Periodic Reporting for period 1 - HO2PF (High-order two-phase flow modelling)
Reporting period: 2022-02-01 to 2024-01-31
Two-phase flows are the flows of two immiscible phases separated by an interface such as, for instance, mixtures of air and water or water and oil. They are ubiquitous in nature and central to many engineering applications, with contributions to key sectors such as energy conversion, transportation, manufacturing, and healthcare. They are also relevant for the study of climate-change and for understanding how diseases spread, e.g. through coughing and sneezing, which can be of incredibly significant public-health impact. Despite their clear importance, our understanding of the complex dynamics of two-phase flows remains limited. Computer-based simulations have played an increasingly important role in providing new insights into these complex dynamics, for instance as viable alternatives to costly experiments, but they are still limited in their scope, flexibility, efficiency, and accuracy.
This project was concerned with initiating a shift in the way two-phase flows can be accurately simulated and predicted using computing resources, leveraging the development of a new "high-order" numerical framework. Owing to its high order, the proposed numerical framework exhibits unprecedented convergence properties, i.e. an enhanced ability to produce increasingly better results as more computational resources are thrown at the problem at hand. Notably, this framework is the first of its kind ever to be able to simulate two-phase flows while both exactly conserving the mass of fluid and producing a convergent estimation of the surface-tension force distribution that acts at the interface between the two phases. This was made possible by applying one main conceptual change to the start-of-the-art, that is the replacement of planar local approximations of the interface by curved (quadratic) ones for numerically solving the governing equations of the flow. The superior performance of the newly developed framework has been demonstrated with canonical and physically realistic test-cases of two-phase flows.
This project was concerned with initiating a shift in the way two-phase flows can be accurately simulated and predicted using computing resources, leveraging the development of a new "high-order" numerical framework. Owing to its high order, the proposed numerical framework exhibits unprecedented convergence properties, i.e. an enhanced ability to produce increasingly better results as more computational resources are thrown at the problem at hand. Notably, this framework is the first of its kind ever to be able to simulate two-phase flows while both exactly conserving the mass of fluid and producing a convergent estimation of the surface-tension force distribution that acts at the interface between the two phases. This was made possible by applying one main conceptual change to the start-of-the-art, that is the replacement of planar local approximations of the interface by curved (quadratic) ones for numerically solving the governing equations of the flow. The superior performance of the newly developed framework has been demonstrated with canonical and physically realistic test-cases of two-phase flows.
Over the course of this project, several key numerical algorithms have been developed in order to make the proposed framework a reality. This includes:
(1) A numerical algorithm for calculating the first geometrical moments (i.e. the volume and barycenter) of any arbitrary polyhedron that is cut by a curved "paraboloid" surface. In order to be a viable toolbox for the numerical simulation of large-scale cases of two-phase flows, this calculation must be exact, robust, and very fast -- three criteria that our proposed algorithm satisfies. This algorithm constitutes the fundamental building block of the proposed numerical framework. We have implemented it in the C++ language and made it available to the research community under the open-source MPL-2 license.
(2) A numerical algorithm for solving the spatio-temporal evolution of the two fluid phases based on piecewise-parabolic interface approximations. We have shown that this new method converges with third-order accuracy, instead of the second-order accuracy of the state-of-the-art, meaning that our proposed method reduces errors faster than the state-of-the-art.
(3) A numerical algorithm for reconstructing parabolic interface approximations from geometrical moments and for estimating the corresponding curvature of the interface, which is a quantity that must be known to estimate the surface-tension force distribution acting on the interface. We have shown that this enables unprecedented convergence and accuracy of the surface-tension estimation, resulting in more accurate and stable simulations of two-phase flows.
These three main developments and their application to two-phase flow problems have been presented at 6 international conferences and 6 invited seminar talks, and have directly led to 2 peer-reviewed journal publications and 1 peer-reviewed conference proceedings publication.
(1) A numerical algorithm for calculating the first geometrical moments (i.e. the volume and barycenter) of any arbitrary polyhedron that is cut by a curved "paraboloid" surface. In order to be a viable toolbox for the numerical simulation of large-scale cases of two-phase flows, this calculation must be exact, robust, and very fast -- three criteria that our proposed algorithm satisfies. This algorithm constitutes the fundamental building block of the proposed numerical framework. We have implemented it in the C++ language and made it available to the research community under the open-source MPL-2 license.
(2) A numerical algorithm for solving the spatio-temporal evolution of the two fluid phases based on piecewise-parabolic interface approximations. We have shown that this new method converges with third-order accuracy, instead of the second-order accuracy of the state-of-the-art, meaning that our proposed method reduces errors faster than the state-of-the-art.
(3) A numerical algorithm for reconstructing parabolic interface approximations from geometrical moments and for estimating the corresponding curvature of the interface, which is a quantity that must be known to estimate the surface-tension force distribution acting on the interface. We have shown that this enables unprecedented convergence and accuracy of the surface-tension estimation, resulting in more accurate and stable simulations of two-phase flows.
These three main developments and their application to two-phase flow problems have been presented at 6 international conferences and 6 invited seminar talks, and have directly led to 2 peer-reviewed journal publications and 1 peer-reviewed conference proceedings publication.
Having made the building blocks of the proposed high-order numerical framework available under open-source license, we expect them to facilitate the adoption of the framework by members of the academic and industrial two-phase flow research communities. This promises to enable new insights into the complex dynamics of two-phase flows, potentially leading to new advances in energy conversion or manufacturing, supporting the EU's industry and its Green Deal objectives. These same numerical tools can contribute to better predicting climate-change or the spread of pathogens via respiratory droplets, and help shaping future EU environmental and public-health policies.