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    Modeling of aggregation kernels for fluidized beds using discrete particle model simulations
    Aggregation is one of the many important processes in chemical and process engineering. Several researchers have attempted to understand this complex process in fluidized beds using the macro-model of population balance equations (PBEs). The aggregation kernel is an effective parameter in PBEs, and is defined as the product of the aggregation efficiency and collision frequency functions. Attempts to derive this kernel have taken different approaches, including theoretical, experimental, and empirical techniques. The present paper calculates the aggregation kernel using micro-model computer simulations, i.e., a discrete particle model. We simulate the micro-model without aggregation for various initial conditions, and observe that the collision frequency function is in good agreement with the shear kernel. We then simulate the micro-model with aggregation and calculate the aggregation efficiency rate. © 2013 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences.
    Publicationtype: Journal Article
      19
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      26
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    Some modelling aspects of aggregation kernels and the aggregation population balance equations
    Aggregation is one of the important processes in chemical and process engineering. To model this process aggregation population balance equation is widely used. The aggregation kernel is one of the most effective parameter of this aggregation equation. This is usually defined as the product of the aggregation efficiency and collision frequency functions. Several authors attempted to model the aggregation kernel using different approaches like theoretical, experimental and empirical approaches. In the present paper we are giving some important modelling aspects of these kernels. One can use these modelling aspects in other variants of the population balance equations with breakage, nucleation, growth, ..., etc.
    Publicationtype: Conference Paper
      37
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      24
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      38
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    Item type:Publication,
    Numerical Methods on Population Balances
    Publicationtype: Book Part
      32
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    Three-dimensional numerical study of heat and mass transfer in fluidized beds with spray nozzle
    The numerical computations of temperature and concentration distributions inside a fluidized bed with spray injection in three-dimensions are presented. A continuum model, based on rigorous mass and energy balance equations developed from Nagaiah et al., is used for the three-dimensional simulations. The three-dimensional model equation for nozzle spray is reformulated in comparison to Heinrich. For solving the non-linear partial differential equations with boundary conditions a finite element method is used for space discretization and an implicit Euler method is used for time discretization. The time-dependent behavior of the air humidity, air temperature, degree of wetting, liquid film temperature and particle temperature is presented using two different sets of experimental data. The presented numerical results are validated with the experimental results. Finally, the parallel numerical results are presented using the domain decomposition methods.
    Publicationtype: Journal Article
      33
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    An efficient numerical technique for solving population balance equation involving aggregation, breakage, growth and nucleation
    A new discretization for simultaneous aggregation, breakage, growth and nucleation is presented. The new discretization is an extension of the cell average technique developed by the authors [J. Kumar, M. Peglow, G. Warnecke, S. Heinrich, and L. Mörl. Improved accuracy and convergence of discretized population balance for aggregation: The cell average technique. Chemical Engineering Science 61 (2006) 3327-3342.]. It is shown that the cell average scheme enjoys the major advantage of simplicity for solving combined problems over other existing schemes. This is done by a special coupling of the different processes that treats all processes in a similar fashion as it handles the individual process. It is demonstrated that the new coupling makes the technique more useful by being not only more accurate but also computationally less expensive. At first, the coupling is performed for combined aggregation and breakage problems. Furthermore, a new idea that considers the growth process as aggregation of existing particle with new small nuclei is presented. In that way the resulting discretization of the growth process becomes very simple and consistent with first two moments. Additionally, it becomes easy to combine the growth discretization with other processes. The new discretization of pure growth is a little diffusive but it predicts the first two moments exactly without any computational difficulties like appearance of negative values or instability etc. The numerical scheme proposed in this work is consistent only with the first two moments but it can easily be extended to the consistency with any two or more than two moments. Finally, the discretization of pure and coupled problems is tasted on several analytically solvable problems.
    Publicationtype: Journal Article
      28
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    Chapter 2 Fluidized bed spray granulation
    (Elsevier, 2007-12) ; ;
    Publicationtype: Book Part
      42