Two-dimensional Rarefaction Waves in the High-speed Two-phase Flow
Two-dimensional Rarefaction Waves in the High-speed Two-phase Flow
复制标题
高速两相流中的二维稀疏波
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
A. Harada
中科院分区：
文献类型：
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作者：
M. Nakagawa;A. Harada
两相流喷嘴用于地热电厂的全流系统和制冷剂循环的喷射器等。两相流喷嘴最重要的功能之一就是将热能转化为两相流动能。从喷嘴中排出的两相流动能适用于所有这类应用。当喷管的工作条件选择较多时，在非最佳膨胀条件下，超音速喷管出口处存在激波或稀疏波。本研究的目的是从理论上阐明超音速两相流喷管出口稀疏波的特性。介绍了考虑相间动量传递的可压缩两相流的二维基本方程。利用单色波近似，从这些方程中得到声速。这取决于决定动量转移的松弛时间。松弛时间大的两相流有冻结声速，松弛时间小的两相流有平衡声速。用CIP方法计算了两相流喷管后的稀疏波。尽管冻结的马赫数小于1控制了这些基本方程，但在较小的驰豫时间内出现了稀疏波。膨胀开始的马赫线取决于入口速度和松弛时间。这些关系在本文中得到了展示。在松弛时间小于0.1的情况下，压力膨胀曲线只是喷管出口拐角转角的函数。对于较大的松弛时间，由于相间动量传递引起的内耗，压力衰减，膨胀曲线不仅是角度的函数，也是流动方向的函数。并将计算的膨胀曲线与实验结果进行了比较。这些计算只考虑了气相的可压缩性，但与发生相变的实验曲线相似。
Two-phase flow nozzles are used in the total flow system for geothermal power plants and in the ejector of the refrigerant cycle, etc. One of the most important functions of a two-phase flow nozzle is to convert the thermal energy to the kinetic energy of the two-phase flow. The kinetic energy of the two-phase flow exhausted from a nozzle is available for all applications of this type. There exist the shock waves or rarefaction waves at the outlet of a supersonic nozzle in the case of non-best fitting expansion conditions when the operation conditions of the nozzle are widely chosen. The purpose of the present study is to elucidate theoretically the character of the rarefaction waves at the outlet of the supersonic two-phase flow nozzle. Two-dimensional basic equations for the compressible two-phase flow are introduced considering the inter-phase momentum transfer. Sound velocities are obtained from these equations by using monochromatic wave approximation. Those depend on the relaxation time that determines the momentum transfer. The two-phase flow with large relaxation times has a frozen sound velocity, and with small one has an equilibrium sound velocity. Rarefaction waves which occurred behind the two-phase flow nozzle are calculated by the CIP method. Although the frozen Mach number, below one, controls these basic equations, the rarefaction waves appeared for small relaxation time. The Mach line behind which the expansion starts depends on the inlet velocity and the relaxation time. Those relationships are shown in this paper. The pressure expansion curves are only a function of the revolution angle around the corner of the nozzle outlet for the relaxation time less than 0.1. For the larger relaxation time, the pressure decays because of internal friction caused by inter phase momentum transfer, and the expansion curves are a function of not only the angle but also the flow direction. The calculated expansion curves are compared with the experimental ones. The calculations considered only the compressibility of the gas phase, but those resembled with the curve of the experiment in which the phase changes occurred.