Dimensional analysis for estimating wetness terms of condensing steam using dry flow data

During rapid expansion in supersonic nozzles and turbine blades, under special conditions, steam may become supercooled vapor, and the heat release rate (\(\dot{Q}\)) due to phase change is substantial. Droplet radius (r) and wetness fraction (WF) are important parameters in designing wet steam equipment. Until now, cost-intensive and complicated methods are applied for designing wet steam equipment. In this paper, an innovative method based on Buckingham Pi dimensional analysis is proposed for predicting r and WF using dry vapor data. A dimensionless droplet radius (DDR) is obtained from the influential parameters at the Wilson point (named DWP). First, DWP, DDR, and WF are obtained from the results of the analytical modeling, and then, two regression equations are proposed for calculating DDR and WF with DWP. Finally, results of the proposed regression relationships are compared for seven analytical cases; the average percent errors associated with the presented equations for the droplet radius or DDR and WF percentage (\(\dot{Q}\)) are found to be less than 30% and 12%, respectively.