Reconstruction of Three-Dimensional Structures From Two-Dimensional Sectional Flow Fields of Cavitating Turbulent Flows Using Machine-Learning-Based Super-Resolution

Abstract A method is proposed for reconstructing spanwise cross-sectional data of a cavitating turbulent flow field around a 2D hydrofoil to a 3D flow field using supervised machine learning (ML). One of the variables of interest was the cross-sectional pseudomeasurement data of particle image velocimetry. Therefore, the spanwise component w of velocity was not obtained; that is, it cannot be input into neural networks (NN). To compensate for this, we introduced a mass conservation error into the loss function of ML. The computational fluid dynamics (CFD) data for the training were obtained using large-eddy simulation with a homogeneous fluid model for cavitation. The super-resolution convolutional neural network (SRCNN) was adopted for the supervised ML framework. As a result, under the attached sheet cavitation mode, which corresponds to a quasi-steady condition, prediction was relatively simple. In contrast, under sheet/cloud cavitation mode, which is a strongly unsteady condition, the learning curve exhibited oscillations, suggesting that learning is difficult. Physical variables with a uniform distribution in the homogeneous spanwise direction can be reconstructed with high accuracy even under unsteady conditions, whereas the rotational components of streamwise vortices, which are nonuniform in the spanwise direction and have high spatiotemporal frequencies, fluctuate even under quasi-steady conditions, making them extremely difficult to reconstruct. When the loss function is augmented with a mass conservation error, the accuracy of the w reconstruction is improved as the NN attempts to satisfy the conservation of mass.