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...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.展开更多
<正> With respect to small deformation gradient tensor,the displacement gradientmoduli Φ_(iLjM)~* at the reference system are introduced by taking into account the rela-tion of the first Piola-Kirchhoff stress ...<正> With respect to small deformation gradient tensor,the displacement gradientmoduli Φ_(iLjM)~* at the reference system are introduced by taking into account the rela-tion of the first Piola-Kirchhoff stress tensor T_(iL) and displacement gradient tensor u_(jM)in the paper.Then the specific expression of Φ_(iLjM) is derived by the comparison of theexpansion terms of Helmholtz free energy H.Finally,the coefficients (?)_(iLjM) related toΦ_(iLjM) are obtained by using ultrasonic measurement and the elastic tensor C_(iLjM) whichdepends on (?)_(iLjM) and initial stresses in the reference system are given.展开更多
文摘基于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.
文摘<正> With respect to small deformation gradient tensor,the displacement gradientmoduli Φ_(iLjM)~* at the reference system are introduced by taking into account the rela-tion of the first Piola-Kirchhoff stress tensor T_(iL) and displacement gradient tensor u_(jM)in the paper.Then the specific expression of Φ_(iLjM) is derived by the comparison of theexpansion terms of Helmholtz free energy H.Finally,the coefficients (?)_(iLjM) related toΦ_(iLjM) are obtained by using ultrasonic measurement and the elastic tensor C_(iLjM) whichdepends on (?)_(iLjM) and initial stresses in the reference system are given.
