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Article

Effect of Periodic Inertial Forces on Particle Flow Behavior in Spacetime

1
School of Chemical Engineering, Hebei University of Technology, Tianjin 300132, China
2
National and Local Joint Laboratory of Chemical Energy Saving Process Integration and Resource Utilization, Tianjin 300130, China
3
School of Energy and Environmental Engineering, Hebei University of Technology, Tianjin 300401, China
*
Authors to whom correspondence should be addressed.
Processes 2026, 14(11), 1761; https://doi.org/10.3390/pr14111761
Submission received: 6 May 2026 / Revised: 22 May 2026 / Accepted: 26 May 2026 / Published: 28 May 2026
(This article belongs to the Section Chemical Processes and Systems)

Abstract

To improve the operational stability and mass transfer performance of fluidized bed reactors under dynamic conditions, this study examines radial particle velocity distributions at different bed cross-sections using a dual-probe measurement method across a range of rocking frequencies and superficial gas velocities. The analysis identifies the dominant influence of additional inertial forces generated by rocking motion, including the Euler force and Coriolis force, in determining the time-averaged flow structure, leading to the development of a spatiotemporally averaged flow field model and clarification of the interaction mechanisms between these forces. Results indicate that the flow field exhibits two representative macroscopic patterns governed by the interplay between inertial forcing and particle response characteristics: at low frequencies, the slowly varying Euler force combines with gravity to produce a coherent large-scale single-circulation structure, whose stability is sustained under higher gas velocities due to reduced internal energy dissipation associated with stronger drag; at high frequencies, the Coriolis force promotes structural division while the rapidly oscillating Euler force introduces disturbances, resulting in the formation and persistence of double or multi-circulation flow structures under their combined action.
Keywords: additional inertial forces; rocking fluidized bed; force analysis; gas–solid flow; spatiotemporal effects additional inertial forces; rocking fluidized bed; force analysis; gas–solid flow; spatiotemporal effects

Share and Cite

MDPI and ACS Style

Yuan, X.; Wang, R.; Wang, D.; Xu, R.; Gao, X.; Zhao, B.; Zhang, S. Effect of Periodic Inertial Forces on Particle Flow Behavior in Spacetime. Processes 2026, 14, 1761. https://doi.org/10.3390/pr14111761

AMA Style

Yuan X, Wang R, Wang D, Xu R, Gao X, Zhao B, Zhang S. Effect of Periodic Inertial Forces on Particle Flow Behavior in Spacetime. Processes. 2026; 14(11):1761. https://doi.org/10.3390/pr14111761

Chicago/Turabian Style

Yuan, Xiaopei, Ruojin Wang, Dewu Wang, Ruofeng Xu, Xuefang Gao, Bin Zhao, and Shaofeng Zhang. 2026. "Effect of Periodic Inertial Forces on Particle Flow Behavior in Spacetime" Processes 14, no. 11: 1761. https://doi.org/10.3390/pr14111761

APA Style

Yuan, X., Wang, R., Wang, D., Xu, R., Gao, X., Zhao, B., & Zhang, S. (2026). Effect of Periodic Inertial Forces on Particle Flow Behavior in Spacetime. Processes, 14(11), 1761. https://doi.org/10.3390/pr14111761

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