Estimating heat release due to a phase change of high-pressure condensing steam using the Buckingham Pi theorem

. The flow of steam, at the Wilson point, begins to condensate through nucleation, and its non-equilibrium conditions are suppressed by forming the critical droplets that decrease the Gibbs energy, and then the condensation shock occurs. Droplet radius ( r ) and Wetness fraction ( WF ) or the heat release rate due to phase change ( Q ˙ ) are important parameters in the design and operation of high-pressure (HP) wet steam equipment. The experimental, analytical, and numerical methods have been considered as cost-intensive, complicated, and time-consuming, respectively. Therefore, in this study, using only dry vapor data, an innovative method based on the Buckingham Pi theorem is proposed to estimate the droplet radius and WF or Q ˙ . Also, an acceptable threshold for the identification of the Wilson point location is suggested. First, the results of analytical modeling are in good agreement with the experimental data at the range of 25-35bars. Next, using dimensional analysis, the droplet-wetness parameter (DWP) is obtained as a dimensionless number which is a function of effective parameters. By curve fittings, two regression equations are proposed for calculating r and WF at the end of nozzles. Finally, the results of the proposed equations are compared with those of the available analytical models. There is good agreement between the current method and the available models in the literature. This innovative method, based on dimensional analysis, is introduced for preliminary design of HP nucleating steam equipment.