Homogeneous Nucleation in Steam Nozzle Condensation

Abstract

AFTER the introduction of Laval nozzles into steam turbine design, it became apparent that steam may be expanded beyond saturation before it condenses. Stodola1 observed that condensation was delayed and appeared in the supersonic part of the nozzle and pointed out that the expansion time was too short for appreciable condensation to take place on any heterogeneous nuclei likely to be present. It was found2,3 that the steam attains a supersaturation ratio 3 < p/p ∞ < 8; the locus of the onset of condensation in rapid nozzle expansions when plotted in a Mollier diagram is called “the Wilson line”; this empirical line lies about 33 kcal kg−1 below the saturation curve. Oswatitsch4 suggested that such condensation is initiated by homogeneous nucleation5–9. By combining a solution of the equations of motion of compressible nozzle flow involving heat addition with the “classical” rate equation7 of homogeneous nucleation and his own expressions for the growth rate of droplets, Oswatitsch found agreement between theory and experiment2,3. Hill10 and other authors11 using improved computational techniques obtained similar agreement. Consequently it is generally considered that the “classical” theory of condensation predicts not only the condensation of water vapour when in the presence of air, as in a cloud chamber12–15, but the condensation of pure steam as well. We show here that in the case of pure steam in nozzles the use of the “classical” theory of nucleation does not lead to agreement with experiment.