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浙江大学学报(工学版)
浙江大学学报(工学版)  2021, Vol. 55 Issue (6): 1128-1134    DOI: 10.3785/j.issn.1008-973X.2021.06.013
能源工程、机械工程     
湍流火焰切向应变率的低维近似模型
任嘉豪(),王海鸥*(),邢江宽,罗坤,樊建人
浙江大学 能源清洁利用国家重点实验室，浙江 杭州 310027
Lower-dimensional approximation models of tangential strain rate of turbulent flames
Jia-hao REN(),Hai-ou WANG*(),Jiang-kuan XING,Kun LUO,Jian-ren FAN
State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, China
 全文: PDF(1241 KB)   HTML
摘要：

利用理论方法，提出切向应变率二维与三维概率密度函数（PDF）之间的关系. 基于3种不同湍流强度的自由传播预混火焰直接数值模拟（DNS）数据库，建立人工神经网络（ANN）和随机森林（RF）模型，从低维量预测三维切向应变速率. 机器学习模型的输入特征包括组分质量分数、二维火焰面法向量梯度和二维速度梯度张量. 模型预测结果与DNS结果对比表明，理论模型预测的PDF与DNS的真实PDF吻合较好. RF模型的预测值与DNS实际值间的相关系数大于0.97，优于ANN模型. RF模型得到的PDF与真实PDF间的误差小于理论模型得到的PDF与真实PDF间的误差. RF模型能够由低维量准确预测三维切向应变率.
关键词： 湍流燃烧;  燃烧模型;  直接数值模拟;  切向应变率;  机器学习    
Abstract:

The relationship between two-dimensional (2D) and three-dimensional (3D) probability density functions (PDF) of tangential strain rate was proposed by theoretical method. Artificial neural network (ANN) and random forest (RF) models were developed to predict the 3D tangential strain rate from lower-dimensional quantities based on a direct numerical simulation (DNS) database of freely propagating premixed flames with three different turbulent intensities. The input features of the machine learning models include species mass fraction, 2D gradient of the flames normal vector and 2D velocity gradient tensor. The comparison of the model predictions and the DNS results showed that the PDF predicted by the theoretical model accorded with that of the DNS. The correlation coefficient of the RF predictions and actual values of the DNS was greater than 0.97, which was superior to that of the ANN model. The difference of the RF model predicted and actual PDF was smaller than that of the theoretical model predicted and actual PDF. 3D tangential strain rate can be accurately predicted by the RF model from lower-dimensional quantities.
Key words: turbulent combustion    combustion model    direct numerical simulation    tangential strain rate    machine learning
收稿日期: 2021-02-24 出版日期: 2021-07-30
CLC:  TK 5  
基金资助: 国家自然科学基金重大研究计划资助项目（91841302）；国家自然科学基金资助项目（51976185）
通讯作者: 王海鸥     E-mail: renjh@zju.edu.cn;wanghaiou@zju.edu.cn
作者简介: 任嘉豪（1997—），男，硕士生，从事湍流燃烧的直接数值模拟及模型研究. orcid.org/0000-0001-7415-3147. E-mail： renjh@zju.edu.cn
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任嘉豪
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邢江宽
罗坤
樊建人

引用本文:

任嘉豪,王海鸥,邢江宽,罗坤,樊建人. 湍流火焰切向应变率的低维近似模型[J]. 浙江大学学报(工学版), 2021, 55(6): 1128-1134.

Jia-hao REN,Hai-ou WANG,Jiang-kuan XING,Kun LUO,Jian-ren FAN. Lower-dimensional approximation models of tangential strain rate of turbulent flames. Journal of ZheJiang University (Engineering Science), 2021, 55(6): 1128-1134.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2021.06.013    或    https://www.zjujournals.com/eng/CN/Y2021/V55/I6/1128

算例 u′/（m·s?1） lt /mm τe /ms Re Ka
L 0.78 0.66 0.85 33 38
M 3.88 0.66 0.17 163 390
H 9.70 0.66 0.07 408 1710
表 1  DNS参数
图 1   $x{\text{-}}y$平面过程变量切片
图 2  坐标系示意图
图 3  机器学习模型的拓扑结构
图 4  理论模型预测概率密度函数与二维、三维真实概率密度函数的对比
图 5  模型超参数调优结果
图 6  测试样本预测值与真实值的散点关系图
模型 算例 R R2 MAPE /%
ANN L 0.908 0.822 22.15
ANN M 0.818 0.669 53.43
ANN H 0.792 0.623 71.82
RF L 0.997 0.994 4.14
RF M 0.984 0.968 11.73
RF H 0.981 0.960 16.23
表 2  ANN模型和RF模型性能的对比
图 7  RF模型测试样本预测概率密度函数与二维、三维真实概率密度函数的对比
图 8  基于RF模型的特征重要性分析
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