摘要
基于Pope修正的有效黏度假设,张量基神经网络(tensor based neural network,TBNN)构建了从雷诺平均方程湍流模型(RANS)的平均应变率张量和平均旋转率张量到高精度数值解的雷诺应力各向异性张量的映射.将高精度数值解用于TBNN的训练,从而使TBNN根据RANS求解的湍动能、湍流耗散率和速度梯度预测其雷诺应力各向异性张量,并与对应的高精度数值模拟结果以及风洞实验结果对比以评估TBNN的预测能力.本工作将TBNN的预测能力从低速域拓展至高超声速工况,分别对低速槽道流、低速NACA0012翼型以及高超声速平板边界层3种工况进行了小样本的训练并成功预测,并以槽道流训练的TBNN较好地预测了低速平板边界层,验证了模型的泛化能力.对于外推的低速槽道流算例,TBNN预测的结果在y^(+)>5的区域与直接数值模拟(DNS)以及实验的误差均在10%以内,预测结果揭示了TBNN对雷诺应力各向异性张量的良好预测能力;对于翼型的预测效果尽管相较于槽道流略有下降,但近壁关键区域较RANS结果仍有显著提升;对于高超声速平板,TBNN在边界层内展现出了良好的预测能力,在y^(+)>5的区域与DNS的误差同样在10%以内.基于Pope本构关系的TBNN方法在平板的高超声速工况下仍能较准确预测边界层内的雷诺应力各向异性张量,方法在宽速域下的预测能力具有较好的表现,且模型泛化能力亦得到了验证.
Tensor based neural network(TBNN)is constructed based on Pope’s effective viscosity hypothesis,and it’s used to produces a mapping from the mean strain rate tensor,mean rotation rate tensor calculated by Reynolds averaged Navier-Stokes(RANS)to the high resolution Reynolds stress anisotropy tensor.The high resolution data is used to train TBNN,then TBNN will give prediction results of Reynolds stress anisotropic tensor from the RANS result.The prediction of TBNN will be compared with high resolution numerical simulation and wind tunnel results to evaluate the prediction ability of TBNN.This work expands the predictive ability of TBNN from the low speed domain to hypersonic conditions.Small sample training is performed on low speed channel flow,NACA0012 and hypersonic boundary layer and the prediction accuracy is satisfactory.In addition,the TBNN trained with channel flow accurately predicts the boundary layer of the low-speed flat plate,which verifies the generalization ability of the model.For the extrapolation channel flow at low-speed,TBNN can predict the Reynolds stress anisotropy tensor well in the range of y^(+)>5,the error between direct numerical simulation(DNS),experiment and TBNN is inside 10%.Although the prediction accuracy of the low-speed airfoil is slightly lower than that of the channel flow,the cloud images predicted in the key area have significant improvement compared with RANS.For the hypersonic boundary layer,TBNN shows good predictive ability in the boundary layer,and the error between TBNN and DNS is also within 10%in the range of y^(+)>5.Although Pope’s constitutive law is proposed for most incompressible flows,TBNN can still predict the Reynolds stress anisotropy tensor under hypersonic conditions.The predictive ability of this method in a wide speed range is confirmed and the generalization ability of the model has also been verified.
作者
任海杰
袁先旭
陈坚强
孙东
朱林阳
向星皓
Ren Haijie;Yuan Xianxu;Chen Jianqiang;Sun Dong;Zhu Linyang;Xiang Xinghao(State Key Laboratory of Aerodynamics,Mianyang 621000,Sichuan,China;Computational Aerodynamics Institute of China Aerodynamics Research and Development Center,Mianyang 621000,Sichuan,China)
出处
《力学学报》
EI
CAS
CSCD
北大核心
2022年第2期347-358,共12页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家重点研发计划(2019 YFA0405204)
国家自然科学基金(92052301,12002355)资助项目。
关键词
张量基神经网络
雷诺应力各向异性张量
湍流建模
宽速域
小样本
tensor based neural network
Reynolds stress anisotropy tensor
turbulence modeling
wide speed range
small sample
