力学与实践 ›› 2020, Vol. 42 ›› Issue (3): 277-281.DOI: 10.6052/1000-0879-19-458

• 应用研究 • 上一篇    下一篇

基于动边界微积分关系再论 任意运动控制体的雷诺输运方程推导

刘沛清1)()   

  1. 北京航空航天大学陆士嘉实验室,北京 100191
  • 收稿日期:2019-12-06 出版日期:2020-06-20 发布日期:2020-06-30
  • 通讯作者: 刘沛清
  • 作者简介:1) 刘沛清,教授,主要研究方向为空气动力学。 E-mail: lpq@buaa.edu.cn

THE DERIVATION OF REYNOLDS TRANSPORT EQUATION FOR ARBITRARY MOTION CONTROL VOLUME BASED ON THE DYNAMIC BOUNDARY CALCULUS

LIU Peiqing1)()   

  1. Lushijia Laboratory, Beihang University, Beijing 100191, China
  • Received:2019-12-06 Online:2020-06-20 Published:2020-06-30
  • Contact: LIU Peiqing

摘要:

严格而言,流体力学中所有守恒定律均是针对物质体系的(或称流体系统),如质量、动量、动量矩和能量等守恒定律。如果跟随物质体系描述和表征流体质点系的运动行为,即为Lagrange描述方法;如果把物质体系的运动和守恒定律转换到空间坐标系中,即为人们常说的Euler描述方法。因此,对于具体考察(跟随的)的流体物质系统而言,各守恒定律存在由物质体系表征到空间体系表征的转换,这个转换关系就是著名的Reynolds输运方程。本文从动边界微积分关系式出发,系统推导了在不同运动速度控制体上的雷诺输运方程,并通过讨论进一步阐明各种不同形式输运方程的物理意义。

关键词: 物质体系, 空间体系, 雷诺输运方程

Abstract:

Strictly speaking, all conservation laws in hydrodynamics are for a material system (or a fluid system), such as the conservation laws of mass, momentum, momentum moment and energy. The Lagrange method is used to describe and characterize the motion behavior of the fluid particle system. If the motion and the conservation laws of the material system are put into the space coordinate system, the Euler method is often used. Therefore, for the observed (followed) fluid material system, each conservation law makes a transformation from the material system to the control volume, which is the famous Reynolds transport equation. In this paper, the Reynolds transport equations for different velocity control volumes are derived based on the boundary calculus. The physical significance of various transport equations is also discussed.

Key words: material system, space system, Reynolds transport equation

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