AbstractThe multidisciplinary design optimization (MDO) of re-entry vehicles presents many challenges associated with the plurality of the domains that characterize the design problem and the multi-physics interactions. Aerodynamic and thermodynamic phenomena are strongly coupled and relate to the heat loads that affect the vehicle along the re-entry trajectory, which drive the design of the thermal protection system (TPS). The preliminary design and optimization of re-entry vehicles would benefit from accurate high-fidelity aerothermodynamic analysis, which are usually expensive computational fluid dynamic simulations. We propose an original formulation for multifidelity active learning that considers both the information extracted from data and domain-specific knowledge. Our scheme is developed for the design of re-entry vehicles and is demonstrated for the case of an Orion-like capsule entering the Earth atmosphere. The design process aims to minimize the mass of propellant burned during the entry maneuver, the mass of the TPS, and the temperature experienced by the TPS along the re-entry. The results demonstrate that our multifidelity strategy allows to achieve a sensitive improvement of the design solution with respect to the baseline. In particular, the outcomes of our method are superior to the design obtained through a single-fidelity framework, as a result of the principled selection of a limited number of high-fidelity evaluations. Aerodynamic and thermodynamic phenomena are strongly coupled and relate to the heat loads that affect the vehicle along the re-entry trajectory, which drive the design of the thermal protection system (TPS). The preliminary design and optimization of re-entry vehicles would benefit from accurate high-fidelity aerothermodynamic analysis, which are usually expensive computational fluid dynamic simulations. We propose an original formulation for multifidelity active learning that considers both the information extracted from data and domain-specific knowledge. Automotive Engineering Body, Aerodynamics, Design Computer-Aided Engineering (CAD, CAE) and Design Engineering Design Vehicle Engineering Aerospace Technology and Astronautics Aerodynamic Design Optimization Methods 1 Introduction Modern space missions are increasingly supported by vehicles able to perform complex assignments and return safely to the Earth’s surface. Examples are manned capsules used for the transfer of astronauts to the international space station and for future Lunar and Martian explorations (Smith et al. 2020 ; Williamson 2017 ). 1 Full size image Re-entry through the Earth atmosphere: conceptual phases Our framework aims at capturing the multi-physics nature of the mission and of the design of a re-entry vehicle, accounting for the contributions introduced by the propulsion system, the re-entry trajectory at a given entry point, the aerothermodynamic effect characterizing the re-entry path and the thermo-structural aspects associated with the sizing of the thermal protection system. In particular, we consider the case of an Orion-like capsule re-entering the Earth atmosphere. 2 Full size image Geometry of the Orion-like re-entry capsule considered in this work Table 1 Design parameters of the Orion-like geometry Full size table Table 2 Design parameters of the primary and the secondary thrusters Full size table Table 3 Design parameters of the re-entry trajectory Full size table Table 4 Design parameters of the thermal protection system Full size table 2.1 Propulsion system model The model of the propulsion system evaluates the mass of the propellant required to complete the entry maneuver, given the propulsive thrust and the engines specifications (Table  2 ). 5 Full size image Heat flux evaluated with the low-fidelity aerothermodynamic model, for the case of an unpowered re-entry of the Orion-like capsule 2.5 Thermo-structural model of the thermal protection system The Thermo-structural model evaluates the temperature of the TPS structure \(T_{{{\text{TPS}}}}\) and the mass of the TPS frame \(m_{{{\text{TPS}}}}\) , given the total heat load \(\dot{q}\) provided by either the low or the high-fidelity aerothermodynamic model (Sects. 2.4 – 2.3 ), the thickness of the TPS structure \(s_{{{\text{TPS}}}}\) , the material property of the TPS (Table  4 ) and the geometry of the capsule (Table  1 ). The model of the thermal protection system computes the mass of the structural frame of the TPS \(m_{{{\text{TPS}}}}\) : $$m_{{{\text{TPS}}}} = \rho _{{{\text{TPS}}}} S_{{{\text{TPS}}}} s_{{{\text{TPS}}}}$$ (14) where \(S_{{{\text{TPS}}}}\) is the frontal surface of the spherical shell that approximates the structure of the TPS, given by the area of the circle with radius equal to the radius of the nose of the capsule \(R_N\) . Fig. The aerothermodynamic models compute the heat flux at the stagnation point \(\dot{q}\) , which is used to compute the temperature \(T_{{{\text{TPS}}}}\) and the mass \(m_{{{\text{TPS}}}}\) of the TPS structure through the model of the thermal protection system (Sect. 2.5 ). The computational flow includes two feedback loops: one couples the model of the trajectory with the aerothermodynamic block through the aerodynamic forces coefficients \(C_L\) and \(C_D\) , the other couples the aerothermodynamics and the model of the TPS through the temperature \(T_{{{\text{TPS}}}}\) . IEEE Trans Eng Manage 28(1981):1 Google Scholar Stewart M, Koenig WJ, Harris RF (2018) Thermal protection systems technology transfer from Apollo and space shuttle to the Orion program Sutherland W (1893) Lii. the viscosity of gases and molecular force. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of. Science 36(223):507–531 Sutton GP, Biblarz O (2016) Rocket propulsion elements. Wiley, Hoboken Google Scholar Sutton K, Graves RA Jr (1971) A general stagnation-point convective-heating equation for arbitrary gas mixtures. Work 50:7885 Google Scholar Tauber ME,