含源流场流动相似参数推导及其物理意义

现有的相似参数能够较好地解决无源流动的动力学相似和热力学相似问题。然而,如果流场中存在质量、动量和能量等源项,则须引入新的相似参数来指导实验的设计。首先,在连续介质假设、斯托克斯流体假设、量热完全气体假设和单相流假设的前提下,推导出了41个相似参数;然后,将之归纳整理成9个独立的相似参数,其中,3个与源项有关;最后,讨论了它们各自的物理意义。现有的单相流相似参数均可通过9个相似参数组合而来。实际应用中,可根据具体流动情况选择这9个相似参数中的某几个进行模拟。

Flow Similarity Parameters and Their Physical Significance

Flow similarity parameters in existence have solved the dynamic similarity and thermodynamic similari- ty problems well. But new similarity parameters are needed to guide the design of experiments if there are source terms such as mass sources and momentum sources or energy sources existing in the flow field. On the other hand, thermodynamic similarity parameters in existence are multifarious, and not all of what are unat- tached. For these reasons, it is necessary to trim similarity parameters to make them more terser in guiding ex- periments. First, 41 similarity parameters were derived on the hypothesis of continuous media, Stokes fluid, calo- rically perfect gas and single-phase flow, then these 41 similarity parameters were trimed to 9 unattached ones （3 of those were obtained for the first time）, and their physical significance was discussed at last. All the simi- larity parameters for single-phase flows could be obtained by combination of these 9 unattached similarity param- eters. Several parameters between these 9 should be chosen to consider according to the specified problems in application to actual problems.