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边界层

边界层示意图,图中可看出由层流演变为紊流的过程

边界层,又称附面层是一个流体力学名词,表示流体中紧接着管壁或其他固定表面的部分。边界层是由黏滞力产生的效应,和雷诺数Re有关。

一般提到的边界层是指速度的边界层。在边界层外,流体的速度接近定值,不随位置而变化。在边界层内,在固定表面上流速为0,距固定表面越远,速度会趋近一定值。

流体速度及自由速度

边界层厚度

若流体的速度为为该点和固定表面的距离,而流体在不受黏滞力影响的速度为自由速度,则可依下式定义边界层厚度(也称作速度边界层厚度),即速度到达99%自由速度的位置:

边界层厚度越小,边界层内速度的变化率越大,可以视为速度的扩散率越大。

不可压缩流中,位移厚度displacement thickness)δ*或δ1可以用以下的方式定义:

而在可压缩流中对应的定义如下(为流体密度):

位移厚度可视为若流体没有黏滞力,其速度为自由速度,若其流量(可压缩流中为质量流量)和原来流场的流量相同,流体可以减少的厚度。位移厚度可以量度在一流场中,因黏滞力而减少的流量。

以类似的方式可以定义动量厚度momentum thickness)θ或δ2

动量厚度可视为若流体没有黏滞力,其速度为自由速度,若其总动量和原来流场的动量相同,流体可以减少的厚度。

热传的边界层厚度

热传导中也有热的边界层。热边界层厚度定义和边界层厚度类似,是从边界到温度为99%原始流体温度位置的距离。 热的边界层厚度越小,表示热传的效果越好。

热传的边界层厚度及速度边界层厚度的关系由普兰特尔数Pr控制。若 Pr=1,两者厚度相同;若Pr> 1,热传边界层厚度较薄,热传的效果较好;若 Pr < 1,热传边界层厚度较厚,热传的效果较差(如空气)。

参考文献

  • A.D. Polyanin and V.F. Zaitsev, Handbook of Nonlinear Partial Differential Equations, Chapman & Hall/CRC Press, Boca Raton - London, 2004. ISBN 1-58488-355-3
  • A.D. Polyanin, A.M. Kutepov, A.V. Vyazmin, and D.A. Kazenin, Hydrodynamics, Mass and Heat Transfer in Chemical Engineering, Taylor & Francis, London, 2002. ISBN 0-415-27237-8
  • Herrmann Schlichting, Klaus Gersten, E. Krause, H. Jr. Oertel, C. Mayes "Boundary-Layer Theory" 8th edition Springer 2004 ISBN 3-540-66270-7
  • John D. Anderson, Jr, "Ludwig Prandtl's Boundary Layer", Physics Today, December 2005
  • Anderson, John. Fundamentals of Aerodynamics 2nd edition. Toronto: McGraw-Hill. 1991: 711–714. ISBN 0-07-001679-8. 
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边界层
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