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Research Papers: Multiphase Flows

Comparison of Moment-Based Methods for Representing Droplet Size Distributions in Supersonic Nucleating Flows of Steam

[+] Author and Article Information
Ali Afzalifar

School of Energy Systems,
Lappeenranta University of Technology,
Lappeenranta 53850, Finland
e-mail: ali.afzalifar@lut.fi

Teemu Turunen-Saaresti

School of Energy Systems,
Lappeenranta University of Technology,
Lappeenranta 53850, Finland
e-mail: teemu.turunen-saaresti@lut.fi

Aki Grönman

School of Energy Systems,
Lappeenranta University of Technology,
Lappeenranta 53850, Finland
e-mail: aki.gronman@lut.fi

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received July 30, 2016; final manuscript received May 6, 2017; published online October 19, 2017. Assoc. Editor: Olivier Coutier-Delgosha.

J. Fluids Eng 140(2), 021301 (Oct 19, 2017) (13 pages) Paper No: FE-16-1486; doi: 10.1115/1.4037979 History: Received July 30, 2016; Revised May 06, 2017

This paper investigates the performance of moment-based methods and a monodispersed model (Mono) in predicting the droplet size distribution and behavior of wet-steam flows. The studied moment-based methods are a conventional method of moments (MOM) along with its enhanced version using Gaussian quadrature, namely the quadrature method of moments (QMOM). The comparisons of models are based on the results of an Eulerian–Lagrangian (E–L) method, as the benchmark calculations, providing the full spectrum of droplet size. In contrast, for the MOM, QMOM, and Mono an Eulerian reference frame is chosen to cast all the equations governing the phase transition and fluid motion. This choice of reference frame is essential to draw a meaningful comparison regarding complex flows in wet-steam turbines as the most important advantage of the moment-based methods is that the moment-transport equations can be conveniently solved in an Eulerian frame. Thus, the moment-based method can avoid the burdensome challenges in working with a Lagrangian framework for complicated flows. The main focus is on the accuracy of the QMOM and MOM in representing the water droplet size distribution. The comparisons between models are made for two supersonic low-pressure nozzle experiments reported in the literature. Results show that the QMOM, particularly inside the nucleation zone, predicts moments closer to those of the E–L method. Therefore, for the test case in which the nucleation is significant over a large proportion of the domain, the QMOM provides results in clearly better agreements with the E–L method in comparison with the MOM.

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References

Figures

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Fig. 1

Normalized dimensions of nozzles (top) and distributions of supersaturation across the nozzles (bottom) obtained by the E–L method

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Fig. 2

Comparison of weights from QMOM using grid sizes of 1000, 2000, and 3000 elements for nozzle A. Ng denotes the grid size.

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Fig. 3

Comparison of radii from QMOM using grid sizes of 1000, 2000, and 3000 elements for nozzle A. Ng denotes the grid size.

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Fig. 4

Comparison of pressure distributions in nozzle A

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Fig. 5

Comparison of droplet mean diameter distributions in nozzle A

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Fig. 6

Distributions of normalized moments, relative to the E–L, of MOM (top) and QMOM (bottom) over the nucleation zone in nozzle A

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Fig. 7

Comparison of distributions for weights (top) and radii (bottom) between QMOM and MOM in nozzle A

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Fig. 8

Comparison of discrete size distributions using Gaussian quadrature for QMOM and MOM with E–L at X/s = 0.3(top), X/s = 1.5 (center) and X/s = 7.0 (bottom)

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Fig. 9

Distributions of nucleation rates and growth rates of droplet sizes present in calculations of QMOM and MOM in Nozzle A

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Fig. 10

Distributions of nucleation rates and growth rates of droplet sizes present in calculations of QMOM and MOM in Exp. 252

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Fig. 11

Distributions of normalized moments, relative to the E–L, of MOM (top) and QMOM (bottom) over the nucleation zone in Exp. 252

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Fig. 12

Comparison of distributions for weights (top) and radii (bottom) between QMOM and MOM in Exp. 252

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Fig. 13

Comparison of pressure distributions in Exp. 252

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Fig. 14

Comparison of droplet mean diameter distributions in Exp. 252

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