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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

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.

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.

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 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.

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

In the past decades, numerical simulation tools have developed much, becoming a reliable instrument for design and failure analysis of components in the field of aero- and hydrodynamics. The focus of research continuously shifts towards challenges that are more complex, such as multiphase flow problems. These flows typically involve strong dynamics, a number of complex physical phenomena as well as a large range of length and time scales, which are mainly connected to interfacial and turbulence structures. Such problems are particularly prevalent in the chemical and process industries. Typically, the development of tools for the numerical simulation focuses on a single morphology: a) disperse interfacial structures, which are not captured by the computational grid (Euler-Euler or Euler-Lagrange) or b) approaches resolving the interface between two different phases (volume-of-fluid or level-set). In many practical applications, the occurring flow morphology is unknown in advance and therefore, the most appropriate numerical model cannot be easily identified a-priori. Corresponding industrial facilities are flotation cells, refrigeration systems, biological and chemical reactors, distillation columns, swirl separators or centrifugal pumps, to name a few examples. In the past years, special hybrid simulation approaches have been developed to describe the aforementioned problems: 2-field methods considering blending between different morphologies, 4-field methods, where two phases represent the same physical phase, but with different morphology, drift-flux models based on the volume-of-fluid approach or methods blending between Euler-Euler and level-set models. We present a 4-field approach, which is developed and validated at Helmholtz-Zentrum Dresden – Rossendorf as an add-on to the public domain library OpenFOAM. Central development criteria and goals are: - Robust applicability to engineering problems at the industrial scale - A unified set of conservation equations

The numerical simulation of gas-liquid flows is a challenging task, when dynamics of systems at industrial scales are considered. A significant contribution to this complexity arises due to the coexistence and interaction of different flow morphologies, such as bubbly and stratified flows. One of the phenomena is the entrainment of small gas bubbles into the liquid bulk at a large-scale gas-liquid interface in regions of high shear rates. In order to capture such phenomena and make reliable predictions, hybrid modelling approaches are used. One of those is the morphology adaptive multifield model developed by Meller et al. (2021), which combines an Euler-Euler method with an algebraic Volume-of-Fluid method for disperse and continuous gas structures, respectively. The interfacial drag coupling is adapted to the local grid resolution at the interface location (Meller et al., 2022). In such a modelling framework, morphology changes are realised by transfers between numerical phases, which are treated differently according to the basic simulation methodologies mentioned above. In that sense, entrainment processes are characterised by multiple numerical aspects: 1) entrapping of large-scale gas structures, which subsequently disintegrate into smaller ones and 2) direct conversion of continuous towards disperse portions of gas due to processes taking place at sub-grid scales, which are described by dedicated entrainment models, such as the one of Ma et al. (2011). In this work, the individual effects as well as the interplay of the aforementioned processes are assessed and validated in comparison to experimental data of a liquid plunging jet (Chanson et al., 2004). This also considers the balance between the two numerical aspects mentioned above. The goal is to improve the reliability of predictions of gas entrainment with high as well as with low spatial resolution.

In the past decades, numerical simulation tools have developed much, becoming a reliable instrument for design and failure analysis of components in the field of aero- and hydrodynamics. The focus of research continuously shifts towards challenges that are more complex, such as multiphase flow problems. These flows typically involve strong dynamics, a number of complex physical phenomena as well as a large range of length and time scales, which are mainly connected to interfacial and turbulence structures. Such problems are particularly prevalent in the chemical and process industries. Typically, the development of tools for the numerical simulation focuses on a single morphology: a) disperse interfacial structures, which are not captured by the computational grid (Euler-Euler or Euler-Lagrange) or b) approaches resolving the interface between two different phases (volume-of-fluid or level-set). In many practical applications, the occurring flow morphology is unknown in advance and therefore, the most appropriate numerical model cannot be easily identified a-priori. Corresponding industrial facilities are flotation cells, refrigeration systems, biological and chemical reactors, distillation columns, swirl separators or centrifugal pumps, to name a few examples. In the past years, special hybrid simulation approaches have been developed to describe the aforementioned problems: 2-field methods considering blending between different morphologies, 4-field methods, where two phases represent the same physical phase, but with different morphology, drift-flux models based on the volume-of-fluid approach or methods blending between Euler-Euler and level-set models. We present a 4-field approach, which is developed and validated at Helmholtz-Zentrum Dresden – Rossendorf as an add-on to the public domain library OpenFOAM. Central development criteria and goals are: - Robust applicability to engineering problems at the industrial scale - A unified set of conservation equations

The numerical simulation of gas-liquid flows is a challenging task, when dynamics of systems at industrial scales are considered. A significant contribution to this complexity arises due to the coexistence and interaction of different flow morphologies, such as bubbly and stratified flows. One of the phenomena is the entrainment of small gas bubbles into the liquid bulk at a large-scale gas-liquid interface in regions of high shear rates. In order to capture such phenomena and make reliable predictions, hybrid modelling approaches are used. One of those is the morphology adaptive multifield model developed by Meller et al. (2021), which combines an Euler-Euler method with an algebraic Volume-of-Fluid method for disperse and continuous gas structures, respectively. The interfacial drag coupling is adapted to the local grid resolution at the interface location (Meller et al., 2022). In such a modelling framework, morphology changes are realised by transfers between numerical phases, which are treated differently according to the basic simulation methodologies mentioned above. In that sense, entrainment processes are characterised by multiple numerical aspects: 1) entrapping of large-scale gas structures, which subsequently disintegrate into smaller ones and 2) direct conversion of continuous towards disperse portions of gas due to processes taking place at sub-grid scales, which are described by dedicated entrainment models, such as the one of Ma et al. (2011). In this work, the individual effects as well as the interplay of the aforementioned processes are assessed and validated in comparison to experimental data of a liquid plunging jet (Chanson et al., 2004). This also considers the balance between the two numerical aspects mentioned above. The goal is to improve the reliability of predictions of gas entrainment with high as well as with low spatial resolution.