# Dedicated experiments for the development and validation of closure models

## Purpose

Bubbly flows can be found in many applications in chemical, biological and power engineering. Reliable simulation tools of such flows that allow the design of new processes and optimization of existing one are therefore highly desirable. CFD simulations applying the multi-fluid approach are very promising to provide such a design tool for complete facilities. In the multi-fluid approach, however, closure models have to be formulated to model the interaction between the continuous and dispersed phase. Due to the complex nature of bubbly flows, different phenomena have to be taken into account and for every phenomenon different closure models exist. For a validation of models, experiments that describe as far as possible all relevant phenomena of bubbly flows are needed. Since such data are rare in the literature, several CFD grade experiments are conducted at the department. Concepts to measure gas fraction distributions with corresponding bubble size, shape and velocity together with liquid velocity fields are developed for this purpose.

## Methods: Continous Phase

**Particle Shadow Velocimetry (PSV)**

Particle Image Velocimetry (PIV) is a commonly used tool to determine liquid velocity fields and derive important quantities like vorticity, strain or any kind of turbulence parameter. In bubbly flows, however, the dispersed gas phase can cause an inhomogeneous illumination due to unwanted lateral shadows of the bubbles as well as strong light scattering and reflection at the gas-liquid interfaces. To circumvent these problems, we recently developed particle shadow velocimetry (PSV) method for dispersed two-phase flows. The feature of such a measurement is to use a volumetric direct in-line illumination with e.g. LED-backlights for the region of interest, whereby scattering effects are strongly reduced and no lateral bubble shadows occur. By using a shallow depth of field (DoF), sharp tracer particle shadows positioned inside the DoF region can be identified and the particle displacement is evaluated in a PIV-like manner [1].

Figure1: Liquid velocity field in a bubbly flow using the PSV technique.

**3D Lagrangian Particle Tracking (LPT)**

For 3D measurements, we use the open source code OpenLPT [2], which uses the Shake-the-Box algorithm to track densely seeded tracer particles in a Lagrangian manner. Images are recorded with multiple high-speed cameras and the flow is again background illuminated with high-intensity LED clusters (similar to the aforementioned PSV technique, cf. Figure 2 left).

Figure 2 Left: Octagonal test section with multiple cameras and LEDs. Right: 3,000 sample trajectories from 3D LPT measurements in a bubble column.

**Methods: Dispersed Phase**

**2D Bubble identification**

An automated and reliable processing of bubbly flow images is highly needed to analyse large data sets of comprehensive experimental series. For single bubbles, which occur isolated in recorded images, edge-detection algorithms have proven high reliability and accuracy. A particular difficulty arises in bubbly flow recordings due to overlapping bubble projections in the images, which highly complicates the identification of individual bubbles. Due to the recent advances of deep learning models in the field of pattern recognition and the related task object detection, we are also pursuing developments in this field in order to detect and reconstruct overlapping bubbles in images [3].

**2D Bubble tracking**

The subsequent tracking of multiple detected bubbles in close proximity poses further challenges. The tracker not only has to be robust against inaccuracies of the detector, i.e. missing or false detections, but also has to be able to track bubbles that are fully occluded even for multiple times steps, while at the same time having numerous possible associations in the near vicinity. To solve these issues, we also utilize deep learning models and use a graph-based tracking formalism capable of tracking multiple bubbles in bubble swarms over long time spans [4].

## Experiment: Bubble Induced Turbulence

Bubble-induced turbulence (BIT) plays an important role in mixing, transport and collision of small particles in many natural and industrial applications. We investigate the properties of bubble-laden turbulent flows at different scales, focusing on the flow kinetic energy, anisotropy, energy transfer and extreme events. The experiments employed either 2D PSV or 3D LPT measurements to measure the flow in a column generated by a homogeneous bubble swarm rising in water. Furthermore, we also explore the Lagrangian description of BIT, e.g. the relative particle pair dispersion, based on the relative separation of tracer particles. The aim is both to develop a fundamental understanding and characterization of the multiscale physics [5,6] of these flows as well develop new models to predict their behavior [7,8].

Figure 5 Left: 2D small-scale PSV measurements. Right: Transverse (a) and longitudinal (b) second order structure function along the horizontal direction for different bubble sizes (Sm-Small/La-Large) and gas fractions (Less/More).

## Experiment: Bubble cluster

We study the evolution of bubble clusters in a swarm of freely rising bubbles under different flow conditions. Our machine learning-aided algorithm [3,4] allows us to identify and track bubbles in clusters and measure the cluster lifetimes/orientation. This comprehensive information is essential for understanding the collective dynamics of bubbles and can be used for instance to investigate the rise velocity of bubble swarms [4], which can be significantly different from that of a single bubble.

Figure 6: Identified bubble clusters in the center of an homogenously aerated bubble column.

## Experiment: Single bubble lift force in low-viscous systems

The lift force, which strongly inﬂuences the spatial bubble distribution, is one of the most important non-drag forces. However, measuring the lift force of ellipsoidal bubbles in a shear field is a very challenging task. Recently, our group developed a special experimental design that allows creating a stable linear shear field in air-water systems. Together with an averaging procedure suitable to address irregular movements of bubbles with high Reynolds number, we were able to experimentally determine the lift coefficient of ellipsoidal bubbles [9]. Furthermore, we could reveal how surfactants and even tiny amounts of impurities in tap water can alter the strength of the lift force [10,11,12].

Figure 7 Left: Experimental design to create linear shear flow. Right: Averaging procedure to obtain average bubble rise path.

Figure 8: Lift coefficient for different modified Eötvös numbers of ellipsoidal bubbles in water.

## Experiment: Stability of bubble columns

The role of the lift force is crucial to describe the regime transition in bubble columns [13]. The force is acting mainly horizontal due to the gravity aligned reactor design. The sign of the pre-factor can change due to the flow situation; in bubble columns, bubbles with a positive lift force coefficient are traveling to the wall, in particular away from velocity peaks, and vice versa. At the wall, the wall lubrication forces are acting against the lift force and are pushing the bubbles away from it. Experiments were conducted in a high aspect ratio bubble column for air/purified water. The sparger consists of 6 holes that can be equipped with different needles. The holes are separated in two groups which hold different needle sizes to produce a certain polydispersed flow. The total gas volume flow was fixed to 1.0 l/min. The gas flow through the sparger group was varied to vary the partial gas fraction of the small and large bubbles. Due to this variation, the regime of the bubble column could be manipulated [14].

## References

- [1] H. Hessenkemper, T. Ziegenhein
**Particle Shadow Velocimetry (PSV) in bubbly flows.**

International Journal of Multiphase Flow 106 (2018) 268-279 - [2] S. Tan, A. Salibindla, A. Masuk, R. Ni
**Introducing OpenLPT: new method of removing ghost particles and high-concentration particle shadow tracking.**

Experiments in Fluids 61 (2020) 47 - [3] H. Hessenkemper, S. Starke, Y. Atassi, T. Ziegenhein, D. Lucas
**Bubble identification from images with machine learning methods.**

International Journal of Multiphase Flow 155 (2022) 104169 - [4] T. Ma, H. Hessenkemper, D. Lucas, A. Bragg
**Fate of bubble clusters rising in a quiescent liquid.**

Journal of Fluid Mechanics 973 (2023) A15 - [5] T. Ma, H. Hessenkemper, D. Lucas, A. Bragg
**An experimental study on the multiscale properties of turbulence in bubble-laden ﬂows.**

Journal of Fluid Mechanics 936 (2022) A42 - [6] T. Ma, H. Hessenkemper, D. Lucas, A. Bragg
**Effects of surfactants on bubble-induced turbulence.**

Journal of Fluid Mechanics 970 (2023) A13 - [7] T. Ma, C. Santarelli, T. Ziegenhein, D. Lucas, J. Fröhlich
**Direct numerical simulation–based Reynolds-averaged closure for bubble-induced turbulence.**

Physical Review Fluids 2 (2017) 034301 - [8] T. Ma, D. Lucas, A. Bragg
**Explicit algebraic relation for calculating Reynolds normal stresses in flows dominated by bubble-induced turbulence.**

Physical Review Fluids 5 (2020) 084305 - [9] T. Ziegenhein, a. Tomiyama, D. Lucas
**A new measuring concept to determine the lift force for distorted bubbles in low Morton number system: Results for air/water.**

International Journal of Multiphase Flow 108 (2018) 11-24 - [10] H. Hessenkemper, T. Ziegenhein, R. Rzehak, D. Lucas, A. Tomiyama
**Lift force coefficient of ellipsoidal single bubbles in water.**

International Journal of Multiphase Flow 138 (2021) 103587 - [11] H. Hessenkemper, T. Ziegenhein, D. Lucas
**Contamination effects on the lift force of ellipsoidal air bubbles rising in saline water solutions**

Chemical Engineering Journal 386 (2020) 121589 - [12] H. Hessenkemper, T. Ziegenhein, D. Lucas, A. Tomiyama
**Influence of surfactant contaminations on the lift force of ellipsoidal bubbles in water.**

International Journal of Multiphase Flow 145 (2021) 103833 - [13] D. Lucas, H.-M. Prasser, A. Manera
**Influence of the lift force on the stability of a bubble column.**

Chemical Engineering Science 60 (2005) 3609-3619 - [14] D. Lucas, T. Ziegenhein
**Influence of the bubble size distribution on the bubble column flow regime.**

International Journal of Multiphase Flow 120(2019) 103092