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Research Papers: Gas Turbines: Turbomachinery

A Comparison of Modeling Techniques for Polydispersed Droplet Spectra in Steam Turbines

[+] Author and Article Information
Fiona R. Hughes

Hopkinson Laboratory,
Department of Engineering,
University of Cambridge,
Cambridge CB2 1PZ, UK
e-mail: frh25@cam.ac.uk

Jörg Starzmann

Hopkinson Laboratory,
Department of Engineering,
University of Cambridge,
Cambridge CB2 1PZ, UK
e-mail: js2145@cam.ac.uk

Alexander J. White

Hopkinson Laboratory,
Department of Engineering,
University of Cambridge,
Cambridge CB2 1PZ, UK
e-mail: ajw36@cam.ac.uk

John B. Young

Hopkinson Laboratory,
Department of Engineering,
University of Cambridge,
Cambridge CB2 1PZ, UK
e-mail: jby@cam.ac.uk

1Corresponding author.

Contributed by the Turbomachinery Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 17, 2015; final manuscript received August 13, 2015; published online October 21, 2015. Editor: David Wisler.

J. Eng. Gas Turbines Power 138(4), 042603 (Oct 21, 2015) (9 pages) Paper No: GTP-15-1344; doi: 10.1115/1.4031389 History: Received July 17, 2015; Revised August 13, 2015

Within steam turbine flows, condensation phenomena give rise to complex droplet spectra that can span more than two orders of magnitude in size. To predict the behavior of the two-phase flow and the resulting losses, the interactions between the vapor phase and droplets of all sizes must be accurately calculated. The estimation of thermodynamic losses and droplet deposition rates, in particular, depends on the size range and shape of the droplet spectrum. These calculations become computationally burdensome when a large number of droplet groups are present, and it is therefore advantageous to capture the complete droplet spectrum in a compressed form. This paper compares several methods for reducing the complexity of the droplet spectrum: a single representative droplet size (equivalent monodispersion), the moment method (including various growth rate approximations), the quadrature method of moments (QMOM), and spectrum pruning. In spectrum pruning, droplet groups are individually nucleated, but their number is subsequently reduced by combining groups together in a manner that preserves droplet number, wetness fraction, and the shape of the initial spectrum. The various techniques are compared within a Lagrangian framework by tracking the two-phase behavior along predefined pressure–time trajectories. Primary and secondary nucleation, droplet evaporation, and a representative turbomachinery case are modeled. The calculations are compared in terms of speed, accuracy, and robustness. It is shown that both the moment methods and spectrum pruning provide an appreciable improvement in accuracy over the use of an “equivalent” monodispersion without compromising calculation speed. Although all the examined methods are adequate for primary nucleation and droplet growth calculations, spectrum pruning and the QMOM are most accurate over the range of conditions considered.

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References

Figures

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Fig. 1

Normalized Wilson point pressure (top), Sauter diameter (centre), and droplet number (bottom) as functions of expansion rate

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Fig. 2

The droplet number density functions resulting from primary nucleation at p˙ = 4000 s−1

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Fig. 3

The droplet number density functions resulting from secondary nucleation at p˙ = 8000 s−1 with droplet clusters

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Fig. 4

Specific droplet number as a function of time for secondary nucleation followed by evaporation; no droplet clusters

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Fig. 5

Sauter mean diameter as a function of time for secondary nucleation followed by evaporation; no droplet clusters

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Fig. 6

Pressure and expansion rate versus time for an idealized expansion in an LP turbine stage

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Fig. 7

Specific droplet number as a function of time near the Wilson point of idealized expansion in an LP turbine

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