High-Resolution Simulations of Gas-Solids Jet Penetration Into a High- Density Riser Flow

High-resolution simulations of a gas-solids jet in a 0.3 m diameter and 15.9 m tall circulating fluidized bed (CFB) riser were conducted with the open source software-MFIX. In the numerical simulations, both gas and solids injected through a 1.6 cm diameter radial-directed tube 4.3 m above the bottom distributor were tracked as tracers, which enable the analysis of the characteristics of a two-phase jet. Two jetting gas velocities of 16.6 and 37.2 m/s were studied with the other operating conditions fixed. Reasonable flow hydrodynamics with respect to overall pressure drop, voidage, and solids velocity distributions were predicted. Due to the different dynamic responses of gas and particles to the crossflow, a significant separation of gas and solids within the jet region was predicted for both cases. In addition, the jet characteristics based on tracer concentration and tracer mass fraction profiles at different downstream levels are discussed. Overall, the numerical predictions compare favorably to the experimental measurements made at NETL

Numerical Simulations of a Circulating Fluidized Bed with a Square Cross-Section

In this study, both 2D and 3D numerical simulations of a well-documented circulating fluidized bed with a square cross-section were conducted. With some assumptions, a series of 2D simulations was first carried out to study the influence of grid resolution, initial flow field, and boundary condition on the flow hydrodynamics. It was found that 2D simulations under-predicted the solids inventory even with the finest grid (10-particle-diameter grid size). On the other hand, a 3D simulation with relatively coarse grid was found in better agreement with the experimental data. Differences between 2D and 3D simulations were briefly discussed

Formation Control with Unknown Directions and General Coupling Coefficients

Generally, the normal displacement-based formation control has a sensing mode that requires the agent not only to have certain knowledge of its direction, but also to gather its local information characterized by nonnegative coupling coefficients. However, the direction may be unknown in the sensing processes, and the coupling coefficients may also involve negative ones due to some circumstances. This paper introduces these phenomena into a class of displacement-based formation control problem. Then, a geometric approach have been employed to overcome the difficulty of analysis on the introduced phenomena. The purpose of this approach is to construct some convex polytopes for containing the effects caused by the unknown direction, and to analyze the non-convexity by admitting the negative coupling coefficients in a certain range. Under the actions of these phenomena, the constructed polytopes are shown to be invariant in view of the contractive set method. It means that the convergence of formation shape can be guaranteed. Subsequently, an example is given to examine the applicability of derived result

NUMERICAL INVESTIGATION OF GAS SAMPLING FROM FLUIDIZED BEDS

Gas mixing in a tall narrow fluidized bed operated in the slugging fluidization regime is studied with the aid of computational fluid dynamics. Three-dimensional numerical simulations are performed with an Eulerian-Eulerian model. Predicted axial and radial tracer concentration profiles for various operating conditions are generally in good agreement with experimental data from the literature. Different field variables including voidage, tracer concentration, and gas velocity at upstream and downstream levels are analysed to study gas mixing. Mean tracer concentrations in the dense phase and the bubble phase are evaluated and significant differences between them are found. The time-mean concentration is weighted heavily towards the dense phase concentration which may lead to misinterpretation of sampling data in dispersion models. Caution is needed when interpreting time-mean tracer concentration data. A flux-based mean tracer concentration is introduced to characterize the gas mixing in numerical simulations of two-phase fluidized beds

Exponential Stability of Time-Switched Two-Subsystem Nonlinear Systems with Application to Intermittent Control

This paper studies the exponential stability of a class of periodically time-switched nonlinear systems. Three cases of such systems which are composed, respectively, of a pair of unstable subsystems, of both stable and unstable subsystems, and of a pair of stable systems, are considered. For the first case, the proposed result shows that there exists periodically switching rule guaranteeing the exponential stability of the whole system with (sufficient) small switching period if there is a Hurwitz linear convex combination of two uncertain linear systems derived from two subsystems by certain linearization. For the second case, we present two general switching criteria by means of multiple and single Lyapunov function, respectively. We also investigate the stability issue of the third case, and the switching criteria of exponential stability are proposed. The present results for the second case are further applied to the periodically intermittent control. Several numerical examples are also given to show the effectiveness of theoretical results

Sub-grid drag model for immersed vertical cylinders in fluidized beds

Immersed vertical cylinders are often used as heat exchangers in gas-solid fluidized beds. CFD simulations are computationally expensive for large scale systems with bundles of cylinders. Therefore sub-grid models are required to facilitate simulations on a coarser grid, where internal cylinders are treated as a porous medium. The influences of cylinders on the gas-solid flow tend to enhance segregation and affect the gas-solid drag. A correction of gas-solid drag must be modeled via suitable sub-grid constitutive relationship. In the past, Sarkar et al. 2013 (1) have developed a sub-grid drag model for horizontal cylinder arrays based on 2D simulations. However, the effect of vertical cylinder arrangement was not considered due to computational complexities. In this work, highly resolved 3D simulations with vertical cylinders were performed in a periodic domain with imposed pressure drop. These simulations were filtered to construct a sub-grid drag model, which can be implemented in coarse-grid simulations. Gas-solid drag was filtered for different average solids fractions; instantaneous snap shots for various average solid fractions are shown in Fig. 1. A reduction in drag was identified as shown in Fig. 2 (a), when compared with simulation without cylinders, and with horizontal cylinders. Fig 2 (b) shows that slip velocities significantly increases when vertical cylinders are present. Vertical suspension drag due to vertical cylinders is insignificant, but substantial horizontal suspension drag is observed. REFERENCE 1.A. Sarkar, X. Sun and S. Sundaresan. Sub-grid drag models for horizontal cylinder arrays immersed in gas-particle multiphase flows. Chem. Eng. Sci.104399–412, 2013. Please click Additional Files below to see the full abstract

Stability and Bifurcation Analysis of a Modified Epidemic Model for Computer Viruses

We extend the three-dimensional SIR model to four-dimensional case and then analyze its dynamical behavior including stability and bifurcation. It is shown that the new model makes a significant improvement to the epidemic model for computer viruses, which is more reasonable than the most existing SIR models. Furthermore, we investigate the stability of the possible equilibrium point and the existence of the Hopf bifurcation with respect to the delay. By analyzing the associated characteristic equation, it is found that Hopf bifurcation occurs when the delay passes through a sequence of critical values. An analytical condition for determining the direction, stability, and other properties of bifurcating periodic solutions is obtained by using the normal form theory and center manifold argument. The obtained results may provide a theoretical foundation to understand the spread of computer viruses and then to minimize virus risks

Label Enhanced Event Detection with Heterogeneous Graph Attention Networks

Event Detection (ED) aims to recognize instances of specified types of event triggers in text. Different from English ED, Chinese ED suffers from the problem of word-trigger mismatch due to the uncertain word boundaries. Existing approaches injecting word information into character-level models have achieved promising progress to alleviate this problem, but they are limited by two issues. First, the interaction between characters and lexicon words is not fully exploited. Second, they ignore the semantic information provided by event labels. We thus propose a novel architecture named Label enhanced Heterogeneous Graph Attention Networks (L-HGAT). Specifically, we transform each sentence into a graph, where character nodes and word nodes are connected with different types of edges, so that the interaction between words and characters is fully reserved. A heterogeneous graph attention networks is then introduced to propagate relational message and enrich information interaction. Furthermore, we convert each label into a trigger-prototype-based embedding, and design a margin loss to guide the model distinguish confusing event labels. Experiments on two benchmark datasets show that our model achieves significant improvement over a range of competitive baseline methods