The space sector is undergoing rapid expansion due to the transformations it is experiencing, evolving from government-funded traditional space initiatives to commercially driven NewSpace activities. The surge of government and private investments in the space domain has positioned it as one of the world's fastest-growing sectors, making it crucial to assess the impact of already operational launch assets and to adopt design-to-sustainability strategies for under-development and future launchers. To actively contribute to this transition, this paper proposes a methodology for deriving novel analytical formulations to estimate nitrogen oxide (NOx) emissions of a hydrogen-fueled reusable access-to-space vehicle. Throughout the paper, the Skylon spaceplane and its Synergetic Air Breathing Rocket Engine are used as a case study. In particular, the SABRE engine presents a highly integrated dual propulsion architecture supporting both air-breathing and rocket modes. This study specifically focuses on the former, enabling the Single Stage To Orbit (SSTO) Skylon reaching the hypersonic speed regime before transitioning to rocket mode. This paper proposes novel analytical formulations to be integrated into the Fuel Flow (FF) and P3-T3 methods for estimating NOx Emission Index (EINOx), since the early design phase. These estimation techniques currently enable the calculation of the emission index of pollutants and GreenHouse Gases (GHGs) produced by any subsonic aero-engines powered by traditional fuels (i.e. kerosene) only. The methodology presented in this paper allows for upgrading the original mathematical formulations of the methods to ensure the applicability to high-speed flight and hydrogen fuel conditions. This involves the propulsive modelling of the engine and the chemical-kinetic modelling of the combustion process, representative of various on-ground and in-flight operating conditions, to generate updated and reliable propulsive and emissive databases for the engine. To this end, 0D chemical-kinetic air/hydrogen combustion numerical simulations are employed. The results of the performance analysis and emission modeling of the SABRE engine are reported and discussed. Regarding the calculated EINOx trend for the air-breathing phase of the engine operation, it reaches a peak of 45 gNOx/kgH2burnt under hypersonic conditions. Through the analysis of correlations between the propulsive characteristics of the SABRE and its NOx production, a series of parameters (such as Mach Number, Fuel to Air Ratio, Water to Fuel Ratio, and others) are selected to be integrated into the original formulations of the P3-T3 and FF methods via mathematical interpolation to adapt them to the case study. Finally, the EINOx trends resulting from the application of the new H2-P3T3 and H2-FF methods to the SABRE are graphically reported, along with the corresponding estimation errors relative to the reference trend from the engine emission database. Additionally, a discussion regarding the chemical-physical justifications for the mathematical contributions to the formulations for EINOx of the newly introduced parameters is provided.
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