This paper describes an Eulerian/Lagrangian two-phase model for nucleating steam based on classical nucleation theory. The model provides an approach for including spontaneous homogeneous nucleation within a full Navier-Stokes solution scheme where the interaction between the liquid and gas phases for a pure fluid is through appropriately modeled source terms. The method allows for the straightforward inclusion of droplet heat, mass, and momentum transfer models along with nucleation within complex flow systems as found, for example, in low pressure steam turbines. The present paper describes the solution method, emphasizing that the important features of nucleating steam flow are retained through comparison with well-established 1-D solutions for Laval nozzle flows. Results for a two-dimensional cascade blade and three-dimensional low pressure turbine stage are also described.
Issue Section:
Additional Technical Papers
Keywords:
two-phase flow,
Navier-Stokes equations,
nucleation,
nozzles,
turbines,
finite volume methods,
finite element analysis,
flow simulation
Topics:
Drops,
Flow (Dynamics),
Nozzles,
Nucleation (Physics),
Pressure,
Particulate matter,
Steam,
Momentum,
Water
1.
Gyarmathy, G., and Meyer, H. 1965, “Spontane Kondensation,” VDI Forschungsheft 508, VDI-Verlag, Dusseldorf.
2.
Hill
, P. G.
, 1966
, “Condensation of Water Vapor During Supersonic Expansion in Nozzles
,” J. Fluid Mech.
, 25
, Part 3, pp. 593
–620
.3.
Bakhtar
, F.
, and Tochai
, M. T. Mohammadi
, 1980
, “An Investigation of Two-Dimensional Flows of Nucleating and Wet Steam by the Time-Marching Method
,” Int. J. Heat Fluid Flow
, 2
, No. 1
, pp. 5
–18
.4.
Young
, J. B.
, 1984
, “Critical Conditions and the Choking Mass Flow Rate in Nonequilibrium Wet Steam Flows
,” ASME J. Fluids Eng.
, 106
, pp. 452
–458
.5.
Young
, J. B.
, 1992
, “Two-Dimensional, Nonequilibrium, Wet Steam Calculations for Nozzles and Turbine Cascades
,” ASME J. Turbomach.
, 114
, pp. 569
–579
.6.
White
, A. J.
, and Young
, J. B.
, 1993
, “Time-Marching Method for the Prediction of Two-Dimensional, Unsteady Flows of Condensing Steam
,” J. Propul. Power
, 9
, No. 4
, pp. 579
–587
.7.
Bakhtar
, F.
, Mahpeykar
, M. R.
, Abbas
, K. K.
, 1995
, “An Investigation of Nucleating Flows of Steam in a Cascade of Turbine Blading-Theoretical Treatment
,” ASME J. Fluids Eng.
, 117
, pp. 138
–144
.8.
White
, A. J.
, Young
, J. B.
, Walters
, P. T.
, 1996
, “Experimental Validation of Condensing Flow Theory for a Stationary Cascade of Steam Turbine Blades
,” Philos. Trans. R. Soc. London
, 354
, pp. 59
–88
.9.
Denton, J. D., 1982, “An Improved Time-Marching Method for Turbomachinery Flow Calculations,” ASME paper 82-GT-239.
10.
Gerber
, A. G.
, 2000
, “Nonequilibrium Droplet Interactions in Rapidly Expanding Steam Flow
,” Turbomachinery, Journal of the Turbomachinery Society of Japan
, 28
, No. 12
, pp. 45
–48
.11.
Dukowicz
, J. K.
, 1980
, “A Particle-Fluid Numerical Model for Liquid Sprays
,” J. Comput. Phys.
, 35
, pp. 229
–253
.12.
Vukalovich, M. P. 1958, Thermodynamic Properties of Water and Steam, Mashgis, Moscow, 6th edition.
13.
Bakhtar
, F.
, and Piran
, M.
, 1979
, “Thermodynamic Properties of Supercooled Steam
,” Int. J. Heat Fluid Flow
, 1
, no. 2
, pp. 53
–62
.14.
McDonald
, J. E.
, 1962
–3, “Homogeneous Nucleation of Water Vapor Condensation. I. Thermodynamic Aspects
,” Am. J. Phys.
, 30
, pp. 870
–877
.15.
McDonald
, J. E.
, 1962
–3, “Homogeneous Nucleation of Water Vapor Condensation. II. Kinetic Aspects
,” Am. J. Phys.
, 131
, pp. 31
–41
.16.
Moore, M. J., Walters, P. T., Crane, R. I., and Davidson, B. J. 1973, “Predicting the Fog Drop Size in Wet Steam Turbines,” Inst. of Mechanical Engineers (UK), Wet Steam 4 Conf., University of Warwick, paper C37/73.
17.
Gyarmathy, G. 1976, “Condensation in Flowing Steam,” Two-Phase Steam Flow in Turbines and Separators, M. J. Moore and C. H. Sieverding, ed., Hemisphere, pp. 127–189.
18.
Raw, M. J. 1995, “A Coupled Algebraic Multigrid Method for the 3D Navier-Stokes Equations,” Proceedings of the 10th GAMM-Seminar Kiel, January 14–16. Notes on Numerical Fluid Mechanics, Vol. 49, Vieweg-Verlag, Braunschweig, Wiesbaden, Germany.
19.
Moore, M. J., and Sieverding, C. H. 1976, Two-Phase Steam Flow in Turbines and Separators, Hemisphere.
20.
Bakhtar
, F.
, Ebrahimi
, M.
, and Webb
, R. A.
, 1995
, “On the Performance of a Cascade of Turbine Rotor Tip Section Blading in Nucleating Steam. Part 1: Surface Pressure Distributions
,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
, 209
, pp. 115
–124
.21.
Bakhtar
, F.
, Ebrahimi
, M.
, and Bamkole
, B. O.
, 1995
, “On the Performance of a Cascade of Turbine Rotor Tip Section Blading in Nucleating Steam. Part 2: wake traverses
,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
, 209
, pp. 169
–177
.22.
Gerber, A. G. 2000, “Modeling the Steady and Transient Dynamics of Nucleating Two-Phase Steam Flow,” Proc. of the 2000 National Heat Transfer Conf., August 20–22, ASME paper NHTC2000-12117.
23.
Skillings, S. A., Moore, M. J., Walters, P. T., and Jackson, R. 1988, “A Reconsideration of Wetness Loss in LP Steam Turbines,” Proceedings of the BNES (British Nuclear Energy Society), Conference on Technology of Turbine Plant Operating with Wet Steam, London, pp. 171–177.
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