Supercritical Carbon Dioxide Shock Behavior Near the Critical Point

This paper aims to provide an understanding of sCO₂ inviscid adiabatic normal shock behavior near the critical point and to develop an explicit tool for faster prediction of the shock relations that can aid the supercritical turbomachinery design process. An iterative algorithm was developed to compute shockwave behaviors for nonideal fluids. Three important shock behavior parameters were investigated: postshock Mach number, shock strength, and polytropic efficiency. A comparative study was carried out between air (ideal gas assumption), ideal gas CO₂ (ideal gas assumption), and nonideal fluid CO₂ (Span–Wagner equation of state). The distinct differences show the inadequacy of the perfect gas shock relations when predicting sCO₂ shock behavior near the critical point. The results of nonideal fluid calculations show a general trend of stronger shock strengths and higher polytropic efficiencies toward lower preshock entropy conditions. This is also distinctive near the critical point due to the reduced speed of sound. Finally, explicit expressions for these parameters were retrieved using symbolic regression. The fitted models have significant improvements compared to the prediction from perfect gas shock relations with a 5–20% point reduction in relative errors. This study also shows the potential for machine learning to be applied in nonideal fluid effects modeling and the methodology developed in this paper can be easily introduced to other working fluids in their ranges of interest.