Multi-scale flow and hydraulic force decomposition in a pump-turbine operating in synchronous condenser mode

The Synchronous Condenser Pump (SCP) operation is a critical operational state for the pumping start-up and reactive power compensation in pumped-storage. However, the complex boundary conditions and high-pressure air–water two-phase flow characteristics pose long-standing challenges for numerical research. This study proposes a comprehensive simulation framework for SCP conditions, incorporating full geometric details such as clearances, labyrinth seals, and auxiliary piping. A multi-scale grid coupling strategy is employed to bridge scales from meters to millimeters, and the Peng-Robinson real gas model is introduced to describe the compressibility of high-pressure air. Utilizing this framework, the study investigates the force characteristics of the runner and their underlying flow mechanisms. Results indicate that hydraulic force in clearance channels is non-negligible, scaling comparably with the main passage hydraulic force. Within these clearances, a Batchelor-type rotating shear flow develops, governed by centrifugal effects and affected by the circumferential momentum dilution from cooling water and by air–water mixing. Runner blades experience minimal axial force (only 2.72% of total), driven mainly by water ring intrusion, while the radial force on the blades dominates the overall radial force, with a viscous contribution significantly higher than in conventional pump or turbine operations. This shift stems from the collapse of the pressure differential across the blade surfaces and the localized viscous stress induced by an asymmetric water ring at a characteristic frequency of 0.5fn. This research establishes a high-fidelity benchmark for simulating synchronous condenser operations and provides a theoretical framework for load prediction and operational optimization.