Self-oscillatory flow in the Hartmann resonator is numerically calculated within the framework of ideal (inviscid and non-heat-conducting) gasdynamics. The calculations are performed for the case of a sonic jet impinging on a tube varying from that with a sealed inlet (rod) to a fairly deep cavity. The spacing between the tube and the nozzle and the nozzle pressure ratio are also varied in the calculations. On the basis of the calculated results the oscillation process is described in detail and its mechanism is revealed for both shallow and deep tubes. For shallow tubes and a rod it is due to an imbalance in the flow rate and momentum between two regions in the jet that impinges on the obstacle. For deep tubes the oscillations are due to the tube filling and evacuation somewhat reminiscent of the process occurring in a one-quarter-wave resonator. In any case no signature of a feedback loop in the external acoustic field of the jet was detected. The results of the calculations are in good agreement with experimental data. The effects of mounting a lip on the tube (transition from a low- to high-frequency operation mode) and heating in the Hartmann tube are also discussed.

中文翻译：

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哈特曼谐振器中的自振荡流——数值模拟

Hartmann 谐振器中的自振荡流动是在理想（无粘性和非导热）气体动力学框架内进行数值计算的。计算是针对声波射流撞击管子的情况进行的，管子从带有密封入口（杆）的管子到相当深的空腔。管子和喷嘴之间的间距和喷嘴压力比在计算中也有所不同。在计算结果的基础上，详细描述了振荡过程，揭示了浅管和深管的振荡机制。对于浅管和杆，这是由于射流中撞击障碍物的两个区域之间的流速和动量不平衡。对于深管，振荡是由于管填充和抽空引起的，这有点让人想起四分之一波谐振器中发生的过程。在任何情况下，都没有检测到射流外部声场中反馈回路的特征。计算结果与实验数据吻合良好。还讨论了在管上安装唇缘（从低频到高频操作模式的过渡）和哈特曼管中加热的影响。