Supersonic impulse turbines are commonly used to harvest waste heat from systems based on organic Rankine cycles, automotive applications, and gas-generator liquid rocket engines. This research aims to design and analyze a single-stage supersonic turbine with a rated power of approximately 440 KW. We present a comprehensive preliminary design roadmap followed by design parameters optimization. The preliminary sizing is carried out using one-dimensional flow analysis, while the blade geometrical design is performed using the two-dimensional method of characteristics. The turbine performance is then analyzed through numerical simulations on three-dimensional models. Comprehensive parametric analyses are conducted to examine the turbine performance sensitivity to changes in partial admission (PA), mean radius, and turbine blade height using three-dimensional sliding mesh techniques (SMT). The current analysis simulates the full turbine to capture PA effects, rather than focusing on a single periodic sector as is common in turbomachinery simulation practices. Different PA scenarios are investigated, emphasizing a single rotor passage over a complete rotor cycle in a partially admitted turbine, and examining its charging and discharging mechanisms. Flow tracking over such a blade shows that the turbine rotor exhibits compressor-like behavior over most of the unadmitted zone, contributing to efficiency drops and severe transients.