Stability Of Thermoacoustic System With Time-delay

Large-amplitude self-exited thermoacoustic oscillations are unwanted in many premixed propulsion systems,such as rocket motors and aeroengines.Thus,predicting the stability behaviors of such system and a better understanding of the instability mechanism are important.Acting feedback controls on instability systems has the important project value.However,the problems of time-delay tin feedback controls come out.In this paper,the stability of SDOF and two DOFs thermoacoustic systems is investigated theoretically and numerically.The coupling between the unsteady heat release and oncoming flow disturbance is characterized by using interaction index-delay H-? model.By using the expansion of the Galerkin series to convert infinite dimensional systems to finite dimensional systems,the thermoacoustic system is described mathematically by DDE.Firstly,the thermoacoustic phenomena and the instability mechanism are discussed in this paper.Based on the conclusions of thermoacoustic instability,this paper puts forward realistic assumptions.Furthermore,the physical model of thermoacoustic system is introduced,and the energy equations of sound pressure and boundary conditions are given,which provides a theoretical basis for the stability of thermoacoustic system with time delay.Secondly,the effects of time-delay τ,acoustic loss ξ and combustion-flow interaction index H on the stability behaviors of the SDOF thermoacoustic system are researched.It is found that there are two stability regions: delay-independent region and stability switches region.If the thermoacoustic system is in the stability switches region,a continuous increase in the time-delay can lead to stability switches between stability and instability.By solving the structure of boundary solution of system parameters and drawing the three-dimensional figures,rich dynamical behaviors are described.Finally,the time-delay dynamical behaviors of a two DOFs thermoacoustic system are investigated.By giving boundary conditions of stability switches and calling the MATLAB-based package DDE-BIFTOOL,the theoretical results are verified.By comparison with the SDOF thermoacoustic system,the richer time-delay dynamical behaviors in the two DOFs thermoacoustic system are given.The results and analysis in this paper can provide some reference to the future studies on time-delay dynamical behaviors in thermoacoustic systems and the design of combustion chamber in engines,superchargers and industrial boilers.