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Volume 113
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Calibration of the volume fraction model for particle drag, experimental validation, and numerical study of shock-driven nozzle gas-solid jet
Lite Zhang *, Shenghao Li, Xiangbo Meng, Heng Zhang, Hao Guan
School of Mechanical Engineering, Zhejiang Sci-Tech University, Hangzhou, 310018, China
10.1016/j.partic.2026.03.023
Volume 113, June 2026, Pages 123-139
Received 14 January 2026, Revised 26 February 2026, Accepted 12 March 2026, Available online 27 March 2026, Version of Record 2 April 2026.
E-mail: langzichsh@zstu.edu.cn
Highlights

• New drag model includes compressibility, inertia, high volume fraction.

• The volume-fraction correction exponent is calibrated using shock-tube experiments.

• Interchangeable-nozzle shock-tube tests provide robust validation data.

• The modified drag model outperforms classical correlations in predictive accuracy.

• Mach number, particle size, and nozzle geometry strongly influence jet performance.


Abstract

Based on experimental observations of shock-driven dense particle flows, this work extends and refines the volume-fraction correction framework originally proposed by Sangani. By incorporating realistic particle spatial distributions, the drag model is modified to more accurately describe gas–solid momentum exchange under dense flow conditions. Following model calibration, the volume-fraction correction exponent is identified as n∗ = 3.8, which yields improved predictive accuracy compared with commonly used drag models. To validate the model and investigate the influence of nozzle geometry on particle transport behavior, a shock-tube experimental system equipped with three representative nozzle configurations—converging, converging–diverging, and diverging nozzles—was constructed. Experimental and numerical results demonstrate that the modified drag model accurately captures the dynamics of shock-driven particle jets: converging nozzles enhance particle concentration, diverging nozzles promote particle acceleration and dispersion, while converging–diverging nozzles exhibit combined regulation characteristics at different stages. These findings provide physically consistent modeling support for understanding shock–particle interaction mechanisms and for optimizing shock-driven particle transport systems, such as dry powder fire extinguishers.

Graphical abstract
Keywords
Shock wave; Particle group; Modified resistance coefficient model; Gas-particle jet
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