0
Research Papers

Second Law Analysis of Condensing Steam Flows

[+] Author and Article Information
Marius Grübel

Institute of Thermal Turbomachinery and
Machinery Laboratory (ITSM),
University of Stuttgart,
Stuttgart 70569, Germany
e-mail: marius.gruebel@itsm.uni-stuttgart.de

Markus Schatz

Institute of Thermal Turbomachinery and
Machinery Laboratory (ITSM),
University of Stuttgart,
Stuttgart 70569, Germany
e-mail: markus.schatz@itsm.uni-stuttgart.de

Damian M. Vogt

Institute of Thermal Turbomachinery and
Machinery Laboratory (ITSM),
University of Stuttgart,
Stuttgart 70569, Germany
e-mail: damian.vogt@itsm.uni-stuttgart.de

Manuscript received June 22, 2018; final manuscript received June 25, 2018; published online August 20, 2018. Editor: Jerzy T. Sawicki.

J. Eng. Gas Turbines Power 140(12), 121003 (Aug 20, 2018) (8 pages) Paper No: GTP-18-1285; doi: 10.1115/1.4040711 History: Received June 22, 2018; Revised June 25, 2018

A numerical second law analysis is performed to determine the entropy production due to irreversibilities in condensing steam flows. In the present work, the classical approach to calculate entropy production rates in turbulent flows based on velocity and temperature gradients is extended to two-phase condensing flows modeled within an Eulerian–Eulerian framework. This requires some modifications of the general approach and the inclusion of additional models to account for thermodynamic and kinematic relaxation processes. With this approach, the entropy production within each mesh element is obtained. In addition to the quantification of thermodynamic and kinematic wetness losses, a breakdown of aerodynamic losses is possible to allow for a detailed loss analysis. The aerodynamic losses are classified into wake mixing, boundary layer, and shock losses. The application of the method is demonstrated by means of the flow through a well-known steam turbine cascade test case. Predicted variations of loss coefficients for different operating conditions can be confirmed by experimental observations. For the investigated test cases, the thermodynamic relaxation contributes the most to the total losses and the losses due to droplet inertia are only of minor importance. The variation of the predicted aerodynamic losses for different operating conditions is as expected and demonstrates the suitability of the approach.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Denton, J. D. , 1993, “Loss Mechanisms in Turbomachines,” ASME J. Turbomach., 115(4), pp. 621–656. [CrossRef]
Bejan, A. , 1996, Entropy Generation Minimization, CRC Press, Boca Raton, FL.
Grübel, M. , Dovik, R. M. , Schatz, M. , and Vogt, D. M. , 2017, “A Methodology for a Detailed Loss Prediction in Low Pressure Steam Turbines,” ASME Paper No. GT2017-63404.
Kock, F. , and Herwig, H. , 2005, “Entropy Production Calculation for Turbulent Shear Flows and Their Implementation in CFD Codes,” Int. J. Heat Fluid Flow, 26(4), pp. 672–680. [CrossRef]
Iandoli, C. L. , Sciubba, E. , and Zeoli, N. , 2008, “The Computation of the Entropy Generation Rate for Turbomachinery Design Applications: Some Theoretical Remarks and Practical Examples,” Int. J. Energy Technol. Policy, 6(1/2), pp. 64–95. [CrossRef]
Sciubba, E. , 2009, “Some Remarks About the Computation of the Entropy Generation Rate in Turbomachinery,” Int. J. Trans. Phen., 11(1), pp. 79–96. http://www.oldcitypublishing.com/journals/ijtp-home/ijtp-issue-contents/ijtp-volume-11-number-1-2009-10/ijtp-11-1-p-79-96/
Zlatinov, M. B. , Tan, C. S. , Montgomery, M. , Islam, T. , and Harris, M. , 2012, “Turbine Hub and Shroud Sealing Flow Loss Mechanisms,” ASME J. Turbomach., 134(6), p. 061027. [CrossRef]
Palenschat, T. , Newton, P. , Martinez-Botas, R. F. , Müller, M. , and Leweux, J. , 2017, “3-D Computational Loss Analysis of an Asymmetric Volute Twin-Scroll Turbocharger,” ASME Paper No. GT2017-64190.
Young, J. B. , 1995, “The Fundamental Equations of Gas-Droplet Multiphase Flow,” Int. J. Multiphase Flow, 21(2), pp. 175–191. [CrossRef]
Starzmann, J. , Casey, M. , Mayer, J. F. , and Sieverding, F. , 2014, “Wetness Loss Prediction for a Low Pressure Steam Turbine Using CFD,” Proc. Inst. Mech. Eng., Part A, 228(2), pp. 216–231. [CrossRef]
Gerber, A. G. , 2008, “Inhomogeneous Multifluid Model for Prediction of Nonequilibrium Phase Transition and Droplet Dynamics,” ASME J. Fluids Eng., 130(3), p. 031402.
Wagner, W. , Cooper, J. R. , Dittmann, A. , Kijima, J. , Kretzschmar, H. J. , Kruse, A. , Mares, R. , Oguchi, K. , Sato, H. , Stöcker, I. , Sifner, O. , Takaishi, Y. , Tanishita, I. , Trübenbach, J. , and Willkommen, T. , 2000, “The IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam,” ASME J. Eng. Gas Turbines Power, 122(1), pp. 150–182. [CrossRef]
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, 219(12), pp. 1315–1333. [CrossRef]
Grübel, M. , Starzmann, J. , Schatz, M. , and Vogt, D. M. , 2017, “Modelling of Condensing Steam Flows in Laval Nozzles With ANSYS CFX,” Proc. Inst. Mech. Eng., Part A (epub).
Young, J. B. , 1982, “The Spontaneous Condensation of Steam in Supersonic Nozzles,” Physicochem. Hydrodyn., 3(1), pp. 57–82.
White, A. J. , 1992, “Condensation in Steam Turbine Cascades,” Ph.D. thesis, University of Cambridge, Cambridge, UK.
Starzmann, J. , Hughes, F. R. , White, A. J. , Halama, J. , Hric, V. , Kolovratnik, M. , Lee, H. , Sova, L. , Stastny, M. , Schuster, S. , Grübel, M. , Schatz, M. , Vogt, D. M. , Patel, Y. , Patel, G. , Turunen-Saaresti, T. , Gribin, V. , Tishchenko, V. , Gavrilov, I. , Kim, C. , Baek, J. , Wu, X. , Yang, J. , Dykas, S. , Wroblewski, W. , Yamamoto, S. , Feng, Z. , and Li, L. , 2016, “Results of the International Wet Steam Modelling Project,” Wet Steam Conference, Prague, Czech Republic, Sept. 12–14, Paper No. 11.
Starzmann, J. , 2014, “Numerische Untersuchung der Zweiphasenströmung und Analyse von Nässeverlusten in Niederdruckdampfturbinen,” Ph.D. thesis, University of Stuttgart, Stuttgart, Germany (in German).
Grübel, M. , Starzmann, J. , Schatz, M. , Eberle, T. , Vogt, D. M. , and Sieverding, F. , 2015, “Two-Phase Flow Modeling and Measurements in Low-Pressure Turbines—Part 1: Numerical Validation of Wet Steam Models and Turbine Modeling,” ASME J. Eng. Gas Turbines Power, 137(4), p. 042602. [CrossRef]
Gyarmathy, G. , 1962, “Grundlagen einer Theorie der Naßdampfturbine,” Ph.D. thesis, ETH Zürich, Juris-Verlag Zürich, Switzerland (in German).
Herwig, H. , and Schmandt, B. , 2014, “How to Determine Losses in a Flow Field: A Paradigm Shift Towards the Second Law Analysis,” Entropy, 16(6), pp. 2959–2989. [CrossRef]
Naterer, G. F. , 2003, Heat Transfer in Single and Multiphase Systems, CRC Press, Boca Raton, FL.
Sun, J. , 2014, “Two-Phase Eulerian Averaged Formulation of Entropy Production for Cavitation Flow,” Ph.D. thesis, University of Manitoba, Winnipeg, MB, Canada. https://mspace.lib.umanitoba.ca/handle/1993/23987
Vreman, A. W. , 2007, “Macroscopic Theory of Multicomponent Flows: Irreversibility and Well-Posed Equations,” Physica D, 225(1), pp. 94–111. [CrossRef]
Crowe, C. , Sommerfeld, M. , and Tsuji, Y. , 1998, Multiphase Flows With Droplets and Particles, CRC Press, Boca Raton, FL.
Schiller, L. , and Naumann, A. , 1933, “Über die grundlegenden Berechnungen bei der Schwerkraftaufbereitung,” Z. Ver. Dtsch. Ing., 77(12), pp. 318–320.
Herwig, H. , and Wenterodt, T. , 2012, Entropie für Ingenieure, Vieweg+Teubner, Wiesbaden, Germany (in German).
White, A. J. , Young, J. B. , and Walters, P. T. , 1996, “Experimental Validation of Condensing Flow Theory for a Stationary Cascade of Steam Turbine Blades,” Philos. Trans. R. Soc. A, 354(1704), pp. 59–88. [CrossRef]
ANSYS, 2017, “ANSYS CFX-Solver Theory Guide, Release 18.0,” Ansys, Inc., Canonsburg, PA.

Figures

Grahic Jump Location
Fig. 1

Geometry and computational domain for the cascade of White [16]

Grahic Jump Location
Fig. 6

Classification of losses for different operating conditions: (L) low inlet superheat, (M) medium inlet superheat, (H) high inlet superheat, (W) wet inflow; (*) flow is still subcooled at the outlet of the CFD domain. (a) Entropy loss coefficient and (b) total entropy production rate.

Grahic Jump Location
Fig. 7

Interphase mass transfer rate and resulting entropy production due to thermodynamic relaxation for case L1: (a) Interphase mass transfer rate and (b) entropy production rate

Grahic Jump Location
Fig. 2

Predicted nucleation rate and comparison between predicted static pressure contours and Schlieren photographs for case L1 (SSS: suction side shock, SPS: pressure side shock, and SC: condensation induced pressure rise)

Grahic Jump Location
Fig. 3

Measured and predicted distributions of normalized static pressure and wetness at the traverse plane for case L1

Grahic Jump Location
Fig. 4

Comparison between measured and predicted loss coefficients for experiments with low (L), medium (M), and high (H) inlet superheat

Grahic Jump Location
Fig. 5

Illustration of mesh elements considered for boundary layer, wake mixing, and thermodynamic relaxation losses for case L1

Grahic Jump Location
Fig. 8

Pressure profile distribution for case W1 with different inlet conditions and comparison to experiment (W1A: r1 = 2r1,W1, W1B: r1 = 3r1,W1, W1C: y1 = 0.01, and W1D: y1 = 0.01, r1 = 3r1,W1)

Grahic Jump Location
Fig. 9

Illustration of the shadow region due to droplet inertia for case W1B with r1 = 3r1,W1: (a) Wetness fraction y for phase Pin and (b) streamlines

Grahic Jump Location
Fig. 10

Classification of losses for case W1 with different inlet conditions (W1A: r1 = 2r1,W1, W1B: r1 = 3r1,W1, W1C: y1 = 0.01, and W1D: y1 = 0.01, r1 = 3r1,W1)

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In