Three-Dimensional Reconstruction of Fluidized Beds from Limited Measurements via a Physics Guided cGAN

Xue Li; Jie Xiang; Ting Zhang; Cheng Zhang; Anqi Li; Mao Ye; Zhongmin Liu

doi:10.53941/sce.2025.100002

Abstract

Characterizing multiphase flows in fluidized beds remains challenging due to complex hydrodynamics, harsh operating conditions, and sensor limitations that restrict data acquisition. A physics guided conditional Generative Adversarial Network (PG-cGAN) framework is designed to reconstruct detailed three-dimensional (3D) fields from limited measurements. This hybrid approach integrates a gap-filling preprocess to mitigate data incompleteness, employs a multiscale strategy to enhance feature extraction from sparse inputs, and incorporates empirical correlations as physical constraints to ensure realistic reconstructions. Validation against computational fluid dynamics (CFD) simulations demonstrates close agreement between reconstructed and ground-truth fields. Furthermore, application of the PG-cGAN to 2D cross-sectional slices obtained from mobile Electrical Capacitance Tomography (ECT) experiments enables 3D fluidization analysis. The PG-cGAN framework provides potential for online characterization of complex flows by enabling rapid reconstruction from limited data.

References

1.
Bi, H.; Grace, J.J. Flow Regime Diagrams for Gas-Solid Fluidization and Upward Transport. Int. J. Multiph. Flow 1995, 21, 1229–1236.
2.
Gidaspow, D. Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions; Academic Press: San Diego, CA, USA, 1994.
3.
Francia, V.; Wu, K.; Coppens, M.-O. Dynamically Structured Fluidization: Oscillating the Gas Flow and Other Opportunities to Intensify Gas-Solid Fluidized Bed Operation. Chem. Eng. Process. 2021, 159, 108143.
4.
Sykes, J.A.; Weston, D.; Adio, N.; et al. Validation of Simulations of Particulate, Fluid and Multiphase Systems Using Positron Emission Particle Tracking: A Review. Particuology 2025, 101, 117–145.
5.
Yang, W.Q.; Spink, D.M.; York, T.A.; et al. An Image-Reconstruction Algorithm Based on Landweber’s Iteration Method for Electrical-Capacitance Tomography. Meas. Sci. Technol. 1999, 10, 1065–1069.
6.
Zhang, C.; Li, A.; Li, C.; et al. Combing Mobile Electrical Capacitance Tomography with Fourier Neural Operator for 3D Fluidized Beds Measurement. AIChE J. 2025, 71, e18641.
7.
Liu, Z.; Wang, H.; Sun, S.; et al. Investigation of Wetting and Drying Process in a Spout-Fluid Bed Using Acoustic Sensor and Electrical Capacitance Tomography. Chem. Eng. Sci. 2023, 281, 119160.
8.
Wang, H.; Fu, T.; Du, Y.; et al. Scientific Discovery in the Age of Artificial Intelligence. Nature 2023, 620, 47–60.
9.
Zeni, C.; Pinsler, R.; Zügner, D.; et al. A Generative Model for Inorganic Materials Design. Nature 2025, 625, 281–286.
10.
Li, Z.; Han, W.; Zhang, Y.; et al. Learning Spatiotemporal Dynamics with a Pretrained Generative Model. Nat. Mach. Intell. 2024, 6, 1566–1579.
11.
Shaham, T.R.; Dekel, T.; Michaeli, T. SinGAN: Learning a Generative Model from a Single Natural Image. arXiv 2019, arXiv:1905.01164.
12.
Hinz, T.; Fisher, M.; Wang, O.; et al. Improved Techniques for Training Single-Image GANs. In Proceedings of the 2021 IEEE Winter Conference on Applications of Computer Vision (WACV), Waikoloa, HI, USA, 3–8 January 2021; IEEE: Piscataway, NJ, USA, 2021; pp. 1300–1309.
13.
Ouyang, X.; Chen, Y.; Zhu, K.; et al. Image Restoration Refinement with Uformer GAN. In Proceedings of the 2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), Seattle, WA, USA, 17–21 June 2024; IEEE: Piscataway, NJ, USA, 2024; pp. 1234–1243.
14.
Xia, Z.; Cui, Z.; Chen, Y.; et al. Generative Adversarial Networks for Dual-Modality Electrical Tomography in Multi-Phase Flow Measurement. Measurement 2021, 173, 108608.
15.
Zhang, C.; Li, C.; Li, X.; et al. A General Physics-Informed Neural Network Approach for Deriving Fluid Flow Fields from Temperature Distribution. Chem. Eng. Sci. 2025, 302, 120950.
16.
Rao, C.; Ren, P.; Wang, Q.; et al. Encoding Physics to Learn Reaction–Diffusion Processes. Nat. Mach. Intell. 2023, 5, 765–779.
17.
Zhang, T.; Xiang, J.; Li, X.; et al. 3D Reconstruction of Fluidized Bed Phase Distribution Based on Multi-Scale Conditional Generative Adversarial Network. Eng. Appl. Artif. Intell. 2025, submitted.
18.
Bohling, G. GSLIB: Geostatistical Software Library and User’s Guide; Computers & Geosciences: Oxford, UK, 1994; pp. 1063–1064.
19.
Huang, K.; Meng, S.; Guo, Q.; et al. Effect of Electrode Length of an Electrical Capacitance Tomography Sensor on Gas–Solid Fluidized Bed Measurements. Ind. Eng. Chem. Res. 2019, 58, 21827–21841.
20.
Goodfellow, I.; Pouget-Abadie, J.; Mirza, M.; et al. Generative Adversarial Nets. In Advances in Neural Information Processing Systems 27; Ghahramani, Z., Welling, M., Cortes, C., et al., Eds.; Curran Associates: Red Hook, NY, USA, 2014; pp. 2672–2680.
21.
Adler, J.; Lunz, S. Banach Wasserstein GAN. In Proceedings of the 32nd International Conference on Neural Information Processing Systems (NeurIPS 2018), Montréal, QC, Canada, 2–8 December 2018; Curran Associates: Red Hook, NY, USA, 2018; pp. 6755–6764.
22.
Clift, R.; Grace, J.R. Continuous Bubbling and Slugging. In Fluidization, 2nd ed.; Davidson, J.F., Clift, R., Harrison, D., Eds.; Academic Press: London, UK, 1985; pp. 73–131.
23.
Mori, S.; Wen, C.Y. Estimation of Bubble Diameter in Gaseous Fluidized Beds. AIChE J. 1975, 21, 109–115.
24.
Xu, G.; Sun, G.; Gao, S. Estimating Radial Voidage Profiles for All Fluidization Regimes in Circulating Fluidized Bed Risers. Powder Technol. 2004, 139, 186–192.

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