This thesis investigates the use of solid oxide fuel cells (SOFCs) to consume waste hydrogen and improve the overall performance of a Hybrid Aluminum Combustor (HAC): a novel underwater power system based on the exothermic reaction of aluminum with seawater. The system is modeled using a NASA-developed framework called Numerical Propulsion System Simulation (NPSS) by assembling thermodynamic models developed for each component. Results show that incorporating the SOFC is not beneficial in cases where venting hydrogen overboard is permissible. However, when venting hydrogen is not permissible - which is the situation for most missions - the HAC-SOFC provides a 5 to 7 fold increase in range/endurance compared to equivalent battery powered systems. The utility of NPSS was demonstrated for evaluating and optimizing underwater propulsion system performance. Methodologies for predicting how system volume and mass scale with power were also developed to enable prediction of power and energy density.