Comparison of Non-Dimensional Parameters for Flow Dynamics at Supercritical Pressures

This paper presents a comparison between two sets of dimensionless parameters for analysing flow stability of heated channels operating at supercritical pressures. These dimensionless parameters were developed independently in previous work and were applied in stability analyses of supercritical fluid systems. Both sets of dimensionless parameters, though quite different from each other, were derived on the basis of 1D mass, momentum and energy balance equations and this common root raises the issue to clarify the relations existing among them. One set of parameters results in very compact stability criteria for the different kinds of instability phenomena expected in these systems. The compactness and the generality of these formulations are two of the attractive features of the adopted dimensionless parameters and of the related stability criteria, which were shown to correctly represent marginal stability thresholds calculated independently. The other set of parameters was instead developed in similarity with dimensionless numbers adopted in the past for boiling channels. It makes reference to the pseudo-critical conditions at each operating pressure and the obtained definitions were found to result in a useful generality of the relationship between dimensionless density and dimensionless enthalpy. Both sets of parameters are discussed herein and are compared to each other with particular attention to the Ledinegg instability phenomenon.