Unsteady flow analysis in a pump as turbine impeller based on proper orthogonal decomposition and dynamic mode decomposition methods

Abstract

Pump as turbine (PAT) is an efficient, simple, and cost-effective equipment combining pump and turbine and is one of the excellent energy recovery devices. It is helpful to master the flow characteristics of the key component impeller for the further optimization and design of the PAT. To analyze the unsteady flow features in the impeller of a double-suction pump operating as a turbine, numerical simulations were conducted using the shear stress transport (SST) k-ω turbulence model at the designed operating conditions. By utilizing proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) methods on the unsteady velocity field of a single cycle, the dominant modes up to the fourth order, along with their respective space–time information, can be extracted. The velocity field and vorticity field analysis were performed on the first four modes extracted using two different methods. Additionally, the vortex structures were extracted using the Ω method. The analysis demonstrates that the POD and DMD methods effectively decompose the intricate flow characteristics within the impeller into dynamic–static interference modes, fundamental modes, and dissipative modes. The dynamic–static interference mode is dominant, reflecting the flow characteristics influenced by the stationary components within the impeller. The vortex structure is mainly small tubular vortex and point vortex. The fundamental mode captures the steady flow field characteristics caused by the blade channel geometry. The vortex structure is mainly continuous tubular vortex and the diameter becomes larger. The dissipative mode reflects the flow separation generated on the blades by disturbances from the stationary components. The vortex structure is dominated by point vortex and discontinuous tubular vortex. Comparing the outcomes of the two modal analysis methods shows that the POD method has a distinct advantage in showcasing key changing nodes. In contrast, the DMD method is superior in isolating modes with a single frequency and in determining their stability.