Impact of nozzle area ratio on performance of small turbojet engines
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摘要:
为了研究喷管出口面积变化对小型涡喷发动机性能的影响，选取一台某型100 daN级涡喷发动机为实验对象，探讨其在
33000 ～60000 r/min转速范围内，在恒定转速和恒定燃油流量两种工况下的响应特性。基于实验数据建立了量化发动机参数间耦合效应的数学模型并提出了优化策略。结果表明：在54000 r/min恒速工况下，当量面积比（EAR）从1.240降至0.850，可使静推力提高107%，出口排气温度（EGT）提高400 K，单位燃油消耗率（SFC）降低10.6%；在恒定燃油流量工况下，EAR减小导致转速下降14.8%，推力降低4%，EGT上升121 K， SFC增加6%。定量分析发现，当EAR为0.925时，60～80 daN推力区间内SFC达到最小值，此时燃料燃烧与气体膨胀匹配最佳；对比高EAR（1.240），低EAR（0.850～0.925）可使SFC降低10%～20%，EGT升高300 K。研究确定最佳工作区间为EAR 为0.925～1.000，对应静推力为60～80 daN、EGT为 800～950 K。该区间内SFC可降低15%～20%，静推力提升30%～40%，同时EGT保持在材料耐受范围内。该研究为无人机推进系统的自适应喷管设计和实时控制提供了参考依据。Abstract:To investigate the impact of nozzle exit area variations on small turbofan engine performance, a 100 daN-class engine across 33 000 r/min to 60 000 r/min speed range under constant speed and constant fuel flow conditions was studied. A mathematical model was developed to quantify the coupling effects between engine parameters, and an optimization strategy was proposed. The results showed that at 54 000 r/min, reducing the equivalent area ratio (EAR) from 1.240 to 0.850 increased the static thrust by 107%, raised the exhaust gas temperature (EGT) by 400 K, and decreased the specific fuel consumption (SFC) by 10.6%. Under constant fuel flow conditions, decreasing EAR led to a 14.8% reduction in speed, a 4% decrease in thrust, a 121 K increase in EGT, and a 6% rise in SFC. Analysis revealed that at EAR of 0.925, SFC was minimized within the 60—80 daN thrust range, indicating the best matching between fuel combustion and gas expansion. Compared with high EAR (1.240), operating with low EAR (0.850—0.925) reduced SFC by 10%—20%, with a 300 K increase in EGT. The optimal operating range was identified as EAR of 0.925—1.000, corresponding to static thrust of 60—80 daN and EGT of 800—950 K. In this range, SFC can be reduced by 15%—20%, static thrust increased by 30%—40%, while EGT remained within material resistance range. These findings could offer valuable insights for adaptive nozzle design and real-time control in unmanned aerial vehicle propulsion systems.
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图 2 涡喷发动机涡轮及喷管示意图
Figure 2. Schematic diagram of turbine and nozzle structure of turbojet engine
图 9 在不同当量面积比下EGT随转速变化曲线图
Figure 9. Variations of EGT with speed at different equivalent area ratios
图 10 在不同当量面积比下燃油流量与空气流量随转速变化曲线图
Figure 10. Variations of fuel flow rate and air flow rate with speed at different equivalent area ratios
图 11 压气机效率和压比随转速变化图
Figure 11. Variations in compressor efficiency and pressure ratio with increasing rotation speed
图 12 在不同当量面积比下推力随转速变化曲线图
Figure 12. Variations of static thrust with speed at different equivalent area ratios
图 13 在不同当量面积比下SFC随转速变化曲线图
Figure 13. Variation of SFC with speed at different equivalent area ratios
图 15 喷管压力与出口速度随当量面积比变化曲线图
Figure 15. Variations in nozzle pressure and outlet velocity with EAR
图 17 参数随当量面积比变化曲线图（供油量恒定）
Figure 17. Parameter variation with EAR （constant fuel supply）
表 1 某型涡喷发动机技术指标
Table 1. Technical specifications of the turbojet engine
发动机技术参数 数值 发动机转速工作区间/（r/min） 0～ 60000 额定压比 4.1 质量流量/（kg/s） 1.93 推质比 10 推力/kN 0.98 进气道总压恢复系数 0.99 压气机等熵效率 0.79 燃烧室效率 0.98 燃烧室出口温度/K 1070 燃烧室压比 0.97 涡轮效率 0.82 喷管收敛角度/（°） 12 
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表 2 各喷管出口面积参数
Table 2. Outlet area parameters of each nozzle
计算模型序号 当量面积比 实际面积/mm2 1 1.240 10527 2 1.120 9508 3 1.000 8500 4 0.925 7853 5 0.850 7216
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表 3 某型涡喷发动机涡轮及喷管结构主要参数
Table 3. Main parameters of turbine and nozzle of a turbojet engine
参数 数值 喷管入口直径D 中心锥顶部至喷管安装面距离L2/D 0.4368 中心锥底部至喷管安装面距离L3/D 0.0422 固定导叶至喷管安装面距离L4/D 0.1713 中心锥半径R1/D 0.6588 喷管收敛角度θ1/（°） 8.5～13.1 固定导叶安装角度θ2/（°） 90
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表 4 实验使用传感器型号及参数
Table 4. Experimental bench model of sensors
传感器名称 传感器型号 测量范围 精度/% 推力计 WD-3K 0～300 kg ±1 燃油流量表 OF04ZAT-1 0～300 kg/h ±2 霍尔传感器 Rcexl CDL 0～ 80000 r/min±0.1 温度传感器 K型热电偶 −200～ 1300 ℃±0.7
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表 5 测试结果的不确定性分析
Table 5. Uncertainty analysis of test results
参数 标准值 不确定度 占比/% 转速/（r/min） 54000 56.8 0.105 燃油流量/（L/h） 105.5 1.03 0.977 静推力/daN 59.2 0.22 0.372 排气温度/K 771 3.8 0.493 注：表中数据为EAR为1.0 和转速为54 000 r/min下所得。
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表 6 RP-3 燃油的物理性质
Table 6. Physical properties of RP-3 fuel
参数 数值 密度$ {\rho } $/（kg/m3） 804 动力黏度$ {\mu } $/（mPa·s） 1.64 比定压热容$ {{c}}_{{p}}$/（kJ/（kg·K）） 2.0～2.3 汽化潜热L/（kJ/kg） 250～270 低热值（LHV）/（MJ/kg） 43.124 注：上述数据适用环境温度约为298 K，但高温高压下可能会变化。
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表 7 耦合公式系数
Table 7. Coupling formula coefficients
参数 数值 置信区间 P00 5.554 （−8.833, 19.94） P10 − 0.2654 （− 0.5469 ,0.01614 ）P01/10−3 8.304 （−61.46, 78.07） P20/10−3 1.101 （− 0.9767 , 3.18）P11/10−4 4.766 （−4.616, 14.15） P02/10−5 −3.213 （−14.57, 8.142） P30/10−5 −1.597 （−2.288, − 0.9068 ）P21/10−6 2.513 （−1.092, 6.118） P12/10−7 −4.932 （−12.74, 2.876） P03/10−8 2.736 （−3.439, 8.912） P1/10−3 1.209 （ 0.2552 , 2.163）P2 − 0.1234 （− 0.2681 ,0.02134 ）P3 6.423 （− 0.0432 , 12.89）P4 594.3 （513.3, 675.2）
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