Noble-Abel刚性气体流体的可压缩流动
Compressible flow in a Noble-Abel Stiffened-Gas fluid
摘要：
虽然可压缩流理论在过去的一个世纪里依赖于完美的气体模型作为其主力，但稠密气体、固体和液体中的可压缩动力学依赖于许多复杂的状态方程，对所解决问题的流体动力学方面的了解有限。最近，Le Metayer和Saurel研究了一个简单但有前途的状态方程，因为它能够模拟介质的热和压缩性方面。它是Noble-Abel状态方程和刚性气体模型的混合，称为Noble-Able刚性气体（NASG）状态方程。在目前的工作中，我们推导出封闭形式的分析框架，模拟可压缩流的介质近似的NASG状态方程。我们推导出了等熵、声速、等熵指数、特征描述中的黎曼变量以及激波、爆燃和爆轰的跳跃条件的表达式。我们还说明了解决黎曼问题的实用性。封闭形式的解决方案概括了一个透明的方式完善的模型，一个完美的气体，突出了介质的可压缩性的作用。
英文摘要：
While compressible flow theory has relied on the perfect gas model as its workhorse for the past century, compressible dynamics in dense gases, solids and liquids have relied on many complex equations of state, yielding limited insight on the hydrodynamic aspect of the problems solved. Recently, Le Métayer and Saurel studied a simple yet promising equation of state owing to its ability to model both the thermal and compressibility aspects of the medium. It is a hybrid of the Noble-Abel equation of state and the stiffened gas model, labeled the Noble-Able Stiffened Gas (NASG) equation of state. In the present work, we derive the closed form analytical framework for modelling compressible flow in a medium approximated by the NASG equations of state. We derive the expressions for the isentrope, sound speed, the isentropic exponent, Riemann variables in the characteristic description, and jump conditions for shocks, deflagrations and detonations. We also illustrate the usefulness by addressing the Riemann problem. The closed form solutions generalize in a transparent way the well-established models for a perfect gas, highlighting the role of the medium's compressibility.
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