黎开管振荡的简单理论
Simple theory of Rijke tube oscillation
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摘要: 根据瑞利定性解释的黎开管振荡的机理,推出了黎开管的波动方程,并取得了严格解。基本要领是把黎开管看做两端开口的均匀管,其中有一点的温度较高。冷空气进入后,通过热点,密度突变,成为声源。据此列出的波动方程可严格求解,并求得黎开管振荡的特性。首先黎开管是反馈系统。热点在其节点或腹点部不发生反馈,也不产生振荡,热点位置决定有无反馈。黎开管振荡必须有气流,所产生的质点速度与气流平均速度成正比。热点温度决定反馈大小.温度低时,反馈基本不影响质点速度的大小,它小于平均速度,并和温度成正比。温度高时,反馈迅速增加。在另一方面,在刚加上温度或气流时,振荡的建立要靠反馈逐渐积累,所以很缓慢。但气流停止后,振荡立刻停止,与室内声场的建立和混响完全不同。如果用阀门或盖板在管的一端控制气流时,发声很有特色。Abstract: A Simple theory of Rijke tube oscillation is presented based on mathematical realization of Rayleigh's qualitative explanation of the mechanism of Rijke tube. This is done assuming a single point of high temperature in an otherwise uniform tube and the sound source produced when cold air flows passing this point. The wave equation thus obtained is then rigorously solved, It is found that the Rijke tube oscillation is a feedback system. There is no feeback nor oscillation when the hot spot is at a node or antinode in the tube. The mean flow is necessary for the oscillation, the particle velocity of which is proportional to the mean velocity, and the ratio is proportional to the gauze temperature when the later is low and the feedback does not effect much the magnitude of the particle velocity. When the temperature is high, the feedback increases rapidly. Otherwise the growth is rather slow, when the mean flow or high temperature is first applied. The oscillations stop immediately when the mean flow is stopped. If the mean flow is controlled by a valve or a paddle at one end of the tube, an interesting sound is controlled by a valve or a paddle at one end of the tube, an interesting sound produced.