Multi-solution characteristic and thrust-specific impulse trade-off in a methane-fueled expander cycle engine

For application scenarios such as UAVs, combined-cycle vehicles, and high-altitude test platforms, the methane-fueled expander cycle (MFEC) engine offers advantages including high thrust-to-weight ratio and low cost. The core challenge of this configuration lies in the strong system coupling induced by the dual role of methane as both coolant and power-generation working fluid. Existing studies have primarily focused on performance evaluation of the engine. To explain the off-design performance distribution of the MFEC engine, this work first establishes its common operating equations and reveals that the matching of a low-flow-rate, high-expansion-ratio methane turbine with a high-flow-rate, low-pressure-ratio air compressor leads to a multi-solution characteristic — at a given compressor operating point, multiple equivalence ratio solutions can exist, both above and below unity. Based on these common operating equations, a steady-state control strategy with rotational speed and equivalence ratio as control variables is proposed. Subsequently, using a zero-dimensional component-level thermodynamic cycle model, control laws targeting maximum thrust and optimal specific impulse along the flight profile are obtained. Specifically, the maximum-thrust states are distributed in the high-equivalence-ratio, high-rotational-speed region, while the optimal specific-impulse states lie mainly in the low-equivalence-ratio, low-rotational-speed region. This leads to the steady-state control strategy centered on rotational speed and equivalence ratio. Notably, below Mach 0.6, the optimal thrust and optimal specific-impulse trajectories largely coincide (specific-impulse difference ' 50 s), whereas at Mach 3 the two trajectories diverge significantly: the thrust-optimal scheme increases specific thrust by 213 m/s at the cost of a specific-impulse penalty of about 88 s. Furthermore, the study finds that the primary constraints are compressor surge and rotational speed limits, rather than the conventional turbine inlet temperature limit. These findings reveal the multi-solution characteristic and performance trade-off behavior of the methane-fueled expander cycle engine, offering practical guidance for thrust-specific impulse coordination in supersonic propulsion applications.