管道中超声速旋涡运动的数值模拟

本文利用ＥＮＮ格式通过求解ＮＳ方程，数值模拟了超声速旋涡在管道中沿其轴向的演变规律。结果表明，当流动处于顺压区，在涡轴附近，截面流线为不稳定的螺旋点形态；当流动处于逆压区，在涡轴附近，截面流线为稳定的螺旋点形态；当从顺压区过渡到逆压区，涡心附近出现不稳定极限环；反之，出现稳定极限环。数值模拟结果同张涵信的拓扑分析理论十分相符。

Numerical Simulation of Supersonic Vortex Flows in a Duct

The supersonic vortex evolution along its axis in a duct is investigated by solving NS equations with ENN scheme. The numerical results show that in the favorable pressure region, the sectional streamlines near the axis in the transveral plane possess an unstable spiral (out ward), and in the adverse pressure region, the transveral streamlines are a stable spiral (inward). As the vortex moves forward along the axis from the favorable pressure region to the adverse pressure region or vice versa,the flow pattern in the transversal plane will yield a Hopf bifurcation, the former is an unstable limiting cycle and the later a stable one.The numerical results given by this paper agree well with the topological theory of professor Zhang.