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Author
Date
2023Type
- Doctoral Thesis
ETH Bibliography
yes
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Abstract
The modeling of multi-phase flow has not yet achieved the same degree of understanding than its single-phase counterpart, given the range of scales as well as the diversity of flow regimes that one encounters in this context. We revisit the discrete equation method (DEM) for two-phase flow in the absence of heat conduction and mass transfer. We analyze resulting probability coefficients and prove their local convexity, rigorously establishing that our version of DEM can model different flow regimes ranging from the disperse to stratified (or separated) flow. Moreover, we reformulate the underlying mesoscopic model in terms of an one-parameter family of PDEs that interpolates between different flow regimes. The one-parameter family of PDEs provides an unified framework for modeling mean quantities for a multiphase flow, while at the same time identifying two key parameters that model the inherent uncertainty in terms of the underlying microstructure. Subsequently we deal with the delicate problem of designing a suitable solution paradigm for two-phase flow problems. Under the classical assumption of small-BV data, we exploit the Front-Tracking (FT) method to prove well-posedness in the one-dimensional case. The methodology is later translated into a numerical procedure for the concrete computation of sharp-interface problems, carefully analyzed on a suite of test cases. Due to the intrinsic necessity of describing two-phase flow phenomena in a statistical per- spective, we propose a novel Monte-Carlo based ab-initio algorithm for directly computing the statistics of macroscopic quantities. Our algorithm samples the underlying probabil- ity space and evolves these samples with the aforementioned sharp interface front-tracking scheme. Consequently, statistical information is generated without resorting to any closure assumptions and information about the underlying microstructure is implicitly included/- constructed. The proposed algorithm is tested on a suite of numerical experiments and we observe that the ab-initio procedure can simulate a variety of flow regimes robustly and converges with respect of refinement of number of samples as well as number of bubbles per volume. The methodology is later extended to a Multi-level version to enhance convergence. Numerical investigation of stability with respect to the underlying distribution is also per- formed. Results produced with the novel ab-initio framework are finally compared with the state- of-the-art discrete equation method presented at the beginning of this work to reveal the inherent limitations of existing macroscopic models. Show more
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https://doi.org/10.3929/ethz-b-000617618Publication status
publishedExternal links
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Publisher
ETH ZurichSubject
two-phase flowOrganisational unit
03851 - Mishra, Siddhartha / Mishra, Siddhartha
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ETH Bibliography
yes
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