基于相似换算<i>N</i>-dot的涡扇发动机全包线加速控制计划研究

王心怡; 郑前钢; 张海波

doi:10.13224/j.cnki.jasp.20240351

基于相似换算N-dot的涡扇发动机全包线加速控制计划研究

doi: 10.13224/j.cnki.jasp.20240351

南京航空航天大学能源与动力学院，南京 210016

详细信息

作者简介:
王心怡（2000-），女，硕士生，主要研究领域为航空发动机建模与控制。E-mail：wxy_hncn@163.com

中图分类号: V231
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出版历程
- 收稿日期: 2024-05-30
- 网络出版日期: 2024-12-14

Study on turbofan engine full envelope acceleration control schedule based on similarity conversion of N-dot

College of Energy and Power Engineering，Nanjing University of Aeronautics and Astronautics，Nanjing 210016，China

摘要

摘要:
针对转子加速度（N-dot）加速控制计划存在全包线范围内适用性不足的问题，提出了一种基于相似换算N-dot的全包线加速控制方法。推导并验证了在等风扇进口总温线上涡扇发动机风扇转速、压气机转速、涡轮前温度等参数稳态相似换算误差小；研究了N-dot可以直接反映剩余功率的大小，保证动态过程相似换算精度高；选择覆盖发动机全工作包线的有限个等温线工作点，构建了不同总温下换算的N-dot加速控制计划；通过相邻等温线线性插值将加速控制计划拓展至非等温线上工作点，实现N-dot加速控制方法全包线内适用。仿真结果表明：相比于传统开环油气比加速控制计划，在同一等温线不同工作点的加速过程，所提方法的加速时间分别缩短了5.31%和10.32%，在非等温线工作点的加速过程，加速时间缩短了57.74%，且全工作包线点的加速时间在2.3～12.3 s内，加速过程均不会出现参数超限问题。所提方法在发动机全包线内的加速控制均能满足快速性和安全性的需求。
- N-dot加速控制计划 /
- 相似换算 /
- 涡扇发动机 /
- 全包线 /
- 等温线
Abstract:
To solve the problem that the rotor acceleration (N-dot) acceleration control schedule has insufficient applicability in the full envelope range, a full envelope acceleration control method based on similarity conversion N-dot was proposed. It was proved and verified that the steady-state similar conversion error of fan speed, compressor speed and turbine front temperature of the turbofan engine was small on total temperature line of fan inlet. Then, it was analyzed that N-dot can directly reflect the size of residual power to ensure high precision of dynamic process similarity conversion. A finite number of isotherm operating points covering the full operating envelope of the engine were selected, and the converted N-dot acceleration control schedule under different total temperature was constructed. By expanding the accelerated control schedule to work points on non-isothermal lines by linear interpolation of neighboring isotherms, the application of N-dot acceleration control method in full envelope was realized. The simulation results showed that compared with the traditional method on open-loop fuel-to-air ratio acceleration control schedule, the acceleration time of the proposed method was shortened by 5.31% and 10.32% at different operating points of the same isotherm, and the acceleration time of the non-isotherm operating point was shortened by 57.74%. The acceleration time of the full operating envelope was within 2.3—12.3 s and each parameter did not exceed the limit. The proposed method can satisfy the control requirements of rapidity and safety in the full envelope range of the engine.
- N-dot acceleration control schedule /
- similarity conversion /
- turbofan engine /
- full envelope /
- isotherm

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图 1 小涵道比涡扇发动机结构简图

Figure 1. Schematic diagram of small bypass ratio turbofan engine structure

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图 2 发动机加速过程的约束限制

Figure 2. Constraints imposed on the engine acceleration process

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图 3 压气机加速度特性图

Figure 3. Acceleration in compressor characteristics diagram

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图 4 N-dot加速控制计划基于等温线插值示意图

Figure 4. Interpolated N-dot acceleration control schedule based on isotherm

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图 5 传统方法示意图^[24]

Figure 5. Traditional method diagram^[24]

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图 6 小涵道比发动机飞行包线示意图

Figure 6. Flight envelope schematic of small bypass ratio engines

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图 7 换算的N-dot加速控制计划优化结果

Figure 7. Optimization results of converted N-dot acceleration control schedules

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图 8 等温线上两种不同方法加速过程对比

Figure 8. Comparison of acceleration process of two different methods on isotherm

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图 9 加速控制过程中压气机工作点的变化

Figure 9. Changes of compressor operating point during acceleration control process

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图 10 等温线上插值两种不同计划加速对比

Figure 10. Comparison of acceleration of interpolating two different schedules on isotherm

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图 11 全包线加速起点、终点

Figure 11. Starting and ending points of full envelope acceleration

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图 12 全包线加速仿真

Figure 12. Full envelope acceleration simulation

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表 1 常用发动机参数相似换算准则

Table 1. Common gas turbine parameter corrections

发动机参数	相似换算准则
转速	$ {N_{{\text{cor}}}} = N/\sqrt {{T_{{\text{t2}}}}} $
温度	$ {T_{{\text{cor}}}} = T/{T_{{\text{t2}}}} $
压力	$ {p_{{\text{cor}}}} = p/{p_{{\text{t2}}}} $
燃油流量	$ {W_{{\text{fb,cor}}}} = {W_{{\text{fb}}}}/ （{p_{{\text{t2}}}}\sqrt {{T_{{\text{t2}}}}}） $
注：表中下标cor表示对应的相似换算参数，T_t2和p_t2分别表示风扇进口总温度和进口总压。

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表 2 不同等温线上稳态参数换算到地面点的误差

Table 2. Errors of converting steady-state parameters to ground on different isotherms

误差/%	$ \begin{gathered} H = 6.5\;{\text{km}},Ma = 0.7, \\ {T_{{\text{t2}}}} = 270\;{\text{K}} \\ \end{gathered} $	$\begin{gathered} H = 8.4\;{\text{km}},Ma = 1.08 ,\\ {T_{{\text{t2}}}} = 288.15\;{\text{K}} \\ \end{gathered} $	$\begin{gathered} H = 7.5\;{\text{km}},Ma = 1.45, \\ {T_{{\text{t2}}}} = 340\;{\text{K}} \\ \end{gathered} $
e（N_f）	1.77	0.115	3.42
e（N_c）	1.49	0.006	2.66
e（S_mf）	1.76	0.702	20.14
e（S_mc）	2.38	0.795	6.27
e（T_t4）	2.68	0.266	4.30

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表 3 不同等温线上典型工作点的飞行条件

Table 3. Flight conditions at typical operating points on different isotherms

风扇进口总温T_t2/K	飞行条件
风扇进口总温T_t2/K	H/km	Ma
240	9.00	0.474
270	6.50	0.700
300	2.40	0.710
340	7.50	1.450
380	3.52	1.469

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