Prediction of the Flow Dynamics of a Sphere Translating near a Plane Wall at Low Reynolds Numbers Using a Multi-Output Deep Learning Model

This study uses data generated by Direct Numerical Simulations (DNS) to develop a multi-output feedforward neural network (FNN) model that is able to accurately and efficiently predict the drag and lift forces on a sphere translating next to a plane wall in laminar flow conditions. The FNN model was trained using 715 Immersed Boundary Direct Numerical Simulation method (IB-DNS) samples with a 15% validation split. The training samples were comprised of Reynolds numbers ranging from 0.5 to 20, the ratio of distance from the plane wall to the centerline of the sphere and the sphere diameter 0.75 ≤ L/D ≤ 2.5, and the angular velocity Reynolds number -5 ≥ Reω ≥ 5 as input features and drag and lift coefficients as the output labels. K-fold cross validation method was implemented to assess the final model's architectural stability, with a training validation split of 15% used for learning and approximately 20% test split for each fold. The final FNN model was able to predict 100% of the train samples within ±5% deviation from the known drag coefficients, and 91% of the train samples within ±10% of the known lift coefficients. Overall, this work demonstrates that a densely connected multi-output regression FNN architecture can be designed and optimized to accurately predict the near-wall flow dynamics of a sphere with only a few dimensionless inputs. Correlations for drag and lift were also developed for the DNS data using a curve fitting method for a fixed value of Reω, which also highlights the advantage of using a FNN regression model approach.