匀动螺旋状集中涡的流函数解析表达及其证明

旨在推导在圆柱直管中作均匀运动的右旋单螺旋状集中涡管诱导无粘流场流函数的解析表达式，并将结果回代到涡与流函数的微分方程中，证明这一解析解的正确性．结果显示：涡管流函数是时间的周期函数，并被表征为一系列在涡核内均匀分布螺旋涡丝流函数的叠加．当螺旋涡管沿自身轴线移动一个节距，同时绕自身轴线旋转一圈时，螺旋涡管诱导的流场退化为定常场．若令圆柱直管半径趋于无穷大，则获得在无穷大域中作均匀运动的三维螺旋状圆柱集中涡管的流函数．

Analytical solution and its proof of the stream function of the uniformly moving helical vortexes

This paper discussed the deducing analytical expression of the stream function of the inviscid velocity field induced by the concentrated helical vortex tube with single right handed that moved uniformly and rigidly without changing the form in the cylindrical straight pipe. It was different from the previous discussion about the stream function of vortex filament and the vortex core size was considered. The result showed that the stream function of vortex tube was expressed as the superposition of the stream functions of vortex filament within the vortex core. When the cylindrical pipe radius tended to infinitely large quantity, the stream function of vortex tube in an unbound space was obtained. The analytical expression was proved to be correct by substituting it into the differential relationship between the stream function and vorticity inside flow field.