工业燃气轮机的轴向分级燃烧技术显著拓宽了功率调节比，并有效降低了NOX污染物排放。然而，二级喷嘴的相关参数对燃烧不稳定性的影响仍需深入研究。为此，本文建立了一个三维理论分析模型，来考虑多热源与穿孔板阻抗边界的耦合作用，以此分析分级燃烧对燃烧不稳定性的影响及声衬的控制机理。研究结果表明，一级喷嘴的热源响应对轴向一阶模态影响显著，而二级喷嘴的相关参数主要影响周向一阶模态。此外，当二级喷嘴位于轴向一阶模态的声压反节点，即燃烧室进出口附近时，对频率和增长率的影响更加明显。当两个二级喷嘴的周向角度差为π/2时，其热源响应对周向一阶分裂模态的综合影响相对微弱；而当周向角度差为π时，二级喷嘴的热源响应对周向一阶分裂模态的综合影响较为显著。此外，二级喷嘴的存在导致周向一阶模态出现轴向声压分布，从而使声衬在接近二级喷嘴的轴向位置能够有效抑制燃烧不稳定性。

The axial staging combustion for industrial gas turbines significantly widens the power regulation range and effectively reduces NOX emissions. However, the impact of secondary nozzle parameters on the combustion instability requires further investigation. To address this, a three-dimensional theoretical model is developed to consider the coupling of multiple nozzles with the perforated plate, analyzing the effects of axial staging combustion on combustion instability and the control mechanisms of the perforated liner. Results show that the flame response of the primary nozzle has a notable effect on the first-order axial modes, while the parameters of the secondary nozzle mainly affect the first-order azimuthal modes. Furthermore, when the secondary nozzle is located at the acoustic pressure antinode of the first-order axial mode, i.e., near the inlet and outlet of the combustion chamber, the effects on frequency and growth rate become more pronounced. When the circumferential angular difference between the two secondary nozzles is π/2, the combined effects of their flame responses on the nondegenerate azimuthal modes are relatively weak. In contrast, when the circumferential angular difference is π, the combined effects of the the secondary nozzles’ flame responses on the nondegenerate azimuthal modes become more significant. In addition, the presence of the secondary nozzles leads to an axial sound pressure distribution for the first-order azimuthal mode, allowing the perforated liner positioned close to the secondary nozzle to effectively suppress the combustion instability.