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Volume 102
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On scaling laws of fast-fluidized-bed dynamics: Critical remarks and final solution (Open Access)
Ming-Chuan Zhang *
Institute of Thermal Energy Engineering, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China
10.1016/j.partic.2025.04.004
Volume 102, July 2025, Pages 53-69
Received 7 October 2024, Revised 17 March 2025, Accepted 3 April 2025, Available online 16 April 2025, Version of Record 24 April 2025.
E-mail: mczhang@sjtu.edu.cn
Highlights

• Problems/limitations of scaling laws missing Ar number in the past were revealed.

• Simplified scaling laws with explicit Ar for mesoscale similarity were derived.

• Semi-spontaneous scaling with non-isothermal fluidizing gas shift was identified.

• Scaling down from hot CFB combustor to 1/20 cold model was demonstrated successfully.

• Macroscopic scaleup laws of two identities were derived for beds with same gas and particles.


Abstract

Archimedes number (Ar) is the most important parameter characterizing the fluid-particle two-phase-flow system, which determines the ratio of terminal velocity of single particle to minimum gas velocity for fluidization, and then the possibility of two fluidized systems being similar in fast-fluidization flow-regime. After brief revisit of the scaling laws reported in literatures, the problem/limitations of missing Ar were revealed/identified. Starting from Glicksman's full set scaling laws, new simplified four identities scaling laws for mesoscale similarity were derived. They were confirmed, also, by the unified model for fast fluidization dynamics established by the present author and his co-workers. When the new criteria were applied for scaling-down a high-temperature CFB combustor to a cold-air model, about one tenth semi-spontaneous scaling for bed size was identified and declared. With this benefit, scaling down from a large CFB combustor, of 15 m in diameter, to a 1/20 cold model was demonstrated successfully. Further simplification was also conducted to the beds using same gas and particles for partial/macroscale similarity. With guidance of the unified model, the simplest scaling laws having two similitude identities were obtained. And this is coincident well with Qi and Zhu's empirical correlation, deduced from dozens more literature data sets and their own.

Graphical abstract
Keywords
Fast bed; Scaleup laws; Ar number; Mesoscale similarity; Macroscale similarity; CFB combustor
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