A new method of solving Oseen’s equations and its application to the flow past an inclined elliptic cylinder
A new method of solving Oseen’s equations and its application to the flow past an inclined elliptic cylinder
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求解Oseen方程的新方法及其在倾斜椭圆柱流场中的应用
DOI：
10.1098/rspa.1954.0148
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发表时间：
1954
期刊：
影响因子：
--
通讯作者：
I. Imai
中科院分区：
文献类型：
--
作者：
I. Imai
本文发展了一种求解粘性流体二维定常绕流任意圆柱体的Oseen线性化方程的一般方法。该方法是基于这样的事实，即在附近的圆柱体的速度一般可以表示为一对解析函数，从适当的边界条件的确定，可以影响的雷诺数，R的幂的逐次逼近。该方法使人们能够获得附近的圆柱体的速度分布和升力和阻力作用在它的幂级数的形式在R中，而不求助于操作的更高的超越函数，如贝塞尔函数和马蒂厄函数的圆形和椭圆形的圆柱体，分别。作为应用该方法的一个例子，考虑了以任意入射角流过椭圆柱的均匀流。得到了升阻系数的解析表达式，其精度为R阶，最低阶项为O（R-1），并对厚度比t = 0，0.1，0.5，1和雷诺数R = 0.1，1进行了数值计算。结果表明，阻力随壁厚比或攻角的增大而略有增大，升力随壁厚比的增大而减小，但在45°附近有一个最大值。
In this paper is developed a general method of solving Oseen’s linearized equations for a two-dimensional steady flow of a viscous fluid past an arbitrary cylindrical body. The method is based on the fact that the velocity in the neighbourhood of the cylinder can be generally expressed in terms of a pair of analytic functions, the determination of which from the appropriate boundary condition can be effected by successive approximations in powers of the Reynolds number, R. The method enables one to obtain the velocity distribution near the cylinder and the lift and drag acting on it in the form of power series in R, without recourse to manipulation of higher transcendental functions such as Bessel and Mathieu functions for circular and elliptic cylinders, respectively. As an example of the application of the method, the uniform flow past an elliptic cylinder at an arbitrary angle of incidence is considered. Analytical expressions for the lift and drag coefficients are obtained, which are correct to the order of R, the lowest order terms being O(R-1) and numerical calculations are carried out for the thickness ratio t = 0, 0.1, 0.5, 1 and the Reynolds number R = 0.1, 1. It is found that drag increases slightly with increase of either thickness ratio or angle of incidence, and that lift decreases with increase of thickness ratio while, as a function of the angle of incidence, it has a maximum at about 45°.