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力学学报  1966 

横向曲率对轴对称可压缩层流边界层的影响

DOI: 10.6052/0459-1879-1966-2-1966-003, PP. 150-172

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Abstract:

在轴对称细长体的绕流中,同物体当地横向曲率半径相比,粘性边界层厚度可能不是一个小量,而可能是大好多倍的量;这时在经典的Prandtl边界层方程中,以物体的横向曲率半径来代替边界层中任一一点到对称轴的距离,这种简化方法已不适用.因此,本文老虑了横向曲率对轴对称可压缩层流边界层流动的影响.首先研究了强影响区.在完全气体,Prandtl数等于1,粘性系数与温度成正比,以及压力梯度可以忽略等假定下,以一个表示横向曲率影响的量θ为小参数,将流函数展成幂级数,从而求得了强影响区域中的摩阻系数和热传递系数的渐近解.为了使这个展开式一致有效,文中用FLK方法消除了二级近似(卽级数中的第三项少在物面附近的奇异性。结果表明,对于幂次物体rw~xn来说,在强影响区,物面摩阻系数Cf和热传递系数St有下面的形式Cf=4Ce/RexTw/Tex/rwcosφ{θ+[0.577-In(1+2n)]θ2}+O(θ3,St=1/2Cf.其次,采用动量积分关系方法研究了横向曲率在整个流动区域中的影响,文中采用Crocco变量下的形式,选择适当的切应力τ和速度μ的关系,求得了圆柱和圆锥的Cf,St表达式,井与弱影响区、强影响区的渐近解作了比较.

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