Theoretical investigation of effects of local cooling of a nozzle divergent section for controlling condensation shock in a supersonic two-phase flow of steam

In supersonic adiabatic two-phase flows of steam, under the influence of supersonic acceleration, the fluid loses its equilibrium conditions and becomes supersaturated. Following this condition and to restore the fluid to equilibrium, micro droplets of water form in the absence of any surface or foreign particles. This phenomenon is called homogeneous nucleation and the formed minute small droplets grow along the fluid flow path. The formation of these droplets and their growth causes the release of the latent heat of evaporation to the gas phase particularly in the nucleation region, and results in an increase in the flow pressure which is called the condensation shock. In this paper, and in continuation of the series of papers by the authors, in addition to analytically solving the adiabatic gas-liquid supersonic flow of steam in a convergent-divergent channel, a novel solution to controlling the undesired effects of this pressure rise (condensation shock) is presented. In the proposed method, with the help of cooling the divergent section of the nozzle, the analytical model for the 1D non-adiabatic two-phase steam flows is further developed which shows considerable decrease in the intensity of the formed condensation shock. Also the growth rate of the formed droplets due to the cooling of the steam flow has higher importance than the nucleation itself.

[1]  Barbara N Hale,et al.  Temperature dependence of homogeneous nucleation rates for water: near equivalence of the empirical fit of Wölk and Strey, and the scaled nucleation model. , 2005, The Journal of chemical physics.

[2]  M. R. Mahpeykar,et al.  Effects of Friction Factor and Inlet Stagnation Conditions on the Self-Condensation of Steam in a Supersonic Nozzle , 2004 .

[3]  M. Sunar,et al.  Study into nucleation of steam during expansion through a nozzle , 1997 .

[4]  Robert J. Anderson,et al.  Homogeneous nucleation rate measurements for water over a wide range of temperature and nucleation rate , 1983 .

[5]  Esmail Lakzian,et al.  REDUCTION OF THERMODYNAMIC LOSSES IN A SUPERSONIC NUCLEATING STEAM NOZZLE BY SPRAYING WATER DROPLETS , 2009 .

[6]  M. R. Mahpeykar,et al.  Reducing entropy generation by volumetric heat transfer in a supersonic two-phase steam flow in a Laval nozzle , 2011 .

[7]  J. B. Young,et al.  A Study of Choking Conditions in the Flow of Wet Steam , 1978 .

[8]  M. Kermani,et al.  A pressure based Eulerian–Eulerian multi-phase model for non-equilibrium condensation in transonic steam flow , 2004 .

[9]  J. M. Rodríguez-Lelis,et al.  A comparative study of treatment of two-dimensional two-phase flows of steam by a Runge-Kutta and by Denton's methods , 2007 .

[10]  Mikhail P. Anisimov,et al.  Nucleation: theory and experiment , 2003 .

[11]  F Bakhtar,et al.  Studies of nucleating and wet steam flows in two-dimensional cascades , 2004 .

[12]  J. Wölk,et al.  Empirical function for homogeneous water nucleation rates , 2002 .

[13]  Shigeki Senoo,et al.  Numerical Simulations of Unsteady Wet Steam Flows With Non-Equilibrium Condensation in the Nozzle and the Steam Turbine , 2006 .

[14]  M. R. Mahpeykar,et al.  Suppression of Condensation Shock in Wet Steam Flow by Injection of Water Droplets in Different Regions of a Laval Nozzle , 2010 .

[15]  R. Strey,et al.  Homogeneous Nucleation of H2O and D2O in Comparison: The Isotope Effect† , 2001 .

[16]  Sławomir Dykas,et al.  Steam condensing flow modeling in turbine channels , 2009 .

[17]  A. White,et al.  Classical Nucleation Theory and Its Application to Condensing Steam Flow Calculations , 2005 .

[18]  Thomas F. Irvine.  CHAPTER 1 – THERMODYNAMIC PROPERTIES OF STEAM , 1984 .

[19]  G. Schnerr,et al.  Nucleating unsteady flows in low-pressure steam turbine stages , 2001 .