Providing a clear description of the theory of polydisperse multiphase flows, with emphasis on the mesoscale modelling approach and its relationship with microscale and macroscale models, this ...all-inclusive introduction is ideal whether you are working in industry or academia. Theory is linked to practice through discussions of key real-world cases (particle/droplet/bubble coalescence, break-up, nucleation, advection and diffusion and physical- and phase-space), providing valuable experience in simulating systems that can be applied to your own applications. Practical cases of QMOM, DQMOM, CQMOM, EQMOM and ECQMOM are also discussed and compared, as are realizable finite-volume methods. This provides the tools you need to use quadrature-based moment methods, choose from the many available options, and design high-order numerical methods that guarantee realizable moment sets. In addition to the numerous practical examples, MATLAB scripts for several algorithms are also provided, so you can apply the methods described to practical problems straight away.
At sufficient mass loading and in the presence of a mean body force (e.g. gravity), an initially random distribution of particles may organize into dense clusters as a result of momentum coupling ...with the carrier phase. In statistically stationary flows, fluctuations in particle concentration can generate and sustain fluid-phase turbulence, which we refer to as cluster-induced turbulence (CIT). This work aims to explore such flows in order to better understand the fundamental modelling aspects related to multiphase turbulence, including the mechanisms responsible for generating volume-fraction fluctuations, how energy is transferred between the phases, and how the cluster size distribution scales with various flow parameters. To this end, a complete description of the two-phase flow is presented in terms of the exact Reynolds-average (RA) equations, and the relevant unclosed terms that are retained in the context of homogeneous gravity-driven flows are investigated numerically. An Eulerian–Lagrangian computational strategy is used to simulate fully developed CIT for a range of Reynolds numbers, where the production of fluid-phase kinetic energy results entirely from momentum coupling with finite-size inertial particles. The adaptive filtering technique recently introduced in our previous work (Capecelatro et al., J. Fluid Mech., vol. 747, 2014, R2) is used to evaluate the Lagrangian data as Eulerian fields that are consistent with the terms appearing in the RA equations. Results from gravity-driven CIT show that momentum coupling between the two phases leads to significant differences from the behaviour observed in very dilute systems with one-way coupling. In particular, entrainment of the fluid phase by clusters results in an increased mean particle velocity that generates a drag production term for fluid-phase turbulent kinetic energy that is highly anisotropic. Moreover, owing to the compressibility of the particle phase, the uncorrelated components of the particle-phase velocity statistics are highly non-Gaussian, as opposed to systems with one-way coupling, where, in the homogeneous limit, all of the velocity statistics are nearly Gaussian. We also observe that the particle pressure tensor is highly anisotropic, and thus additional transport equations for the separate contributions to the pressure tensor (as opposed to a single transport equation for the granular temperature) are necessary in formulating a predictive multiphase turbulence model.
A long-standing paradigm in astrophysics is that collisions- or mergers-of two neutron stars form highly relativistic and collimated outflows (jets) that power Y-ray bursts of short (less than two ...seconds) duration. The observational support for this model, however, is only indirect. A hitherto outstanding prediction is that gravitational-wave events from such mergers should be associated with Y-ray bursts, and that a majority of these bursts should be seen off-axis, that is, they should point away from Earth. Here we report the discovery observations of the X-ray counterpart associated with the gravitational-wave event GW170817. Although the electromagnetic counterpart at optical and infrared frequencies is dominated by the radioactive glow (known as a 'kilonova') from freshly synthesized rapid neutron capture (r-process) material in the merger ejecta, observations at X-ray and, later, radio frequencies are consistent with a short Y-ray burst viewed off-axis. Our detection of X-ray emission at a location coincident with the kilonova transient provides the missing observational link between short Y-ray bursts and gravitational waves from neutron-star mergers, and gives independent confirmation of the collimated nature of the Y-ray-burst emission.
Kinetic equations arise in a wide variety of physical systems and efficient numerical methods are needed for their solution. Moment methods are an important class of approximate models derived from ...kinetic equations, but require closure to truncate the moment set. In quadrature-based moment methods (QBMM), closure is achieved by inverting a finite set of moments to reconstruct a point distribution from which all unclosed moments (e.g. spatial fluxes) can be related to the finite moment set. In this work, a novel moment-inversion algorithm, based on 1-D adaptive quadrature of conditional velocity moments, is introduced and shown to always yield realizable distribution functions (i.e. non-negative quadrature weights). This conditional quadrature method of moments (CQMOM) can be used to compute exact
N-point quadratures for multi-valued solutions (also known as the multi-variate truncated moment problem), and provides optimal approximations of continuous distributions. In order to control numerical errors arising in volume averaging and spatial transport, an adaptive 1-D quadrature algorithm is formulated for use with CQMOM. The use of adaptive CQMOM in the context of QBMM for the solution of kinetic equations is illustrated by applying it to problems involving particle trajectory crossing (i.e. collision-less systems), elastic and inelastic particle–particle collisions, and external forces (i.e. fluid drag).
SN 2014J in M82 is the closest detected Type Ia supernova (SN Ia) in at least 28 yr and perhaps in 410 yr. Despite its small distance of 3.3 Mpc, SN 2014J is surprisingly faint, peaking at ...V = 10.6 mag, and assuming a typical SN Ia luminosity, we infer an observed visual extinction of A
V
= 2.0 ± 0.1 mag. But this picture, with R
V
= 1.6 ± 0.2, is too simple to account for all observations. We combine 10 epochs (spanning a month) of HST/Space Telescope Imaging Spectrograph (STIS) ultraviolet through near-infrared spectroscopy with HST/Wide Field Camera 3 (WFC3), Katzman Automatic Imaging Telescope, and FanCam photometry from the optical to the infrared and nine epochs of high-resolution TRES (Tillinghast Reflection Echelle Spectrograph) spectroscopy to investigate the sources of extinction and reddening for SN 2014J. We argue that the wide range of observed properties for SN 2014J is caused by a combination of dust reddening, likely originating in the interstellar medium of M82, and scattering off circumstellar material. For this model, roughly half of the extinction is caused by reddening from typical dust (E(B − V) = 0.45 mag and R
V
= 2.6) and roughly half by scattering off Large Magellanic Cloud-like dust in the circumstellar environment of SN 2014J.
Inertial particles in turbulent flows are characterised by preferential concentration and segregation and, at sufficient mass loading, dense particle clusters may spontaneously arise due to momentum ...coupling between the phases. These clusters, in turn, can generate and sustain turbulence in the fluid phase, which we refer to as cluster-induced turbulence (CIT). In the present work, we tackle the problem of developing a framework for the stochastic modelling of moderately dense particle-laden flows, based on a Lagrangian probability-density-function formalism. This framework includes the Eulerian approach, and hence can be useful also for the development of two-fluid models. A rigorous formalism and a general model have been put forward focusing, in particular, on the two ingredients that are key in moderately dense flows, namely, two-way coupling in the carrier phase, and the decomposition of the particle-phase velocity into its spatially correlated and uncorrelated components. Specifically, this last contribution allows us to identify in the stochastic model the contributions due to the correlated fluctuating energy and to the granular temperature of the particle phase, which determine the time scale for particle–particle collisions. The model is then validated and assessed against direct-numerical-simulation data for homogeneous configurations of increasing difficulty: (i) homogeneous isotropic turbulence, (ii) decaying and shear turbulence and (iii) CIT.
Gas-particle and other dispersed-phase flows can be described by a kinetic equation containing terms for spatial transport, acceleration, and particle processes (such as evaporation or collisions). ...In principle, the kinetic description is valid from the dilute (non-collisional) to the dense limit. However, its numerical solution in multi-dimensional systems is intractable due to the large number of independent variables. As an alternative, Lagrangian methods “discretize” the density function into “parcels” that are simulated using Monte-Carlo methods. While quite accurate, as in any statistical approach, Lagrangian methods require a relatively large number of parcels to control statistical noise, and thus are computationally expensive. A less costly alternative is to solve Eulerian transport equations for selected moments of the kinetic equation. However, it is well known that in the dilute limit Eulerian methods have great difficulty to describe correctly the moments as predicted by a Lagrangian method. Here a two-node quadrature-based Eulerian moment closure is developed and tested for the kinetic equation. It is shown that the method can successfully handle highly non-equilibrium flows (e.g. impinging particle jets, jet crossing, particle rebound off walls, finite Stokes number flows) that heretofore could not be treated accurately with the Eulerian approach.
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