基于支持向量回归模型的弹用冲压发动机性能预测及优化

doi:10.12382/bgxb.2022.0493

摘要/Abstract

摘要：

为提高弹用固体燃料冲压发动机的工作性能和优化设计效率,提出一种与弹内有限空间适配的发动机性能预测及优化方法。采用带转捩的剪切应力输运和涡概念耗散方程,建立其内弹道计算模型,获得流场结构与性能参数;在此基础上,基于支持向量回归方法构建了发动机性能参数的预测模型,并结合改进非支配排序遗传算法对发动机结构进行优化。研究结果表明:新建立的内弹道计算模型,可较好地模拟发动机内燃烧与流动过程;构建的预测模型可靠性较高,与高可信度模型相比,最大相对误差小于3%;发动机结构优化后,燃烧室缩短了13.88%,补燃室增长了13.50%,燃烧效率、推力和比冲分别提高12.02%、24.22%、20.28%。

关键词: 固体燃料冲压发动机, 代理模型, 多目标优化模型, 性能预测

Abstract:

To improve the working performance of solid fuel ramjet for projectiles and shorten the optimization period, the transitionshear stress transfer and vortex concept dissipation equations are used to establish an internal ballistic calculation model, and the flow field and performance parameters are obtained. Then, based on the support vector regression method,a prediction model of the performance parameters is built, and the ramjet structure is optimized using the NSGA-Ⅱ algorithm. The results show that the internal ballistic calculation model can simulate the combustion and flow process in the ramjet well. At the same time, the constructed prediction model has high reliability, and the maximum relative error is less than 3% compared with that of the high-confidence model. After the ramjet is optimized, the combustion chamber is shortened by 13.88%, the aft mixing chamber is increased by 13.50%, and the combustion efficiency, thrust and specific impulse are increased by 12.02%,24.22% and 20.28%, respectively.

Key words: solid fuel ramjet, surrogate model, multi-objective optimization model, performance prediction

中图分类号:

张宁, 史金光, 王中原, 赵新新. 基于支持向量回归模型的弹用冲压发动机性能预测及优化[J]. 兵工学报, 2023, 44(10): 2944-2953.

ZHANG Ning, SHI Jinguang, WANG Zhongyuan, ZHAO Xinxin. Performance Prediction and Optimization of Ramjet for Projectiles Using Support Vector Regression Model[J]. Acta Armamentarii, 2023, 44(10): 2944-2953.

图/表 20

图1 弹用冲压发动机几何模型

Fig.1 Structure of SFRJ for projectile

图2 冲压发动机网格

Fig.2 Meshing of simulation cases

表1 HTPB主要物性参数[20]

Table 1 Main parameters of HTPB[20]

参数	数值
ρ/(kg·m^-3)	930
A/(m·s^-1)	3.964 (T<722K) 0.011(T>722K)
E_a/(J·mol^-1)	55803(T<722K) 20523(T>722K)

表2 C4H6主要物性参数

Table 2 Main parameters of C4H6

参数	数值
密度/(kg·m^-3)	612
标准生成焓/(J·mol^-1)	110000
标准熵/(J·mol^-1·K^-1)	278.78
标准热容/(J·mol^-1·K^-1)	79.88
燃烧热/(J·mol^-1)	-2541490

表3 网格收敛性分析

Table 3 Grid convergence analysis

网格数/10⁴	F/N	η/%	$r ·$ 平均值/(mm·s^-1)
14	253.27	79.17	0.6664
21	328.45	80.77	0.6847
32	383.06	84.26	0.7484
48	402.51	85.15	0.7598
72	412.83	86.31	0.7740
108	414.00	87.15	0.7795

表3 网格收敛性分析

Table 3 Grid convergence analysis

网格数/10⁴	F/N	η/%	$r ·$ 平均值/(mm·s^-1)
14	253.27	79.17	0.6664
21	328.45	80.77	0.6847
32	383.06	84.26	0.7484
48	402.51	85.15	0.7598
72	412.83	86.31	0.7740
108	414.00	87.15	0.7795

图3 冲压发动机优化流程

Fig.3 Optimization workflow of theramjet

图4 冲压发动机几何模型

Fig.4 Geometric model of the ramjet

图5 带有罚函数的NSGA-Ⅱ流程

Fig.5 NSGA-Ⅱ flow witha penalty function

图6 燃烧室中心轴向速度

Fig.6 Mean axial velocity alongthe combustor centerline

表4 计算结果与实验结果的对比

Table 4 Comparison between the calculated results and experimental results

算例	条件		结果
算例	流量/ (kg·m^-2·s^-1)	温度/ K	$r · ¯ r e f$ / (mm·s^-1)	$r · ¯ c a l$ / (mm·s^-1)
1	0.293	624	0.576	0.583
2	0.308	615	0.578	0.589

表4 计算结果与实验结果的对比

Table 4 Comparison between the calculated results and experimental results

算例	条件		结果
算例	流量/ (kg·m^-2·s^-1)	温度/ K	$r · ¯ r e f$ / (mm·s^-1)	$r · ¯ c a l$ / (mm·s^-1)
1	0.293	624	0.576	0.583
2	0.308	615	0.578	0.589

图7 预测值与计算值对比

Fig.7 Comparison between predicted and calculated values

图8 冲压发动机多目标优化设计的帕累托解集

Fig.8 Pareto solution set for multi-objective optimization design

图9 λ=1时优化后的冲压发动机结构

Fig.9 Optimizedramjet shape when λ=1

表5 优化后发动机结构参数

Table 5 Structural parameters of the optimized ramjet

结构	参数值/mm	变化量/%
l_c	212.72	-13.88
h_c	24.00	20.00
d_m	41.67	-16.67
l_m	306.45	13.50
h_p	8.40	-30.00
d_r	15.18	-15.67
l_s	34.68	-7.96
d_out	23.55	13.49
l_e	19.98	-5.33

图10 发动机中C4H6的质量分数

Fig.10 C4H6 mass fraction of the ramjet

图11 发动机中O2的质量分数

Fig.11 O2 mass fraction of the ramjet

图12 初始冲压发动机的温度和流线图

Fig.12 Temperaturecontour and streamline of the initial ramjet

图13 优化后冲压发动机的温度和流线图

Fig.13 Temperature contour and streamline of the optimized ramjet

图14 燃速沿轴向分布情况

Fig.14 Regression rate along grain surface

表6 优化前后发动机性能指标

Table 6 Performance of the ramjet

性能指标	优化前	优化后
$r · ¯$ /(mm·s^-1)	0.774	0.822
$m · b$ /(kg·s^-1)	0.041	0.043
F/N	412.83	512.82
I/(N·s·kg^-1)	999.68	1107.81
η/%	86.31	98.33

表6 优化前后发动机性能指标

Table 6 Performance of the ramjet

性能指标	优化前	优化后
$r · ¯$ /(mm·s^-1)	0.774	0.822
$m · b$ /(kg·s^-1)	0.041	0.043
F/N	412.83	512.82
I/(N·s·kg^-1)	999.68	1107.81
η/%	86.31	98.33

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