1,721,194 research outputs found
Prediction of Multimodal Distributions in Breakage Processes
No full textThe prediction of multimodal distributions through the population balance equation (PBE) in breakage processes is addressed. A numerical approach based on physical arguments is suggested and applied. The time-dependent unknown distribution is approximated by a weighted sum of beta-subdistributions. The parameters of the beta-PDFs and their weights are treated as unknown functions of time. The method allows for the tracking of the evolution of multimodal distributions through few unknown functions, determined by ordinary differential equations. The method is applied here to PBEs for pure breakage processes, although it can be further developed to include growth and coalescence
A model of fine particles deposition on smooth surfaces: I - Theoretical basis and model development
No full textA model of fine particles deposition from a flowing suspension on smooth surfaces is developed. It is based on a common Eulerian-Lagrangian particle tracking approach, that allows a force-based description of the interactions between particles and surface. Hydrodynamics and particle-wall forces are included, with emphasis on a detailed account of Van der Waals forces. Diffusion has also been included and combined with the Lagrangian approach resulting in a stochastic process. Efficient and physically consistent techniques to solve the resulting stochastic differential equations are discussed, with specific algorithms to manage transition from small to extremely strong forcing function, and to precisely determine when and where particle trajectories reach the boundary. Quantitative evidences of the usefulness of techniques are shown. (c) 2006 Elsevier Ltd. All rights reserved
Analysis of reaction mechanisms through stochastic simulation
No full textStochastic approaches have been widely employed for simulating the dynamics of complex reacting systems. These approaches allow the structure of a complex mechanism and its dynamics to be analysed easily, since evolution is discretized and the main reaction paths can be clearly identified. Other features of the mechanism, such as closed reaction sequences and key species, may be identified by statistical analysis of the sequence of steps. The technique is explained by the application to a standard mechanism for homogeneous NOx removal through NH3 (Thermal DcNOx, including 73 reversible reactions. NO redution is shown to take place thanks to a few reaction cycles driven by a limited number of key radicals, i.e. H, OH, O, NH2, N2H, HNO. © 2001 Elsevier Science Ltd. All rights reserved
Method of moments for the dilute granular flow of inelastic spheres
No full textSome peculiar features of granular materials (smooth, identical spheres) in rapid flow are the normal pressure
differences and the related anisotropy of the velocity distribution function f (1). Kinetic theories have been
proposed that account for the anisotropy, mostly based on a generalization of the Chapman-Enskog expansion
[N. Sela and I. Goldhirsch, J. Fluid Mech. 361, 41 (1998)]. In the present paper, we approach the problem
differently by means of the method of moments; previously, similar theories have been constructed for the
nearly elastic behavior of granular matter but were not able to predict the normal pressures differences. To
overcome these restrictions, we use as an approximation of the f (1) a truncated series expansion in Hermite
polynomials around the Maxwellian distribution function. We used the approximated f (1) to evaluate the
collisional source term and calculated all the resulting integrals; also, the difference in the mean velocity of the
two colliding particles has been taken into account. To simulate the granular flows, all the second-order
moment balances are considered together with the mass and momentum balances. In balance equations of the
Nth-order moments, the (N+1)th-order moments (and their derivatives) appear: we therefore introduced
closure equations to express them as functions of lower-order moments by a generalization of the ‘‘elementary
kinetic theory,’’ instead of the classical procedure of neglecting the (N+1)th-order moments and their derivatives.
We applied the model to the translational flow on an inclined chute obtaining the profiles of the solid
volumetric fraction, the mean velocity, and all the second-order moments. The theoretical results have been
compared with experimental data [E. Azanza, F. Chevoir, and P. Moucheront, J. Fluid Mech. 400, 199 (1999);
T. G. Drake, J. Fluid Mech. 225, 121 (1991)] and all the features of the flow are reflected by the model: the
decreasing exponential profile of the solid volumetric fraction, the parabolic shape of the mean velocity, the
constancy of the granular temperature and of its components. Besides, the model predicts the normal pressures
differences, typical of the granular materials
Improving the Quantitative Description of Reacting Porous Solids: Critical Analysis of the Shrinking Core Model by Comparison to the Generalized Grain Model
No full textA numerical comparison between the shrinking core model and the grain model is carried out, in the case of a single noncatalytic gas-solid reaction within a spherical particle. The study is focused on the mathematical quantification of the divergence between the time dependent particle conversions predicted by the two models, taking into account the different relationships between kinetics and intraparticle diffusion. Sensitivity tests have been carried out, depending on the controlling regime (chemical, diffusive, intermediate). The comparison was extended to a generalized form of the grain model, in which the superficial area of the porous matrix can be described as nonspherical micrograins, with possible sintering phenomena occurring. The comparison between the two models is first made by trying to fit the shrinking core model kinetics to the more realistic continuous model. Finally, errors introduced by the shrinking core model extrapolated to particle sizes different from that used to identify its apparent kinetics are discussed and quantified. Unexpectedly, the largest errors introduced by the shrinking core model are in the intermediate regime, instead of the kinetic one, where it is farthest from the actual physics of the process. The results prove that the common choice of using a shrinking core model instead of a continuous model can lead to severe errors in the conversion prediction, also beyond the regime where its assumptions are clearly violated
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