Journal of Thermal Analysis and Calorimetry

, Volume 137, Issue 6, pp 2121–2134 | Cite as

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

  • Fahime Salmani
  • Mohammad Reza MahpeykarEmail author


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.


Nucleating steam flow Wilson point Latent heat Wetness fraction Dimensional analysis Buckingham Pi 

List of symbols


Area (m2)


Virial coefficients


Sonic velocity (m s−1)


Specific heat capacity of liquid (J/kg K)


Number of main dimensions


Diffusion coefficient


Hydraulic diameter


Dimensionless droplet radius


Droplet–wetness parameters


Total energy


Friction coefficient


Gibbs free energy change


Enthalpy (J kg−1)


Latent heat (J kg−1)


Number of repeated variables


Nucleation rate (#/m3 s)


Knudsen number


Divergent section length (m)


Mach number


Mass flow rate (kg s−1)


Droplet mass (kg)


Liquid mass flow rate (kg s−1)


Total mass flow rate (kg s−1)


Total number of dimensional (physical) variables


Number of molecules per unit mass


Pressure (kPa)


Pressure ratio


Dry expansion rate


Condensation coefficient


Heat release rate due to phase change (W)


Droplet radius (μm)


Gas constant for steam (= 461.4 J/kg K)


Schmidt number \(\left( {\mu_{\text{G}} /\rho_{\text{G}} D} \right)\)


Temperature (K)


X-component velocity (m s−1)


Velocity (m s−1)


Wetness fraction (ML/MT)


Cartesian direction (m)

Greek symbols


Droplet convectional heat transfer coefficient (W/m2 K)


Time (s)


Tolman coefficient


Degree of supercooling (K)


Thermal conductivity of vapor (W/m K)


Viscosity (m2 s−1)


Density (kg m−3)


Dimensionless group


Viscous stress tensor (N m−2)


Thermal (K)


Liquid surface tension (N m)


Density of interfacial region







Kalva’s surface tension correction








Gas (vapor)


Wilson point

Flat surface tension



Critical condition



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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Faculty of EngineeringHakim Sabzevari UniversitySabzevarIran
  2. 2.Department of Mechanical Engineering, Faculty of EngineeringFerdowsi University of MashhadMashhadIran

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