# README for Multiphase Cases Repository by HZDR [[_TOC_]] ## Multiphase Cases Repository by HZDR This repository contains simulation setups of the Multiphase Cases Repository by HZDR for OpenFOAM Foundation Software [^19]. The simulation setups are divided into mono- and polydisperse bubbly flows utilising the set of Baseline models of HZDR[^20], setups using the morphology-adaptive multifield two-fluid model[^21] (unresolved and resolved interfaces) and miscellaneous cases. **Acknowledgement:** OpenFOAM(R) is a registered trade mark of OpenCFD Limited, producer and distributor of the OpenFOAM(R) software via [www.openfoam.com](https://openfoam.com). The Multiphase Cases Repository by HZDR for OpenFOAM Foundation Software is not compatible with the software released by OpenCFD Limited, but is based on the software released by the OpenFOAM Foundation via [www.openfoam.org](https://openfoam.org). ## Highlights of the Multiphase Cases Repository by HZDR ### Cases using the Baseline model set by HZDR | Folder | Reference for Experiment | Reference for Case Setup | |-------------------------------------------|----------------------------------------------------|--------------------------------------------------------------| | cases/baseline/1986_Sun_and_Faeth | Sun and Faeth (1986)[^50],[^51] | Kamble et al. (2025)[^52] | | cases/baseline/1987_Wang | Wang (1986)[^53], Wang et al. (1987)[^54] | :x: | | cases/baseline/1993_Liu_and_Bankoff | Liu (1989)[^55], Liu and Bankoff (1993)[^56],[^57] | :x: | | cases/baseline/1998_Liu | Liu (1998)[^11] | Rzehak et al. (2021)[^15], Kriebitzsch and Rzehak (2016)[^8] | | cases/baseline/1999_Pfleger_et_al | Pfleger et al. (1999)[^36] | Schlegel et al. (2025)[^63] | | cases/baseline/2000_Deen_et_al | Deen et al. (2000)[^37] | Schlegel et al. (2025)[^63] | | cases/baseline/2001_Hibiki | Hibiki et al. (2000)[^58] | :x: | | cases/baseline/2005_Lucas_et_al | Lucas et al. (2005)[^12] | Lehnigk et al. (2022)[^9] | | cases/baseline/2008_Shawkat | Shawkat et al. (2008)[^16] | Kriebitzsch and Rzehak (2016)[^8] | | cases/baseline/2009_Hosokawa | Hosokawa and Tomiyama (2009)[^4] | Rzehak et al. (2021)[^15] | | cases/baseline/2009_Mudde_et_al | Mudde et al. (2009)[^40] | Draw and Rzehak (2024)[^61] | | cases/baseline/2010_Lucas_et_al | Lucas et al. (2010)[^59] | :x: | | cases/baseline/2012_Akbar_et_al | Akbar et al. (2012)[^38] | Schlegel et al. (2025)[^63] | | cases/baseline/2013_Hosokawa_and_Tomiyama | Hosokawa and Tomiyama (2013)[^5] | Kriebitzsch and Rzehak (2016)[^8], Liao et al. (2020)[^10] | | cases/baseline/2016_Kim_et_al | Kim et al. (2016)[^7] | Liao et al. (2020)[^10] | | cases/baseline/2019_Ziegenhein_and_Lucas | Ziegenhein and Lucas (2019)[^39] | Schlegel et al. (2025)[^63] | | cases/baseline/2020_Neumann-Kipping | Neumann-Kipping et al. (2020)[^60] | :x: | | cases/baseline/2021_Seo_and_Kim | Seo and Kim (2021)[^66] | Kamble et al. (2026)[^67] | | cases/baseline/2023_Sommer | Sommer et al. (2023)[^62] | Sommer et al. (2024)[^62] | ### Cases using the morphology-adaptive modelling approach | Folder | Reference for Experiment/Direct Numerical Simulation | Reference for Case Setup | |--------------------------------------------------------|--------------------------------------------------------|-----------------------------------------------------| | cases/multimorph/1937_Taylor_and_Green | Taylor and Green (1937)[^49] | :x: | | cases/multimorph/1987_Fabre_et_al | Fabre et al. (1987)[^64] | Meller et al. (2023)[^65] | | cases/multimorph/2007_Staebler | Staebler (2007)[^17] | Tekavcic et al. (2021, 2022)[^18],[^44] | | cases/multimorph/2009_Hysing_et_al | Hysing et al. (2009)[^6] | Hysing et al. (2009)[^6], Meller et al. (2021)[^13] | | cases/multimorph/2014_Adelsberger_et_al | :x: | Adelsberger et al. (2014) [^28] | | cases/multimorph/2014_Cubero_et_al | :x: | Cubero et al. (2014)[^31] | | cases/multimorph/2015_Balcazar_et_al | Bhaga and Weber (1981)[^3], Balcazar et al. (2015)[^2] | Meller et al. (2021)[^13] | | cases/multimorph/2021_Porombka_et_al | Porombka et al. (2021)[^46] | Porombka (2023)[^47], Riviera (2024)[^48] | | cases/multimorph/2023_Wiedemann_et_al | Wiedemann et al. (2023)[^33] | Wiedemann et al. (2023)[^33] | | cases/multimorph/hydraulicJump2D | :x: | :x: | | cases/multimorph/plungingJetChansonEtAl2004 | Chanson et al. (2004)[^32] | Meller et al. (2024)[^45] | | cases/multimorph/risingBubbleFrederixEtAl2021/regimeII | Tripathi et al. (2015)[^29] | Frederix et al. (2021)[^30] | | cases/multimorph/risingBubbleHysingEtAl2009 | :x: | Meller et al. (2021, 2022)[^13],[^14] | | cases/multimorph/risingBubbleMellerEtAl2022 | :x: | Meller et al. (2022)[^14] | | cases/multimorph/shipHullAirLubrication | Elbing et al. (2008)[^43] | :x: | ### Miscellaneous cases | Folder | Reference for Experiment | Reference for Case Setup | |---------------------------------------------------------|--------------------------|---------------------------| | cases/misc/multiphase/multiphaseEuler/1991_Akhtar_et_al | Akhtar et al. (1991)[^1] | Lehnigk et al. (2022)[^9] | ## Installation ### Prerequisites For running the cases in this repository, you need to install the software provided through the Multiphase Code Repository by HZDR for OpenFOAM Foundation Software. Depending on what you have access to * **Helmholtz Code Base**[^22]: For Helmholtz and Friends via Helmholtz AAI[^23] or using a HZDR guest account * **Rossendorf Data Repository (RODARE)**[^19]: For everybody you can install the software in several ways: * as Debian packages * by compiling from sources * by pulling the provided Docker or Apptainer Images Follow the installation instructions for your preferred approach and make sure your environment is setup correctly, e.g. by running `foamVersion`. ### General remarks The installation instructions will use the following environment variable: * `FOAM_RUN`: directory where simulation setups are stored ### Multiphase Cases Repository by HZDR from Helmholtz Code Base Note that this repository includes content that is versioned using git-lfs[^27] to store large binary files in the repository ```shell sudo apt update sudo apt install git-lfs ``` After successful installation, simply clone the repository ```shell mkdir -p $FOAM_RUN git clone --single-branch git@codebase.helmholtz.cloud:fwdc/multiphase/cases.git $FOAM_RUN ``` ### Multiphase Cases Repository by HZDR from Rossendorf Data Repository (RODARE) Download tar archive [^24] from RODARE and unpack it ```shell mkdir -p $FOAM_RUN tar -xzf Multiphase-Cases-Repository-.tgz -C $FOAM_RUN ``` ### Snakemake workflow for Computational Fluid Dynamics software This repository is configured for convenient batch-processing of the contained simulation setups both on workstations and HPC systems using Snakemake. In order to use this functionality an installation of the _multiphasepy_ package is required. You can obtain it from [PYPI](https://pypi.org). For usage information refer to the [documentation](https://multiphase-python-repository-by-hzdr.readthedocs.io/en/latest/) of the package. ## Model Testing For efficiently testing the influence of a certain model or parameter selection for a range of simulation setups, e.g. in the scope of a Snakemake workflow, the corresponding dictionary entry can be placed at a central location and included in individual cases using the `#include` directive provided by OpenFOAM. In the following example, the lift model selection in `constant/phaseProperties` for a case using the `multiphaseEuler` solver module is centralized. ```cpp lift { air_dispersedIn_water { #include "~/OpenFOAM/cases/models/lift.cfg" } } ``` The content of `~/OpenFOAM/cases/models/lift.cfg` could be ```cpp type Tomiyama; aspectRatio { type Wellek; } ``` **Note**: To allow parallel testing of different model selections, the directory containing the files to be included should be relative to the directory to which the Cases Repository was cloned. Globally overwriting a model via the `#includeEtc` is discouraged for this reason. ## Quantification of the CFD Prediction Quality A systematic analysis of results can be supported by a quantification of the agreement of simulation results and experimental data. For that purpose a fuzzy logic controller [^35] is introduced that allows a comparison of two one- dimensional data sets, e.g. line samples or probes. It generates a concise value between 0 and 1 quantifying the prediction quality or performance of a simulation result. This performance evaluation is performed for all available validation data individually. For details on the fuzzy controller please checkout the `mpyfuzzy` utility of the `multiphasepy` package [^34] and use `mpyfuzzy --help` for further options. For plotting purposes a jupyter notebook to be found under `workflow/scripts/plotCFDPerformance.ipynb` can be used and a working environment for launching the notebook is provided with the `multiphasepy` package [^34]. Note that for the notebook script to work it has to be copied into the top-level workflow directory. The script plots the error metrics and performance results for all validation fields for the selected cases. The script also averages performance results over all the individual validation data in order to produce an overall performance value for each case, and plots this for all selected cases. ## Analysing the Feature Hierarchy of Cases Results of [Model testing](#model-testing) can be visualized using a decision tree analysis [^41]. Keywords describing each case and listed in the `case.yml` files serve as labels, while the values computed as a [Quantification of the prediction quality](#Quantification of the prediction quality) can be used as the target feature for building decision tree models. An automated script for plotting a decision tree from the change in performance after model testing can be found under `workflow/scripts/decisionTreeAnalysis.ipynb`. In order to use the script the `sklearn`[^42] package needs to be installed, everything else is provided with the `multiphasepy` package [^34]. ## Repository Structure The repository includes the following main directories and files: | Directory | Description | |------------------|----------------------------------------------------------------------------------------------------| | etc | header templates for dictionaries, scripts and Snakefiles, template for case setup, keyword list | | profiles | contains configuration files for executing the Snakemake[^25] workflow locally or on a cluster | | cases/baseline | directory containing mono- and poly-disperse bubbly flow cases | | cases/flotation | directory for three-phase flotation cases | | cases/misc | directory for various `incompressibleVoF` and `multiphaseEuler` setups with experimental data | | cases/multimorph | directory for cases using the morphology-adaptive modelling approach | | workflow | stores files relevant for batch processing with Snakemake workflow execution and report generation | | codemeta.json | software metadata according to The CodeMeta Project[^26] | | CONTRIBUTING.md | how to contribute to the project | | LICENSE | licensing information | | workflow.yml | top-level configuration file for batch runs | ## How to cite us? When using the Multiphase Cases Repository by HZDR cite as >>> Haensch, S. et al. (2026). Multiphase Cases Repository by HZDR for OpenFOAM Foundation Software. Rodare. >>> [^1]: Akhtar, M. K., Xiong, Y., & Pratsinis, S. E. (1991). Vapor synthesis of titania powder by titanium tetrachloride oxidation. AIChE Journal, 37(10), 1561-1570. [^2]: Balcazar, N., Lehmkuhl, O., Jofre, L., & Oliva, A. (2015). Level-set simulations of buoyancy-driven motion of single and multiple bubbles. International Journal of Heat and Fluid Flow, 56, 91-107. [^3]: Bhaga, D., & Weber, M. E. (1981). Bubbles in viscous liquids: shapes, wakes and velocities. Journal of fluid Mechanics, 105, 61-85. [^4]: Hosokawa, S., & Tomiyama, A. (2009). Multi-fluid simulation of turbulent bubbly pipe flows. Chemical Engineering Science, 64(24), 5308-5318. [^5]: Hosokawa, S., & Tomiyama, A. (2013). Bubble-induced pseudo turbulence in laminar pipe flows. International journal of heat and fluid flow, 40, 97-105. [^6]: Hysing, S. R., Turek, S., Kuzmin, D., Parolini, N., Burman, E., Ganesan, S., & Tobiska, L. (2009). Quantitative benchmark computations of two-dimensional bubble dynamics. International Journal for Numerical Methods in Fluids, 60(11), 1259-1288. [^7]: Kim, M., Lee, J. H., & Park, H. (2016). Study of bubble-induced turbulence in upward laminar bubbly pipe flows measured with a two-phase particle image velocimetry. Experiments in Fluids, 57(4), 1-21. [^8]: Kriebitzsch, S., & Rzehak, R. (2016). Baseline model for bubbly flows: simulation of monodisperse flow in pipes of different diameters. Fluids, 1(3), 29. [^9]: Lehnigk, R., Bainbridge, W., Liao, Y., Lucas, D., Niemi, T., Peltola, J., & Schlegel, F. (2022). An open-source population balance modeling framework for the simulation of polydisperse multiphase flows. AIChE Journal, 68(3), e17539. [^10]: Liao, Y., Upadhyay, K., & Schlegel, F. (2020). Eulerian-Eulerian two-fluid model for laminar bubbly pipe flows: Validation of the baseline model. Computers & Fluids, 202, 104496. [^11]: Liu, T. J. (1998, June). The role of bubble size on liquid phase turbulent structure in two-phase bubbly flow. In Proc. Third International Congress on Multiphase Flow ICMF (Vol. 98, pp. 8-12). [^12]: Lucas, D., Krepper, E., & Prasser, H. M. (2005). Development of co-current air-water flow in a vertical pipe. International Journal of Multiphase Flow, 31(12), 1304-1328. [^13]: Meller, R., Schlegel, F., & Lucas, D. (2021). Basic verification of a numerical framework applied to a morphology adaptive multifield two-fluid model considering bubble motions. International Journal for Numerical Methods in Fluids, 93(3), 748-773. [^14]: Meller, R., Schlegel, F., & Klein, M. (2022). Sub-grid Scale Modelling and a-Posteriori Tests with a Morphology Adaptive Multifield Two-Fluid Model Considering Rising Gas Bubbles. Flow, Turbulence and Combustion 108, 895-922. [^15]: Rzehak, R., Liao, Y., Meller, R., Schlegel, F., Lehnigk, R., & Lucas, D. (2021). 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In Proceedings of the 11th world congress on computational mechanics (WCCM XI), Barcelona, Spain (Vol. 179). [^29]: Tripathi, M. K., Sahu, K. C., & Govindarajan, R. (2015). Dynamics of an initially spherical bubble rising in quiescent liquid. Nature communications, 6(1), 1-9. [^30]: Frederix, E. M. A., Dovizio, D., Mathur, A., & Komen, E. M. J. (2021). All-regime two-phase flow modeling using a novel four-field large interface simulation approach. International Journal of Multiphase Flow, 145, 103822. [^31]: Cubero, A., Sanchez-Insa, A., & Fueyo, N. (2014). A consistent momentum interpolation method for steady and unsteady multiphase flows. Computers & chemical engineering, 62, 96-107. [^32]: Chanson, H., Aoki, S. I., & Hoque, A. (2004). Physical modelling and similitude of air bubble entrainment at vertical circular plunging jets. Chemical engineering science, 59(4), 747-758. [^33]: Wiedemann, P., Meller, R., Schubert, M., & Hampel, U. (2023). 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Multiphase Science and Technology, 24, 197-222. [^39]: Ziegenhein, T. and Lucas, D. 2019. The critical bubble diameter of the lift force in technical and environmental, buoyancy-driven bubbly flows. International Journal of Multiphase Flow, 116, 26-38. [^40]: Mudde, R. F., Harteveld, W. K., and van den Akker, H. E. A., (2009). Uniform flow in bubble-columns. Industrial & Engineering Chemistry Research 48, 148-158. [^41]: Evdokimov, I. & Haensch, S. (2021). Quality Assessment of CFD Software Using Workflows and Decision Trees. In: Ivannikov ISPRAS Open Conference, Moscow, Russian Federation. [^42]: [^43]: Elbing, B. R., Winkel, E. S., Lay, K. A., Ceccio, S. L., Dowling, D. R., & Perlin, M. (2008). Bubble-induced skin-friction drag reduction and the abrupt transition to air-layer drag reduction. Journal of Fluid Mechanics, 612, 201-236. [^44]: Tekavcic, M., Meller, R., Krull, B., & Schlegel, F. (2022). Simulation of Liquid Waves With Flow Reversal in Stratified Counter-Current Flow With a Hybrid Multi-Fluid Model. Proceedings of the International Conference Nuclear Energy for New Europe, 31, 408. [^45]: Meller, R., Krull, B., Schlegel, F., & Tekavcic, M. (2024). Numerical transfer towards unresolved morphology representation in the MultiMorph model. Nuclear Engineering and Design, 428, 113470. [^46]: Porombka, P., Boden, S., Lucas, D., & Hampel, U. (2021). Horizontal annular flow through orifice studied by X-ray microtomography. Experiments in Fluids, 62, 1-14. [^47]: Porombka, P. (2023). Experimental Investigation and Modelling of Annular Flow in Pipes and the Prediction of the Liquid Distribution in Compact Heat Exchangers. PhD Thesis, Technische Universitaet Dresden. [^48]: Riviera, E. (2024). CFD Simulation of Horizontal Annular Flow in Simple Pipe and through an Orifice Plate using a Hybrid Morphology-Adaptive Two-Fluid Model. Master Thesis, Politecnico di Milano. 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(1987). 3-D turbulence structure and phase distribution measurements in bubbly two-phase flows. International Journal Multiphase Flow, 13(3), 327-343. [^55]: Liu, T. J. (1989). Experimental investigation of turbulence structure in two-phase bubble flow. PhD Thesis, Northwestern University, Illinois, 251 pages. [^56]: Liu, T. J., & Bankoff, S. G. (1993). Structure of air-water bubbly flow in a vertical pipe. I: Liquid mean velocity and turbulence measurements. Journal of Heat Transfer, 36, 1049-1060. [^57]: Liu, T. J., & Bankoff, S. G. (1993). Structure of air-water bubbly flow in a vertical pipe. II: Void fraction, bubble velocity and bubble size distribution. Journal of Heat Transfer, 36, 1061-1972. [^58]: Hibiki, T., Ishii, M., & Xiao, Z. (2001). Axial interfacial area transport of vertical bubbly flows. International Journal of Heat and Mass Transfer, 44, 1869-1888. [^59]: Lucas, D., Beyer, M., Szalinski, L., & Schuetz, P. (2010). A new database on the evolution of air-water flows along a large vertical pipe. International Journal of Thermal Sciences, 49(4), 664-674. [^60]: Neumann-Kipping, M. and Bieberle, A. and Hampel, U. 2020. Investigations on bubbly two-phase flow in a constricted vertical pipe. International Journal of Multiphase Flow, 130, 103340. [^61]: Draw, M., and Rzehak, R. (2024). Euler-Euler simulation of a bubble column flow up to high gas fraction. International Journal of Multiphase Flow, 181, 104969. [^62]: Sommer, A.-E., Draw, M., Wang, L., Schmidtpeter, J., Hessenkemper, H., Gatter, J., Nam, H., Eckert, K., & Rzehak, R. (2023). Hydrodynamics in a bubble column - part 1: Two-phase flow. Chemical Engineering & Technology. [^63]: Schlegel, F., Haensch, S., Krull, B. et al. (2025). Comparison of upper boundary treatments for bubble column simulations with the two-fluid model. Experimental and Computational Multiphase Flow 7, 227-244. [^64]: Fabre, J., Masbernat, L., & Suzanne, C. (1987). Experimental Data Set No. 7: Stratified Flow, Part I: Local Structure. Multiphase Science and Technology, 3(1-4), 285-301. [^65]: Meller, R., Tekavcic, M., Krull, B., & Schlegel, F. (2023). Momentum exchange modeling for coarsely resolved interfaces in a multifield two-fluid model. International Journal for Numerical Methods in Fluids, 95(9), 1521-1545. [^66]: Seo, H., & Kim, C.K. (2021). Experimental study on flow and turbulence characteristics of bubble jet with low void fraction. Int. J. Multiphase Flow Vol. 142, pp. 103738. [^67]: Kamble, V., Froehlich, J. & Rzehak, R. (2026). Eulerian Simulation of Premixed Submerged Multiphase Turbulent Jets. Experimental and Computational Multiphase Flow.