Prediction of pulsating turbulent pipe flow by deep learning with generalization capability

The spatiotemporal development of turbulent pipe flows with various conditions of pulsation is predicted by deep learning. In the present model, convolutional autoencoder (CAE) extracts the spatial features of the input as latent space vectors and long short-term memory (LSTM) evolves them in time. Time-delay neural network (TDNN) is accompanied by LSTMs to treat general unsteady variations of the spatial mean pressure gradient of the pulsatile flows. Temporal evolution is processed in a sequence-to-sequence manner. Note that the pulsating turbulent pipe flows are statistically unsteady flows for which the spatiotemporal development has been seldom predicted by the deep learning technique. The flow field obtained by direct numerical simulation (DNS) was used to train the model. When the pulsating parameters for the training and prediction are the same, several model parameters are validated. To examine further generalization capability, the present model was trained by data from four pulsation conditions. The model was tested afterward by test data from twenty different pulsation conditions of which the range of parameters is either within or out of the range covered by the training data. The model successfully predicts the various pulsating flow fields with reasonable accuracy. The change in the period yields a larger influence on prediction accuracy than the change in the amplitude. The degradation of the prediction accuracy of the bulk velocity for the case with a long period and large amplitude is not caused by the latent space vectors themselves, but by the decoder which reconstructs the flow field from the latent space vectors.