### Abstract

Accurate prediction of turbulence statistics in marine hydrokinetic (MHK) turbine wakes is important in turbine layout optimization. However, the high-fidelity simulation for the turbulence statistics prediction is computationally expensive due to the large computational domain size and the long sampling time. Therefore, we developed a physics-informed autoencoder convolutional neural networks (CNNs) algorithm to reconstruct the turbulence statistics of wake flow of MHK turbines at a small fraction of the computational cost of high-fidelity simulations.

The proposed algorithm consists of two parts. The first part is an autoencoder CNN which uses several instantaneous flow field snapshots as the inputs to reconstruct the time-averaged velocity field. The second part is another autoencoder CNN to reconstruct the Reynolds stresses field using the instantaneous velocity fluctuations calculated from instantaneous velocity and predicted time-averaged velocity. Physics constraints, such as mass and momentum conservation, are considered in the prediction of time-averaged velocity field through additional physicscal constraints terms in the loss function, to ensure the prediction results are coincident with the physics laws.

To examine the performance of the proposed physics-informed autoencoder CNNs algorithm, large eddy simulations (LES) of turbulent flow around MHK turbines in three different configurations (one training case and two validation cases) are conducted in large-scale waterways to generate training and validation data. In the simulation, the MHK turbines are modeled by the actuator line method. The inputs of the physics-informed autoencoder CNNs algorithm are five instantaneous flow field snapshots obtained from LES, and the targets of the outputs are the time-averaged velocity and normal Reynolds stresses calculated by LES. The CNNs are trained using the LES data of the training case, then the developed CNN is validated using the two validation cases. The predicted results of the two validation cases are compared against the LES result, showing good agreement, while the computational cost of the CNNs is orders of magnitude less than the LES.