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Closed equation model for cavity evolution in granular media

Published online by Cambridge University Press:  26 September 2024

Junsheng Zeng Open the ORCID record for Junsheng Zeng [Opens in a new window] ,
Baoqing Meng Open the ORCID record for Baoqing Meng [Opens in a new window] ,
Xiaoyan Ye Open the ORCID record for Xiaoyan Ye [Opens in a new window]  and
Baolin Tian
Junsheng Zeng
Affiliation:
School of Aeronautic Science and Engineering, Beihang University, Beijing, PR China Shanghai Zhangjiang Institute of Mathematics, Shanghai, PR China
Baoqing Meng*
Affiliation:
Institute of Mechanics, Chinese Academy of Sciences, Beijing, PR China
Xiaoyan Ye*
Affiliation:
Key Laboratory of Mechanics on Disaster and Environment in Western China, Ministry of Education, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou, PR China
Baolin Tian
Affiliation:
School of Aeronautic Science and Engineering, Beihang University, Beijing, PR China Shanghai Zhangjiang Institute of Mathematics, Shanghai, PR China
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

Cavity evolution in granular media is crucial in explosion-driven gas–particle flows, particularly in many engineering applications. In this study, a theoretical model was first proposed to describe the cavity evolution in granular media by extending the classical Rayleigh–Plesset model. A closed equation set comprising the radius, pressure and gas leak-off velocity equations was built by considering the gas expansion and non-Darcy gas-penetration effects. Both centrally symmetric and non-centrally symmetric cases of gas injection into granular media were investigated. Especially for modelling the non-symmetric scenario, the radius and gas leak-off velocity equations were proposed in each radial direction with angle $\theta$, and then the pressure equation was built up based on the integral gas leak-off along the cavity outline. Through non-dimensionalizing the theoretical equations, four key dimensionless numbers $\varPi_1,\ \varPi_4$ were obtained to characterize the response time of cavity expansion and the intensity of non-Darcy effects for both cases. This allowed us to determine a scaling law of effective cavity radius $R_{eff}^*=\sqrt {2\varPi _2/(7{\rm \pi} )}t^{*1/2}$ and the critical time $t_{cr}^*=\sqrt {12.5/\varPi _1}$ for two-dimensional cavity evolution. Additionally, the necessity of incorporating non-Darcy effects was ascertained under conditions of $\varPi _4>400$. The findings demonstrate that the proposed theoretical equations effectively predict the cavity evolution results under various operational conditions ($0.7<\varPi _1<7\times 10^2, 3<\varPi _4<1.1\times 10^3$), as validated by refined Euler–Lagrange numerical simulations.

JFM classification

Compressible Flows: Gas dynamics Drops and Bubbles: Bubble dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 996 , 10 October 2024 , A15
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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