Aerodynamic design method of contra-rotating open rotor
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摘要:
提出一种基于升力线理论的对转开式转子（contra-rotating open rotor，CROR）气动设计方法。以推力为设计目标，基于拉格朗日乘子法构建气动设计控制方程组。考虑高飞行马赫数对流动特征的影响，根据激盘模型，采用一道正激波模拟转子的增压过程。完成速度场预测后，利用压气机三维造型方法完成初始设计。初始设计完成后，对翼型折转角进行修正从而满足目标推力。研究表明，整个设计过程中只需2次计算流体力学（CFD）计算与再设计便可满足目标推力，所需翼型折转角修正量为−0.486°，设计结果的推力与目标推力的相对误差为−0.32%，设计方法高效且具有高的设计精度。
Abstract:An aerodynamic design method of contra-rotating open rotor (CROR) based on lifting line theory was proposed. Utilizing Lagrange multiplier method, the aerodynamic design control equation of CROR was constructed to find the CROR meeting the thrust demand. Due to the influence of high flight Mach number on the flow characteristics, a positive shock wave was used to simulate the pressure rising process of rotor according to the actuator disk model. Based on the predicted velocity field, preliminary design of CROR was completed utilizing three-dimensional modeling method of compressor. After the preliminary design, turning angle was corrected to meet the thrust demand. The results showed that only two computational fluid dynamics (CFD) calculations and redesign in the whole design process were required to meet the thrust demand. The required turning angle correction was −0.486°. The relative error between design result and thrust demand was −0.32%. The design method was efficient and had good design accuracy.
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图 6 升力系数径向分布对比结果
Figure 6. Comparison result of radial distribution of lift coefficient
图 8 一维气动设计结果（设计实例）
Figure 8. One dimensional aerodynamic design results （design example）
图 11 对转开式转子不同叶高位置截面云图（设计实例）
Figure 11. Contour of CROR at different cross sections （design example）
图 12 一维气动设计结果（验证算例）
Figure 12. One-dimensional aerodynamic design results （validation example）
图 13 对转开式转子不同叶高位置截面云图（验证算例）
Figure 13. Contour of CROR at different cross sections （validation example）
表 1 实验与数值模拟结果对比
Table 1. Comparison of experiment and CFD results
项目 推力系数 功率系数 推进效率 实验 0.786 2.734 0.821 CFD 0.834 2.778 0.857 相对误差/% 6.048 1.593 4.385 
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表 2 对转开式转子设计参数（设计实例）
Table 2. Design parameters of the CROR （design example）
参数 数值 飞行条件 飞行高度/m 10668 飞行马赫数 0.785 前排转子 叶片数 12 转速/（r/min） 1100 转子直径/m 3.6 轮毂直径/m 1.44 后排转子 叶片数 12 转速/（r/min） −1100 转子直径/m 3.6 轮毂直径/m 1.44 前/后排间距/m 0.72
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表 3 一维气动设计结果（设计实例）
Table 3. Results of one-dimensional aerodynamic design （design example）
性能参数 前排 后排 整体 推力/N 11394.7 14605.3 26000.0 扭矩/（N·m） 30322.0 30322.0 60644.1 推进效率 0.759 0.973 0.866
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表 4 修正前对转开式转子性能（设计实例）
Table 4. Performance of the CROR before correction （design example）
性能参数 前排 后排 整体 推力/N 12265.8 15458.5 27724.3 扭矩/（N·m） 33212.9 34111.0 67323.8 推进效率 0.746 0.916 0.832 推力相对误差/% 6.632
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表 5 修正后对转开式转子性能（设计实例）
Table 5. Performance of the CROR after correction （design example）
性能参数 前排 后排 整体 推力/N 程序 11394.7 14605.3 26000.0 CFD 11787.9 14128.9 25916.8 相对误差/% 3.45 −3.26 −0.32 扭矩/（N·m） 程序 30322.0 30322.0 60644.1 CFD 31506.8 30998.9 62505.7 相对误差/% 3.91 2.23 3.07 推进效率 程序 0.759 0.973 0.866 CFD 0.756 0.921 0.838 相对误差/% −0.44 −5.37 −3.29
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表 6 修正前对转开式转子性能（验证算例）
Table 6. Performance of the CROR before correction （validation example）
性能参数 前排 后排 整体 推力/N 11103.4 12150.3 23253.7 扭矩/（N·m） 22931.6 22166.4 45098.0 推进效率 0.774 0.876 0.824 推力相对误差/% 2.665
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表 7 修正后对转开式转子性能（验证算例）
Table 7. Performance of the CRP after correction （validation example）
性能参数 前排 后排 整体 推力/N 10905.6 11742.9 22648.5 扭矩/（N·m） 22439.0 21362.2 43801.2 推进效率 0.776 0.878 0.826 推力相对误差/% −0.007
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