{'fraction_non_alphanumeric': 0.013636363636363636, 'fraction_numerical': 0.0, 'mean_word_length': 5.592814371257485, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Low Frequency Beating Instability in a Rijke Burner and its Active Control

A special pattern of thermoacoustic oscillation has been observed in a Rijke burner. The acoustic pressure histories show obvious amplitude modulation at very low frequencies, namely beating instability. Accompanied with the amplitude modulation, the porous-plug stabilized flame also shows low frequency pulsations. This beating can be caused by the interaction of flame dynamics at different time scales. Accordingly, dynamic models of a ceramics stabilized flat flame are developed at two distinctive time scales and embedded in an acoustic network system. Simulation results show that low frequency flame temperature pulsation can lead to obvious amplitude modulation. Furthermore, aiming to suppress the beating instability with active control, the effects of amplitude modulation on thermoacoustic oscillation control have been studied. A phase shift controller and a phase lag compensator are tested, and the simulation results illustrate the challenge that may be encountered in the control of beating instabilities.