Daniel Deising

Dipl.-Ing. Daniel Deising

+49 6151 16-21464

Mass Transfer at Fluid Interfaces

Research Motivation

The optimization of bubble column reactors is an important topic in the chemical and biological industry. In recent years, also numerical simulation techniques are employed to get a deeper understanding of the physico-chemical processes within these reactors, using detail-reduced two-fluid models (TFM). Since detail-reduction is achieved by averaging, information about local flow phenomena beyond averaging-scale is inherently lost and closure modeling becomes necessary.

Therefore, this work aims at the deduction of a closure model for interfacial species transfer by means of Direct Numerical Simulation of single rising bubbles and bubble swarms.

Project Description

Fig. 1 (left): LIV-Measurements of oxygen concentation in water-air (Prof. Schlüter, TUHH), Fig. 2 (right): Direct Numerical Simulation of oxygen-transfer in water-air (CST model, D. Deising)
Fig. 1 (left): LIV-Measurements of oxygen concentation in water-air (Prof. Schlüter, TUHH), Fig. 2 (right): Direct Numerical Simulation of oxygen-transfer in water-air (CST model, D. Deising)

The challenge in capturing the interfacial species transfer over fluid interfaces by Direct Numerical Simulations (DNS) are the steep concentration gradients at the interface and the abrupt interfacial concentration jumps, which impose severe requirements onto the underlying numerical methods (cf. Figures 1,2).

Fig. 3: Dynamic local adaptive mesh refinement and dynamic load balancing (Image: D. Deising)
Fig. 3: Dynamic local adaptive mesh refinement and dynamic load balancing (Image: D. Deising)

The simulation of species transfer is incorporated by means of the Continuous Species Transfer (CST) model which is based on the work of [1] and further developed in the course of this project [2]. To capture the thin concentration boundary layer, a dynamic local adaptive mesh refinement and dynamic load balancing are applied (Figure 3), which has been accomplished in the OpenFOAM C++ library for computational continuum mechanics. Basis of our numerical investigations is the interFoam solver which was significantly modified and enhanced.

Fig. 4 (left): Species concentration profile around a single rising bubble (Eo=40, Mo=1e-05), Fig. 5 (right):.Velocity field around five bubbles rising in a fully periodic domain (Images: D. Deising)
Fig. 4 (left): Species concentration profile around a single rising bubble (Eo=40, Mo=1e-05), Fig. 5 (right):.Velocity field around five bubbles rising in a fully periodic domain (Images: D. Deising)

The project so far consisted mainly of model development, implementation and validation. Recently, the derived methodology has been successfully applied to the numerical simulation of species transfer from rising single bubbles and bubble swarms (see Figures 4,5).

CST Model Description

The Continuous Species Transfer (CST) model is a single field model formulation for interfacial species transfer across fluid interfaces for Volume-Of-Fluid (VOF) interface capturing methods. The model derivation is based on the Conditional Volume Averaging (CVA) technique, which reveals additional interfacial terms that inherently take care of the interfacial jump conditions within the single field formulation. Further, the application of the CVA technique enables the derived model to consistently smear out the cross interfacial concentration jump onto the underlying available spatial resolution provided by the computational mesh (i.e. the finite volumes or equivalently the averaging volumes). This makes the CST model also applicable to numerical methods which do not provide a strictly sharp interface (e.g. algebraic VOF methods).

Acknowledgements

This work is supported by the German Federal Ministry of Education and Research (BMBF) in scope of the project 'Multi-Phase' (FKZ: 01RC1102).

Literature

[1] H. Marschall, K. Hinterberger, C. Schüler, F. Habla, O. Hinrichsen, 2012. “Numerical simulation of species transfer across fluid interfaces in free-surface flows using OpenFOAM.” Chemical Engineering Science 78, 111 – 127.

[2] D. Deising, H. Marschall, D. Bothe, 2015. “A unified single-field model framework for Volume-Of-Fluid simulations of interfacial species transfer applied to Bubbly Flows.” Chemical Engineering Science, accepted manuscript

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