基于直接数值模拟数据和神经网络的湍流封闭模型构建

Turbulence closure model based on neural network and direct numerical simulation data

雷诺平均Navier-Stokes方程(Reynolds-averagedNavier-StokesRANS)是目前工程上高效数值模拟湍流的基本方法,但这一方法需要给出关于雷诺应力的湍流封闭模型。该文从环形方管流场的直接数值模拟(DirectNumerical Simulation,DNS)数据出发,构建了一种基于神经网络的湍流封闭模型。文中利用环形方管流场DNS结果中的平均速度场及其梯度场作为流动特征输入量,与雷诺应力张量中各分量分别建立神经网络映射,从而构造出平均速度场及其梯度场与湍流雷诺应力的非参数化映射关系。计算结果表明,通过对环形方管DNS数据的深度学习,神经网络模型可有效地表达湍流时平均流场与雷诺应力之间的映射关系,并且能够准确地重构DNS所给出的雷诺应力,进而采用RANS基本方程捕捉到传统湍流模型中难以模拟的湍流驱动二次流现象,为新型湍流封闭模型的构建及其工程计算的实现提供创新思路。

The Reynolds-averaged Navier-Stokes(RANS) equations are commonly regarded as the most popular approach to efficiently simulate turbulent flow in engineering. However, the RANS method requires a turbulence closure model for Reynolds stresses. Based on the direct numerical simulation(DNS) data for the turbulence in a square annular duct, the neural-network(NNW) deep-learning method is applied to construct the closure model. The time-averaged velocity and the its gradients from the DNS data are used as the characteristic inputs and the NNW mapping with these inputs is established for each component in the Reynolds stresses, which constitutes a non-parameterized mapping from the time-averaged flow to the Reynolds stresses. The numerical experiments indicate that the NNW mapping can effectively generate the correlation between the mean flow field and the Reynolds stress components, and therefore accurately predict the Reynolds stresses in the NNW deep-learning process. The NNW-predicted Reynolds stresses are then applied to the RANS computation, which yields the accurate mean flow fields, including the mean streamwise velocity and the turbulence-driven secondary flow. The current turbulence closure model based on the NNW and DNS overcomes the difficulty in the traditional RANS models. In the paper, the practice provides a concept proofing for the NNW approach and DNS data to be applied to the turbulence engineering simulation.