Studies on the onset of carbon dioxide condensation undergoing rapid expansion through a converging–diverging nozzle

Carbon dioxide (CO2) is emerging as a natural, eco-friendly working fluid in refrigeration, energy conversion, and carbon-capture technologies, where rapidly expanding flows in nozzles are encountered in the transcritical domain involving condensation. Rapid expansion delays condensation onset, impacting nozzle efficiency, which is dependent on nozzle geometry and inlet conditions. Previous studies have explored limited factors, and broader questions regarding the cohesive prediction of condensation onset delay remain open, motivating this study. Experiments are conducted in an optically accessible CO2 supersonic nozzle test section over carefully chosen inlet states spanning supercritical and superheated conditions, with a critical supersaturation ratio between 1.01 and 1.14. High-speed shadowgraphy, wall static pressure measurements, and laser Doppler anemometry are employed, with condensation onset identified from reduced light transmittance. Corroborative Quasi-one-dimensional (Quasi-1D) analysis and computational fluid dynamics simulations based on classical nucleation theory (CNT) are performed and compared with isentropic homogeneous equilibrium (IHE) predictions. CNT-based approaches show closer agreement with experiments, predicting pressure and velocity profiles within 17%, compared to 31% for IHE. A notable observation is that inlet states with similar entropy exhibit identical condensation onset delays, highlighting the role of inlet entropy. This motivates the derivation of a non-dimensional parameter (Uf) incorporating geometric and operational parameters. Condensation onset data from the present and previous studies collapse onto a power–law with Uf, which is validated using untested geometries. The proposed correlation provides a robust metric for characterizing condensation delay in CO2 nozzles flows and offers potential applicability to other working fluids.