Title: Natural frequency for exponential shaped thermoacoustic resonator

Author(s): FENG Heying; PENG Yehui; JIANG Lingli; LI Xuejun

Affiliation(s): Hunan Provincial Key Laboratory of Health Maintenance for Mechanical Equipment, Hunan University of Science and Technology; et al.

Abstract: The two-dimensional nonlinear acoustic field of eleven exponential shaped resonators was simulated with a computational fluid dynamics software Fluent. The influence of driving frequency and driving intensity on pressure in resonator as well as its natural frequency was investigated. The relationship between natural frequency and theoretical calculation resonance frequency was also explored. It is found that beating phenomena can be observed in the resonator when the driving frequency deviates from the natural frequency. Moreover, the natural frequency of resonator increases with the increasing of driving intensity, which shows a hard spring effect. However, the driving intensity plays little effect on natural frequency and the natural frequencies are smaller than the theoretical calculation values in any driving intensity. Meanwhile, a formula between the natural frequency and its first-order resonance frequency from theoretical calculation was obtained by linear fitting for all these exponential shaped resonators under consideration. It is also found that the highest pressure amplitude and highest pressure ratio can be obtained from the exponential shaped resonator of m=2.8 under the same driving intensity. Moreover, the relation between natural frequency and the theoretical resonance frequency for m=2.8-tube is slightly different from other tubes in consideration.