Unsteady Incompressible Potential Flow
Unsteady Incompressible Potential Flow
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非定常不可压缩势流
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
A. Plotkin
中科院分区：
文献类型：
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作者：
J. Katz;A. Plotkin
我们在前面的章节中已经看到，在不可压缩、不可旋转的流体中，速度场可以通过求解连续性方程来获得。但是，不可压缩连续性方程不直接包含含时项，而是通过边界条件引入含时项。因此，第一个目标是证明为定常流动开发的求解方法只需稍加修改即可使用。这些修改将包括“固体表面上的零法向流”边界条件的处理和非定常伯努利方程的使用。此外，由于非均匀运动的结果，尾迹变得比相应的定常流动情况更加复杂，应该适当考虑。因此，本章分为三个部分，如下：a.问题的表述和关于将稳态流动方法转换为处理非恒定流的拟议修改(第13.1-13.6节)。B.转换分析模型以处理随时间变化的流动的实例(例如，第13.8-13.9节中的薄升力翼型和细长机翼)。C.转换数值模型以处理随时间变化的流动的实例(第13.10-13.13节)。对于数值例子，只给出了最简单的模型；然而，强烈建议将该方法应用于第11章的任何其他方法(例如，可以作为学生项目给出)。在一般情况下，浸没在流体中的固体(例如机动机翼或飞行器)的任意运动，其运动路径由组合的动力学和流体动力学方程确定。
We have seen in the previous chapters that in an incompressible, irrotational fluid the velocity field can be obtained by solving the continuity equation. However, the incompressible continuity equation does not directly include time-dependent terms, and the time dependency is introduced through the boundary conditions. Therefore, the first objective is to demonstrate that the methods of solution that were developed for steady flows can be used with only small modifications. These modifications will include the treatment of the “zero normal flow on a solid surface” boundary conditions and the use of the unsteady Bernoulli equation. Furthermore, as a result of the nonuniform motion, the wake becomes more complex than in the corresponding steady flow case and it should be properly accounted for. Consequently, this chapter is divided into three parts, as follows: a. Formulation of the problem and of the proposed modifications for converting steady-state flow methods to treat unsteady flows (Sections 13.1–13.6). b. Examples of converting analytical models to treat time-dependent flows (e.g., thin lifting airfoil and slender wing in Sections 13.8–13.9). c. Examples of converting numerical models to treat time-dependent flows (Sections 13.10–13.13). For the numerical examples only the simplest models are presented; however, application of the approach to any of the other methods of Chapter 11 is strongly recommended (e.g., can be given as a student project). In the general case of the arbitrary motion of a solid body submerged in a fluid (e.g., a maneuvering wing or aircraft) the motion path is determined by the combined dynamic and fluid dynamic equations.