适用于纯物质流体工质S2流面半反命题和A型杂交命题的变分原理族

文献2]建立了轴流式叶轮机S_2流面半反命题、A型杂交命题的变分原理族。文献1]在此基础上提出混流式叶轮机S_2流面半反命题和A型杂交命题的变分原理族,避免混流式中可能出现解的不确定性及分区处理的麻烦。但这些文章中所提出的变分原理均只适用于完全气体工质,使这些变分原理的应用受到一定的限制。例如对水蒸汽及氟里昂等工质,在某些极限工况下,如果再以完全气体的模型求解,会与实际情况相差较大。本文提出可将以上各变分原理推广至纯物质流体工质,从而使这些变分原理具有较强的适应性。

FAMILIES OF VARIATIONAL PRINCIPLES FOR SEMI-INVERSE AND TYPE 'A'HYBRID PROBLEMS ON A S_2-STREAMSHEET FOR FLUIDS OF PURE SUBSTANCE

In this paper, two families of variational principles for semi-inverse and type 'A' hybrid problems on a S2-streamsheet suitable for the fluid of pure substance are established. The momentum equation in an arbitrary qusi-orthogonal direction Y is chosen as the primary equation, and for the hybrid problem a corresponding image plane is introduced. Thus, these variational principles provide a reliable theoretical basis for finite element applications in fluid machanics of a variety of pure substances, especially for imperfect gases such as steam and Freon,etc.