TY - JOUR

T1 - Computational Study of Three-Dimensional Lagrangian Transport and Mixing in a Stirred Tank Reactor  

AU - Weiland, Christian

AU - Steuwe, Eike

AU - Fitschen, Jürgen

AU - Hoffmann, Marko

AU - Schlüter, Michael

AU - Padberg-Gehle, Kathrin

AU - von Kameke, Alexandra

N1 - The authors gratefully acknowledge the financial support provided by the German Research Foundation (DFG) within the project 395843083 (KA 4854/1-1) and the project 316204571 as part of the Priority Programme DFG-SPP 1881 “Turbulent Superstructures”. The authors thank Johannes Wutz from M-Star Simulations, LCC. for the fruitful discussions. Further, the authors thank Marc Maly and Sebastian Hofmann for proofreading. Publisher Copyright: © 2023 The Author(s)

PY - 2023/5/15

Y1 - 2023/5/15

N2 - The detection of compartments and dead zones as well as the estimation of the mixing efficiency in stirred tanks are of vital interest for a variety of biochemical and chemical processes. Here, numerically derived time-dependent 3D fluid velocity fields of a stirred tank reactor are computed using the Lattice Boltzmann Method. Mixing in the stirred tank reactor is analysed by means of Lagrangian Coherent Structures which allow to unravel the mixing states of complex flows. This Lagrangian analysis is achieved by computing Finite Time Lyapunov Exponents and applying recent trajectory-based network methods on the three-dimensional flow. The results reveal a zone of low interaction in the upper region of the stirred tank reactor and five additional transient compartments. The trajectory-based network analysis detects low cross-mixing of fluid parcels between different compartments but a very high mixing of fluid parcels inside of each compartment. This high interaction is also found in an analysis of the Finite Time Lyapunov Mixing Intensity. Time-averaging of the fluid velocity field prior to the Lagrangian analysis is considered to extract the most influential Lagrangian Coherent Structures.

AB - The detection of compartments and dead zones as well as the estimation of the mixing efficiency in stirred tanks are of vital interest for a variety of biochemical and chemical processes. Here, numerically derived time-dependent 3D fluid velocity fields of a stirred tank reactor are computed using the Lattice Boltzmann Method. Mixing in the stirred tank reactor is analysed by means of Lagrangian Coherent Structures which allow to unravel the mixing states of complex flows. This Lagrangian analysis is achieved by computing Finite Time Lyapunov Exponents and applying recent trajectory-based network methods on the three-dimensional flow. The results reveal a zone of low interaction in the upper region of the stirred tank reactor and five additional transient compartments. The trajectory-based network analysis detects low cross-mixing of fluid parcels between different compartments but a very high mixing of fluid parcels inside of each compartment. This high interaction is also found in an analysis of the Finite Time Lyapunov Mixing Intensity. Time-averaging of the fluid velocity field prior to the Lagrangian analysis is considered to extract the most influential Lagrangian Coherent Structures.

KW - Mathematics

KW - Lagrangian coherent structures

KW - Mixing

KW - Finite time lyapunov exponent

KW - Stirred tank reactor

KW - Compartments

KW - Network methods

UR - http://www.scopus.com/inward/record.url?scp=85146445937&partnerID=8YFLogxK

U2 - 10.1016/j.ceja.2023.100448

DO - 10.1016/j.ceja.2023.100448

M3 - Journal articles

VL - 14

JO - Chemical Engineering Journal Advances

JF - Chemical Engineering Journal Advances

SN - 2666-8211

M1 - 100448

ER -