The quadrature method of moments (QMOM) has recently attracted much attention in representing the size distribution of liquid droplets in wet-steam flows using the -point Gaussian quadrature. However, solving transport equations of moments using high-order advection schemes is bound to corrupt the moment set, which is then termed as a nonrealizable moment set. The problem is that the failure and success of the Gaussian quadrature are unconditionally dependent on the realizability of the moment set. First, this article explains the nonrealizability problem with the QMOM. Second, it compares two solutions to preserve realizability of the moment sets. The first solution applies a so-called “quasi-high-order” advection scheme specifically proposed for the QMOM to preserve realizability. However, owing to the fact that wet-steam models are usually built on existing numerical solvers, in many cases modifying the available advection schemes is either impossible or not desired. Therefore, the second solution considers correction techniques directly applied to the nonrealizable moment sets instead of the advection scheme. These solutions are compared in terms of accuracy in representing the droplet size distribution. It is observed that a quasi-high-order scheme can be reliably applied to guarantee realizability. However, as with all the numerical models in an Eulerian reference frame, in general, its results are also sensitive to the grid resolution. In contrast, the corrections applied to moments either fail in identifying and correcting the invalid moment sets or distort the shape of the droplet size distribution after the correction.
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January 2017
Research-Article
Nonrealizability Problem With Quadrature Method of Moments in Wet-Steam Flows and Solution Techniques
Ali Afzalifar,
Ali Afzalifar
School of Energy Systems,
Lappeenranta University of Technology,
Lappeenranta 53850, Finland
e-mail: ali.afzalifar@lut.fi
Lappeenranta University of Technology,
Lappeenranta 53850, Finland
e-mail: ali.afzalifar@lut.fi
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Teemu Turunen-Saaresti,
Teemu Turunen-Saaresti
School of Energy Systems,
Lappeenranta University of Technology,
Lappeenranta 53850, Finland
e-mail: teemu.turunen-saaresti@lut.fi
Lappeenranta University of Technology,
Lappeenranta 53850, Finland
e-mail: teemu.turunen-saaresti@lut.fi
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Aki Grönman
Aki Grönman
School of Energy Systems,
Lappeenranta University of Technology,
Lappeenranta 53850, Finland
e-mail: aki.gronman@lut.fi
Lappeenranta University of Technology,
Lappeenranta 53850, Finland
e-mail: aki.gronman@lut.fi
Search for other works by this author on:
Ali Afzalifar
School of Energy Systems,
Lappeenranta University of Technology,
Lappeenranta 53850, Finland
e-mail: ali.afzalifar@lut.fi
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
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
Lappeenranta University of Technology,
Lappeenranta 53850, Finland
e-mail: aki.gronman@lut.fi
1Corresponding author.
Contributed by the Turbomachinery Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received June 20, 2016; final manuscript received June 22, 2016; published online August 16, 2016. Editor: David Wisler.
J. Eng. Gas Turbines Power. Jan 2017, 139(1): 012602 (9 pages)
Published Online: August 16, 2016
Article history
Received:
June 20, 2016
Revised:
June 22, 2016
Citation
Afzalifar, A., Turunen-Saaresti, T., and Grönman, A. (August 16, 2016). "Nonrealizability Problem With Quadrature Method of Moments in Wet-Steam Flows and Solution Techniques." ASME. J. Eng. Gas Turbines Power. January 2017; 139(1): 012602. https://doi.org/10.1115/1.4034196
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