论文标题
雷诺（Reynolds
Reynolds Stress Anisotropy Tensor Predictions for Turbulent Channel Flow using Neural Networks
论文作者
论文摘要
雷诺（Reynolds）平均的Navier-Stokes（RANS）方法由于其高成本效益而仍然是湍流建模的骨干。它的精度主要基于可靠的雷诺应力各向异性张量闭合模型。旨在改善传统闭合模型的工作量，而对某些复杂的流程配置仍然不满意。近年来，计算能力的进步为解决此问题的新方法开辟了新方法：机器学习辅助的湍流建模。在本文中，我们采用神经网络来充分预测不同摩擦雷诺数在不同摩擦雷诺数上的雷诺各向异性各向异性张量。多层感知器（MLP）类型的几种通用神经网络经过不同的输入特征组合训练，以完全了解每个参数的作用。最佳性能是由模型产生的，无尺寸的平均流速度梯度$α$，无尺寸壁距$ y^+$和摩擦reynolds $ \ mathrm {re}_τ$作为输入。对张量基碱神经网络（TBNN）的更深入的理论洞察力阐明了文献中有关其在教皇的一般涡流粘度模型的应用中发现的剩余歧义。我们强调TBNN对持续张量$ \ textbf {t}^{*（0）} $对动荡的通道流数据集的敏感性，并新提出了一个广义的$ \ textbf {t}^{*（0）} $，从而大大提高了其性能。 Through comparison between the MLP and the augmented TBNN model with both $\{α, y^+, \mathrm{Re}_τ\}$ as input set, it is concluded that the former outperforms the latter and provides excellent interpolation and extrapolation predictions of the Reynolds stress anisotropy tensor in the specific case of turbulent channel flow.
The Reynolds-Averaged Navier-Stokes (RANS) approach remains a backbone for turbulence modeling due to its high cost-effectiveness. Its accuracy is largely based on a reliable Reynolds stress anisotropy tensor closure model. There has been an amount of work aiming at improving traditional closure models, while they are still not satisfactory to some complex flow configurations. In recent years, advances in computing power have opened up a new way to address this problem: the machine-learning-assisted turbulence modeling. In this paper, we employ neural networks to fully predict the Reynolds stress anisotropy tensor of turbulent channel flows at different friction Reynolds numbers, for both interpolation and extrapolation scenarios. Several generic neural networks of Multi-Layer Perceptron (MLP) type are trained with different input feature combinations to acquire a complete grasp of the role of each parameter. The best performance is yielded by the model with the dimensionless mean streamwise velocity gradient $α$, the dimensionless wall distance $y^+$ and the friction Reynolds number $\mathrm{Re}_τ$ as inputs. A deeper theoretical insight into the Tensor Basis Neural Network (TBNN) clarifies some remaining ambiguities found in the literature concerning its application of Pope's general eddy viscosity model. We emphasize the sensitivity of the TBNN on the constant tensor $\textbf{T}^{*(0)}$ upon the turbulent channel flow data set, and newly propose a generalized $\textbf{T}^{*(0)}$, which considerably enhances its performance. Through comparison between the MLP and the augmented TBNN model with both $\{α, y^+, \mathrm{Re}_τ\}$ as input set, it is concluded that the former outperforms the latter and provides excellent interpolation and extrapolation predictions of the Reynolds stress anisotropy tensor in the specific case of turbulent channel flow.
