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摘要: 针对查表法外推能力不可靠以及采用单一曲线拟合法时在压气机不同工作区域的预测与外推精度不一致的问题, 提出了一种船用大型压气机质量流量分区域建模方法; 通过定义区域划分函数, 将压气机整个工作区域划分为设计工况区、低转速区、高转速区与低压比区, 通过对比与分析经典的和近年提出的压气机质量流量数学模型的预测和外推精度, 为每个区域选择精度最高的数学模型; 为防止在动态仿真过程中当压气机运行点由其他区进入低压比区时可能出现的不连续间断点, 应用一种曲线融合方法来保证等转速线的平滑过渡; 为验证所提出的建模方法的正确性与有效性, 将其应用于一台船用大型低速二冲程柴油机仿真模型中开展稳态与瞬态仿真试验。研究结果表明: 相比查表法, 提出的建模方法可有效提升主机仿真模型增压器转速的稳态预测精度, 平均绝对百分误差由3.54%下降至0.61%, 在改变主机转速与负载这2种瞬态工况下, 压气机的运行点可平稳、连续地由设计工况区过渡至非设计工况区; 提出的建模方法既能准确预测压气机设计工况区内的已有样本数据点, 又能合理、稳健地外推至非设计工况区, 既可直接应用于涡轮增压发动机的动态仿真研究中, 也可用于离线生成压气机在全工况范围内的性能图谱, 进而应用于商业发动机性能仿真软件中。Abstract: To address the problems of unreliability of extrapolation when using a look-up table and inconsistent accuracy in prediction and extrapolation when using a single curve-fitting method in different operating zones of a compressor, a zonal modeling method was proposed for the mass flow of a large-scale marine compressor. After a zone division function was defined, the entire operating area of compressor was divided into the design, low-speed, high-speed, and low-pressure ratio zones. Following a comparison and analysis of the accuracies of prediction and extrapolation with the classical and proposed compressor mass flow models, a mathematical model with the highest accuracy was selected for each zone. A curve blending method was adopted to guarantee a smooth transition of the iso-speed line to prevent the possible discontinuity when the operating point enters the low pressure ratio zone from other operating zones during the dynamic simulation process. To validate the correctness and effectiveness of the proposed modeling method, it was applied to the simulation experiment of a large-scale low-speed two-stroke marine diesel engine model conducted under steady and transient operating conditions. Research result shows that compared with the look-up table method, the proposed modeling method can effectively improve the steady-state prediction accuracy of turbocharger rotational speed for the main engine simulation model, while reducing the mean absolute percentage error from 3.54% to 0.61%. The operating point of compressor can transition steadily and continuously from the design operating zone to the non-design operating zones under the transient operating condition when the speed and load of main engine change. The proposed modeling method not only accurately predicts the existing sample data points in the design operating zone of compressor, it also reasonably and robustly extrapolates the data to the non-design operating zones. The method can be applied directly to dynamic simulation research of turbocharged engines, and can be used to generate the compressor performance map for the full range of operating conditions offline. Accordingly, the method can be used in commercial engine performance simulation software.
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图 2 压气机叶片进出口速度三角形
Figure 2. Velocity triangles at inlet and outlet of compressor impeller
图 3 实际比焓变与质量流量线性拟合结果
Figure 3. Linear fitting results of actual specific enthalpy change and mass flow
图 4 A270-L59型船用大型压气机叶片直径估算结果
Figure 4. Estimation result of impeller diameter of A270-L59 large-scale marine compressor
图 6 各压气机质量流量模型在设计工况区内的预测结果(A270-L59)
Figure 6. Prediction results of various compressor mass flow models in design operating zone (A270-L59)
图 7 各压气机质量流量模型在设计工况区内的预测结果(TCA88-25070)
Figure 7. Prediction results of various compressor mass flow models in design operating zone (TCA88-25070)
图 8 阻塞压比和阻塞流量测量值与预测值(TCA88-25070)
Figure 8. Measured and predicted choking pressures and choking flows (TCA88-25070)
图 9 各压气机质量流量模型的LS区外推结果(A270-L59)
Figure 9. Extrapolation results of LS zone with various compressor mass flow models (A270-L59)
图 10 各压气机质量流量模型的LS区外推结果(TCA88-25070)
Figure 10. Extrapolation results of LS zone with various compressor mass flow models (TCA88-25070)
图 11 各压气机质量流量模型的HS区外推结果(A270-L59)
Figure 11. Extrapolation results of HS zone with various compressor mass flow models (A270-L59)
图 12 各压气机质量流量模型的HS区外推结果(TCA88-25070)
Figure 12. Extrapolation results of HS zone with various compressor mass flow models (TCA88-25070)
图 14 喘振区与LPR区边界线上压比与质量流量测量与拟合结果
Figure 14. Measured and fitting results of pressure ratios and mass flows at border of surging and LPR zones
图 17 压气机质量流量分区域建模方法预测与外推结果
Figure 17. Prediction and extrapolation results of zonal modeling method for mass flow of compressor
图 18 主机转速改变时压气机的运行点轨迹
Figure 18. Trajectory of compressor operating points when main engine speed changes
图 19 主机负载改变时压气机的运行点轨迹
Figure 19. Trajectory of compressor operating points when main engine loading changes
表 1 两类压气机叶片直径估算方法的预测误差
Table 1. Prediction errors of two estimation methods for compressor impeller diameter
型号 实际值/m 文献[19]中的方法 本文方法 估计值/m 误差/% 估计值/m 误差/% TCA88-25070 0.893 0 0.836 2 -6.36 0.886 4 -0.74 TCA55 0.500 0 0.468 2 -6.36 0.496 7 -0.66 
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表 2 A270-L59与TCA88-25070型船用大型压气机主要技术参数
Table 2. Main technical parameters of A270-L59 and TCA88-25070 large-scale marine compressors
型号 A270-L59 TCA88-25070 叶片直径/m 0.59 0.893 最大流量/(m3·s-1) 23 60 最大转速/(r·min-1) 16 800 11 763 样本点数 289 54
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表 3 各压气机质量流量模型在设计工况区内的预测精度(A270-L59)
Table 3. Prediction accuracies of various compressor mass flow models in design operating zone (A270-L59)
模型名称 R E/% δ5%/% δ10%/% 管聪模型 0.999 6 0.56 100.00 100.00 Karlson-Ⅰ模型 0.998 9 1.00 98.96 99.65 Karlson-Ⅱ模型 0.998 9 0.91 99.31 100.00 Malkhede模型 0.990 5 3.20 82.00 97.92 Kolmanovsky模型 0.989 0 3.39 82.00 92.73 Müller-Ⅰ模型 0.986 4 2.13 89.27 98.96 Müller-Ⅱ模型 0.971 4 3.52 77.51 95.85 Leufvén-Llamas椭圆模型 0.913 3 6.81 77.85 84.78
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表 4 各压气机质量流量模型在设计工况区内的预测精度(TCA88-25070)
Table 4. Prediction accuracies of various compressor mass flow models in design operating zone (TCA88-25070)
模型名称 R E/% δ5%/% δ10%/% 管聪模型 0.992 6 2.28 88.89 98.15 Karlson-Ⅰ模型 0.987 0 2.96 85.19 96.30 Karlson-Ⅱ模型 0.991 6 2.53 90.74 94.44 Malkhede模型 0.970 3 5.39 66.67 90.74 Kolmanovsky模型 0.961 8 6.76 57.41 75.93 Müller-Ⅰ模型 0.972 2 4.37 66.67 90.74 Müller-Ⅱ模型 0.945 6 6.28 51.85 83.33 Leufvén-Llamas椭圆模型 0.919 1 7.61 64.81 70.37
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表 5 不同转速下Leufvén-Llamas椭圆模型与Karlson-Ⅰ模型阻塞流量的预测精度
Table 5. Prediction accuracies of choking flows by Leufvén-Llamas ellipse model and Karlson-Ⅰ model at different rotational speeds
模型名称 不同叶梢圆周速度下(m·s-1)的相对误差/% 550 525 500 475 450 400 350 300 250 Leufvén-Llamas椭圆模型 1.08 0.29 1.07 0.55 0.38 1.07 0.92 0.85 0.57 Karlson-Ⅰ模型 0.53 1.66 1.64 1.90 2.00 0.31 1.88 3.04 1.30
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表 6 各压气机质量流量模型的LS区外推精度(A270-L59)
Table 6. Extrapolation accuracies of LS zone with various compressor mass flow models (A270-L59)
模型名称 管聪模型 Karlson-Ⅰ模型 Karlson-Ⅱ模型 Kolmanovsky模型 E/% 2.53 5.53 2.97 16.34 模型名称 Malkhede模型 Leufvén-Llamas椭圆模型 Müller-Ⅰ模型 Müller-Ⅱ模型 E/% 12.49 38.53 1.60 3.07
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表 7 各压气机质量流量模型的LS区外推精度(TCA88-25070)
Table 7. Extrapolation accuracies of LS zone with various compressor mass flow models (TCA88-25070)
模型名称 管聪模型 Karlson-Ⅰ模型 Karlson-Ⅰ模型 Kolmanovsky模型 E/% 5.45 14.06 16.08 44.41 模型名称 Malkhede模型 Leufvén-Llamas椭圆模型 Müller-Ⅰ模型 Müller-Ⅱ模型 E/% 13.77 23.36 3.51 8.90
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表 8 各压气机质量流量模型的HS区外推精度(A270-L59)
Table 8. Extrapolation accuracies of HS zone with various compressor mass flow models (A270-L59)
模型名称 管聪模型 Karlson-Ⅰ模型 Karlson-Ⅱ模型 Kolmanovsky模型 E/% 28.73 2.57 1.01 7.68 模型名称 Malkhede模型 Leufvén-Llamas椭圆模型 Müller-Ⅰ模型 Müller-Ⅱ模型 E/% 4.73 32.47 5.76 6.94
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表 9 各压气机质量流量模型的HS区外推精度(TCA88-25070)
Table 9. Extrapolation accuracies of HS zone with various compressor mass flow models (TCA88-25070)
模型名称 管聪模型 Karlson-Ⅰ模型 Karlson-Ⅱ模型 Kolmanovsky模型 E/% 17.58 4.97 2.28 7.85 模型名称 Malkhede模型 Leufvén-Llamas椭圆模型 Müller-Ⅰ模型 Müller-Ⅱ模型 E/% 5.58 40.43 5.16 8.47
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