In many industrial applications one aims for the design of efficient chemical reactions. This is often done by combining the experimental analysis of the reactors with numerical twins. The simultaneous modelling of flow, mixing and chemical reaction, however, remains a complicated task, because the computational costs are still significant and often prohibitive.
In this work, mixing processes of chemical substances are modelled and analysed by a transfer operator method that uses the Lagrangian trajectories of passive particles. In practice, the spatial distributions of the concentrations of the chemical species are represented by density vectors. These are evolved by means of a stochastic transition matrix, which is obtained as a numerical approximation of a transfer operator. In a further step, the reaction of the fluids is modelled by specific rules that update the density vectors.
The method is applicable to closed and to open example systems and to different chemical processes, such as competitive consecutive reactions. The authors demonstrate that the dynamic processes are reflected well by this method.
Furthermore, the interdependence of the reaction fronts with Lagrangian coherent structures is evaluated. These structures are defined with set oriented methods that also work well on data in three dimensions.
The study is a collaboration between the Institute of Mathematics and its Didactics at Leuphana University Lüneburg and the Hamburg University of Applied Sciences, carried out within the Collaborative Research Centre CRC 1615 (SMART Reactors). It builds on simulated Lagrangian trajectory data of a stirred tank reactor on laboratory scale that are published separately.
Anja Göbel, Anna Klünker, Alexandra von Kameke, Kathrin Padberg-Gehle (2026). Model-based computational study of reactive fluid systems using transfer operator methods. PubData, Leuphana University Lüneburg.
