层流边界层方程的近似分析解
An Approximate Analytical Solution of the Laminar Boundary Layer Equations
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摘要: 文献[1]引用压力梯度作为新的自变量以代替通常的纵坐标x.从而将经典的边界层方程变为新的形式.在此基础上,文献[1]用图解法求定任一截面处的摩擦应力因子.本文仍然采用文献[1]的变量置换,但用级数法求得了层流边界层方程的一级近似分析解;并得到了计算摩擦应力因子的公式(4.13).对于主函数中不含常数项的一类流动说,本文求得的摩擦应力因子和文献[1]的结果十分符合;对于主函数中含有常数项的另一类流动,文中作了更进一步的简化,求得的摩擦应力因子和文献[1]的结果相比较,误差也低于10%.Abstract: Using the pressure gradient as the new variable instead of. the ordinary longitudinal coordinate x, Liu transformed the ordinary laminar boundary equations into a new form. On this base Liu obtained the frictional stress factor by using the graphical method.In this paper the same variable replacement as in [1] is used and an approximate analytical solution of the laminar boundary layer equations by the series method is obtained. The author also obtains a formula of frictional stress factor. For the case of the main function without the term of constant, the author makes a further simplification. The error of the frictional stress factor obtained by the author is still less than 10%, compared with that of [1].
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Key words:
- Laminar boundary layer /
- pressure gradient /
- frictional stress factor
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[1] 刘钮,力学学报,4(1981),347-352. [2] Chang,Lang Mann and Chen Ching-jen,AIAA Journal,19(12)(1981),1551-1557. [3] 蔡树棠,空气动力学学报,(1)(1984),49-55. [4] 巴特勒雪夫,A,H 《流体力学》(下册,戴昌晖等译),高等教育出版社(1959),644-660. [5] 复旦大学数学系编,《流体力学》(1960),267. [6] Aziz,A.and T,Y.Na,AIAA Journal,9(1981),1242-1244. [7] Швед,А.Е.,ПММ,(3)(1949). -
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