ON SOUND GENERATED AERODYNAMICALLY .1. GENERAL THEORY
ON SOUND GENERATED AERODYNAMICALLY .1. GENERAL THEORY
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DOI：
10.1098/rspa.1952.0060
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发表时间：
1952-01-01
影响因子：
--
通讯作者：
LIGHTHILL, MJ
中科院分区：
文献类型：
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作者：
LIGHTHILL, MJ
在气体运动方程的基础上提出了一种理论，用于估计具有刚性边界的流体辐射的声音，由于不稳定，流体流动包含规则的涨落或湍流。声场是由单位体积瞬时强度为ρvivj+pij-A20ρδij的声学四极子静态分布所产生的声场，其中ρ是密度，通过速度向量pij是压缩应力张量，以及流外的声速。在许多情况下，该四极强度密度可以近似为ρ0vivj。用延迟势解的方法推导出辐射场。在它中，强度主要取决于四极杆的频率和强度，结果是与流动中典型速度U的高功率成比例增加，接近八分之一。从物理上讲，能量从动能到声能的转换机制是基于固定表面上的动量流的涨落，在§2中解释了这是如何解释这一过程的相对低效和U的效率提高的原因。在§7中显示了如何提高效率，特别是对于向前发出的声音，在马赫数为不可忽略的波动的情况下。
A theory is initiated, based on the equations of motion of a gas, for the purpose of estimating the sound radiated from a fluid flow, with rigid boundaries, which as a result of instability contains regular fluctuations or turbulence. The sound field is that which would be produced by a static distribution of acoustic quadrupoles whose instantaneous strength per unit volume isρvivj+pij-a20ρδij, whereρis the density,vithe velocity vector,pijthe compressive stress tensor, anda0the velocity of sound outside the flow. This quadrupole strength density may be approximated in many cases asρ0vivj. The radiation field is deduced by means of retarded potential solutions. In it, the intensity depends crucially on the frequency as well as on the strength of the quadrupoles, and as a result increases in proportion to a high power, near the eighth, of a typical velocityUin the flow. Physically, the mechanism of conversion of energy from kinetic to acoustic is based on fluctuations in the flow of momentum across fixed surfaces, and it is explained in § 2 how this accounts both for the relative inefficiency of the process and for the increase of efficiency withU. It is shown in § 7 how the efficiency is also increased, particularly for the sound emitted forwards, in the case of fluctuations convected at a not negligible Mach number.