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The Wave Disk Engine (WDE) is a novel engine that has the potential for higher efficiency and power density of power-generation systems. A recent version of wave disk engine architecture known as the two-stage WDE has been studied to address existing challenges of an existing WDE. After describing the engine operation, a cold air-standard thermodynamic model supporting the physical phenomena occurring inside the device is introduced to evaluate performance of the engine. The developed model is general and does not depend on the shape of the wave rotor, it can be applied to radial and axial combustion wave rotors integrated with turbomachinery devices. The analysis starts with predicting internal waves propagating inside the channels of the engine and linking various flow states to each other using thermodynamics relationships. The goal is to find analytical expressions of work output and efficiency in terms of known pressure and temperature ratios.