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Two-Phase Eulerian/Lagrangian Model for Nucleating Steam Flow

[+] Author and Article Information
A. G. Gerber

Department of Mechanical Engineering, University of New Brunswick, Fredericton, N.B., Canada, E3B-5A3

J. Fluids Eng 124(2), 465-475 (May 28, 2002) (11 pages) doi:10.1115/1.1454109 History: Received April 14, 2000; Revised October 29, 2001; Online May 28, 2002
Copyright © 2002 by ASME
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References

Gyarmathy, G., and Meyer, H. 1965, “Spontane Kondensation,” VDI Forschungsheft 508, VDI-Verlag, Dusseldorf.
Hill,  P. G., 1966, “Condensation of Water Vapor During Supersonic Expansion in Nozzles,” J. Fluid Mech., 25, Part 3, pp. 593–620.
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.
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.
Young,  J. B., 1992, “Two-Dimensional, Nonequilibrium, Wet Steam Calculations for Nozzles and Turbine Cascades,” ASME J. Turbomach., 114, pp. 569–579.
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.
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.
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.
Denton, J. D., 1982, “An Improved Time-Marching Method for Turbomachinery Flow Calculations,” ASME paper 82-GT-239.
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.
Dukowicz,  J. K., 1980, “A Particle-Fluid Numerical Model for Liquid Sprays,” J. Comput. Phys., 35, pp. 229–253.
Vukalovich, M. P. 1958, Thermodynamic Properties of Water and Steam, Mashgis, Moscow, 6th edition.
Bakhtar,  F., and Piran,  M., 1979, “Thermodynamic Properties of Supercooled Steam,” Int. J. Heat Fluid Flow, 1, no. 2, pp. 53–62.
McDonald,  J. E., 1962–3, “Homogeneous Nucleation of Water Vapor Condensation. I. Thermodynamic Aspects,” Am. J. Phys., 30, pp. 870–877.
McDonald,  J. E., 1962–3, “Homogeneous Nucleation of Water Vapor Condensation. II. Kinetic Aspects,” Am. J. Phys., 131, pp. 31–41.
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.
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.
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.
Moore, M. J., and Sieverding, C. H. 1976, Two-Phase Steam Flow in Turbines and Separators, Hemisphere.
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.
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.
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.
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.

Figures

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Schematic describing nucleating particle injection relative to flux-element and control-volume locations
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Centerline nucleation rate, pressure, and wetness predictions using the Laval nozzle of Moore et al. 16 with one and eight droplets injected per flux-element
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Centerline nucleation rate, pressure, and wetness predictions using the rotor tip profile of Bakhtar et al. 20 with one and eight droplets injected per flux-element
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Centerline nucleation rate, pressure, and wetness predictions using the Laval nozzle of Moore et al. 16 with three levels of grid refinement
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Finite-volume discretization within a finite-element representation of the geometry
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Nucleation rate and Mach number obtained with the present model. Flow conditions are the same as that described for Fig. 7.
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Comparison with 1-D nonequilibrium solution of Gyramathy and Meyer 1
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Nonequilibrium solution compared with the equilibrium solution for the same nozzle and inflow conditions used by Gyramathy and Meyer 1
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Centerline pressure levels in a condensing converging-diverging nozzle-present model compared to the results of Moore et al. 16
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Centerline mass-averaged droplet size in a condensing converging-diverging nozzle-present model compared to the results of Moore et al. 16
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Typical model predictions for nucleating flow over a two-dimensional rotor tip cascade (Bakhtar 2021). Flow conditions Po=0.999 bar,Ts(P)−Tg=10 K, and Pe=0.427 bar.
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Total and static pressure profiles (for superheated and nucleating cases) before and after expansion through the rotor tip blade of Bakhtar et al. 2021. Flow conditions were Po=0.999 bar and Pe=0.427 bar with 20 K superheat and 10 K supercooling respectively at the inlet.
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Component efficiency, enthalpy loss and exit droplet size over a range of inlet supercooling and expansion ratios compared to the experimental data of Bakhtar et al. 21
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Low pressure turbine stage calculation results at mid-span. On the left the nucleation index (n=log10(J+1)) is shown with nmin=0,nmax=25 and Δn=2.5. On the right, supercooling (Tsc=Ts(P)−Tg) with Tsc,min=−10 K,Tsc,max=60 K and ΔTsc=5 K.
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Low pressure turbine stage calculation results at mid-span. On the left the mass averaged droplet size is shown where rmin=0 μm,rmax=0.012 μm and Δr=0.001 μm. On the right, relative Mach number with Mmin=0,Mmax=1.4 and ΔM=0.1.
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Low pressure turbine stage results showing nucleation index (n=log10(J+1)) near the shroud. Nucleation index is shown with nmin=0,nmax=25 and Δn=2.5.

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