Effect of Important Thermophysical Properties on Condensation Shock in a Steam Flow

Abstract

When pure steam (i.e., steam that does not contain any impurities and external particles) expands in the turbine and crosses the saturation line it is not condensed instantly but rather first enters supersaturated (supercooled) conditions. The supercooled steam is in an unstable state and during a set time period, which depends on the supercooling degrees by way of nucleation (i.e., the sudden formation and growth of numerous minute liquid droplets), returns to stable state and consequently, equilibrium two-phase flow is reached. The modeling of this two-phase vapor-liquid flow, which starts with droplet formation (nucleation) and continues with rapid droplet growth and condensation shock, depends highly on our understanding of nucleation and defining its main thermophysical properties. Despite numerous research conducted in this area, there still exists a great deal of uncertainty around the value of the influential parameters affecting nucleation, in particular the droplet surface tension, which require further investigation. The factors which need the most attention are the ones related to the properties of the fluid’s molecule sets, such as the surface tension of tiny droplets, the supercooled state equation for calculating the isentropic index, and finally, the condensation coefficient. In this paper, using a proposed equation for nucleation and vapor state, and also employing genetic algorithm, the simultaneous reciprocal effects of three important factors on the nucleation phenomenon are investigated; namely, the surface tension, isentropic index, and the condensation coefficient. For this purpose, the one-dimensional analytical model for nonequilibrium nucleating flows is applied to two Laval nozzles with different boundary conditions. The results indicate that droplet surface tension has the highest impact on the nucleation phenomenon and the sudden condensation and that the effects of the other two factors are relatively limited. In this regard, using the results of genetic algorithm, an improved equation is proposed for calculating the surface tension of the tiny liquid droplets by modifying the surface tension of bulk water. The use of this equation leads to a better and more accurate solution of the two-phase flow for predicting the condensation of low supersaturation steam in convergent–divergent supersonic nozzles.