Natural frequency for exponential shaped thermoacoustic resonator

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 studied. 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 frequencies deviate from the natural frequency. Moreover, the natural frequency of resonator increased with the increasing of driving intensity, which showed a hard spring effect. However, the driving intensity play 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 revealed for all these exponential shaped resonators in 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 formula between natural frequency and the theoretical calculation resonance frequency for the tube of m=2.8 is slightly different from others tubes in consideration.