The quadrature method of moments (QMOM) is applied to the particle size distribution (PSD) present in nucleating steam flow, with a particular emphasis on conditions relevant to low-pressure steam turbines. These machines exhibit heterogeneous and homogeneous phase transition in the presence of strong flow discontinuities due to shocks and complex geometry. They offer a particularly difficult two-phase modeling situation. The present work shows that QMOM is a robust and efficient method and, in comparison to current practice of using a monodispersed PSD in computational fluid dynamics (CFD) models, offers promise for dealing with the complex two-phase conditions present in real machines.

1.
Bakhtar
,
F.
,
Mahpeykar
,
M. R.
, and
Abbas
,
K. K.
, 1995, “
An Investigation of Nucleating Flows of Steam in a Cascade of Turbine Blading-Theoretical Treatment
,”
ASME Trans. J. Fluids Eng.
0098-2202,
117
, pp.
138
144
.
2.
Young
,
J. B.
, 1992, “
Two-Dimensional, Nonequilibrium, Wet Steam Calculations for Nozzles and Turbine Cascades
,”
ASME J. Turbomach.
0889-504X,
114
, pp.
569
579
.
3.
Gerber
,
A. G.
, 2002, “
Two-Phase Lagrangian/Eulerian Model for Nucleating Steam Flow
,”
ASME J. Fluids Eng.
0098-2202,
124
2
, pp.
465
475
.
4.
White
,
A. J
, 2003, “
A Comparison of Modeling Methods for Polydispersed Wet-Steam Flow
,” Int. J. Numerical Methods in Engineering,
57
, pp.
819
834
.
5.
White
,
A. J.
, and
Hounslow
,
M. J.
, 2000, “
Modelling Droplet Size Distribution in Polydispersed Wet-Steam Flows
,”
Int. J. Heat Mass Transfer
0017-9310,
43
, pp.
1873
1884
.
6.
Gerber
,
A. G.
,
Sigg
,
R.
,
Volker
,
L.
, and
Casey
,
M. V.
, 2007, “
Predictions of Nonequilibrium Phase Transition in a Model Low Pressure Steam Turbine
,”
Seventh European Turbomachinery Conference (ETC)
, Athens, March 5–9, Paper no. 176.
7.
Hesketh
,
J. A.
, and
Walker
,
P. J.
, 2005, “
Effects of Wetness in Steam Turbines
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
0954-4062,
219
, pp.
1301
1314
.
8.
Hulburt
,
H. M.
, and
Katz
,
S.
, 1964, “
Some Problems in Particle Technology
,”
Chem. Eng. Sci.
0009-2509,
19
, pp.
555
574
.
9.
Gerber
,
A.
, and
Mousavi
,
A.
, 2006 “
Application of Quadrature Method of Moments to the Polydispersed Droplet Spectrum in Transonic Steam Flows With Primary and Secondary Nucleation
,”
Appl. Math. Model.
0307-904X,
31
,
1518
1533
10.
Marchisio
,
D. L.
, and
Fox
,
R. O.
, 2005, “
Solution of Population Balance Equations Using the Direct Quadrature Method of Moments
,”
J. Aerosol Sci.
0021-8502,
36
, pp.
43
73
.
11.
Hoffmann
,
K. A.
, and
Chiang
,
S. T.
, 1993, “
Computational Fluid Dynamics for Engineers
,”
Engineering Education System
, Wichita, Kansas, Vol.
2
.
12.
McGraw
,
R.
, 1997, “
Description of Aerosol Dynamics by the Quadrature Method of Moments
,”
Aerosol Sci. Technol.
0278-6826,
27
, pp.
255
265
.
13.
Marchisio
,
D. L.
,
Fox
,
O.
, and
Vigil
,
R. D.
, 2003, “
Quadrature Method of Moments for Population-Balance Equation
,”
AIChE J.
0001-1541,
49
, pp.
1266
1276
.
14.
McDonald
,
J. E.
, 1962, “
Homogeneous Nucleation of Water Vapor Condensation. I. Thermodynamic Aspects
,”
Am. J. Phys.
0002-9505,
30
, pp.
870
877
.
15.
Bakhtar
,
F.
,
Young
,
J. B.
,
White
,
A. J.
, and
Simpson
,
D. A.
, 2005 “
Classical Nucleation Theory and Its Application to Condensing Steam Flow Calculations
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
0954-4062,
219
, pp.
1315
1333
.
16.
Lee
,
T. D.
, 1998, “
Surface Characterization by Heterogeneous Nucleation from the Vapor
” Ph. D. thesis, Harvard University.
17.
Lee
,
Y. L.
,
Chou
,
W. S.
, and
Chen
,
L. H.
, 1998, “
The Adsorption and Nucleation of Water Vapor on an Insoluble Spherical Solid Particle
Surf. Sci.
0039-6028,
414
, pp.
363
373
.
18.
Hirsch
,
C.
, 1990,
Numerical Computation of Internal and External Flows
,
Wiley
,
New York
, Vol.
2
.
19.
Anderson
,
D. A.
,
Tannehill
,
J. C.
, and
Pletcher
,
R. H.
, 1997,
Computational Fluid Rechanics and Heat Transfer
, 2nd ed.,
Taylor & Francis
,
London
.
20.
Moore
,
M. J.
,
Walters
,
P. T.
,
Crane
,
R. I
, and
Davidson
,
B. J.
, 1975, “
Predicting the Fog Drop Size in Wet Steam Turbines
,” Institute of Mechanical Engineers (UK), Wet Steam 4 Conference, University of Warwick, Paper No. C37/73.
You do not currently have access to this content.