Bell Ian H, Jäger Andreas
National Institute of Standards and Technology, Boulder, CO 80305.
Technische Universität Dresden, Professur für Technische Thermodynamik, Helmholtzstr. 14, 01062 Dresden, Germany.
J Res Natl Inst Stand Technol. 2016 Jun 20;121:238-263. doi: 10.6028/jres.121.011. eCollection 2016.
Comprehensive sets of derivatives of Helmholtz energy transformations of several common cubic equations of state are presented. These derivatives can be used for implementing cubic equations of state into complex multi-fluid mixture models when no multiparameter equation of state is available for a mixture component. Thus, pure fluids (or mixtures) for which no accurate model exists in literature can be modeled with a relatively small set of fluid property data. Composition derivatives have been calculated for the cases where the last mole fraction is either an independent or dependent variable. Analytic derivatives are presented up to fourth order in the independent variables combined with composition derivatives up to third order; this set covers the common requirements for derivatives needed in the state-of-the-art thermophysical property libraries. A C++ implementation of the presented analyses, data for computer code validation, and information about the computer algebra tools used to calculate the intermediate derivatives are provided as supplementary information.
给出了几种常见立方状态方程的亥姆霍兹能量变换的综合导数集。当混合物组分没有多参数状态方程可用时，这些导数可用于将立方状态方程应用于复杂的多流体混合物模型。因此，对于文献中不存在精确模型的纯流体（或混合物），可以用相对较少的一组流体性质数据进行建模。已针对最后一个摩尔分数是自变量或因变量的情况计算了组成导数。给出了自变量的四阶解析导数以及三阶组成导数；这组导数涵盖了最新热物理性质库中所需导数的常见要求。作为补充信息，提供了所提出分析的C++实现、用于计算机代码验证的数据以及用于计算中间导数的计算机代数工具的信息。
