匀动螺旋单涡管诱导压力场的解析解

Analytical solution of the pressure field induced by uniformly moving helical vortex tube

推导了在圆柱直管中作均匀运动的螺旋单涡管诱导核外压力场的解析表达式 ,若令柱管直径趋于无穷大 ,该表达式也能够描述在无限域中螺旋单涡管诱导核外压力场 .假设相对速度场定常且具有螺旋对称性 ,并利用已获得的涡管诱导相对速度场和相对坐标系下动量方程求其诱导压力场 .获得的结果显示 :压力场是时间的周期函数 ,仅当螺旋涡管静止或沿自身的空间螺旋线轴滑移时 ,螺旋涡诱导的压力场退化为定常场 ,该退化现象已被实验证实 ;圆柱直管壁上的压力极值点计算位置与现有实验的测量位置一致 .压力公式显示管壁压力脉动频率是均匀分布的 ,这一结论也与现有压力实验的频域特性相符合 .

This paper presented analytic solution of pressure field of inviscid fluid induced by a helical vortex tube moving uniformly and rigidly in a cylindrical pipe. The relative coordinate system was set on moving the vortex tube. The analytical solutions of the pressure field was obtained on the assumption that relative velocity field induced was time independent and helically symmetrical. If the diameter of the cylindrical pipe approached infinity, this solution was available for unbounded space. The result shows that the pressure field is periodical in time, and may reduce to time independent when the helical vortex tube is immobile or slips along the vortex itself. The calculated locations of pressure peak and valley on pipe wall agree with their experimental results.