Unsteady flow analysis in a double-suction pump as turbine impeller based on finite-time Lyapunov exponent

Pump as turbine (PAT) is an excellent energy recovery device. Understanding the flow characteristics of the key component, the impeller, is essential for further optimization and design of PAT. To analyze the unsteady flow characteristics inside the impeller of a double-suction PAT from a Lagrangian perspective, numerical simulations were conducted using the shear stress transport k–ω turbulence model for the design conditions. The finite-time Lyapunov exponent (FTLE) method was employed to extract the two-dimensional and three-dimensional Lagrangian coherent structures (LCSs) of the impeller over one cycle of unsteady velocity field. Results indicate that with time, the scale of the FTLE field gradually decreases, suggesting enhanced flow stability, reduced mixing efficiency, smoother flow structures, and increased flow convergence. In the two-dimensional perspective, high FTLE values concentrate at the inlet region of the passage, pressure side of the blades, and outlet region of the passage, spreading gradually over the entire blade surface, while low FTLE values predominantly concentrate on the blade surface with a diminishing area. The flow separation occurs at the leading edge of the impeller, the suction side of the impeller and the inlet region of the flow channel. In the three-dimensional perspective, different LCSs show varied changes at specific FTLE values, reflecting the impact of FTLE variation on the distribution of LCSs and indicating the evolution of flow states in fluid dynamics. Each moment of LCS exhibits a growth–stability–dissipation status transition. The FTLE method effectively reveals the flow variations inside the impeller of a double-suction PAT, offering a new perspective and tool for analyzing the turbulent structures in the complex flow field of PAT.