Model reduction techniques for the simulation of particle populations in fluid flow

Zusammenfassung Der Beitrag beschreibt den Einsatz der Proper Orthogonal Decomposition (POD) für die Modellreduktion von Partikelprozessen in fluider Strömung. Diese Prozessklasse ist von großer Bedeutung für die chemische und pharmazeutische Industrie. Physikalische Modelle solcher Prozesse sind häufig sehr komplex und für Regelungsaufgaben wenig geeignet. POD bietet hier eine attraktive Möglichkeit, zu reduzierten Prozessmodellen zu gelangen, da das Verfahren sehr flexibel ist, keine spezielle Struktur des Referenzmodells erfordert und interne und externe Koordinaten in einheitlicher Weise behandelt. Der Beitrag stellt das Reduktionsverfahren vor und illustriert es an Beispielen. Summary This paper discusses the application of Proper Orthogonal Decomposition (POD) to the model reduction of particle processes in fluid flow. This class of processes is highly relevant for chemical and pharmaceutical industry. As detailed first principle models of such processes tend to be very complicated, reduced models are required for process control and process design. POD is an attractive method to obtain the reduced models, as it is highly flexible, does not require a special structure of the reference model and treats internal and external coordinates in the same manner. The method is presented and illustrated by examples.

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“….., N c erhält man durch Einsetzen der Approximationen in die Bilanzgleichungen (11,12) und Gewichtung des Residuums mit den Basisfunktionen:…”

Section: Schritt: Herleitung Der Differentialgleichungen Des Reduzierunclassified

Modellreduktion von Populationssystemen mit Hilfe von Proper Orthogonal Decomposition

Mangold

Krasnyk

2012

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“…10 is used to simulate the described crystallizer model. A complete list of model parameters is given in Krasnyk et al 9 In simulation a spatially distributed steady-state fluid flow profile has been used. A streamline plot of the fluid flow is shown in Figure 2.…”

Section: Modelmentioning

confidence: 99%

“…This is justified if the particle concentration is sufficiently small. A more detailed description of the experimental setup and of the model is given in Krasnyk et al…”

Section: Reference Modelmentioning

confidence: 99%

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Reduction of a Urea Crystallizer Model by Proper Orthogonal Decomposition and Best-Points Interpolation

Krasnyk

Mangold

2010

Ind. Eng. Chem. Res.

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A reduced model of a urea crystallizer is developed for process control purposes. It is derived from a reference model, which describes the formation of particles in fluid flow and is of very high order. A strong reduction of the system order is achieved by proper orthogonal decomposition (POD). However, it turns out that POD alone does not lead to a satisfactory reduction of the computation time. The reason is the presence of nonlinear terms in the reference model whose evaluation is quite costly in the reduced model. To get a speed-up of the reduced model, the nonlinear terms are approximated by an interpolation technique. The resulting reduced model is 500 times smaller and 100 times faster than the reference model, while the loss of accuracy is marginal.

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Application of Proper Orthogonal Decomposition to Particulate Processes

Mangold

Krasnyk

2012

IFAC Proceedings Volumes

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Particulate processes like industrial crystallisation or granulation are often described by population balances. This leads to mathematical models containing partial integro differential equations. In many cases, the flow conditions of the fluid phase have a strong impact on the particle formation. To describe this properly, Navier Stokes equations have to be solved in addition. The resulting model equation system is too complicated to apply them to typical process control tasks. Reduced models are desirable. In this contribution, the use of proper orthogonal decomposition is suggested as a powerful reduction method. The usefulness of the approach is illustrated by two application examples: a granulation process with particle aggregation and a crystallisation process with particle growth and complex fluid dynamics.

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Model reduction techniques for the simulation of particle populations in fluid flow

Cited by 3 publications

References 20 publications

Modellreduktion von Populationssystemen mit Hilfe von Proper Orthogonal Decomposition

Modellreduktion von Populationssystemen mit Hilfe von Proper Orthogonal Decomposition

Reduction of a Urea Crystallizer Model by Proper Orthogonal Decomposition and Best-Points Interpolation

Application of Proper Orthogonal Decomposition to Particulate Processes

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