EI、Scopus 收录
中文核心期刊

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

融合相似性原理的涡轮叶型流场预测方法研究

郭振东 成辉 陈云 蒋首民 宋立明 李军 丰镇平

郭振东, 成辉, 陈云, 蒋首民, 宋立明, 李军, 丰镇平. 融合相似性原理的涡轮叶型流场预测方法研究. 力学学报, 2023, 55(11): 1058-1071 doi: 10.6052/0459-1879-23-382
引用本文: 郭振东, 成辉, 陈云, 蒋首民, 宋立明, 李军, 丰镇平. 融合相似性原理的涡轮叶型流场预测方法研究. 力学学报, 2023, 55(11): 1058-1071 doi: 10.6052/0459-1879-23-382
Guo Zhendong, Cheng Hui, Chen Yun, Jiang Shoumin, Song Liming, Li Jun, Feng Zhenping. Study on flow field prediction of turbine blades by coupling similarity principle. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(11): 1058-1071 doi: 10.6052/0459-1879-23-382
Citation: Guo Zhendong, Cheng Hui, Chen Yun, Jiang Shoumin, Song Liming, Li Jun, Feng Zhenping. Study on flow field prediction of turbine blades by coupling similarity principle. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(11): 1058-1071 doi: 10.6052/0459-1879-23-382

融合相似性原理的涡轮叶型流场预测方法研究

doi: 10.6052/0459-1879-23-382
基金项目: 国家科技重大专项(2019-II-0008-0028)、国家自然科学基金51936008和52306048资助项目
详细信息
    通讯作者:

    宋立明, 教授, 主要研究方向为热机气动热力学与叶轮机械先进智能设计优化方法. E-mail: songlm@xjtu.edu.cn

  • 中图分类号: TK14

STUDY ON FLOW FIELD PREDICTION OF TURBINE BLADES BY COUPLING SIMILARITY PRINCIPLE

  • 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.

     

  • 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  3  涡轮叶栅网格示意图

    Figure  3.  Schematic of the grids of turbine cascades

    图  4  几何相似性原理验证

    Figure  4.  Verification of geometric 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  6  T1对叶型载荷分布的影响分析

    Figure  6.  The effect of T1 on the blade loading distribution

    图  7  Re对叶型载荷分布的影响分析

    Figure  7.  The effect of Re on blade loading distribution

    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  9  涡轮叶型t-SNE聚类分布

    Figure  9.  Classification of turbine blades by t-SNE

    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  11  不同工况案例平均相对误差

    Figure  11.  MRE of test cases in different conditions

    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  13  测试集叶型的t-SNE分布

    Figure  13.  t-SNE distribution of blades in testing set

    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 parameterMinMax
    inlet geometric angle β1/(°)3060
    outlet airflow angle β2/(°)1530
    upper wedge angle εup/(°)1025
    outlet deflection angle δout/(°)1015
    center line angle γ/(°)2045
    correlation coefficient k0.20.35
    relative axial pitch t/Cx0.91.1
    下载: 导出CSV

    表  2  3个FNN模型的神经网络结构

    Table  2.   Configurations of three FNN

    Network typeFNN-1FNN-2FNN-3
    input layer1 × 4071 × 4071 × 407
    hidden layer3 × 7003 × 8003 × 900
    output layer1 × 4021 × 4021 × 402
    下载: 导出CSV

    表  3  训练模型精度验证

    Table  3.   Validation of the training models

    Network typeTraining setValidation set
    RMSER2RMSER2
    FNN-10.003 30.996 60.003 50.995 9
    FNN-20.002 50.997 50.002 80.996 8
    FNN-30.003 70.996 20.003 80.996 0
    下载: 导出CSV

    表  4  测试案例的工况条件

    Table  4.   Working conditions of the test dataset

    Testing casesMaoutαt/Cx
    case10.537−4.1250.927
    case20.473−3.4750.991
    case30.527−3.8251.045
    case40.499−0.3250.969
    case50.517−1.3751.069
    case60.423−4.5250.979
    case70.543−2.9250.983
    case80.567−4.5751.075
    case90.489−1.5251.027
    case100.441−0.7750.953
    下载: 导出CSV

    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 conditionBlade profilePrediction 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
    下载: 导出CSV
  • [1] Viana FAC, Simpson TW, Balabanov V, et al. Special section on multidisciplinary design optimization: metamodeling in multidisciplinary design optimization: how far have we really come? AIAA Journal, 2014, 52(4): 670-690 doi: 10.2514/1.J052375
    [2] LeCun Y, Bengio Y, Hinton G. Deep learning. Nature, 2015, 521(7553): 436-444 doi: 10.1038/nature14539
    [3] 陈海昕, 邓凯文, 李润泽. 机器学习技术在气动优化中的应用. 航空学报, 2019, 40(1): 52-68 (Chen Haixin, Deng Kaiwen, Li Runze. Utilization of machine learning technology in aerodynamic optimization. Acta Aeronautica et Astronautica Sinica, 2019, 40(1): 52-68 (in Chinese)

    Chen Haixin, Deng Kaiwen, Li Runze. Utilization of machine learning technology in aerodynamic optimization. Acta Aeronautica et Astronautica Sinica, 2019, 40(1): 522480-5224809 (in Chinese)
    [4] 孙刚, 王聪, 王立悦等. 人工智能在气动设计中的应用与展望. 民用飞机设计与研究, 2021(142): 1-9, 147 (Sun Gang, Wang Cong, Wang Liyue, et al. Application and prospect of artificial intelligence in aerodynamic design. Civil Aircraft Design &Research, 2021(142): 1-9, 147 (in Chinese)

    Sun Gang, Wang Cong, Wang Liyue, et al. Application and prospect of artificial intelligence in aerodynamic design. Civil Aircraft Design & Research, 2021, No. 142(03): 1-9 + 147 (in Chinese))
    [5] 刘浩, 李国庆, 张深等. 机器学习在涡轮机械中的应用进展. 工程热物理学报, 2023, 44(04): 938-951

    Liu Hao, Li Guoqing, Zhang Shen, et al. Journal of Engineering Thermophysics, 2023, 44(04): 938-951 (in Chinese)
    [6] 王怡星, 韩仁坤, 刘子扬等. 流体力学深度学习建模技术研究进展. 航空学报, 2021, 42(4): 231-250 (Wang Yixing, Han Renkun, Liu Ziyang, et al. Progress of deep learning modeling technology for fluid mechanics. Acta Aeronautica et Astronautica Sinica, 2021, 42(4): 231-250 (in Chinese)

    Wang Yixing, Han Renkun, Liu Ziyang, et al. Progress of deep learning modeling technology for fluid mechanics. Acta Aeronautica et Astronautica Sinica, 2021, 42(4): 231-250 (in Chinese)
    [7] 张伟伟, 寇家庆, 刘溢浪. 智能赋能流体力学展望. 航空学报, 2021, 42(4): 524689 (Zhang Weiwei, Kou Jiaqing, Liu Yilang. Prospect of artificial intelligence empowered fluid mechanics. Acta Aeronautica et Astronautica Sinica, 2021, 42(4): 524689 (in Chinese)

    Zhang Weiwei, Kou Jiaqing, Liu Yilang. Prospect of artificial intelligence empowered fluid mechanics. Acta Aeronautica et Astronautica Sinica, 2021, 42(4): 524689 (in Chinese)
    [8] 金晓威, 赖马树金, 李惠. 物理增强的流场深度学习建模与模拟方法. 力学学报, 2021, 53(10): 2616-2629 (Jin Xiaowei, Laima Shujinn, Li Hui. Physics-enhanced deep learning methods for modelling and simulating flow fields. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(10): 2616-2629 (in Chinese)

    Jin Xiaowei, Laima Shujinn, Li Hui. Physics-enhanced deep learning methods for modelling and simulating flow fields. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(10): 2616-2629 (in Chinese))
    [9] 陈皓, 郭明明, 田野等. 卷积神经网络在流场重构研究中的进展. 力学学报, 2022, 54(09): 2343-2360 (Chen Hao, Guo Mingming, Tian Ye, et al. Progress of convolution neural networks in flow field reconstruction. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(09): 2343-2360 (in Chinese)

    Chen Hao, Guo Mingming, Tian Ye, et al. Progress of convolution neural networks in flow field reconstruction. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(09): 2343-2360 (in Chinese)
    [10] 惠心雨, 袁泽龙, 白俊强等. 基于深度学习的非定常周期性流动预测方法. 空气动力学学报, 2019, 37(3): 462-469 (Hui Xinyu, Yuan Zelong, Bai Junqiang, et al. A method of unsteady periodic flow field prediction based on the deep learning. Acta Aeronautica et Astronautica Sinica, 2019, 37(3): 462-469 (in Chinese)

    Hui Xinyu, Yuan Zelong, Bai Junqiang, et al. A method of unsteady periodic flow field prediction based on the deep learning. Acta Aeronautica et Astronautica Sinica, 2019, 37(3): 462-469 (in Chinese)
    [11] Sekar V, Jiang Q, Shu C, et al. Fast flow field prediction over airfoils using deep learning approach. Physics of Fluids, 2019, 31(5): 057103 doi: 10.1063/1.5094943
    [12] 李凯, 杨静媛, 高传强等. 基于POD和代理模型的静气动弹性分析方法. 力学学报, 2023, 55: 1-10 (Li Kai, Yang Jingyuan, Gao Chuanqiang, et al. Static aeroelastic analysis based on proper orthogonal decomposition and surrogate model. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55: 1-10 (in Chinese)

    Li Kai, Yang Jingyuan, Gao Chuanqiang, et al. Static aeroelastic analysis based on proper orthogonal decomposition and surrogate model. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55: 1-10 (in Chinese)
    [13] Jin Y, Li S, Jung O. Prediction of flow properties on turbine vane airfoil surface from 3D geometry with convolutional neural network//Turbo Expo: Power for Land, Sea, and Air. American Society of Mechanical Engineers, 2019
    [14] 杜周, 徐全勇, 宋振寿等. 基于深度学习的压气机叶型气动特性预测. 航空动力学报, 2023, 38(9): 2251-2260 (Du Zhou, Xu Quanyong, Song Zhenshou, et al. Prediction of aerodynamic characteristics of compressor blades based on deep learning. Journal of Aerospace Power, 2023, 38(9): 2251-2260 (in Chinese)

    Du Zhou, Xu Quanyong, Song Zhenshou, et al. Prediction of aerodynamic characteristics of compressor blades based on deep learning[J]. Journal of Aerospace Power, 2023, 38(9): 2251-2260 (in Chinese)
    [15] Wang Q, Yang L, Rao Y. Establishment of a generalizable model on a small-scale dataset to predict the surface pressure distribution of gas turbine blades. Energy, 2021, 214: 118878 doi: 10.1016/j.energy.2020.118878
    [16] Chen J, Liu C, Xuan L, et al. Knowledge-based turbomachinery design system via a deep neural network and multi-output Gaussian process. Knowledge-Based Systems, 2022, 252: 109352 doi: 10.1016/j.knosys.2022.109352
    [17] Li J, Liu T, Wang Y, et al. Integrated graph deep learning framework for flow field reconstruction and performance prediction of turbomachinery. Energy, 2022, 254: 124440 doi: 10.1016/j.energy.2022.124440
    [18] 金晓威. 物理启发的钝体绕流场机器学习计算方法. [博士论文]. 哈尔滨: 哈尔滨工业大学, 2021

    Jin Xiaowei. Physics-inspired machine learning methods for flow field around a bluff body. [PhD Thesis]. Harbin: Harbin Institute of Technology, 2021 (in Chinese)
    [19] Raissi M, Perdikaris P, Karniadakis GE. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 2019, 378: 686-707 doi: 10.1016/j.jcp.2018.10.045
    [20] 陈苏, 丁毅, 孙浩等. 物理驱动深度学习波动数值模拟方法及应用. 力学学报, 2023, 55(1): 272-282 (Chen Su, Ding Yi, Sun Hao, et al. Methods and applications of physical information deep learning in wave numerical simulation. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(1): 272-282 (in Chinese)

    Chen Su, Ding Yi, Sun Hao, et al. Methods and applications of physical information deep learning in wave numerical simulation. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(1): 272-282 (in Chinese)
    [21] 刘子俊, 冯勇, 陈景龙等. 基于多源数据的液体火箭发动机智能异常检测. 火箭推进, 2022, 48(03): 79-86 (Liu Zijun, Feng Yong, Chen Jinglong, et al. Intelligent anomaly detection of liquid rocket engine with multi-source data. Journal of Rocket Propulsion, 2022, 48(03): 79-86 (in Chinese) doi: 10.3969/j.issn.1672-9374.2022.03.010

    Liu Zijun, Feng Yong, Chen Jinglong, et al. Intelligent anomaly detection of liquid rocket engine with multi-source data[J]. Journal of Rocket Propulsion, 2022, 48(03): 79-86 (in Chinese) doi: 10.3969/j.issn.1672-9374.2022.03.010
    [22] 王珺, 吕海鑫, 陈景龙等. 液体火箭发动机健康状态智能检测方法. 火箭推进, 2021, 47(4): 52-58 (Wang Jun, Lv Haixin, Chen Jinglong, et al. Intelligent detection method of liquid rocket engine health state. Journal of Rocket Propulsion, 2021, 47(4): 52-58 (in Chinese) doi: 10.3969/j.issn.1672-9374.2021.04.008

    Wang Jun, Lv Haixin, Chen Jinglong, et al. Intelligent detection method of liquid rocket engine health state[J]. Journal of Rocket Propulsion, 2021, 47(04): 52-58(in Chinese) doi: 10.3969/j.issn.1672-9374.2021.04.008
    [23] Anderson JD, Wendt J. Computational Fluid Dynamics. New York: McGraw-Hill, 1995
    [24] 季路成. 高性能叶轮机全3维叶片技术趋势展望. 航空发动机, 2013, 39(4): 9-18, 31 (Ji Lucheng. Trend of full three-dimensional blading techniques for high performance turbomachinery. Aeroengine, 2013, 39(4): 9-18, 31 (in Chinese) doi: 10.3969/j.issn.1672-3147.2013.04.003

    Ji Lucheng. Trend of full three-dimensional blading techniques for high performance turbomachinery. Aeroengine, 2013, 39(04): 9-18 + 31 (in Chinese) doi: 10.3969/j.issn.1672-3147.2013.04.003
    [25] 陈云, 宋立明, 王雷等. 自动优化技术在涡轮设计中的应用. 航空发动机, 2012, 47(4): 59-66 (Chen Yun, Song Liming, Wang Lei, et al. Application of automatic optimization technology in turbine design. Aeroengine, 2012, 47(4): 59-66 (in Chinese) doi: 10.3969/j.issn.1672-3147.2012.04.014

    Chen Yun, Song Liming, Wang Lei, et al. Application of automatic optimization technology in turbine design[J]. Aeroengine, 2012, 47(04): 59-66 (in Chinese) doi: 10.3969/j.issn.1672-3147.2012.04.014
    [26] Xie J, Sage M, Zhao YF. Feature selection and feature learning in machine learning applications for gas turbines: A review. Engineering Applications of Artificial Intelligence, 2023, 117: 105591 doi: 10.1016/j.engappai.2022.105591
    [27] Korakianitis T. Hierarchical development of three direct-design methods for two-dimensional axial-turbomachinery cascades. Journal of Turbomachinery-transactions of The Asme, 1993, 115: 314-324 doi: 10.1115/1.2929237
    [28] Zannetti L, Pandolfi M. Inverse design technique for cascades. NASA, 1984
    [29] 邹正平, 叶建, 刘火星等. 低压涡轮内部流动及其气动设计研究进展. 力学进展, 2007, 37(4): 551-562 (Zhou Zhengping, Ye Jian, Liu Huoxing. Research progress on low pressure turbine internal flows and related aerodynamic design. Advances in Mechanics, 2007, 37(4): 551-562 (in Chinese) doi: 10.6052/1000-0992-2007-4-J2006-131

    Zhou Zhengping, Ye Jian, Liu Huoxing. Research progress on low pressure turbine internal flows and related aerodynamic design[J]. Advances in Mechanics, 2007, 37(4): 551-562(in Chinese) doi: 10.6052/1000-0992-2007-4-J2006-131
    [30] Pritchard LJ. An eleven parameter axial turbine airfoil geometry model//Proceedings of the ASME 1985 International Gas Turbine Conference and Exhibit. Volume 1: Aircraft Engine, Marine, Turbomachinery. Microturbines and Small Turbomachinery. Houston, Texas, USA. March 18–21, 1985
    [31] Maaten L, Hinton G. Visualizing data using t-SNE. Journal of Machine Learning Research, 2008, 9: 2579-2605
    [32] Ning, F. MAP: A CFD package for turbomachinery flow simulation and aerodynamic design optimization//Proceedings of the ASME Turbo Expo 2014: Turbine Technical Conference and Exposition. Volume 2 B: Turbomachinery. Düsseldorf, Germany. June 16–20, 2014
    [33] Rosenblatt, F. The Perceptron—A perceiving and recognizing automaton project para. Ithaca, New York, Cornell Aeronautical Laboratory. 1957, 85-460-1
  • 加载中
图(16) / 表(5)
计量
  • 文章访问数:  40
  • HTML全文浏览量:  13
  • PDF下载量:  7
  • 被引次数: 0
出版历程
  • 网络出版日期:  2023-09-07

目录

    /

    返回文章
    返回