中文摘要：

采用计算流体力学软件Fluent模拟研究了11种不同形状参数的指数型热声谐振管内二维非线性声场特性，分析了驱动频率和驱动强度对管内声压演化过程及固有频率的影响，并探索了指数管的固有频率与理论计算谐频之间的关系。研究发现：当驱动频率偏离谐振管固有频率时，管内将出现明显的“拍”现象；指数管的固有频率随驱动强度的增加而增加，呈现硬弹簧效应，但驱动强度对固有频率的影响较小并且在任何驱动下指数管的固有频率均小于理论计算谐频。针对所研究的指数型管，获得了其固有频率与理论计算谐频之间的关系式。结果表明，相同驱动下，形状参数m值约等于2．8的指数管所能获得的压力幅值及压比最大，且m=2．8指数管的固有频率与理论计算谐频之间的关系式与其他管型略有不同。

英文摘要：

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.