Analysis of non-equilibrium condensation characteristics of supercritical carbon dioxide during transcritical flow in the Laval nozzle

During near critical operation, the non-equilibrium phase transition risk of supercritical carbon dioxide compressors usually poses significant challenges to the stability of the whole system. Analyzing the condensation characteristics in the Laval nozzle is considered an effective and feasible method for understanding condensation behavoir of supercritical carbon dioxide in rotating machinery due to the similarity and measurability of flow. In this paper, the Euler-Euler Source numerical model coupled with high-accuracy carbon dioxide real gas property table is established for transonic compressible flow in the Laval nozzle. The non-equilibrium effects of expansion and condensation during transonic flow in the nozzle are discussed and the relationships between inlet parameters, droplet distribution and nucleation rates are also analyzed. The numerical result shows that the nonequilibrium characteristic during the expansion process causes the delay of condensation in the nozzle, resulting in an overestimation of the prediction of carbon dioxide condensation region based on the homogeneous equilibrium model. Shock wave of transonic flow further amplifies the deviation of results and leads to over 12 % overestimation of liquid mass fraction. Increasing the inlet pressure and decreasing the inlet temperature can cause the forward movement of the condensation onset and the reduce of the nucleation region. For supercritical carbon dioxide in the transonic flow, the value of critical pressure ratio can be taken as 0.54 similar to 0.55. These results provide valuable suggestions in the analysis of non-equilibrium condensing flow and designing inlet conditions for experiments.