Evaporation of a CO₂ Droplet in a High Temperature, Supercritical Pressure Environment

This study presents a numerical investigation of the transient relaxation dynamics of a near-critical CO₂ droplet immersed in a warmer supercritical environment composed of the same fluid. Three thermodynamic regimes were analysed: quasi-critical ( $T_r=1.01,P_r=1.01$), transitional ( $T_r=2.01,P_r=1.01$), and deep supercritical ( $T_r=5.01,P_r=3.01$). The evolution of density, temperature, and velocity fields was examined to characterize the internal structure and stability of the interfacial transition layer. The evolution of density, temperature, and velocity fields highlights the competition between thermal diffusion, compressibility, and mass confinement in shaping the stability of the interfacial transition layer. Near the critical point, strong gradients and flux discontinuities emerge, consistent with known instabilities, whereas higher reduced conditions promote homogenization and stabilized transport. In the deep supercritical regime, smooth and nearly uniform fields indicate robust thermal stability. The model is validated against prior studies on droplet evaporation under supercritical and trans-critical conditions. Beyond theoretical insights, the results underline practical implications for advanced propulsion, heat transfer, and evaporation systems as well as for safe CO₂ supercritical storage and extraction processes in energy, aerospace, pharmaceutical, and materials industries.