温度梯度场中声线传播路径数值研究

NUMERICAL STUDY ON THE PROPAGATION PATH OF SOUND RAY THROUGH THE TEMPERATURE GRADIENT FIELD

该文利用光学 Fermat 原理和数学变分方法,建立了三维温度梯度场中的声传播路径的数学模型,数值计算了一维轴对称和二维单峰圆对称温度梯度场中的声线传播路径,揭示了一维轴对称温度场对声传播具有“墙壁效应”,二维单峰(谷)圆对称温度场对声传播具有“透镜效应”的物理特征。根据温度梯度场中的声线弯曲事实,指出了按等温介质中的声波直线传播规律来诊断声源位置,必然会发生“蜃听”现象,导致源定位失真,并进一步对定位方法及其产生虚源的位置进行了分析,为研究炉内管道泄漏声检测及其定位技术,乃至声学测温技术中的温度场重建提供了基础研究。

By using the Fermat’s theory and the calculus of variations, a mathematic model is established for calculating the propagation paths of sound ray in three-dimension temperature gradient fields, the propagation paths of sound ray in temperature gradient fields of one dimension axial symmetry and two-dimension circular symmetry with one peak (or vale) are calculated respectively. The results reveal that there is a wall-effect in the temperature fields of one-dimension axial symmetry with a peak and a lens-effect in the temperature fields of the two-dimension circular symmetry with a peak (or a vale). The facts of sound ray deviating from straightness in the non-equality temperature fields reveal that the hearing mirage phenomena which leads to locate the distortion sources would appear if the straight-propagation law is used in non-equality temperature fields. The locating method and the distortion-source position produced by the method have been simply analyzed. This study lays a theoretic foundation for detecting the leak trace and measuring the temperature distribution in boilers by using sound method.