Bayesian calibration with model discrepancy of a two-group interfacial area transport model for upward bubbly flow in a square duct
Abstract
Predictive simulation of bubbly flows with the two-fluid model relies on interfacial area transport equations (IATE) whose coalescence and breakup source terms involve empirical coefficients calibrated on restricted sets of experiments. This paper presents a Bayesian calibration, with explicit model discrepancy, of the two-group IATE source term coefficients embedded in the industrial CFD solver Neptune_CFD, using the upward air-water bubbly flow in a vertical square duct measured by Sun as reference data. A close examination of the experimental database reveals internally inconsistent inlet conditions, which motivates a calibration framework in which inlet boundary conditions are treated as uncertain and inferred jointly with the closure coefficients. Global sensitivity analysis shows that the wake-entrainment coefficient dominates the output variance when the inlet conditions are controlled, whereas inlet uncertainty overwhelms all parametric effects when it is present. Because each simulation is quite expensive (approximately 7.9 hours on 280 cores), calibration is made tractable by Gaussian-process surrogates constructed with an adaptive, posterior-driven design strategy that concentrates code evaluations in regions of high posterior probability and converges markedly faster than space-filling designs. Calibrations on synthetic and experimental data demonstrate that neglecting model discrepancy produces biased coefficient estimates and overconfident predictions, while explicitly modeling it separates structural model error from measurement noise and parametric uncertainty. The calibrated model substantially reduces the bias on void fraction and liquid velocity profiles and the inferred discrepancy consistently reveals a structural deficiency of the source term formulation in the near-wall region.
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BibTeX
@misc{idrissi2026bayesian,
title = {{Bayesian calibration with model discrepancy of a two-group interfacial area transport model for upward bubbly flow in a square duct}},
author = {Sanae Janati Idrissi and Maria Giovanna Rodio and Pietro Marco Congedo},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-05788479v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Bayesian calibration with model discrepancy of a two-group interfacial area transport model for upward bubbly flow in a square duct
AU - Sanae Janati Idrissi
AU - Maria Giovanna Rodio
AU - Pietro Marco Congedo
PY - 2026
DA - 2026/10/09
PB - HAL
UR - https://hal.science/hal-05788479v1
AB - Predictive simulation of bubbly flows with the two-fluid model relies on interfacial area transport equations (IATE) whose coalescence and breakup source terms involve empirical coefficients calibrated on restricted sets of experiments. This paper presents a Bayesian calibration, with explicit model discrepancy, of the two-group IATE source term coefficients embedded in the industrial CFD solver Neptune_CFD, using the upward air-water bubbly flow in a vertical square duct measured by Sun as reference data. A close examination of the experimental database reveals internally inconsistent inlet conditions, which motivates a calibration framework in which inlet boundary conditions are treated as uncertain and inferred jointly with the closure coefficients. Global sensitivity analysis shows that the wake-entrainment coefficient dominates the output variance when the inlet conditions are controlled, whereas inlet uncertainty overwhelms all parametric effects when it is present. Because each simulation is quite expensive (approximately 7.9 hours on 280 cores), calibration is made tractable by Gaussian-process surrogates constructed with an adaptive, posterior-driven design strategy that concentrates code evaluations in regions of high posterior probability and converges markedly faster than space-filling designs. Calibrations on synthetic and experimental data demonstrate that neglecting model discrepancy produces biased coefficient estimates and overconfident predictions, while explicitly modeling it separates structural model error from measurement noise and parametric uncertainty. The calibrated model substantially reduces the bias on void fraction and liquid velocity profiles and the inferred discrepancy consistently reveals a structural deficiency of the source term formulation in the near-wall region.
ER -