Andreas Bück

An improved and efficient finite volume scheme for bivariate aggregation population balance equation

In this work, a finite volume scheme for the numerical solution of bivariate pure aggregation population balance equations on non-uniform meshes is derived. The new method has a simple mathematical structure and it provides high accuracy with respect to the number density distribution as well as different moments. The method relies on weights to conserve the total mass of the system. The new method is compared to a recently developed finite volume scheme by Forestier-Coste and Mancini (2012) for some selected benchmark problems. It is shown that the proposed method is not only computationally more efficient but also more accurate than the method by Forestier-Coste and Mancini (2012).

CFD–DEM study of residence time, droplet deposition, and collision velocity for a binary particle mixture in a Wurster fluidized bed coater

ABSTRACT An approach that combines computational fluid dynamics with the discrete element method is applied to investigate the residence time and collision velocity in different processing zones of a Wurster fluidized bed. Ideal and nonideal circulating motions of particles are distinguished to evaluate distributions of cycle times. Solid-like droplets are injected and simulated inside a predefined spray zone to study the droplet deposition rate. The simulation, conducted for a binary mixture of small and large particles, predicts the ideal cycle times and the residence times of both particle sizes in the Wurster tube are in good agreement to the available experimental results.

Prediction of Shell Porosities in Continuous Fluidized Bed Spray Layering

In this work, experimental results for a continuous fluidized bed spray layering process are used to identify product quality influencing process parameters, such as the shell porosity. The prediction of the shell porosity is based on an empirical relation established for fluidized bed layering in batch mode. It uses gas-side properties, which are represented by the drying potential of the gas. It is shown that the shell porosities forming in the continuous mode can be deduced from this relation by comparing experimental data and simulation results. Process stability and seed formation are also discussed using the obtained experimental data.

Adaptive discrepancy based control of continuous fluidized bed spray granulation with internal classification

This paper is concerned with adaptive stabilization of open loop unstable uidized bed spray granulation with internal product classication by means of nonlinear feedback control. Since the process model is represented by a nonlinear partial integro-dierenti al equation, direct stabilization of the particle size distribution in a Lp or L1 norm is dicult. To overcome this problem a stability notion using two generalized distance measures, the discrepancies, is used. It is shown that the adaptive version of the resulting discrepancy based control law is able to cope with uncertainties present in industrial applications.

Low order controller design for continuous fluidized bed spray granulation with internal product classification by robust control methods

Abstract This paper is concerned with stabilizing open loop unstable fluidized bed spray granulation with internal product classification by means of low order control methods. The process under investigation can be described by a population balance equation. In order to design a low order controller numerical approximation and model reduction methods are applied resulting in a low order design model. Stability when applying the low order control to the original plant can be guaranteed under certain conditions on the approximation and reduction methods and the robustness of the designed controller. The controller is validated by simulation of the nonlinear plant model.

Superheated steam drying of single wood particles: A characteristic drying curve model deduced from continuum model simulations and assessed by experiments

ABSTRACT Computational fluid dynamics (CFD) and CFD coupled with discrete element method (DEM) are powerful approaches to describe the drying behavior of real drying towers. In these approaches, the heat and mass interaction between fluid phase and the wet solid is required as an essential input. In this work, a new methodology for establishing simple drying model of single wood particles is presented. First, a spatially resolved continuum-scale model that describes the coupled heat and mass transfer within a single porous wood particle during superheated steam drying under atmospheric pressure is developed. The thermophysical properties of wood particle required as input data for the continuum model are determined experimentally. Then sophisticated continuum model is reduced to a simpler lumped model, which is referred to as the characteristic drying curve (CDC) model. The continuum model simulations are performed in a board range of operating drying conditions and the associated results are used to establish correlations for the CDC model parameters. The results of both sophisticated and reduced models are validated against the experimental observations made using a magnetic suspension balance. The sensitivity analysis performed with the continuum model indicates a strong dependency of the critical moisture content on particle size and drying condition. The established CDC model can be implemented in the CFD or CFD-DEM model of superheated steam dryers.

Bifurcation analysis of process stability of continuous fluidized bed agglomeration with external product classification

Abstract This contribution discusses the process behaviour of continuous fluidised bed agglomeration with external product screening and milling. The stability behaviour is tracked in the parameter plane (aggregation efficiency and milling diameter) by parameter continuation methods. It is shown that for EKE and gravitational kernels, loss of stable operation with onset of oscillatory behaviour has to be expected.

MODELAGEM DE TRANSFERÊNCIA DE CALOR EM LEITO FIXO COLOCADO EM TAMBOR HORIZONTAL PARCIALMENTE PREENCHIDO E COM ROTAÇÃO INTERMITENTE

RESUMO O objetivo deste trabalho foi modelar a transferencia de calor em um leito fixo colocado em tambor rotativo parcialmente preenchido e com rotacao intermitente, visando sua utilizacao futura como biorreator para fermentacao em estado solido. Para tanto, foi feito um estudo de caso utilizando um leito de particulas inertes composto de esferas de vidro acondicionado em um biorreator cilindrico horizontal parcialmente preenchido, com temperatura interna de 45oC mantida atraves da camisa e de aeracao forcada sobre o leito. Foi proposto um modelo bidimensional a uma fase, com variacoes de temperatura com as coordenadas angular e radial, com o tempo. Foram admitidas condicoes de contorno de primeira especie para o raio maximo e de terceira especie para a superficie do leito. Os resultados indicam simetria na distribuicao de temperatura angular e radial e pouca influencia da conveccao devido ao baixo valor do coeficiente convectivo. O aumento de h evidencia a conveccao, mas a vazao de ar necessaria para tal nao e usual em ensaios fermentativos. Em 10 horas de simulacao, a temperatura media correspondeu a 32,9oC sem rotacao e a 36,4oC com rotacao intermitente a cada 2 horas.

Dynamic Modelling of Particle Formulation in Horizontal Fluidized Beds

Abstract A generic multi-compartment, multi-zone population balance model (PBE) is developed. The model considers particle properties as well as the geometric coordinates (apparatus length). Further features of the presented model are the possibility to include different transport mechanisms from one process chamber to the next, the possibility of arbitrary positions of particle recycle as well as different operating conditions in each chamber. By parametric studies the influence of important process parameters on the product quality is investigated. It is the aim of this work to link product properties, in particular the particle size distribution, to a multi-zone model that can be readily applied in an industrial environment for process design and optimization.

Discrepancy based control of systems of population balances

This contribution is concerned with control of systems of population balances, which are frequently used for modeling of particulate processes like granulation or crystallization. Using the model of a pellet coating processes it will be shown that discrepancy based control can be successfully applied for control of systems of population balances. Here, the main idea is to choose a system output being a generalized measure for the distance between the particle size distribution and its desired steady state, which allows a direct Lyapunov design.