多喷嘴燃烧室三维热声不稳定性分析

doi:10.7527/S1000-6893.2025.31843

Abstract

Abstract:

Thermoacoustic instability poses a significant challenge to the operational safety and stability of multi-nozzle combustors in both aero-engines and industrial gas turbines. To achieve a comprehensive understanding and effective control of this phenomenon， this paper employs a three-dimensional Green's function method to characterize the geometric and thermal response differences among multiple nozzles， aiming to reveal the key parameters influencing three-dimensional thermoacoustic instability and the control effects of combining different types of nozzles. The study focuses on analyzing the impact of the average temperature of the combustion chamber， axial length of nozzles， and inlet boundary conditions of nozzles on the azimuthal， radial， and axial modal thermoacoustic instability. The results indicate that when the axial length of nozzles approximates an odd multiple of a quarter wavelength， the thermoacoustic instability evolves gradually； in contrast， when the length approaches an integer multiple of a half wavelength， an abrupt shift in the instability state occurs. Moreover， the inlet boundary conditions of nozzles affect the stability of thermoacoustic modes by altering the acoustic energy dissipation at the inlet and the phase difference between sound pressure and unsteady heat release rate. By leveraging the identified patterns of key parameters， adjusting the geometric structure and heat source response of some nozzles can effectively control three-dimensional unstable modes. Moreover， coordinated adjustments of multiple parameters can significantly enhance the control of first-order axial mode thermoacoustic instability across a broader parameter spectrum.

Key words: multi-nozzle combustor, thermoacoustic instability, three-dimensional theoretical model, axial length of nozzles, boundary conditions

CLC Number:

V231

Yisha HUANG, Xiaoyu WANG, Lei QIN, Guangyu ZHANG, Ronghui CHENG, Xiaofeng SUN. Three-dimensional thermoacoustic instability analysis in a multi-nozzle combustor[J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(18): 131843.

Figures/Tables 20

Fig.1

Fig.2

Table 1

Geometrical and physical parameters of the multi-nozzle combustor

参数	数值
燃烧室腔体的轴向距离 $L c$ /m	2.0
燃烧室腔体的直径 $D c$ /m	0.45
喷嘴轴向长度 $L$ /m	0.27（可变）
喷嘴径向位置 $φ$	0.6
喷嘴横截面积 $S$ /m²	0.001 2
已燃区域平均温度 $T ¯ 2$ /K	1 519.15（可变）
已燃区域平均声速 $c ¯ 2$ /（m·s^-1）	1 104.93（可变）
已燃区域平均密度 $ρ ¯ 2$ /（kg·m^-3）	1.60（可变）
已燃区域平均压力 $p ¯ 1$ /Pa	1 470 000
未燃区域平均温度 $T ¯ 1$ /K	673.15
未燃区域平均声速 $c ¯ 1$ /（m·s^-1）	575
未燃区域平均密度 $ρ ¯ 1$ /（kg·m^-3）	6.22
未燃区域平均压力 $p ¯ 1$ /Pa	1 470 000
喷嘴进口边界声压反射系数 $R$	-1（可变）
增益系数 $g$	0.5
延迟时间 $τ$ /s	可变
周向一阶模态周期 $t 100$ /s	0.000 7
径向一阶模态周期 $t 010$ /s	0.000 33
轴向一阶模态周期 $t 001$ /s	0.003 6
周向一阶模态波长 $λ 100$ /m	0.400
径向一阶模态波长 $λ 010$ /m	0.192
轴向一阶模态波长 $λ 001$ /m	2.082

Table 1

Table 2

Fig.3

Fig.4

Table 3

Absolute and relative frequency variations under different mean temperatures

模态	频率/Hz（1 341.65 K）	频率/Hz（1 416.65 K）	频率/Hz（1 519.15 K）	绝对变化 $Δ a c$ /Hz		相对变化 $Δ r c$ /%
周向一阶	1 352.83	1 390.05	1 436.38	37.22	46.33	2.75	3.33
径向一阶	2 814.11	2 891.52	2 993.96	77.41	102.44	2.75	3.54
轴向一阶	260.62	267.74	277.16	7.54	9.42	2.89	3.52

Table 3

Table 4

Absolute and relative growth rate variations under different mean temperatures

模态	增长率/s^-1（1 341.65 K）	增长率/s^-1（1 416.65 K）	增长率/s^-1（1 519.15 K）	绝对变化 $Δ a c$ /s^-1		相对变化 $Δ r c$ /%
周向一阶	0.34	0.27	0.19	0.07	0.08	20.59	29.63
径向一阶	0.25	0.41	0.75	0.16	0.34	64.00	82.93
轴向一阶	1.03	0.98	0.93	0.05	0.05	4.85	5.10

Table 4

Table 5

Values of X(T¯c) related to the first-order axial/circumferential/radial mode

模态	波数 $k m n h$	系数 $X (T ¯ c)$
周向一阶	8.18	8.30
径向一阶	17.03	29.63
轴向一阶	1.57	3.06

Table 5

Fig.5

Fig.6

Fig.7

Table 6

Calculated and theoretical values of circular diameters

模态	圆轨迹直径 $α - 1$ /s^-1	圆轨迹直径 $α 1$ /s^-1	$α - 1 / α 1$	理论比值 $B$
周向一阶	0.384	1.49	0.257 7	0.259 6
径向一阶	1.5	0.68	2.205 9	2.255 1
轴向一阶	1.86	1.98	0.939 4	0.881 8

Table 6

Fig.8

Fig.9

Fig.10

Fig.11

Fig.12

Fig.13

Fig.14

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燃烧室平均温度/K	平均声速/（m∙s^-1）	平均密度/（kg∙m^-3）
1 519.15	1 104.93	1.60
1 416.65	1 067.01	1.72
1 341.65	1 038.38	1.81

Three-dimensional thermoacoustic instability analysis in a multi-nozzle combustor

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