Volume 108
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Wang, B., Jin, H., Su, H., & Guo, L. (2026). Identification of scaling law for supercritical water fluidized bed reactors via CFD and data-driven approach. Particuology, 108, 168-182. https://doi.org/10.1016/j.partic.2025.11.010
Identification of scaling law for supercritical water fluidized bed reactors via CFD and data-driven approach
Bingcheng Wang, Hui Jin, Haozhe Su, Liejin Guo *
State Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong University, Xi'an, 710049, China
10.1016/j.partic.2025.11.010
Volume 108, January 2026, Pages 168-182
Received 26 September 2025, Revised 9 November 2025, Accepted 17 November 2025, Available online 25 November 2025, Version of Record 3 December 2025.
E-mail: lj-guo@mail.xjtu.edu.cn

Highlights

• A data-driven method is proposed to develop a modified scaling law for SCWFBRs.

• The modified scaling law is validated against Glicksman's scaling sets.

• Pressure drop fluctuations, particle volume fraction and axial velocity are analyzed.

• The modified scaling law performs better in both tested Geldart A and B conditions.


Abstract

Supercritical water fluidized bed reactors (SCWFBRs) offer significant potential for large-scale hydrogen production, but their scale-up process remains challenging. Traditional scaling laws, such as Glicksman's sets, simplify or omit interphase and interparticle closure terms in conservation equations, limiting applicability under supercritical water conditions. To address this, a data-driven approach is proposed to develop a modified scaling law for SCWFBRs. A dataset was generated from two-fluid model (TFM) simulations across diverse operating conditions and reactor scales. Dimensional analysis, combined with a multi-layer perceptron (MLP) and a pattern search method, was then applied to identify a composite dimensionless number representing interaction closure terms in two-phase momentum equations. This number, together with dimensionless numbers derived from other momentum terms, was refined via XGBoost and backward stepwise feature selection to preserve essential design degrees of freedom, yielding the modified scaling law. Validation against key hydrodynamic indicators, including pressure drop fluctuations, particle volume fraction, and particle axial velocity, demonstrated that the modified law consistently outperforms Glicksman's criteria for both Geldart A and B particles, with the extent of improvement varying between particle types under a tenfold scale-up. These results highlight the importance of accounting for interphase and interparticle interactions in SCWFBRs and indicate that the data-driven approach is an effective tool for reactor design and scale-up.

Graphical abstract
Keywords
Scaling laws; Fluidized bed; Supercritical water; Data-driven