Journal of Thermal Analysis and Calorimetry

, Volume 133, Issue 2, pp 1023–1039 | Cite as

Analytical investigation of simultaneous effects of convergent section heating of Laval nozzle, steam inlet condition, and nozzle geometry on condensation shock

  • Makan Talebi Somesaraee
  • Ehsan Amiri Rad
  • Mohammad Reza MahpeykarEmail author


Rapid expansion and supercooling of dry vapor in low-pressure steam turbines trigger nucleation phenomenon. Subsequently, following the occurrence of vapor condensation, a vapor–liquid two-phase flow is established. Entropy generation mainly by condensation shock, blade erosion, and ultimately, destruction of equipment and efficiency reduction are among adverse effects of vapor condensation, which should be either attenuated or controlled. In the present research, which is a continuation to the research performed by original authors, a one-dimensional analytical Eulerian–Lagrangian model is used to apply convergent section heating to different supersonic nozzles under various inlet conditions. The results indicate that the flow response to the heating is well dependent on the intensity of condensation shock or inlet conditions. In order to compensate for the mass flow rate resulted from the convergent section heating, effects of simultaneous reduction of inlet stagnation temperature and convergent section heating were investigated. Finally, it was found that, maintaining constant mass flow rate, simultaneous reduction of inlet stagnation temperature and convergent section heating cannot attenuate the condensation shock significantly. Therefore, the best approach to compensate for the reduction in the mass flow rate due to convergent section heating is to simultaneously increase inlet stagnation pressure.


Heating Convergent–divergent nozzle Steam condensation shock Two-phase flow Non-adiabatic 

List of symbols




Virial condensation coefficient


Specific heat at constant pressure


Equivalent diameter


Friction factor



\(\Delta G\)

Change in Gibbs free energy


Rate of formation of critical droplets per unit volume and time


Convergent length


Latent heat


Total mass flow rate


Mass of droplet


Mach number


Number of droplets per unit volume


Vapor pressure

\(P_{\text{S}} \left( {T_{\text{G}} } \right)\)

Saturation pressure at \(T_{\text{G}}\)


Condensation coefficient


Volumetric heat transfer rate (W m−3)


Total heat transfer rate (W)


Gas constant for water vapor


Sauter mean radius


Surface-averaged radius


Volume-averaged radius


Radius of droplet


Total surface of droplets per unit volume





\(T_{\text{S}} \left( P \right)\)

Saturation temperature at P




Total volume of droplets per unit volume


Distance along nozzle axis

X, Y

Functions of temperature and density in equation of state


Heat transfer coefficient




Coefficient of thermal conductivity


Surface tension of droplet



Stagnation condition


Vapor phase


Inlet condition


Liquid phase





Critical droplet


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  • Makan Talebi Somesaraee
    • 1
  • Ehsan Amiri Rad
    • 1
  • Mohammad Reza Mahpeykar
    • 2
    Email author
  1. 1.Hakim Sabzevari UniversitySabzevarIran
  2. 2.Department of Mechanical Engineering, Faculty of EngineeringFerdowsi University of MashhadMashhadIran

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