基于升力线理论的对转桨扇气动耦合建模与特性分析

陈凤萍; 马晓云; 贾琳渊; 陈玉春; 王笑天

doi:10.13224/j.cnki.jasp.20240345

基于升力线理论的对转桨扇气动耦合建模与特性分析

doi: 10.13224/j.cnki.jasp.20240345

1.
西北工业大学动力与能源学院，西安 710072
2.
中国人民解放军 95960部队，西安 710089

基金项目: 国家自然科学基金面上项目（52372397）

详细信息

作者简介:
陈凤萍（1996-），女，博士生，研究领域为开式转子发动机总体设计。E-mail：cfp-chen@mail.nwpu.edu.cn

通讯作者:
贾琳渊（1989-），男，副教授，博士，研究领域为航空发动机总体设计。E-mail：jialinyuan@nwpu.edu.cn

中图分类号: V231.3
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出版历程
- 收稿日期: 2024-05-28
- 网络出版日期: 2024-12-22

Aerodynamic coupling modeling and characteristic analysis of counter-rotating propellers based on lifting-line method

1.
School of Power and Energy，Northwestern Polytechnical University，Xi’an 710072，China
2.
Unit 95960，the Chinese People’s Liberation Army，Xi’an 710089，China

摘要

摘要:
为了高效、准确地生成对转桨扇全工况范围的特性图，基于规定尾迹的升力线法，发展了对转桨扇气动特性预测模型。通过引入相互诱导速度项来考虑前、后排桨扇之间的气动干扰效应；通过不同相位的尾迹叠加方法来考虑周期性影响；利用Kriging法建立了翼型升、阻特性代理模型以提升计算精度。对F7-A7对转桨扇进行了特性预测、模型验证和评估，结果表明：本模型不仅能够较高精度且快速地预测全工况范围内的特性，而且能够有效捕捉干扰效应、周期性特征及轴间距的影响。其中，设计点的净效率与推力误差分别为0.43%和0.37%；在宽广的非设计工况下，仍能保持较高精度，效率误差小于1.2%；单个工作点计算仅需21 s。相较于零维模型，在设计/非设计点的效率和功率预测准确度均显著提升，为开式转子发动机的总体性能仿真与优化设计提供了强有力的支持。
- 对转桨扇 /
- 性能预测 /
- 升力线法 /
- Kriging代理模型 /
- 干扰效应
Abstract:
To predict the performance of counter-rotating propellers, a lifting-line prediction model was developed based on the prescribed wake method. The mutual induction velocity terms were introduced to account for the interference effect, and multiphase wakes were calculated to consider the periodicity. To enhance accuracy, a Kriging method was employed to establish surrogate models for lift and drag coefficients. This model was then applied to the F7-A7 contra-rotating propellers. The results indicated that this model not only provided high-precision and rapid predictions of characteristics across the full range of operating conditions, but also effectively captured interference effects, periodic features, and the impact of axial spacing. Specifically, the errors in net efficiency and thrust at the design point were 0.43% and 0.37%, respectively. Under a wide range of off-design conditions, the model maintained a high accuracy, with efficiency errors remaining below 1.2%. The elapsed time to calculate a single operating condition was approximately 21 s. Compared with zero-dimensional models, the prediction accuracy for efficiency and power at both design and off-design points was significantly improved, providing robust support for the overall performance simulation and optimization design of open rotor engines.
- counter-rotating propellers /
- performance prediction /
- lifting-line method /
- Kriging surrogate model /
- aerodynamic interaction

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图 1 叶片和尾迹涡丝的离散化示意图

Figure 1. Discretization of the blade and the trailing vortex filament

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图 2 对转桨扇升力线模型的尾迹叠加

Figure 2. Counter-rotating propellers wake superposition for lifting-line method

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图 3 对转桨扇的速度三角形

Figure 3. Counter-rotating propellers velocity triangles

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图 4 C_L和C_D的预测值与原始校验样本的对比

Figure 4. Comparison of the predicted values with the original data of C_L and C_D

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图 5 Kriging代理模型的升力系数预测结果示例（NACA 16-504）

Figure 5. Kriging surrogate model prediction results of lift coefficient （NACA 16-504）

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图 6 Kriging代理模型的阻力系数预测结果示例（NACA 16-504）

Figure 6. Kriging surrogate model prediction results of drag coefficient （NACA 16-504）

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图 7 升力线模型的建模流程图

Figure 7. Flow chart of lifting-line method

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图 8 F7叶片设计参数

Figure 8. Design parameters of F7 blade

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图 9 总体性能曲线（Ma=0.72）

Figure 9. Overall performance curves （Ma=0.72）

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图 10 F7-A7 对转桨扇全工况的总体性能对比

Figure 10. Overall performance map comparison of experimental data in full operating conditions for F7-A7

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图 11 Ma对F7-A7总性能的影响

Figure 11. Effect of Ma on F7-A7 overall performance

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图 12 升力线模型与试验数据、零维模型的净效率对比

Figure 12. Comparison of net efficiency between lifting-line model, experimental data, and zero dimensional model

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图 13 桨轴间距和周期性对性能的影响

Figure 13. Effect of propeller spacing and periodicity on counter-rotating propellers performance

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表 1 能量守恒尾迹叠加模型输入参数与能量评估

Table 1. Input parameters for the energy conservation wake superposition model and energy assessment

参数	数值
$ {u_{\text{1}}} $/（m/s）	213.6
$ {u_{{{1W}}}} $/（m/s）	229.7
$ {u_{\text{2}}} $/（m/s）	224.6
$ {u_{{{2W}}}} $/（m/s）	240.2
$ \dot m $/（kg/s）	686.1
$ {P_1} $/kW	3069.4
$ {P_2} $/kW	2847.4
$ \Delta {E_{{\text{total}}}} $/（kJ/s）	4921.8
$ \Delta {E_{{\text{loss}}}} $/（kJ/s）	995.0

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表 2 能量守恒叠加模型与升力线模型评估结果对比

Table 2. Comparison of evaluation results between the energy conservation wake superposition model and the lifting-line method

参数对比	数值
$ {\eta _{{\text{net,LLM}}}} $	0.8243
$ {\eta _{{\text{net,EB}}}} $	0.8318
$ {\eta _{{\text{net,test}}}} $	0.8200
$ {u_{{{W,{\mathrm{EB}}}}}} $/（m/s）	244.9
$ {u_{{{W,{\mathrm{LLM}}}}}} $/（m/s）	243.9
注：LLM为升力线模型；EB为能量守恒模型；test为F7-A7的设计点试验数据。

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表 3 Kriging代理模型的输入、输出参数

Table 3. Input and output parameters of the Kriging surrogate model

代理模型	输入参数	输出参数
升力系数模型	C_L,des, γ_toc, α, Ma	C_L
阻力系数模型	C_L,des, γ_toc, C_L, Ma	C_D

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表 4 F7-A7设计点的试验数据和升力线预测值的对比（Ma=0.72, H=10669 m，ISA）

Table 4. Comparison of F7-A7 experimental data and predicted results by lifting-line model at design points （Ma=0.72, H=10669 m，ISA）

参数	试验值^[5]	预测值	误差/%
净效率	0.8200	0.8243	0.43
总推力/N	22408	22490	0.37

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表 5 不同耦合方式对性能参数的影响（Ma=0.67）

Table 5. Effect of different coupling models on performance parameters （Ma=0.67）

性能参数	孤立模型	向前耦合	向后耦合	相互耦合
P_CRP/kW	3711	3836	4514	4763
P₁/kW	2262	2387	2262	2453
P₂/kW	1449	1449	2252	2310
T_CRP/daN	1530	1584	1904	2013
T₁/daN	918	972	918	1000
T₂/daN	612	612	985	1013
η₁	0.8070	0.8095	0.8070	0.8104
η₂	0.8392	0.8392	0.8697	0.8717
η_net	0.8196	0.8207	0.8382	0.8401
注：向前耦合仅考虑后桨对前桨的诱导作用；向后耦合仅考虑前桨对后桨的诱导作用。

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