as it is possible to construct terms in such a way as to leave growth rates unconstrained. This model, termed the k-φ-L-a-V model, is then applied in simulations of Rayleigh-Taylor, Richtmyer-Meshkov, and Kelvin-Helmholtz mixing layers. These simulations confirm that the expected growth parameters are recovered and high-order spatial profiles are maintained. |
Monday, November 22, 2021 5:49PM - 6:02PM |
P22.00009: Ergodicity and invariant measures for a diffusing passive scalar advected by a random channel shear flow and the connection between the Kraichnan-Majda model and Taylor-Aris Dispersion Lingyun Ding, Robert Hunt, Richard M McLaughlin We study the long time behavior of an advection-diffusion equation with a random shear flow which depends on a stationary Ornstein-Uhlenbeck (OU) process in parallel-plate channels enforcing the no-flux boundary conditions. We derive a closed form formula for the long time asymptotics of the arbitrary N-point correlator using a ground state eigenvalue perturbation approach. In turn, appealing to the conclusion of the Hausdorff moment problem, we discover a diffusion equation with a random drift and deterministic enhanced diffusion possessing the exact same probability distribution function at long times. Such equations enjoy many ergodic properties which immediately translate to ergodicity results for the original problem. In particular, we establish that the first two Aris moments using a single realization of the random field can be used to explicitly construct all ensemble averaged moments. Also, the first two ensemble averaged moments explicitly predict any long time centered Aris moment. Such ergodic results guarantee than an experimentalist need only perform a single realizaiton to fully experience the complete ensemble statistics. We present experimental and Monte-Carlo simulations exploring the convergence of the random solutions to their deterministic limits. Laslty, We present explicit formulae for the decaying passive scalar's long time limiting probability distribution function (PDF) for different types of initial conditions. |
Monday, November 22, 2021 6:02PM - 6:15PM |
P22.00010: Determinism for diffusing passive scalars advected by general unsteady random shear flows Lingyun Ding, Richard M McLaughlin We study the long time behavior of an advection-diffusion equation with a general random shear flow imposing no-flux boundary conditions on channel walls using Center Manifold Theory (CMT). Recent results have explicitly calculated using statistical moment closure the invariant measure for a diffusing passive scalar advected by a class of Gaussian random shear flows. Here we establish how center manifold theory can be used to greatly extend these theories to a much broader class of random (non-Gaussian) shear flows, particularly regarding their temporal statistics. In doing so, we can extend results which show how all the effective diffusion coefficients converge at long times to a deterministic value for this broader class of flows. Such results are important ergodicity-like results in that they assure an experimentalist need only perform a single realization of a random flow to observe the ensemble moment predictions at long time. Monte-Carlo simulations will be presented illustrating how the highly random behavior converges to the deterministic limit at long time. |
Monday, November 22, 2021 6:15PM - 6:28PM |
P22.00011: The effect of the presence of inertial-convective and viscous-convective subranges on the statistics of a passive scalar in Homogeneous Isotropic Turbulence in air and water Kedar Prashant Shete, David J Boucher, James J Riley, Steve M de Bruyn Kops An assumption common to many approaches to understanding and modeling turbulent mixing is that the statistics of a passive scalar at small length scales will approach the analogous statistics of the velocity field as the scale separation increases between the flow-specific outer scales and the small scales of interest. However, it is well recognized that differences in the scalar and velocity dynamics prevent the overall statistics of the two being identically the same, even at either high Reynolds number or high Schmidt number individually. Because of limitations in laboratory measurements, direct numerical simulations (DNSs), and measurements of the ocean and atmosphere, it is difficult to obtain data in which the Reynolds number is high enough for an inertial-convective subrange, and the Schmidt number is simultaneously high enough for a clear viscous-convective subrange. We hypothesize that when both subranges exist, then there is sufficient scale separation in the velocity field for its statistics to be approximately universal, and also sufficient additional scale separation for the scalar to relax so that its small-scale statistics approach those of the velocity. We explore this hypothesis with DNS resolved on up to 14256×14256×14256 grid points, Taylor Reynolds number Reλ=633, and Schmidt number Sc = [0.1, 0.7, 1.0, 7.0]. For high Reynolds number with Schmidt number less than unity, a viscous-convective subrange does not exist and we find that small-scale isotropy, the intermittency exponent, and the probability density function (PDF) of the scalar dissipation rate are all much different from the analogous velocity statistics, as reported widely in literature. However, when the Schmidt number is greater than unity at high Reynolds number, the velocity and scalar statistics are similar. This suggests that at high Reynolds numbers, the modelling assumption of similarity between velocity and scalar statistics is valid for mixing in water, but not in air. |
Monday, November 22, 2021 6:28PM - 6:41PM |
P22.00012: Investigation of intermittency in scalar mixing from concentrated sources by way of higher-order spectral moments Milind V Singh, Emmanuel Germaine, Luca Cortelezzi, Laurent B Mydlarski The effect of intermittency on scalar mixing is investigated by way of higher-order spectral moments. The (hydrodynamic) flow under consideration is fully-developed turbulent channel flow and the scalar mixing within this flow is that generated by a concentrated line source within the flow. In this work, direct numerical simulations were undertaken by way of a spectral method to solve the equations of conservation of mass and momentum, and the advection-diffusion equation was solved using a flux integral method (Germaine et al., J. Comput. Phys., 2013). The intermittency of the scalar plume emitted by the concentrated line source is studied by way of higher-order spectral moments. Particular attention is paid to third- and fourth-order spectral moments, using the definitions formalized by Antoni (Mech. Syst. Signal Process., 2006). Such statistics are sensitive to transients / non-stationarities, and thus provide insight into the intermittency of the scalar field. |
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