Modeling of Disperse Multiphase Flow

多相流的工程描述必须建立在宏观方程的基础上，在宏观方程中，相的不均匀性是一般意义上的，而不是详细的。建立模型的困难在于连续介质力学基本方程的任何平均过程都会导致模型中包含的未知数多于方程。最根本的问题是闭合方程集，即确定用其他未知量表示某些未知量的“本构关系”。这是所提议的分散流动的研究的中心主题，例如流体相中的颗粒。这个问题将依靠一种新的推导平均方程的方法和最先进的数值直接模拟技术来解决。这两个工具之前都是在NSF的支持下开发的。新的平均过程用粒子表面上的积分来表示未知，这些积分可以很容易地从运动的数值模拟中计算出来。计算将通过在大规模并行超级计算机上实现的时空有限元方法进行。如果这项研究取得成功，对方程式结构的洞察将有望回答长期存在的问题，如方程式的数学结构及其与观察现象的关系。开展这项研究所需的数值技术的增强本身就构成了当前直接数值模拟能力的重大进步。这项研究将与约翰·霍普金斯大学的安德烈斯·普洛斯彼莱蒂教授合作进行，他与美国国家科学基金会有单独的关系。＊＊＊

ABSTRACT CTS-9521373 An Engineering description of multi-phase flows by necessity must be made on the basis of macroscopic equations in which the phase inhomogeneties are accounted for in an average sense, rather than in detail. The difficulty in formulating the models resides in the fact that any averaging procedure applied to the fundamental equations of continuum mechanics leads to models containing more unknowns than equations. The fundamental problem is then that of closing the equation set, namely of determining "constitutive relations" that express some unknown quantities in terms of others. This is the central theme of the proposed research for the case of disperse flows, such as particles in a fluid phase. The problem will be attacked by relying on a new method for deriving averaged equations and on the state-of-the-art numerical direct-simulation techniques. Both tools have been previously developed under NSF support. The new averaging procedure expresses the unknown in terms of integrals over the particles surfaces that can readily be calculated from numerical simulations of the motion. The computations will be carried out by means of a space-time finite-element method implemented on massively parallel supercomputers. The insight into the structure of the equations that, if successful, will derive from this research promises to answer long-standing questions as to the mathematical structure of the equations and their relationship to observe phenomena. The enhancement of the numerical techniques necessary to carry out this research constitutes in itself a significant advancement in the current direct numerical simulation capabilities. This research will be carried out in conjunction with Professor Andres Prosperetti of the Johns Hopkins University who has a separate from NSF. ***