Development of Artificial Neural Network Models for Calculating Internal Energies and Specific Heats of Air Species

Reentry vehicles encounter nonequilibrium flows during their flights. For accurate prediction of the aerothermodynamic characteristics of these vehicles, a thorough understanding of non-equilibrium flows is necessary. In the widely used two-temperature model, rigid-rotor harmonic oscillator (RRHO) assumptions are applied to estimate the thermodynamic properties of gas species. Although the RRHO assumptions simplify the calculations, they fail to capture key high-temperature effects, such as anharmonicity, non-rigidity, and coupling between energy modes. In contrast, partition functions, used in statistical mechanics, can predict these properties without assumptions, but their computation is time-consuming. To overcome the limitations of both approaches, this study proposes artificial neural network (ANN)-based models for predicting the internal energies of five air species under non-equilibrium conditions. The models are also capable of predicting specific heat by differentiating the internal energy with respect to the temperature. Training data is generated using the partition function, covering a temperature range of 50 to 50,000 K. ANN models are trained to minimize relative errors using the Levenberg-Marquardt algorithm and validated by comparing their predictions with data based on partition functions, showing excellent agreement with a maximum error of 5\%. ANN models offer an efficient and accurate alternative to traditional methods, with potential integration into computational fluid dynamics (CFD) solvers to enhance high-enthalpy flow simulations.