Analytical formulations for NOx emissions prediction of SABRE engine

With an expected global revenue exceeding 1 trillion USD by 2040, the space industry is one of the world's fastest-growing sectors. Given the booming investment in the space industry and the anticipated space tourism era, it is crucial to assess the impact of already operative launch assets as well as to adopt design-to-sustainability strategies for the under-development and future launchers. This paper discloses novel analytical formulations to estimate nitrogen oxide emissions of a hydrogen-fueled air- breathing concept using a Synergetic Air Breathing Rocket Engine technology. Throughout the paper, the Skylon spaceplane and its Synergetic Air Breathing Rocket Engine are used as a case study. The methodology described specializes in updating the classical formulation of the Boeing Fuel Flow Method 2 (BFFM2) for estimating Nitrogen Oxide (NOx) emissions. This method currently enables the estimation of NOx emissions for any subsonic aircraft powered by traditional fuels. The objective is to derive new mathematical formulations applicable in the case of high-speed engines and hydrogen fuel. The proposed updating strategy is correlation-based and is generally applicable for modifying any analytical method for estimating emissions, including BFFM2. Through the analysis of correlations between the engine's propulsion and emission variables and its NOx production, a series of parameters are derived to integrate into the original formulation of BFFM2 to adapt it to the case study. The input parameters required for the application and validation of the method, both in its original form and in the proposed variations, are obtained through high-fidelity propulsion and emission modeling of the engine, representative of various on-ground and in-flight operating conditions. To this end, 0D chemical-kinetic air/hydrogen combustion numerical simulations are employed. The methodology disclosed allows proving the high competitiveness of these air-breathing space launchers with respect to famous past and current competitors, such as the Space Shuttle and the Falcon 9.