Thermodynamic Interpretation of Cryogenic Injection Experiments

This paper discusses a thermodynamic rather than mechanic discussion and interpretation of cryogenic injection of nitrogen in the vicinity of the critical point. There is no concensus in the literature on how to properly interpret and treat injection phenomena at supercritical pressures. While it is clear that the supercritical fluid loses many distinct liquid properties, such as heat of vaporization and surface tension, flows are being treated like they were liquid. Liquid core lengths are being determined in experiments, distinct droplets are tracked in computational fluid dynamic studies. And in fact, these approaches prove to be very successful. Nevertheless, a more appropriate treatment is desireable, taking into account the specifics of supercritical fluids. A contribution is attempted in this paper. The concept of pseudo-boiling, a maximum in heat capacity associated with a strong increase in specific volume, is discussed. It will be shown that the ensemble of supercritical maximum heat capacity states is in fact an extension to the saturation curve. A novel interpretation of the Clapeyron equation of thermodynamics in the limit of the critical point and beyond will be given. It will be shown that this generalization is able to characterize the pseudo-boiling line. Furthermore it will be shown that the slope (d log p/dT) is constant for supercritical conditions and equals the value at the critical point. The pseudo-boiling approach is then applied to characterize injection experiments. It can be shown that the power needed to reach the pseudo-boiling state correlates with the structure of the axial density distribution.