Mixing in Curved Pipes

Over the previous summer I studied mixing of a passive tracer by flow in a straight cylindrical pipe, under the supervision of prof. Bernoff. The mixing process can be thought of as the successive action of advection by the fluid flow and diffusion modeled by random walks. With this method we were able to distinguish three different regimes. For short times, diffusion is more relevant than advection and we observed a Gaussian longitudinal distribution of the concentration. In an intermediate regime, advection by the shear is dominant over longitudinal diffusion and we observed a distinctively asymmetric distribution which spread much faster than would be expected by the action of diffusion alone. Finally when the tracer had completely mixed across the pipe’s cross- section, we recovered the classical Taylor regime with a longitudinal Gaussian distribution. In each regime we have analytical prediction of tracer distribution, confirmed by numerical calculation. The object of this thesis is to extend our results to curved pipes; we will start by considering curved planar pipes and helical pipes. We will try to determine if mixing in these geometries displays the same three distinctive regimes of mixing. The pipe’s curvature introduces a secondary flow in the form of a transverse recirculation with a dipolar form, discovered by Dean (1928). We believe this transverse flow should enhance mixing, which explains why curved pipes are used in cooling systems and other situations where heat exchange is relevant. Our object is to first understand existing analytical approximations to the flow in a curved pipe due to Dean and others and then to study analytically and numerically the spread of a passive scalar in these flows

Physics of reshock and mixing in single-mode Richtmyer-Meshkov instability

The ninth-order weighted essentially nonoscillatory (WENO) shock-capturing method is used to investigate the physics of reshock and mixing in two-dimensional single-mode Richtmyer-Meshkov instability to late times. The initial conditions and computational domain were adapted from the Mach 1.21 air (acetone)/SF6 shock tube experiment of Collins and Jacobs [J. Fluid Mech. 464, 113 (2002)]: the growth of the bubble and spike amplitudes from fifth- and ninth-order WENO simulations of this experiment were compared to the predictions of linear and nonlinear amplitude growth models, and were shown to be in very good agreement with the experimental data prior to reshock by Latini, Schilling, and Don [Phys. Fluids 19, 024104 (2007)]. In the present investigation, the density, vorticity, baroclinic vorticity production, and simulated density Schlieren fields are first presented to qualitatively describe the reshock process. The baroclinic circulation deposition on the interface is shown to agree with the predictions of the Samtaney-Zabusky model and with linear instability theory. The time evolution of the positive and negative circulation on the interface is considered before and after reshock: it is shown that the magnitudes of the circulations are equal before as well as after reshock, until the interaction of the reflected rarefaction with the layer induces flow symmetry breaking and different evolutions of the magnitude of the positive and negative circulation. The post-reshock mixing layer growth is shown to be in generally good agreement with three models predicting linear growth for a short time following reshock. Next, a comprehensive investigation of local and global mixing properties as a function of time is performed. The distribution and amount of mixed fluid along the shock propagation direction is characterized using averaged mole fraction profiles, a fast kinetic reaction model, and mixing fractions. The modal distribution of energy in the mixing layer is quantified using the spectra of the fluctuating kinetic energy, fluctuating enstrophy, pressure variance, density variance, and baroclinic vorticity production variance. It is shown that a broad range of scales already exists prior to reshock, indicating that the single-mode Richtmyer-Meshkov instability develops nontrivial spectral content from its inception. The comparison of the spectra to the predictions of classical inertial subrange scalings in two-dimensional turbulence shows that the post-reshock spectra may be consistent with many of these scalings over wave number ranges less than a decade. At reshock, fluctuations in all fields (except for the density) are amplified across all scales. Reshock strongly amplifies the circulation, profiles, and mixing fractions, as well as the energy spectra and statistics, leading to enhanced mixing followed by a decay. The mole and mixing fraction profiles become nearly self-similar at late times following reshock; the mixing fraction exhibits an approach toward unity across the layer at the latest time, signifying nearly complete mixing of the gases. To directly quantify the amplification of fluctuations by reshock, the previously considered quantities are compared immediately after and before reshock. Finally, to investigate the decay of fluctuations in the absence of additional waves interacting with the mixing layer following reshock, the boundary condition at the end of the computational domain is changed from reflecting to outflow to allow the reflected rarefaction wave to exit the domain. It is demonstrated that the reflected rarefaction has an important role in breaking symmetry and achieving late-time statistical isotropy of the velocity field

High-resolution simulations and modeling of reshocked single-mode Richtmyer-Meshkov instability: Comparison to experimental data and to amplitude growth model predictions

The reshocked single-mode Richtmyer-Meshkov instability is simulated in two spatial dimensions using the fifth- and ninth-order weighted essentially nonoscillatory shock-capturing method with uniform spatial resolution of 256 points per initial perturbation wavelength. The initial conditions and computational domain are modeled after the single-mode, Mach 1.21 air(acetone)/SF6 shock tube experiment of Collins and Jacobs [J. Fluid Mech. 464, 113 (2002)]. The simulation densities are shown to be in very good agreement with the corrected experimental planar laser-induced fluorescence images at selected times before reshock of the evolving interface. Analytical, semianalytical, and phenomenological linear and nonlinear, impulsive, perturbation, and potential flow models for single-mode Richtmyer-Meshkov unstable perturbation growth are summarized. The simulation amplitudes are shown to be in very good agreement with the experimental data and with the predictions of linear amplitude growth models for small times, and with those of nonlinear amplitude growth models at later times up to the time at which the driver-based expansion in the experiment (but not present in the simulations or models) expands the layer before reshock. The qualitative and quantitative differences between the fifth- and ninth-order simulation results are discussed. Using a local and global quantitative metric, the prediction of the Zhang and Sohn [Phys. Fluids 9, 1106 (1997)] nonlinear Padé model is shown to be in best overall agreement with the simulation amplitudes before reshock. The sensitivity of the amplitude growth model predictions to the initial growth rate from linear instability theory, the post-shock Atwood number and amplitude, and the velocity jump due to the passage of the shock through the interface is also investigated numerically

Transient Anomalous Diffusion in Poiseuille Flow

We revisit the classical problem of dispersion of a point discharge of tracer in laminar pipe Poiseuille flow. For a discharge at the centre of the pipe we show that in the limit of small non-dimensional diffusion, D, tracer dispersion can be divided into three regimes. For small times (t [double less-than sign] D−1/3), diffusion dominates advection yielding a spherically symmetric Gaussian dispersion cloud. At large times (t [dbl greater-than sign] D−1), the flow is in the classical Taylor regime, for which the tracer is homogenized transversely across the pipe and diffuses with a Gaussian distribution longitudinally. However, in an intermediate regime (D−1/3 [dbl greater-than sign] t [dbl greater-than sign] D−1), the longitudinal diffusion is anomalous with a width proportional to t [double less-than sign] Dt2 and a distinctly asymmetric longitudinal distribution. We present a new solution valid in this regime and verify our results numerically. Analogous results are presented for an off-centre release; here the distribution width scales as D1/2t3/2 in the anomalous regime. These results suggest that anomalous diffusion is a hallmark of the shear dispersion of point discharges at times earlier than the Taylor regime

A comprehensive review and classification of unit operations with assessment of outputs quality in lithium-ion battery recycling

Lithium-ion batteries (LIBs) are the core component of the electrification transition, being used in portable electronics, electric vehicles, and stationary energy storage. The exponential growth of LIB use generates a large flow of spent batteries which must be recycled. This paper provides a comprehensive review of industrial realities of LIB recycling companies in Europe, North America, and Asia. An in-depth description of representative pyrometallurgy-based and hydrometallurgy-based processes is reported, providing classification of unit operations, their industrial readiness, and quality of output materials. The analysis shows that the pyrometallurgical route can treat different LIB chemistries without pre-sorting, but Li is not recovered unless the slag is refined. Hydrometallurgy-based processes are more chemistry-specific and in, although being affected by losses of electrode active materials during the mechanical pre-treatments for black mass separation. Efforts are required to promote in Europe the industrial capacity and readiness of hydrometallurgical processes by facilitating sorting and mechanical separations. There is also the need for harmonization of criteria for outputs definitions and rules for calculating recycling efficiency indicators. This represents an opportunity for modeling to support quantitative techno-economic and environmental assessments of the entire LIB recycling chain

Recycling of Lithium-Ion Batteries: Overview of Existing Processes, Analysis and Performance

Lithium-ion batteries (LIBs) have become a widespread technology for electrochemical energy storage in the current era of digitalization and transport electrification, being used as electric stationary storage as well as for powering electric vehicles, e-bikes and portable electronic devices such as smartphones and laptops. However, LIBs contain valuable materials, such as cobalt, nickel, lithium and graphite, whose supply has become critical to meet the increasing demand of batteries. Therefore, proper recycling processes are required in order to recover these materials from spent batteries and re-use them to produce new batteries in a sustainable cycle. This contribution provides an extensive survey of the main recycling routes available today, focusing specifically on pyrometallurgical and hydrometallurgical processes based in Europe, North America and Asia. Attention is also devoted to the recycling behaviour of individuals and companies and to the possible ways to increase their recycling rate. The comparison of different processes allows for the ranking of best practices as well as the drawbacks of different process units, with identification of which materials can be recovered, their recovery rate, and an assessment of the overall recycling efficiency of the process for different battery sizes (small and large, for portable electronics and electric vehicles, respectively). The analysis reveals that pyrometallurgical processes can flexibly treat different LIB chemistries but, since the electrolyte and graphite are burnt in the process, the global recycling efficiency cannot compete with hydrometallurgical processes, especially for small format batteries. Nevertheless, hydrometallurgical processes typically require preliminary mechanical separation treatments to separate the black mass, which contains valuable electrodic materials, as well as complex precipitation steps, which eventually reduce the material recovery rate and the applicability to diverse LIB chemistries. Finally, the study reports an analysis of the electrochemical performance of a battery made with recycled materials, showing that even if recycled cathodic materials had a lower gravimetric capacity and solid-state diffusivity, the performance of a recycled battery could be compensated by simple minor changes to the cell design which would ultimately decrease the specific energy density by a few percent compared to a LIB made with virgin materials

Restrições de termoregulação sobre o comportamento: padrões em uma assembléia de libélulas tropicais

Odonate species are classified in terms of their thermoregulatory behavior into flier and percher categories. Larger perchers could be more efficient thermoregulators in sunny sites and smaller perchers depend more on air temperature. In this paper, an analysis of the behavioral temporal budget of an odonate neotropical assemblage was performed to determine the role of body size on territorial defense and general behavioral strategies. This analysis revealed three groups based on time budget. The first and second groups contained the species that remained perched for most of the activity time, but species of the first group differ from the second group by the larger proportion of transition flights. The third group contained species which were usually observed patrolling or in reproductive activities. The larger species spent more time in patrol and territorial defense activities, while smaller species remained perched. Larger dragonflies, with better thermoregulatory abilities could spend more time in reproductive activities. The behavioral classification of fliers and perchers is considered extremely useful but could oversimplify the behavioral patterns among species that have a wide body size variation. It is proposed that a behavioral continuum associated with the body size variation in perchers could explain some patterns of species interactions in odonate communities.As libélulas são classificadas comportamentalmente em voadoras e pousadoras com relação a sua capacidade de termoregulação. Libélulas de grande tamanho corporal devem termoregular de forma mais eficiente em locais com elevada irradiação solar, ao passo que libélulas menores dependem da temperatura ambiente. Neste estudo, foram realizadas análises de orçamento temporal de uma assembléia de libélulas para determinar como o tamanho corporal pode restringir a defesa de territórios e outros comportamentos. Baseado no orçamento temporal, foram observados três grupos de espécies. O primeiro e o segundo grupos abrangem espécies que permaneceram pousadas grande parte do tempo de atividade, entretanto espécies do primeiro grupo realizaram vôos de transição mais freqüentemente. O terceiro grupo conteve as espécies que foram observadas freqüentemente patrulhando seus territórios ou executando atividades reprodutivas. As espécies maiores permaneceram mais tempo em atividades de patrulha e defesa de seus territórios enquanto as espécies menores ficaram mais tempo pousadas. Libélulas maiores com maior habilidade de termoregulação puderam gastar mais tempo em atividades reprodutivas. A classificação das libélulas em voadoras e pousadoras é considerada extremamente útil, mas simplifica os padrões comportamentais observados entre espécies que têm grande variação de tamanho corporal. É provável que o contínuo comportamental associado com a variação de tamanho corporal, nos pousadores, possa explicar os padrões de interações entre espécies em comunidades de libélulas.15516