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In order to analyze the thermo-acoustic instability in combustion chamber, an unsteady heat release rate model is established, which is based on the linear analysis of chemical reaction kinetics. In this model, the fluctuation of heat release rate is determined by the fluctuation of fuel mass fraction, density, temperature and pressure, and influenced by both the convection of flow and propagation of acoustic wave. To verify this model, the unsteady heat release rate of premixed swirling flame and staged flame are calculated respectively, and compared with the experimental data. It is demonstrated that the transport velocity is the key parameter affecting the heat release rate fluctuation. Subsequently, the heat release rate model is employed to analyse the thermoacoustic instability of the annular combustor. The growth rate of the characteristic frequency of the combustor is obtained by analytically solving multi-dimensional acoustic wave equation in the frequency domain. The solution is used as the basis for determination of the self-excited thermoacoustic instability of the combustor. The results predicted by this model are compared with the results obtained by high fidelity numerical method such as large-eddy simulation. The comparison show that three types of self-excited oscillation frequencies corresponding to the first-order circumferential, first-order longitudinal and first-order circumferential and longitudinal mixed modes of the combustor, can be properly predicted by this model. INTRODUCTION Combustion instability occurs in lean fuel combustion chambers such as civil aviation engines and gas turbines which can cause severe damage to combustor components (Lieuwen, 2005). The mechanism of its inception is due to the acoustic field fluctuation, induced by unsteady combustion, interacting with the combustion flame. If the acoustic fluctuation and heat release rate oscillation occur inphase, the continuous increase of the amplitude of pressure and heat release fluctuation will be initiated, and more intense combustion fluctuations will be introduced, as well as many other undesirable transient combustion phenomena such as flame blowout, flash back and increased emissions. At present the widely used prediction method of combustion instability is based on a linearized small disturbance theory to analyze the growth rate of acoustic pressure in a combustion chamber. The method takes the whole combustion chamber as the research object and the unsteady heat release rate is coupled into the control equation of acoustic field as the source term. The growth rate of the corresponding frequency is obtained by calculating the eigenvalue of the control equation and it is possible to estimate the development trend of the acoustic pressure fluctuation amplitude at this frequency. If the amplitude of the pressure fluctuation increases continuously, it means that the combustion instability has been triggered in the combustion chamber. Although the unsteady heat release in the combustor is influenced by multiple physical factors such as the geometry, boundary conditions, thermal dynamics, and the acoustic pressure modes, the perturbed heat release is usually correlated to the acoustic fluctuation of the combustor in the calculation for the purpose of introducing no new unknown variables. The unsteady heat release fluctuation source term is coupled with the pressure (or velocity) fluctuation, which is called the flame transfer function (Stow and Dowling, 2001), is the core of the model for combustion instability prediction and determines the accuracy of prediction results. The flame transfer functions used currently can be roughly divided into two categories, one based on global or lumped heat release analysis (Crocco and Cheng, 1956; Dowling, 1995; Stow and Dowling, 2001; Dowling and Stow, 2003; Mongia et al., 2003; Evesque and Polifke, 2003; Ecksteom and Sattelmayer, 2006; Temme et al. 2014; Yoon, 2017), the other based on specific flame morphology (Park et al., 2002; Lieuwen, 2003; Schuller et al., 2003; You et al., 2005; Huang et al., 2006; Huang and Yang, 2009; Palies, 2011; Candel et al. 2014; Magina et al., 2015; Magina and Lieuwen, 2016; Rani V, and Rani S, 2018; Li et al., 2018; Yao and Zhu, 2012). A typical global heat release model is

Numerical Analysis of Combustion Instability in Annular Combustion Chamber with Spatially Distributed Heat Release Rate Model