【摘要】 基于Matveev和Culick提出的涡脱落引起的热声不稳定性一维简化模型,对涡脱落引起的热声振荡中的典型非线性现象进行研究,着重研究了系统的初值敏感性、关键参数对热声振荡的影响规律及涡声锁频现象.首先,采用Galerkin方法将控制方程中压力和速度波动在基函数下展开,使偏微分方程组转化为一簇常微分方程;然后,数值求解得到了不同系统参数下声场的压力和速度波动,并详细分析了系统在不同初始条件下的热声不稳定性,同时研究了不同稳态流动速度对系统热声振荡的影响规律,以及在不同稳态流动速度下热声振荡过程中出现的涡声锁频现象.结果表明:该涡脱落热声振荡系统对初值极为敏感,是典型的非线性系统;随着稳态流动速度增大,压力波动的振幅总体有增大趋势,但在几个速度区间内却重复出现振幅先减小后增大的相似结构;系统最终以涡撞击频率(f_s)的整数(f_p/f_s)倍做周期振荡,呈现转数为f_p/f_s的涡声锁频,该涡声锁频可以作为周期性燃烧振荡的重要特征.更多还原

【Abstract】 In engineering, the combustion chamber with a backward step is very popular, and it is a kind of flame stabilizer. In this type of combustion chamber, there will be shedding vortices at the step due to the instability of the flow field. The shedding vortices will carry reactants to move downstream and burn, resulting in unstable heat release and then pressure and velocity fluctuations of the sound field, thereby, finally, forming a combustion-vortex-acoustic interaction process. If a positive feedback loop is formed between the unstable heat release and the pressure fluctuation of sound field, combustion instability will occur, and it is also referred to as thermoacoustic oscillation due to vortex shedding. Combustion instability frequently occurs in many practical systems or equipment, and its induced significant pressure oscillations have a serious influence on the normal operation of the equipment. Recently, the combustion instability has been extensively studied experimentally,but the theoretical investigation on its nature is still rare. Since combustion instability is a complicated nonlinear phenomenon, it is necessary to study its nature from the viewpoint of nonlinear dynamics. Based on the one-dimensional simplified model of thermoacoustic instability involving vortex shedding proposed by Matveev and Culick, the typical nonlinear phenomenon in thermoacoustic oscillation induced by vortex shedding is studied. The study focuses on the initial value sensitivity of the system, the influence of key parameters on thermoacoustic oscillation, and the phenomenon of vortex-acoustic lock-on. Firstly, the Galerkin method is used to approximate the governing equation, and the partial differential equations are reduced to a set of ordinary differential equations. Then, the first ten modes are selected, and the pressure and velocity fluctuations of sound field under different system parameters are obtained by MATLAB program. Finally, the thermoacoustic instability of the system under different initial disturbances, the influences of different steady flow velocity on the thermoacoustic oscillation of the system, and the phenomenon of vortex-acoustic lock-on in thermoacoustic oscillation are studied in detail. The results show that the system of thermoacoustic oscillation involving vortex shedding is extremely sensitive to initial values, and there are a rich variety of nonlinear phenomena. With steady flow velocity increasing, the amplitude of pressure fluctuation augments generally.However, the similar structures are found in several intervals of steady flow velocity, and the amplitude first decreases and then increases. In particular, it is verified that the system oscillates periodically by integer(f_p/f_s)multiple of the vortex impinging frequency(f_s), that is, the vortex-acoustic frequency locking with the number of revolutions f_p/f_s, which is found in experiment and can be regarded as an important characteristic of periodic thermoacoustic oscillation.更多还原