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.

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Fig. 1

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

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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)

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Fig. 3

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

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Fig. 4

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

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Fig. 5

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

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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.

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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

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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)

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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)

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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



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