Lower-dimensional approximation models of tangential strain rate of turbulent flames

doi:10.3785/j.issn.1008-973X.2021.06.013

Journal of ZheJiang University (Engineering Science)

2021, Vol. 55

Issue (6): 1128-1134 DOI: 10.3785/j.issn.1008-973X.2021.06.013

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

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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

Received: 24 February 2021 Published: 30 July 2021

CLC:

TK 5

Fund: 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）

Corresponding Authors: Hai-ou WANG E-mail: renjh@zju.edu.cn;wanghaiou@zju.edu.cn

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Cite this article:

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.

URL:

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

湍流火焰切向应变率的低维近似模型

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

Tab.1 Parameters of DNS

Fig.1 Slices of distributions of progress variable in typical x-y planes

Fig.2 Schematic of coordinate system.

Fig.3 Topological structures of machine learning models

Fig.4 Comparison of two-dimensional, three-dimensional and model predicted probability density functions in theoretical model

Fig.5 Results of hyper-parameter optimization of models

Fig.6 Scatter plots of modeled and actual values for test samples

Tab.2 Comparison of performance of ANN model and RF model

Fig.7 Comparison of two-dimensional, three-dimensional and model predicted probability density functions in RF model

Fig.8 Feature importance based on RF model


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