Learning from sparse flow field observations to unsteady hydrodynamics of pump-jet propulsor via a novel data-driven method

The unsteady hydrodynamic force acting on a pump-jet propulsor is primarily induced by its interaction with the non-uniform wake flow of the underwater vehicle. Accurate estimation of this temporal force is important, as it directly determines the hydraulic as well as acoustic performance of the propulsion system. Performing high-fidelity prediction, however, typically relies on costly experiments or time-consuming unsteady numerical simulations, which limit the design efficiency. The challenge is further compounded by the difficulty of obtaining global flow field observations. To this end, a reduced-order surrogate modeling framework, termed Gappy Proper Orthogonal Decomposition with Time-delayed Gaussian Process Regression (GappyPOD-TGPR), is proposed to quickly reconstruct the wake flow field based on sparse observations using GappyPOD, and to predict the associated unsteady force response through the POD-assisted Gaussian process for time-delayed regression. Numerical evaluations on the well-known Suboff model with pump-jet propulsor show that both the reconstructed wake flow field and the predicted force closely match the high-fidelity computational fluid dynamics (CFD) results. For the investigated case, the trained GappyPOD-TGPR model reduces the computational time from approximately 72 h required by a single high-fidelity unsteady CFD simulation to the millisecond scale during online prediction, indicating its potential for rapid inverse reconstruction and performance assessment from sparse wake observations.