The focal phase shift of waves of a circular membrane, applied to underexpanded supersonic jet structure
The focal phase shift of waves of a circular membrane, applied to underexpanded supersonic jet structure
复制标题
圆形膜波的焦点相移，应用于欠膨胀超音速喷气结构
DOI：
--
复制
发表时间：
1995
期刊：
影响因子：
--
通讯作者：
A. Powell
中科院分区：
文献类型：
--
作者：
A. Powell
本文指出，圆形张力膜上的会聚波在焦点处发生−π/2相移，从根本上影响随后的波型。考虑了膜在除固定周长附近以外的其他地方均匀位移的情况。从简正波的解出发，导出了一个纯周期的行波近似(有效r/RHilbert=0.7，r/R=无量纲半径)：运动的周期为8r/c(c=波速)，其中一半的周期被作为初始阶跃波的类脉冲(有限)≳变换的波占据。对于r/R≳0.2时，更好的近似使用了级数解的精化第一项。通过Rayleigh的类比，这一结果可以直接应用于由于均匀超音速圆形喷流轻微过度膨胀或膨胀不足而引起的空间压力摄动。然后，第一个正弦变化项对应于Prandtl的单元长度，其余所有项都显式地描述熟悉的钻石p。
It is pointed out that a convergent wave on a circular taut membrane undergoes a −π/2 phase shift at the focus that radically affects the ensuing pattern of waves. The case of a membrane initially uniformly displaced everywhere except close to the fixed perimeter is considered. From the normal modes solution, a purely periodic approximation (valid r/R≳0.7, r/R=nondimensional radius) in terms of traveling waves is derived: The motion has a period of 8R/c (c=wave speed), half of the period being taken up by waves that are the impulselike (finite) Hilbert transforms of the initial step wave. A better approximation valid for r/R≳0.2 uses a refined first term of the series solution. By Rayleigh’s analogy, the result can be applied directly to the spacewise pressure perturbation due to slight over‐ or underexpansion of an otherwise uniform supersonic circular jet. The first, sinusoidally varying, term then corresponds to Prandtl’s cell length, all the remaining terms explicitly describing the familiar diamond p...