Rijke管热声振荡的稳定性切换行为研究  

Stability switching behavior of thermoacoustic oscillation in Rijke tube

作　　者：党南南 张正元 张家忠[1] Dang Nan-Nan;Zhang Zheng-Yuan;Zhang Jia-Zhong(School of Energy and Power Engineering, Xi＇an Jiaotong University, Xi＇an 710049, China)

机构地区：[1]西安交通大学能源与动力工程学院,西安710049

出　　处：《物理学报》2018年第13期318-327,共10页Acta Physica Sinica

基　　金：国家重点基础研究发展计划(批准号:2012CB026002);国家自然科学基金(批准号:51775437);陕西省重点研发计划(批准号:2017ZDCXL-GY-02-02)资助的课题~~

摘　　要：采用数值方法模拟了强弱两种阻尼条件下传热迟滞时间对一维Rijke管热声系统稳定性的影响,发现Rijke管系统存在稳定性切换现象.在推导了无量纲形式的管内声波动量方程和能量方程之后,利用Galerkin方法对控制方程进行展开并在时间域内数值求解.分析了强阻尼和弱阻尼条件下,给定热源的Rijke管热声振荡的稳定性与传热迟滞时间的关系.结果显示:在两类阻尼条件下,持续增大传热与速度的迟滞时间,系统均呈现出稳定性切换现象,即系统在稳定和不稳定两个状态间持续转变;但弱阻尼系统的不稳定区域宽于强阻尼系统的不稳定区域,系统最大振幅相对增大,且系统热声振荡的主模态在不同模态之间发生转换.最后,通过求解系统各阶模态极限环幅值随传热迟滞时间的变化,发现Rijke管热声振荡稳定性切换现象与迟滞时间存在近似周期性关系.Large-amplitude self-excited thermoacoustic oscillations arising due to the interaction between unsteady heat release and acoustic pressure fluctuations have been encountered in many thermal devices. These oscillations may lead to unwanted structural vibrations and efficiency reduction while emitting loud noises, and thus the predicting of such oscillations is very important. Physically, oscillation is a kind of instability, so stability analysis can be applied to understanding such a phenomenon. The present work focuses on the role of time delay between unsteady heat release and flow perturbation in the stability of thermoacoustic system. To this end, one-dimensional Rijke tube model with both open ends is numerically investigated. In the Rijke tube model, an electric heater is located at the first quarter of the Rijke tube and its unsteady heat release rate is modeled by an empirical model proposed by Heckl. Non-dimensional momentum equation and energy equation of the acoustic perturbation are derived and solved in time domain by using the Galerkin technique. The time evolution of the thermoacoustic oscillations with continuous increase in the time delay is calculated in two different acoustic damping cases, namely the heavily damped case and the weakly damped case, while other parameters are fixed. It is found that in both the heavily damped case and the weakly damped case, the system stability switches between stability and instability as the time delay increases, which is called stability switching and is a typical nonlinear phenomenon in a delay-dependent system. However, compared with in the heavily damped case, in the weakly damped case, the stability region is enlarged and the amplitude of the limit cycle oscillation is increased.Besides, in the weakly damped system, the dominating mode of system shifts in the first three modes instead of keeping in the first mode during increasing the time delay, which suggests that for the weakly damped system, the higher modes cannot be neglected and the system cannot

关 键 词：热声振荡 RIJKE管 稳定性切换 

分 类 号：O551.3[理学—热学与物质分子运动论]