The reciprocal theorem in fluid dynamics and transport phenomena
The reciprocal theorem in fluid dynamics and transport phenomena
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DOI：
10.1017/jfm.2019.553
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发表时间：
2019-11-25
影响因子：
3.7
通讯作者：
Stone, Howard A.
中科院分区：
文献类型：
--
作者：
Masoud, Hassan;Stone, Howard A.
在流体动力学和传输现象的研究中，感兴趣的关键量通常是物体上的力和扭矩以及从它们传递的热/质的总速率。通常，这些积分量通过首先求解场变量（即速度、压力、温度、浓度等）的详细分布的控制方程来确定。然后在物体的表面上对变量或其导数进行积分。另一方面，守恒方程的发散形式为建立积分恒等式打开了大门，积分恒等式可用于直接计算积分量，而不需要主要变量分布的详细知识。这种捷径的做法构成了互等定理的想法，其最接近的亲戚是绿色的第二身份，读者可能会记得从研究偏微分方程。尽管它的重要性和实用性，该定理可能不那么熟悉的许多研究社区。具有讽刺意味的是，有些人认为该定理的极端简单性和普遍性是抑制其应用的原因！在这篇观点文章中，我们提供了一个关于互等定理的概念和应用的教学介绍，希望能促进它的使用。具体来说，简要的历史上的发展定理作为背景，其次是讨论的主要思想的背景下，小学边值问题。在那之后，我们展示了如何利用互易定理来解决低雷诺数流体力学，空气动力学，声学和热/质传递，包括对流的基本问题。在整篇文章中，我们努力使早期职业研究人员能够使用这些材料，同时让更有经验的科学家和工程师感兴趣。
In the study of fluid dynamics and transport phenomena, key quantities of interest are often the force and torque on objects and total rate of heat/mass transfer from them. Conventionally, these integrated quantities are determined by first solving the governing equations for the detailed distribution of the field variables (i.e. velocity, pressure, temperature, concentration, etc.) and then integrating the variables or their derivatives on the surface of the objects. On the other hand, the divergence form of the conservation equations opens the door for establishing integral identities that can be used for directly calculating the integrated quantities without requiring the detailed knowledge of the distribution of the primary variables. This shortcut approach constitutes the idea of the reciprocal theorem, whose closest relative is Green's second identity, which readers may recall from studies of partial differential equations. Despite its importance and practicality, the theorem may not be so familiar to many in the research community. Ironically, some believe that the extreme simplicity and generality of the theorem are responsible for suppressing its application! In this Perspectives piece, we provide a pedagogical introduction to the concept and application of the reciprocal theorem, with the hope of facilitating its use. Specifically, a brief history on the development of the theorem is given as a background, followed by the discussion of the main ideas in the context of elementary boundary-value problems. After that, we demonstrate how the reciprocal theorem can be utilized to solve fundamental problems in low-Reynolds-number hydrodynamics, aerodynamics, acoustics and heat/mass transfer, including convection. Throughout the article, we strive to make the materials accessible to early career researchers while keeping it interesting for more experienced scientists and engineers.