Continuous subsonic-sonic flows in a two-dimensional semi-infinitely long nozzle
Continuous subsonic-sonic flows in a two-dimensional semi-infinitely long nozzle
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DOI：
10.3934/era.2020122
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发表时间：
2021
影响因子：
0.8
通讯作者：
Mingjun Zhou;Jingxue Yin
中科院分区：
文献类型：
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作者：
Mingjun Zhou;Jingxue Yin
本文重点研究半无限长喷嘴中的二维连续亚音速-音速势流，该喷嘴具有直的下壁和上壁，该上壁在出口处会聚，而在远场处是直的。证明了如果喷管横截面的变化率适当小，则喷管内存在一种独特的连续亚音速-音速流动，使得声速曲线与上壁相交于定点，且流速沿声速曲线处的法线方向。此外，声波曲线是自由的，其中流动是奇异的，即流速仅是霍尔德连续的并且流动加速度爆炸。此外，还显示了远场流速的渐近行为。
This paper focuses on two-dimensional continuous subsonic-sonic potential flows in a semi-infinitely long nozzle with a straight lower wall and an upper wall which is convergent at the outlet while straight at the far fields. It is proved that if the variation rate of the cross section of the nozzle is suitably small, there exists a unique continuous subsonic-sonic flows in the nozzle such that the sonic curve intersects the upper wall at a fixed point and the velocity of the flow is along the normal direction at the sonic curve. Furthermore, the sonic curve is free, where the flow is singular in the sense that the flow speed is only Holder continuous and the flow acceleration blows up. Additionally, the asymptotic behaviors of the flow speed at the far fields is shown.