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The two-fluid model is usually combined with closure forces designed for applications on coarse grids, i.e. bubbles (or particles) are typically assumed to be smaller than a grid cell. Practical applications however include situations where the mesh is comparatively fine, e.g. when meshing the wall boundary layer or in cases with growing bubbles. This may lead to non-convergent behaviour in mesh studies or to void fraction oscillations. To tackle this problem, a filtering approach is proposed, based on an additional diffusion term in the continuity equation. This approach increases the robustness of the results in regions of high spatial resolution, significantly reducing mesh-dependency of the simulation results. The implementation is straightforward, without a need to solve any additional system of equations. It is analysed in four different bubbly flow cases with varying characteristics: 2D/3D, wedge, square, and cuboid computational domains, with resolutions up to 32 cells per bubble diameter, laminar and turbulent flows, and several ways of gas injection. The additional computational effort varies, but is moderate. The proposed approach is applicable in multi-field two-fluid models for which a stable Euler-Euler behaviour on fine meshes is required, for example to prepare the transfer to an interface-resolving volume-of-fluid representation in morphology-adaptive approaches.

This repository contains simulation setups for the www.openfoam.org

The Multiphase Code Repository by HZDR for OpenFOAM Foundation Software is a software publication released by Helmholtz-Zentrum Dresden-Rossendorf according to the morphology-adaptive modelling approach (dispersed and resolved interfaces, Meller et al., 2021) with an interface to the multiphaseEuler fr

Industrial multiphase flows are typically characterized by coexisting morphologies. Modern simulation methods are well established for dispersed (e.g., Euler-Euler) or resolved (e.g., Volume-of-Fluid) interfacial structures. A simulation method that requires less knowledge about the flow in advance would be desirable and should allow describing both types of interfacial structures – resolved and dispersed – in a single computational domain. Such methods that combine interface-resolving and non-resolving approaches are called hybrid models. A morphology adaptive multifield two-fluid model, named MultiMorph Model, is proposed, which is able to handle dispersed and resolved interfacial structures coexisting in the computational domain with the same set of equations. For large interfacial structures an interfacial drag formulation is used to describe them in a volume-of-fluid-like manner. For the dispersed structures, the baseline model developed at Helmholtz-Zentrum Dresden - Rossendorf e.V. (HZDR) is applied. The functionality of the framework is demonstrated by several test cases, including a single rising gas bubble in a stagnant water column. Recent developments focus on the transition region, where bubbles are over- or under-resolved for Euler-Euler or for Volume-of-Fluid, respectively. The contribution will focus on an overview about the fundamentals of the MultiMorph Model and recent simulation results for a plunging jet, a stratified counter-current air-water flow and a column tray of a distillation column.

A typical feature of nuclear safety facilities are multiphase flows with coexisting morphologies, i.e. with phases which occur both in a continuous form (such as in a stratified flow) and in a disperse form (bubbles or droplets). Established simulation methods are usually suitable for either resolved structures (e.g., Volume-of-Fluid) or dispersed structures (e.g., Euler-Euler). We propose a morphology adaptive multifield two-fluid model, which is able to handle both disperse and resolved interfacial structures coexisting in a common computational domain, covered by a unified set of equations. This requires (A) a careful selection of closure models. On the continuous side, the interfacial drag formulation of Štrubelj and Tiselj (Int J Numer Methods Eng, 2011, 85, 575-590) is used to describe large interfacial structures in a volume-of-fluid-like manner. For the dispersed structures, the HZDR baseline model is applied. Meller et al. (Int J for Numer Method Fluid, 2021, 93, 748-773) and Tekavčič et al. (Nucl Eng Des, 379, 111223) presented several test cases to prove that the numerical consistent coexistence of different morphologies is ensured. The interaction of the morphologies is only controlled by the aforementioned closure models without being disturbed by numerical effects. A second requirement is (B) a reliable transition between continuous and disperse states, depending on the size of the structures and the degree of spatial resolution. This is subject of the current work. A prerequisite for reliable transitions is the stable coverage of intermediate situations, where bubbles are either over- or under-resolved for Euler-Euler or Volume-of-Fluid (Fig. 1). An adaptive interfacial drag model and a filtering technique are applied for stable and robust handling of the transition regions. Two morphology transfer models are established, allowing large resolved structures to disintegrate into small unresolved fluid particles and, vice versa, the accumulation of dispe

Physical phenomena in industrial gas-liquid flows typically span a wide range of length and time scales. Individual flow regimes are usually modelled using specific approaches, which are mainly characterised by the level of detail the existing interfaces are handled with. The cross-scale nature of multiphase flows requires the simultaneous application and flexible switching between these methods in a single common framework. For this reason, a morphology-adaptive model is established by combining the Euler- Euler model with the Volume-of-Fluid (VOF) model. Interactions and transitions between different morphologies and scales are taken into account by dedicated models. This work gives an overview over recent advances towards a fully scalable morphology-adaptive multiphase model (MultiMorph). In order to be applicable to realistic, large-scale problems, special care is required to ensure a robust model behaviour, even if the spatial resolution is not optimal in terms of the respective flow phenomena. Large interfaces might be represented on coarse numerical grids. The usual VOF model typically over-predicts the interfacial shear stress in such a situation, resulting in unrealistic interface dynamics. Instead, a resolution-adaptive interfacial coupling is proposed. In that way the phases may slip along each other in the direction parallel to the interface, improving the prediction, i.e., of interface shape or of bubble rising velocity. A central building block of morphology-adaptive methods is the ability of structures to evolve from one morphology to another. For example, unresolved bubbles may coalesce, grow, or enter highly-refined mesh regions, such that a resolved representation becomes possible. Therefore, a transition to a continuous representation is realised, to make optimal use of the available numerical degrees of freedom. The opposite case, the transition from a continuous to a dispersed representation, is handled as well. This becomes relevant in case of

The morphology adaptive multifield two-fluid model OpenFOAM-Hybrid focuses on the reliable and robust simulation of interfacial two-phase flows in real size industrial applications. This requires to combine the Volume-of-Fluid approach with the Euler-Euler model for large and small scale interfacial structures, respectively. The choice of the local representation of interfacial structures, such as bubbles or droplets, by either the first or the second of the aforementioned basic method strongly depends on the ratio of the length scale of the interface feature to the grid spacing. In case the computational grid gets too coarse to locally resolve an interfacial structure anymore, a morphology transfer is required. Such a transfer process allows to convert resolved fluid into non-resolved one, i.e. changing from a continuous description to a dispersed one. A formulation for such a numerically motivated disintegration process is presented and validated with a case of a two-dimensional single rising bubble on a grid with gradually varying cell size. The model is then applied to two further cases: an oil-water phase inversion and a water jet plunging into a free water surface. Hereby, functionality, robustness and feasibility of the proposed morphology transfer mechanism are demonstrated. This work contributes to a hybrid modelling approach for the simulation of two-phase flows adapting the numerical representation depending on local flow morphology and on available computational resources.

Industrial multiphase flows are typically characterized by coexisting morphologies. Modern simulation methods are well established for dispersed (e.g., Euler-Euler) or resolved (e.g., Volume-of-Fluid) interfacial structures. A simulation method that requires less knowledge about the flow in advance would be desirable and should allow describing both interfacial structures – resolved and dispersed – in a single computational domain. Such methods that combine interface-resolving and non-resolving approaches are called hybrid models. A morphology adaptive multifield two-fluid model, named OpenFOAM-Hybrid, is proposed, which is able to handle dispersed and resolved interfacial structures coexisting in the computational domain with the same set of equations. An interfacial drag formulation for large interfacial structures is used to describe them in a volume-of-fluid-like manner. For the dispersed structures, the baseline model developed at Helmholtz-Zentrum Dresden - Rossendorf is applied. The functionality of the framework is demonstrated by several test cases, including a single rising gas bubble in a stagnant water column. Recent developments focus on the transition region, where bubbles are over- or under-resolved either for Euler-Euler or for Volume-of-Fluid.

Process engineering and energy production systems often feature gas-liquid flows with coexisting two-phase flow regimes and a broad range of interfacial and turbulent scales. Suitable simulation methods can be found for each particular morphology, such as Volume-of-Fluid for larger, resolvable and continuous features of stratified flows, and the two-fluid model for unresolved dispersed bubbles or droplets. A morphology-adaptive multifield two-fluid model (MultiMorph) presented here is developed based on the OpenFOAM Foundation Release, with the aim to handle different coexisting dispersed and continuous flow structures for a wide range of spatial resolutions within a common computational tool. The present work highlights specifically the following aspects of the model: a resolution-adaptive momentum transfer for under-resolved flow structures on coarse meshes, interface turbulence damping in strong shear flow near a gas-liquid surface with high density ratios between the phases, and morphology transfer models. This enables both transitions, disintegration and accumulation, between dispersed and continuous phase morphologies of the same fluid. Application of the MultiMorph model is presented on the following selected set of safety related test cases: a stratified counter-current flow case with partial flow reversal and liquid waves, and a plunging jet case, with entrainment of gas bubbles. Results are evaluated with measurements from the corresponding experiments.

Two-phase flows generally occur with various flow regimes, even in fixed geometries. The transition from one regime to another requires careful numerical modeling. In vane-type gas-liquid separators, the transition from bubbly flow to stratified flow is the dominating phenomena. This paper describes the application of a morphology adaptive hybrid multi-field model (OpenFOAM-Hybrid) to predict the complex flow in such vane-type separator, covering different regimes and the corresponding transitions. By means of OpenFOAM-Hybrid, the coexistence of dispersed bubbles and continuous gas core is modelled simultaneously with the same set of equations. The key issue here is the definition of a morphology transition criterion describing the formation of continuous gas out of dispersed gas. Such a transition criterion, based on the local volume fractions of the dispersed and the continuous gas phase, is proposed. It combines coalescence and absorption transfer processes. This model is added to OpenFOAM-Hybrid and validated by predicting both gas bubbles and a continuous gas core as well as transitional regimes in the vane-type separator. The gas core morphology evolution is investigated in detail. OpenFOAM-Hybrid is capable of capturing the gas core dynamics in the vane-type separator and thus proves to be a reliable predictive tool.

The CFD modelling of annular flow is a challenge since it should take into account the continuous liquid film, the continuous gas core, and the dispersed droplets simultaneously. Recently, the CFD department in Helmholtz-Zentrum Dresden - Rossendorf (HZDR) are developing a morphology adaptive multifield two-fluid model that has great potential to simulate the three structures in a single computational domain. To complete the annular flow simulation in the morphology adaptive framework, a new droplet entrainment model is proposed in this work, which describes the mass transfer from the continuous liquid film to the dispersed droplets. The new entrainment model is developed based on the shear-off mechanism on the interfacial wave, implying that the entrainment behavior is dominated by the shear force and surface tension on the gas and liquid interface. Contrarily to previous entrainment models, the new model is correlated to the local flow parameters on the interface, so that it is suitable for the CFD framework. The properties of the new model are discussed and the model performance is verified by laboratory experiments. Qualitatively, the proposed model can simulate the generation of the interfacial wave from the inlet to the downstream. The droplets are mainly entrained at the front tip of the disturbance wave, where the shear force effect is remarkable. These phenomena are identical to the physical understanding of the droplet entrainment. Quantitatively, the characteristics of the droplet fraction matches the experimental results. The liquid film fraction obtained with the new model is analyzed and compared with the experiment. It turns out that the statistical parameters of film fraction's average value, standard deviation, possibility density function, and power spectral density match well with the experiment. Finally, the model comparisons show that the new model outperforms previous models with regard to droplet generation.

In the present contribution, we demonstrate the application of a hybrid multiphase CFD approach, which allows for simulating dispersed phases as well as resolved interfaces within an Eulerian framework, for the flow on distillation trays for the first time. The morphology adaptive multifield two-fluid model is exemplified for a generic tray setup with a single trapezoid fixed valve. Instead of fully resolving its geometry in the computational grid, the gas inlets are emulated by implementing mass and momentum sources that are applied to local cell zones. Different zone types in terms of volume and curtain area are tested and compared. The simulation results are verified with experimental data from a lab-scale test rig with air-water flow. Local phase fractions were measured using a conductivity sensor array. The comparison of simulated and experimental results reveals that the relevant time-averaged and transient flow characteristics can be predicted satisfactorily if at least an approximate representation of the valve's geometry in the computational grid is given. However, local differences are observed among the simulated phase distributions due to the varying cell zone volume and hence maximum intensity of injected momentum.

Morphology-adaptive multiphase models are becoming more established for the numerical description of complex gas-liquid flows adapting dynamically to the local flow morphology. In the present study two different numerical methods originally designed for distinct flow morphologies are combined, namely the Volume-Of-Fluid and the Euler-Euler method. Both edge cases have been proven to be capable of delivering reliable predictions in the respective use cases. The long-term goal is to improve the prediction of gas-liquid flows, regardless of the flow regime in a specific application. To capture the system dynamics with a given grid resolution, the flow fields need to be predicted as precise as possible, while the shape of structures such as gas bubbles need to be recovered adequately in topology and shape. The goal is to obtain reliable predictions on intermediate mesh resolutions rather than relying on fine meshes requiring more computational resources. Therefore, a procedure is proposed to locally measure the degree of resolution. With this information, the hydrodynamics in the interface region can be controlled by means of a dedicated interfacial drag formulation in order to improve simulation results across several levels of spatial resolution. A modified formulation of buoyancy is proposed to prevent unphysical oscillations of vertical velocity near a horizontal interface. The functionality is demonstrated in a three-dimensional case of a gas bubble rising in stagnant liquid and in a co-current stratified air-water channel flow in two-dimensional space. The choice of these different applications demonstrates the general applicability of the proposed model framework.

The simulation of industrial multiphase flows is challenging, because these flows are typically characterized by coexisting morphologies. Modern simulation methods are well established for dispersed (e.g., Euler-Euler) or resolved (e.g., Volume-of-Fluid) interfacial structures. We propose a morphology adaptive multifield two-fluid model, which is able to handle dispersed and resolved interfacial structures coexisting in the computational domain with the same set of equations. The interfacial drag formulation of Štrubelj and Tiselj (Int J Numer Methods Eng, 2011, Vol. 85, 575-590) is used to describe large interfacial structures in a volume-of-fluid-like manner. For the dispersed structures, the HZDR baseline model is applied. The functionality of the framework is demonstrated by investigating a gas bubble, rising in a liquid, which is laden with micro gas bubbles, a 2D stagnant stratification of water and oil, sharing a large-scale interface, which is penetrated by micro gas bubbles, and an isothermal counter-current stratified flow case. For the latter the framework symmetric and asymmetric turbulence damping is used to account for turbulent flow conditions near an interface. Recent developments focus on the transition region, where bubbles are either over- or under-resolved for Euler-Euler or Volume-of-Fluid (Fig. 1). A drag model to allow tangential slip at an interface and a filtering technique are proposed for stable and robust handling interfacial structures in the transition region. Furthermore, a concept is presented for the transition of oversized dispersed bubbles into the resolved phase.

Die numerische Simulation hat sich in den letzten Jahrzehnten stetig weiterentwickelt und ist im Bereich der Aerodynamik und der Hydrodynamik zu einem etablierten Werkzeug für die Auslegung und Fehleranalyse von Bauteilen herangereift. Der Schwerpunkt der Forschung verlagert sich daher zunehmend auf die numerische Simulation mehrphasiger Strömungen. Derartige Mehrphasenströmungen zeichnen sich durch eine hohe Dynamik, komplexe physikalische Vorgänge und eine große Spanne an Längenskalen aus, die überwiegend mit den sich ausbildenden Grenzflächen zusammenhängen. Insbesondere in der Chemie- und Verfahrenstechnik sind solche Problemstellungen häufig anzutreffen und entsprechend viel Forschungsbedarf ist vorhanden. Allerdings liegt der Schwerpunkt der jeweiligen Forschungsarbeit und Modellentwicklung jeweils auf numerischen Simulationen für eine spezifische Morphologie: a) Verfahren zur Simulation von dispersen Strukturen, bei welchen die Grenzflächen durch das numerische Gitter nicht erfasst werden (Euler-Euler, Euler-Lagrange) und b) Verfahren, bei welchen die Grenzflächen aufgelöst werden (Volume-of-Fluid, Level-Set). Jedoch gibt es eine Vielzahl von technischen Fragestellungen, bei denen die auftretenden Morphologien – und damit das am besten geeignete Verfahren – nicht a priori bekannt sind. Hierzu gehören u.a. Flotationszellen, Kältemaschinen, biologische und chemische Reaktoren, Destillationskolonnen, Drall-basierte Abscheider oder Fliehkraftpumpen für mehrphasige Strömungen. Seit einiger Zeit werden für derartige Problemstellungen spezielle hybride Simulationsmethoden entwickelt: 2-Feld-Ansätze mit entsprechendem Morphologieblending, 4-Feld-Ansätze mit spezifischen numerisch motivierten Phasen, Drift-Flux-Methoden auf Volume-of-Fluid-Basis oder auch das Blending zwischen Simulationsmethoden wie Euler-Euler und Level-set. Der vorliegende Beitrag stellt einen 4-Feld-Ansatz vor, welcher seit einiger Zeit am Helmholtz-Zentrum Dresden-Rossendorf in der quelloffenen B