The comparison of pump flow field via decomposition mode dynamic and proper orthogonal decomposition: An analysis of gappy proper orthogonal decomposition

To meet the real-time requirements of digital twin and enhance computational efficiency, this paper explores the application of modal decomposition techniques, proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD), in the field of pump fluid dynamics instead of traditional numerical simulation, which is limited by the complexity of the Navier–Stokes equations. Before decomposition, transient flow field of pump impeller and volute needs to be calculated under 0.6Q and 1.0Q, with significant differences. The results show that the first five modes capture most of the flow field's energy, with errors remaining below 10−2 even at 30 modes. However, the flow at off-design conditions is more unstable, with higher reconstruction errors using POD and more fragmented flow features in the DMD analysis. More importantly, to address potential incomplete data, gappy-POD was used to reconstruct data from single and multiple snapshots with varying levels of data loss. For single snapshots, reconstruction error is minimally affected by data sparsity, with errors below 0.0005 at 20 modes. For multiple snapshots, reconstruction accuracy is more sensitive to the iteration count and sparsity level, with a negative correlation between the sparsity level and the number of modes. Especially, when the sparsity level is less than or equal to 50%, the error does not significantly decrease after 10 iterations. At an 80% sparsity level, the iteration count significantly impacts the data repairing, with the first ten modes being more beneficial for repairing in missing data after 15 iterations.