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In this paper, we develop a machine learning-based Bayesian approach toinversely quantify and reduce the uncertainties of the two-fluid model-basedmultiphase computational fluid dynamics (MCFD) for bubbly flow simulations. Theproposed approach is supported by high-resolution two-phase flow measurementtechniques, including double-sensor conductivity probes, high-speed imaging,and particle image velocimetry. Local distribution of key physical quantitiesof interest (QoIs), including void fraction and phasic velocities, are obtainedto support the modular Bayesian inference. In the process, the epistemicuncertainties of the closure relations are inversely quantified, the aleatoryuncertainties from stochastic fluctuation of the system are evaluated based onexperimental uncertainty analysis. The combined uncertainties are thenpropagated through the MCFD solver to obtain uncertainties of QoIs, based onwhich probability-boxes are constructed for validation. The proposed approachrelies on three machine learning methods: feedforward neural networks andprincipal component analysis for surrogate modeling, and Gaussian processes formodel form uncertainty modeling. The whole process is implemented within theframework of open-source deep learning library PyTorch with graphics processingunit (GPU) acceleration, thus ensuring the efficiency of the computation. Theresults demonstrate that with the support of high-resolution data, theuncertainty of MCFD simulations can be significantly reduced.

Uncertainty quantification for Multiphase-CFD simulations of bubbly  flows: a machine learning-based Bayesian approach supported by  high-resolution experiments