华南理工大学学报(自然科学版) ›› 2003, Vol. 31 ›› Issue (10): 61-64.

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Prandtl 边界层方程推导中的尺度化分析

樊福梅1 梁 平1 龙新峰2   

  1. 1.华南理工大学 电力学院‚广东 广州510640;2.华南理工大学 化工学院‚广东 广州510640
  • 出版日期:2003-10-20 发布日期:2022-06-02
  • 作者简介:樊福梅(1977-)‚女‚硕士生‚主要从事热工过程优化控制研究.

Scaling Analysis for Inducing Prandtl Boundary Layer Equation

Fan Fu-mei 1 Liang Ping 1 Long Xin-feng 2   

  1. 1.College of Electric Power‚South China Univ.of Tech.‚Guangzhou510640‚China; 2.College of Chemical Engineering‚South China Univ.of Tech.‚Guangzhou510640‚China
  • Online:2003-10-20 Published:2022-06-02

摘要: 针对 Navier-Stokes 方程中的各项微商‚通过选择内禀参考尺度‚并根据连续函 数的若干性质‚在结合实验观察结果的基础上‚确定其数量级的大小‚再进一步对方程中 的各项进行尺度化分析‚使得方程中各项的数量级无量纲化‚并评估方程中各项微商的数 量级大小‚略去数量级小于1的项‚从而成功推导出了 Prandtl 边界层微分方程.该方法 在一定程度上揭示了边界层微分方程的数学物理实质.

关键词: 边界层, 尺度化, 数量级

Abstract: By selecting intrinsic reference scaling‚and according to some related properties of continuous function‚the magnitude of each tiny quotient in Navier-Stokes equation was determined based on some experimental materials.Then scaling analysis was carried out to make each part of the equation non-dimensional‚and the magnitude of each tiny quotient of the equation was evaluated.By removing the parts whose magnitude was less than1‚Prandtl boundary layer differential equation was induced successfully.To a certain extent‚this method discloses the mathematical and physical essence of boundary differential equation. 

Key words: boundary layer, scaling, magnitude

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