914 research outputs found
A Quadrature-based Moment Closure for the Williams Spray Equation
Sprays and other dispersed-phase systems 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 describing correctly the moments as predicted by a Lagrangian method. A two-point quadrature-based Eulerian moment closure is developed and tested here for the Williams spray equation. It is shown that the method can successfully handle highly non-equilibrium flows (e.g., impinging particle jets, jet crossing, and particle rebound off walls) that heretofore could not be treated with the Eulerian approach
Direct comparison of EulerianâEulerian and EulerianâLagrangian simulations for particleâladen vertical channel flow
Particleâladen flows in a vertical channel were simulated using an EulerianâEulerian, Anisotropic Gaussian (EEâAG) model. Two sets of cases varying the overall mass loading were done using particle sizes corresponding to either a large or small Stokes number. Primary and turbulent statistics were extracted from these results and compared with counterparts collected from EulerianâLagrangian (EL) simulations. The statistics collected from the small Stokes number particle cases correspond well between the two models, with the EEâAG model replicating the transition observed using the EL model from shearâinduced turbulence to relaminarization to clusterâinduced turbulence as the mass loading increased. The EEâAG model was able to capture the behavior of the EL simulations only at the largest particle concentrations using the large Stokes particles. This is due to the limitations involved with employing a particleâphase Eulerian model (as opposed to a Lagrangian representation) for a spatially intermittent system that has a low particle number concentration.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/155968/1/aic16230_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/155968/2/aic16230.pd
Verification of EulerianâEulerian and EulerianâLagrangian simulations for turbulent fluidâparticle flows
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/139111/1/aic15949_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/139111/2/aic15949.pd
Strongly coupled fluid-particle flows in vertical channels. II. Turbulence modeling
In Part I, simulations of strongly coupled fluid-particle flow in a vertical channel were performed with the purpose of understanding, in general, the fundamental physics of wall-bounded multiphase turbulence and, in particular, the roles of the spatially correlated and uncorrelated components of the particle velocity.The exact Reynolds-averaged (RA) equations for high-mass-loading suspensions were presented, and the unclosed terms that are retained in the context of fully developed channel flow were evaluated in an EulerianâLagrangian (EL) framework. Here, data from the EL simulations are used to validate a multiphase Reynolds-stress model (RSM) that predicts the wall-normal distribution of the two-phase, one-point turbulence statistics up to second order. It is shown that the anisotropy of the Reynolds stresses both near the wall and far away is a crucial component for predicting the distribution of the RA particle-phase volume fraction. Moreover, the decomposition of the phase-average (PA) particle-phase fluctuating energy into the spatially correlated and uncorrelated components is necessary to account for the boundary conditions at the wall. When these factors are properly accounted for in the RSM, the agreement with the EL turbulence statistics is satisfactory at first order (e.g., PA velocities) but less so at second order (e.g., PA turbulent kinetic energy). Finally, an algebraic stress model for the PA particle-phase pressure tensor and the Reynolds stresses is derived from the RSM using the weak-equilibrium assumption
Eulerâeuler anisotropic gaussian mesoscale simulation of homogeneous clusterâinduced gasâparticle turbulence
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/137187/1/aic15686.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/137187/2/aic15686_am.pd
Hexabromocyclododecane and hexachlorocyclohexane: How lessons learnt have led to improved regulation
This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2014 Taylor & Francis.The use of chemicals by society has many benefits but contamination of the environment is an unintended consequence. One example is the organochlorine compound hexachlorocyclohexane (HCH). During the 1980s, when HCH was banned in many countries, the brominated flame retardant, hexabromocyclododecane (HBCD), found increasing use. The persistent, bioaccumulative, and toxic characteristics of HBCD are, 30 years later, likely to warrant global action on production and use under the Stockholm Convention on persistent organic pollutants. Historical lessons have taught us that we need to control the use of chemicals and programs are in place worldwide in an attempt to do so.Tertiary Education Trust Fund, Nigeri
A Kato type Theorem for the inviscid limit of the Navier-Stokes equations with a moving rigid body
The issue of the inviscid limit for the incompressible Navier-Stokes
equations when a no-slip condition is prescribed on the boundary is a famous
open problem. A result by Tosio Kato says that convergence to the Euler
equations holds true in the energy space if and only if the energy dissipation
rate of the viscous flow in a boundary layer of width proportional to the
viscosity vanishes. Of course, if one considers the motion of a solid body in
an incompressible fluid, with a no-slip condition at the interface, the issue
of the inviscid limit is as least as difficult. However it is not clear if the
additional difficulties linked to the body's dynamic make this issue more
difficult or not. In this paper we consider the motion of a rigid body in an
incompressible fluid occupying the complementary set in the space and we prove
that a Kato type condition implies the convergence of the fluid velocity and of
the body velocity as well, what seems to indicate that an answer in the case of
a fixed boundary could also bring an answer to the case where there is a moving
body in the fluid
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