Numerical Simulation of Shock Wave in Gas–Water Interaction Based on Nonlinear Shock Wave Velocity Curve

Zongduo Wu, Dapeng Zhang (), Jin Yan, Jianhua Pang and Yifang Sun
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Zongduo Wu: Naval Architecture and Shipping College, Guangdong Ocean University, Zhanjiang 524091, China
Dapeng Zhang: Naval Architecture and Shipping College, Guangdong Ocean University, Zhanjiang 524091, China
Jin Yan: Naval Architecture and Shipping College, Guangdong Ocean University, Zhanjiang 524091, China
Jianhua Pang: Ocean Intelligence Technology Center, Shenzhen Institute of Guangdong Ocean University, Shenzhen 518055, China
Yifang Sun: Naval Architecture and Shipping College, Guangdong Ocean University, Zhanjiang 524091, China

Mathematics, 2024, vol. 12, issue 20, 1-26

Abstract: In a gas–water interaction problem, the nonlinear relationship between shock wave velocity is introduced into a Hugoniot curve, and a Mie–Grüneisen Equation of state (EOS) is established by setting the Hugoiot curve as the reference state. Unlike other simple EOS based on the thermodynamics laws of gas (such as the Tait EOS), the Mie–Grüneisen EOS uses reference states to cover an adiabatic impact relationship and considers the thermodynamics law separately. However, the expression of the EOS becomes complex, and it is not adaptive to many methods. A multicomponent Mie–Grüneisen mixture model is employed in this study to conquer the difficulty of the complex form of an EOS. In this model, some coefficients in the Mie–Grüneisen EOS are regarded as variables and solved using newly constructed equations. The performance of the Mie–Grüneisen mixture model in the gas–water problem is tested by low-compression cases and high-compression cases. According to these two tests, it is found that the numerical solutions of the shock wave under the Mie–Grüneisen EOS agrees with empirical data. When compared to other simple-form EOSs, it is seen that the Mie–Grüneisen EOS has slight advantages in the low-compression case, but it plays an important role in the high-compression case. The comparison results show that the solution of the simple-form EOS clearly disagrees with the empirical data. A further study shows that the gap between the Mie–Grüneisen EOS and other simple-form EOSs becomes larger as the initial pressure and particle velocity increase. The impact effects on the pressure, density and particle velocity are studied. Moreover, the gas–water interaction in a spherical coordinate plane and a two-dimensional coordinate is a significant part of our work.

Keywords: gas–water flow; shock wave; Riemann problem; Mie–Grüneisen mixture model; equation of state (EOS) (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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