基于正交试验的固体火箭超燃冲压发动机优化设计

doi:10.12382/bgxb.2024.0820

摘要/Abstract

摘要：

为研究固体火箭超燃冲压发动机中硼颗粒点火和燃烧特性以及补燃室结构对发动机燃烧性能的影响,编写表征硼颗粒点火和燃烧过程的用户自定义程序,分析超燃冲压发动机中凝相颗粒的燃烧释能动态特征。基于正交设计试验方法,分别从颗粒特征参数和发动机结构角度出发,分析硼颗粒粒径、燃气入射角和凹腔深度以及两两之间交互作用对发动机燃烧效率的影响规律。研究结果表明:通过极差和方差分析,各因素对发动机燃烧效率影响大小排序为硼颗粒粒径>粒径与燃气入射角度的交互作用>燃气入射角>凹腔深度>燃气入射角和凹腔深度的交互作用>粒径与凹腔深度的交互作用,最终确定的最优组合燃烧效率达77.01%;硼颗粒粒径对于固体火箭冲压发动机燃烧效率具有高度显著影响,粒径与燃气入射角的交互作用的影响不容忽视。

关键词: 固体火箭超燃冲压发动机, 硼颗粒, 正交设计, 交互作用, 燃烧效率

Abstract:

The effects of the ignition and combustion characteristics of boron particles in a solid rocket scramjet engine and the combustor structure on the combustion performance of engine are studied.A user-defined function program for characterizing the ignition and combustion processes of boron particles is written,and the dynamic characteristics of combustion energy release of condensed-phase particles in a ramjet is analyzed.Furthermore,based on the orthogonal design experimental method,the effects of boron particle size,gas injection angle and cavity depth,as well as their interactions on engine combustion efficiency are analyzed from the perspectives of particle characteristics and engine structure.Through range and variance analyses,the results indicate that the factors influencing the engine combustion efficiency are ranked as follows:boron particle size > interaction between particle size and gas injection angle > gas injection angle > cavity depth > interaction between gas injection angle and cavity depth > interaction between particle size and cavity depth.The optimal combination achieves a combustion efficiency of 77.01%.The boron particle size has a significant effect on the combustion efficiency of solid rocket scramjet engine,and the interaction between particle size and gas injection angle cannot be ignored.

Key words: solid rocket scramjet engine, boron particle, orthogonal design, interaction, combustion efficiency

冯滢, 付文娟, 胡振坤, 唐勇, 赵马杰, 石保禄. 基于正交试验的固体火箭超燃冲压发动机优化设计[J]. 兵工学报, 2025, 46(9): 240820-.

FENG Ying, FU Wenjuan, HU Zhenkun, TANG Yong, ZHAO Majie, SHI Baolu. Optimization Design of Solid Rocket Scramjet Engine Based on Orthogonal Experiments[J]. Acta Armamentarii, 2025, 46(9): 240820-.

图/表 24

图1 基于正交试验的固冲发动机燃烧效率影响因素分析方法

Fig.1 Analysis method of factors influencing combustion efficiency in solid rocket scramjet engine based on orthogonal experiment

图2 气固两相数值模拟迭代过程

Fig.2 Iterative process for gas-solid two-phase numerical simulation

表1 气相化学反应机理

Table 1 Gas-phase chemical reaction mechanism

`化学反应	A/(m³·kmol^-1·s^-1)	E/(J·kmol^-1)
2CO+O₂→2CO₂	2.239×10¹²	1.7×10⁸
2H₂+O₂→2H₂O	9.87×10⁸	3.1×10⁷
2B₂O₂+O₂→2B₂O₃	1.1×10¹²	1.0×10⁸

表2 碳颗粒表面化学反应机理

Table 2 Surface chemical reaction mechanism of carbon particles

化学反应	A/(kg·m^-2·s^-1·Pa^-1)	E/(J·kmol^-1)	B
C+O₂→2CO	0.86	1.0495×10⁸	0

表3 硼颗粒非均相化学反应机理

Table 3 Heterogeneous chemical reaction mechanism of boron particles

过程	反应速率	反应机理
点火过程	R₁	2/3B(s)+2/3B₂O₃(l)→B₂O₂(g)
	R₂	B₂O₃(l)→B₂O₃(g)
	R₃	B(s)+O₂(g)→BO₂(g)
	R₄	2/3B(s)+2/3B₂O₃(l)+H₂O(g)+ 1/2O₂(g)→2HBO₂(g)
	R₅	B₂O₃(l)+H₂O(g)→2HBO₂(g)
燃烧过程	R₆	2B(s)+O₂(g)→B₂O₂(g)
	R₇	2B(s)+2/3O₂(g)+H₂O(g)→2HBO₂(g)
	R₈	B(l)→B(g)(蒸发)
	R₉	B(l)→B(g)(沸腾)

图3 固体火箭超燃冲压发动机验证模型示意图

Fig.3 Schematic diagram of the verification model for the solid rocket scramjet engine

表4 燃气组分质量分数

Table 4 Mass fraction of gas components

组分	CO	H₂	MgCl₂	N₂
质量分数	0.4063	0.1325	0.3688	0.0924

图4 不同网格数量的补燃室出口截面处中心线压力分布

Fig.4 Centerline pressure distribution at the combustor exit cross-section for different grid quantities

图5 沿程壁面压力对比

Fig.5 Comparison diagram of wall pressure along the length

图6 固体火箭超燃冲压发动机构型示意图[21]

Fig.6 Schematic diagram of the solid rocket scramjet engine[21]

表5 因素水平表

Table 5 Factor level table

编号	因素	水平
编号	因素	1	2	3
A	颗粒粒径/μm	3	6	9
B	燃气入射角/(°)	45	90	135
C	凹腔深度/mm	10	20	30

表6 L27(313)正交设计表

Table 6 L27(313) orthogonal design table

试验号	1	2	3	4	5	6	7	8	9	10	11	12	13
试验号	A	B	A×B	A×B	C	A×C	A×C	B×C			B×C
1	1	1	1	1	1	1	1	1	1	1	1	1	1
2	1	1	1	1	2	2	2	2	2	2	2	2	2
3	1	1	1	1	3	3	3	3	3	3	3	3	3
4	1	2	2	2	1	1	1	2	2	2	3	3	3
5	1	2	2	2	2	2	2	3	3	3	1	1	1
6	1	2	2	2	3	3	3	1	1	1	2	2	2
7	1	3	3	3	1	1	1	3	3	3	2	2	2
8	1	3	3	3	2	2	2	1	1	1	3	3	3
9	1	3	3	3	3	3	3	2	2	2	1	1	1
10	2	1	2	3	1	2	3	1	2	3	1	2	3
11	2	1	2	3	2	3	1	2	3	1	2	3	1
12	2	1	2	3	3	1	2	3	1	2	3	1	2
13	2	2	3	1	1	2	3	2	3	1	3	1	2
14	2	2	3	1	2	3	1	3	1	2	1	2	3
15	2	2	3	1	3	1	2	1	2	3	2	3	1
16	2	3	1	2	1	2	3	3	1	2	2	3	1
17	2	3	1	2	2	3	1	1	2	3	3	1	2
18	2	3	1	2	3	1	2	2	3	1	1	2	3
19	3	1	3	2	1	3	2	1	3	2	1	3	2
20	3	1	3	2	2	1	3	2	1	3	2	1	3
21	3	1	3	2	3	2	1	3	2	1	3	2	1
22	3	2	1	3	1	3	2	2	1	3	3	2	1
23	3	2	1	3	2	1	3	3	2	1	1	3	2
24	3	2	1	3	3	2	1	1	3	2	2	1	3
25	3	3	2	1	1	3	2	3	2	1	2	1	3
26	3	3	2	1	2	1	3	1	3	2	3	2	1
27	3	3	2	1	3	2	1	2	1	3	1	3	2

表7 试验结果

Table 7 Test results

试验号	η_B/%	η_C/%	η_t/%
1	61.46	99.37	72.30
2	62.42	99.56	73.04
3	58.22	99.60	70.05
4	67.80	100.00	77.01
5	67.79	100.00	77.00
6	67.23	100.00	76.60
7	60.90	99.12	71.83
8	60.75	99.28	71.77
9	62.10	95.50	72.79
10	45.89	100.00	61.36
11	44.15	99.98	60.11
12	43.23	99.01	59.18
13	9.26	17.04	11.48
14	9.13	16.75	11.31
15	9.00	16.40	11.12
16	29.73	94.52	48.26
17	28.29	93.88	47.04
18	27.81	92.98	46.44
19	12.01	27.33	16.39
20	12.25	28.00	16.75
21	12.50	28.90	17.20
22	6.00	20.60	10.20
23	5.36	19.72	9.47
24	5.75	20.05	9.84
25	11.90	35.61	18.68
26	11.20	34.20	17.80
27	10.76	32.90	17.09

表8 极差分析表

Table 8 Range analysis table

参数	1	2	3	4	5	6	7	8	11
参数	A	B	A×B	A×B	C	A×C	A×C	B×C	B×C
K₁	662.39	446.38	386.64	302.87	387.51	381.9	383.73	384.22	384.15
K₂	356.3	294.03	464.83	422.69	384.29	387.04	383.82	384.91	386.23
K₃	133.42	411.7	426.55	426.55	380.31	383.17	384.56	382.98	381.73
$K ¯ 1$	73.60	49.60	42.96	33.65	43.06	42.43	42.64	42.69	42.68
$K ¯ 2$	39.59	32.67	51.65	46.97	42.70	43.00	42.65	42.77	42.91
$K ¯ 3$	14.82	45.74	47.39	47.39	42.26	42.57	42.73	42.55	42.41
R	58.77	16.93	8.69	13.74	0.80	0.57	0.09	0.21	0.50

表8 极差分析表

Table 8 Range analysis table

参数	1	2	3	4	5	6	7	8	11
参数	A	B	A×B	A×B	C	A×C	A×C	B×C	B×C
K₁	662.39	446.38	386.64	302.87	387.51	381.9	383.73	384.22	384.15
K₂	356.3	294.03	464.83	422.69	384.29	387.04	383.82	384.91	386.23
K₃	133.42	411.7	426.55	426.55	380.31	383.17	384.56	382.98	381.73
$K ¯ 1$	73.60	49.60	42.96	33.65	43.06	42.43	42.64	42.69	42.68
$K ¯ 2$	39.59	32.67	51.65	46.97	42.70	43.00	42.65	42.77	42.91
$K ¯ 3$	14.82	45.74	47.39	47.39	42.26	42.57	42.73	42.55	42.41
R	58.77	16.93	8.69	13.74	0.80	0.57	0.09	0.21	0.50

表9 方差分析表

Table 9 Analysis of variance table

方差来源、误差项和总和	变差平方和	自由度	均方	F	F_α	显著性
A	15673.18	2	7836.59	10829.63	F_0.01(2,8)=8.65	高度显著
B	1417.02	2	708.51	979.11	F_0.01(2,8)=8.65	高度显著
C	2.89	2	1.45	2.00	F_0.2(2,8)=1.98	有一定影响
A×B	2597.65	4	649.41	897.29	F_0.05(4,8)=7.01	高度显著
A×C	1.64	4	0.41	0.57	F_0.2(4,8)=1.92	无影响
B×C	1.34	4	0.33	0.46	F_0.2(4,8)=1.92	无影响
e	5.79	8	0.72
总和	19699.50	26

表10 颗粒粒径与入射角相应水平组合下的燃烧效率

Table 10 Combustion efficiency under the corresponding level combinations of particle size and injection angle

组合	燃烧效率平均值/%
A1B1	71.80
A1B2	76.87
A1B3	72.13

图7 不同燃气入射角下马赫数云图

Fig.7 Mach number contour plot under different gas injection angles

图8 不同燃气入射角下温度云图

Fig.8 Temperature contour plots under different gas injection angles

图9 不同燃气入射角下的局部温度和流线云图

Fig.9 Local temperature and streamline contour plots under different gas injection angles

图10 不同燃气入射角下B2O3质量分数云图

Fig.10 Mass fraction contour plots of B2O3 under different gas injection angles

表11 不同入射角下硼颗粒氧化层厚度分布

Table 11 Distribution of boron particle oxide layer thickness under different injection angles

燃气入射角/(°)	粒径/μm
燃气入射角/(°)
45
90
135

表12 不同入射角下硼颗粒粒径分布

Table 12 Distribution of boron particle size under different injection angles

燃气入射角/(°)	粒径/μm
燃气入射角/(°)
45
90
135

表13 不同入射角下硼颗粒温度分布

Table 13 Distribution of boron particle temperature under different injection angles

燃气入射角/(°)	粒径/μm
燃气入射角/(°)
45
90
135

表14 颗粒粒径与入射角相应水平组合下的滞留时间和燃烧效率

Table 14 Residence time and combustion efficiency at corresponding levels of particle size and injection angle

硼颗粒粒径/μm	入射角/ (°)	硼颗粒滞留时间/ms	碳颗粒滞留时间/ms	η_t/%
3	45	1.35	1.34	72.30
	90	1.38	1.31	77.01
	135	1.31	1.34	71.83
6	45	1.29	1.11	61.36
	90	1.07	1.10	11.48
	135	1.21	1.22	48.26
9	45	1.10	1.10	16.39
	90	1.06	1.07	10.20
	135	1.14	1.12	18.68

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