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Analytical Solutions to a Model of Inviscid Liquid-gas Two-phase Flow with Cylindrical Symmetry and Free Boundary

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Abstract

In this paper, we consider the free boundary value problem for a model of inviscid liquid-gas two-phase flow with cylindrical symmetry. For simplicity, we assume that the gas velocity is always equal to the liquid one and the gas and liquid are both connected continuously to the outer vacuum through the same free boundary. Furthermore, the free boundary is assumed to move in the radial direction with the radial velocity, which will affect the angular velocity but does not affect the axial velocity. We construct two classes of global analytical solutions by using some ansatzs and show that the free boundary will spread outward linearly in time by using some new averaged quantities.

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Authors and Affiliations

  1. School of Mathematical, Zhengzhou University of Aeronautics, Zhengzhou, 450015, China

    Jian-wei Dong & Yi-hui Zhang

Authors
  1. Jian-wei Dong
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  2. Yi-hui Zhang
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Correspondence to Jian-wei Dong.

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The authors declare no conflict of interest.

Additional information

The project is supported by the the Project of Youth Backbone Teachers of Colleges and Universities in Henan Province (No. 2019GGJS176), the Vital Science Research Foundation of Henan Province Education Department (No. 22A110024 and No. 22A110026), the Scientific Research Team Plan of Zhengzhou University of Aeronautics (No. 23ZHTD01003), the Basic Research Projects of Key Scientific Research Projects Plan in Henan Higher Education Institutions (No. 20zx003) and the Henan Natural Science Foundation (No. 222300420579).

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Dong, Jw., Zhang, Yh. Analytical Solutions to a Model of Inviscid Liquid-gas Two-phase Flow with Cylindrical Symmetry and Free Boundary. Acta Math. Appl. Sin. Engl. Ser. (2024). https://doi.org/10.1007/s10255-024-1074-y

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  • DOI: https://doi.org/10.1007/s10255-024-1074-y

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