STUDY ON FLOW FIELD PREDICTION OF TURBINE BLADES BY COUPLING SIMILARITY PRINCIPLE
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摘要: 计算流体力学(CFD)方法是涡轮叶片等设计阶段性能评估的重要手段. 然而, 基于CFD的数值仿真方法通常比较耗时, 难以满足涡轮叶型设计阶段快速迭代的需求. 为实现快速性能评估并克服纯数据驱动预测模型泛化能力不足的问题, 受到物理增强的机器学习思路的启发, 将相似性原理与深度学习模型相结合, 提出了一种泛化能力强的涡轮叶型流场预测新方法. 以涡轮叶片表面等熵马赫数分布预测为例, 提出采用相似性原理对叶型几何变量和气动参数进行归一化, 进而在归一化参数空间构建训练样本集与深度学习预测模型, 由此建立统一的流场预测模型, 对几何尺寸、边界条件差异较大的叶型气动性能进行评估. 在完成模型训练后, 对归一化条件下不同工况/不同形状叶型的流场、真实环境下不同工况/不同尺寸叶型的流场以及GE-E3低压涡轮不同截面叶型的流场进行预测, 结果表明预测结果的分布曲线与CFD评估结果吻合良好, 平均相对误差在1.0%左右, 由此验证了所提出的融合相似性原理的流场预测模型的精度与泛化能力.Abstract: Computational fluid dynamics (CFD) is an important tool to evaluate the performance of turbine blades and etc. in the design stage. However, the numerical simulation of turbine blades that based on CFD method can be very time-consuming, which makes it rather difficult to meet the need of rapid iteration in the design process of turbine blades. In order to evaluate the performance of turbine blades rapidly and overcome the problem of insufficient generalization ability of pure data-driven prediction models as well, inspired by the concept of physics augmented machine learning, a novel method for turbine blade flow field prediction with strong generalization ability is proposed, by combining the similarity principle with deep learning model. Taking the prediction of the isentropic Mach number distribution at the surface of turbine blades as an example, we propose to make use of the similarity principle to normalize the geometric variables and aerodynamic parameters of turbine blades, and then prepare the training sample set and train the deep learning-based prediction model in the normalized parameter space. And accordingly, a unified prediction model based deep learning can be obtained, which can quickly predict the aerodynamic performance of turbine blades that in very different geometric size and have different boundary condition values. After finishing the model training, the trained prediction model is used to predict the flow fields of the turbine blades that works under different operation condition and of different shape in normalized design space, the flow fields of real-world blades of different size/different working conditions, and the flow fields of different section profiles of GE-E3 low-pressure turbines. The results showed that the predicted results were in good agreement with the CFD evaluation results, and the averaged relative error was less than 1.0%, which verify the accuracy and generalization ability of the proposed flow field prediction model coupling the similarity principle.
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图 1 某涡轮级几何模型及相关运行工况参数
Figure 1. Geometry and related working condition of a turbine stage
图 2 融合相似性原理的流场预测建模流程
Figure 2. Modeling process of the flow prediction model by coupling similarity principle
图 5 采用Maout进行工况归一化处理的可行性分析
Figure 5. Feasibility analysis of normalizing working conditions by Maout
图 8 归一化涡轮叶型数据库生成方法
Figure 8. The generation method of the normalized turbine blade dataset
图 10 融合相似性原理的深度学习模型
Figure 10. Framework of deep learning model coupled by similarity principle
图 12 case1和case7所对应的CFD与预测结果对比
Figure 12. Comparison of CFD and prediction results of testing blades in case 1 and case 7
图 14 测试叶型CFD值和预测值比较结果
Figure 14. Comparison of CFD and prediction results of testing blades
图 15 边界条件数值差异较大情况下模型预测结果
Figure 15. Prediction results for the cases when the values of boundary conditions are very different
图 16 叶型实际尺寸相差较大的情况下模型预测结果
Figure 16. Prediction results for the cases when the geometric size of blades are quite different
表 1 叶型参数化空间
Table 1. Parameterization space of blade profile
Geometric parameter Min Max inlet geometric angle β1/(°) 30 60 outlet airflow angle β2/(°) 15 30 upper wedge angle εup/(°) 10 25 outlet deflection angle δout/(°) 10 15 center line angle γ/(°) 20 45 correlation coefficient k 0.2 0.35 relative axial pitch t/Cx 0.9 1.1 
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表 2 3个FNN模型的神经网络结构
Table 2. Configurations of three FNN
Network type FNN-1 FNN-2 FNN-3 input layer 1 × 407 1 × 407 1 × 407 hidden layer 3 × 700 3 × 800 3 × 900 output layer 1 × 402 1 × 402 1 × 402
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表 3 训练模型精度验证
Table 3. Validation of the training models
Network type Training set Validation set RMSE R2 RMSE R2 FNN-1 0.003 3 0.996 6 0.003 5 0.995 9 FNN-2 0.002 5 0.997 5 0.002 8 0.996 8 FNN-3 0.003 7 0.996 2 0.003 8 0.996 0
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表 4 测试案例的工况条件
Table 4. Working conditions of the test dataset
Testing cases Maout α t/Cx case1 0.537 −4.125 0.927 case2 0.473 −3.475 0.991 case3 0.527 −3.825 1.045 case4 0.499 −0.325 0.969 case5 0.517 −1.375 1.069 case6 0.423 −4.525 0.979 case7 0.543 −2.925 0.983 case8 0.567 −4.575 1.075 case9 0.489 −1.525 1.027 case10 0.441 −0.775 0.953
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表 5 GE-E3低压涡轮级实际叶型算例的测试结果
Table 5. Testing results of GE-E3 low-pressure turbine blades
Working condition Blade profile Prediction results (a) blade profile at the root section of the
second stage of GE-E3 rotor blade$p_0^t$ = 319339 Pa
$ p_1^s $ = 252318 Pa
T1 = 1161 K
$ \alpha $ = −3.5°
t = 1.07
(b) blade profile at the section of middle span of
the third stage of GE-E3 rotor blade$p_0^t$ = 266884 Pa
$ p_1^s $ = 218858 Pa
T1 = 900 K
$ \alpha $ = −2.2°
t = 0.92
(c) blade profile at the section of middle span of
the third stage of GE-E3 vane blade$p_0^t$ = 295699 Pa
$ p_1^s $ = 257337 Pa
T1 = 1080 K
$ \alpha $ = −1.0°
t = 1.02
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