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Research Papers

Condensation in Radial Turbines—Part II: Application of the Mathematical Model to a Radial Turbine Series

[+] Author and Article Information
Sebastian Schuster

University of Duisburg-Essen,
Lotharstr. 1,
Duisburg 47057, Germany
e-mail: s.schuster@uni-due.de

Dieter Brillert

University of Duisburg-Essen,
Lotharstr. 1,
Duisburg 47057, Germany,
e-mail: dieter.brillert@uni-due.de

Friedrich-Karl Benra

University of Duisburg-Essen,
Lotharstr. 1,
Duisburg 47057, Germany
e-mail: friedrich.benra@uni-due.de

1Corresponding author.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received February 23, 2017; final manuscript received July 17, 2018; published online September 28, 2018. Assoc. Editor: Anestis I. Kalfas.

J. Turbomach 140(10), 101002 (Sep 28, 2018) (7 pages) Paper No: TURBO-17-1033; doi: 10.1115/1.4040935 History: Received February 23, 2017; Revised July 17, 2018

In the second part of this two part paper, the condensation process and the movement of the liquid phase near the impeller blades of a radial turbine are studied. The investigation methodology presented in part 1 is applied to a radial turbine type series used for waste heat recovery. First, the subcooling necessary for the beginning of the condensation process is examined and a relationship between the location of maximum subcooling and the onset of droplet deposition at the surfaces of the turbine impeller is determined. Thereafter, the movement of liquid films on the impeller blades is analysed and characterized. Correlations determining the movement of droplets originating from liquid film atomization on the edge of the impeller blade along the casing are derived. Finally, conclusions are drawn depicting the most important findings of condensing flows in radial turbines.

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References

Schuster, S. , Benra, F.-K. , Dohmen, H. J. , König, S. , and Martens, U. , 2012, “ Influence of Different Gas Models on the Numerical Results of High-Velocity Condensation,” Conference on Modelling Fluid Flow (CMFF'12), Budaspet, Hungary, Sept. 4–7, pp. 642–649.
Schuster, S. , Benra, F. K. , Dohmen, H. J. , Koenig, S. , and Martens, U. , 2014, “ Sensitivity of Condensation Calculations on Model Coefficients With Respect to Turbo Machinery Applications,” 15th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery (ISROMAC), Budapest, Hungary, Sept. 4–7, pp. 1–9.
Schuster, S. , Benra, F. K. , Dohmen, H. J. , König, S. , and Martens, U. , 2014, “ Sensitivity Analysis of Condensation Model Constants on Calculated Liquid Film Motion in Radial Turbines,” ASME Paper No. GT2014-25652.
Schuster, S. , Benra, F.-K. , and Brillert, D. , 2017, “ Reliability of Condensation Models for Droplet Deposition Calculations in Radial Turbines,” Wet Steam Conference, pp. 1–12.
Schuster, S. , Benra, F.-K. , and Brillert, D. , 2017, “ Droplet Deposition in Radial Turbines,” Eur. J. Mech.—B/Fluids, 61(2), pp. 289–296. [CrossRef]
Schuster, S. , Brillert, D. , and Benra, F.-K. , 2017, “ Condensation in Radial Turbines—Part 1: Mathematical Modelling,” ASME J. Turbomach. (accepted).
Schuster, S. , 2016, Untersuchung Der Entstehung Und Bewegung Von Flüssigkeitsansammlungen Auf Radialturbinenlaufradschaufeln Mit Einem Erweiterten Navier-Stokes-Löser, Shaker Verlag, Aachen, Germany.
Wagner, W. , and Kretzschmar, H.-J. , 2008, International Steam Tables: Properties of Water and Steam Based on the Industrial Formulation IAPWS-IF97, Springer-Verlag, Berlin.
Hammitt, F. G. , Krzeczkowski, S. , and Krzyzanowski, J. , 1981, “ Liquid Film and Droplet Stability Consideration as Applied to Wet Steam Flow,” Forsch. Ingenieurwes., 47(1), pp. 1–14. [CrossRef]
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Gomaa, H. , and Weigand, B. , 2012, “ Modelling and Investigation of the Interaction Between Drops and Blades in Compressor Cascades With a Droplet Laden Inflow,” 14th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery (ISROMAC), Honolulu, HI, Feb. 27–Mar. 2, pp. 1–10.
Schmehl, R. , Rosskamp, H. , Willmann, M. , and Wittig, S. , 1999, “ CFD Analysis of Spray Propagation and Evaporation Including Wall Film Formation and Spray/Film Interactions,” Int. J. Heat Fluid Flow, 20(5), pp. 520–529. [CrossRef]
Schiller, L. , and Naumann, A. , 1933, “ Über die grundlegende Berechnung bei der Schwerkraftaufbereitung,” Zeitschrift des Vereins Deutscher Ingenieure, 77(12), pp. 318–320.

Figures

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Fig. 6

Turbine E: Maximum subcooling and deposition onset in the meridional view on the pressure and on the suction side

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Fig. 7

Local condensation phenomenon without considering evaporation (left) and with evaporation (right)

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Fig. 8

Correlation for subcooling as a function of expansion velocity

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Fig. 5

Turbine D: Maximum subcooling and deposition onset in the meridional view on the pressure and on the suction side

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Fig. 4

Turbine C: Maximum subcooling and deposition onset in the meridional view on the pressure and on the suction side

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Fig. 3

Turbine B: Maximum subcooling and deposition onset in the meridional view on the pressure and on the suction side

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Fig. 2

Turbine A: Maximum subcooling and deposition onset in the meridional view on the pressure and on the suction side

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Fig. 1

Sketch of the radial turbine

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Fig. 13

Size of droplets resulting from liquid film disintegration in comparison to critical diameter for droplet transport into the nozzle-impeller gap

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Fig. 9

Accordance between CFD-condensation and CFD-correlation for turbine B (left) and turbine C (right) on the S1-surface at 50 % channel height, T0-r = 0 °C, φ0 = 40 %

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Fig. 10

Relationship between location of maximum subcooling obtained with CFD-correlation and onset of deposition for turbine A, φ0 = 40%

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Fig. 11

Force acting on a liquid film element due to surface rotation

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Fig. 12

Droplet diameter above which droplets move into the nozzle-impeller gap

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