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TECHNICAL PAPERS

Calculation of the Expansion Through a Cooled Gas Turbine Stage

[+] Author and Article Information
Leonardo Torbidoni1

 Ansaldo Energia, Via Nicola Lorenzi 8, 16152 Genova, Italyleonardo.torbidoni@aen.ansaldo.it

J. H. Horlock

Whittle Laboratory, University of Cambridge, Madingley Road, CB3 0DY, UK

1

Formerly at TPG, Universitá di Genova, Italy.

J. Turbomach 128(3), 555-563 (Feb 01, 2005) (9 pages) doi:10.1115/1.2185123 History: Received October 01, 2004; Revised February 01, 2005

In recent work by the same authors [Torbidoni, L., and Horlock, J. H., 2005, ASME J. Turbomach, 127, pp. 191–199], a new method for calculating the coolant flow requirements of a high-temperature gas turbine blade was described. It involved consideration of successive chordwise strips of blading; the coolant required in each strip was obtained by detailed study of the heat transfer processes across the wall of the blade and then setting limits on the maximum blade metal temperature. In the present paper, the gas state paths, involving viscous losses, heat transfer, and mixing of the coolant with the mainstream, are determined strip by strip along the whole blade chord for the stator and rotor of the stage and illustrated on an enthalpy-entropy chart. The work output from each rotor strip is obtained together with the losses (entropy creation) through the whole stage. It is then possible to calculate the thermodynamic efficiency for the cooled turbine stage and compare it to that of the uncooled stage. Illustrative calculations are given, a main calculation being based on the mean flow across the blade pitch. But, in a second supplementary calculation, allowance is also made for flow variations across the blade pitch. By comparing these two calculations, it is shown that the mean flow calculation is usually adequate.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Element Δsdy for heat transfer through blade surface to coolant

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Figure 2

Diagram showing the elementary expansion step, where stagnation (dotted lines) and static (continuous lines) specific enthalpies are plotted versus the specific entropy for the mainstream gas flow. The three major phenomena are depicted in succession: (A-B) uncooled expansion, (B-C) convective heat exchange and (C-D) mixing.

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Figure 3

Schematic of the elementary control volume of the preliminary pressure and suction blade surfaces evaluation

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Figure 4

Enthalpy-entropy diagrams for uncooled and cooled nozzle guide vane row (showing both stagnation and static enthalpy for the mainstream gas flow)

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Figure 5

Mainstream gas flow stagnation and static pressure for ten steps along the cooled nozzle-blade chord

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Figure 6

Mainstream gas flow velocity and axial velocity for ten steps along the cooled nozzle-blade chord

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Figure 7

Specific entropy variation for ten steps along the cooled nozzle-blade chord due to uncooled expansion, convective heat transfer across the blade wall, mixing, and trailing-edge discharge

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Figure 8

Entropy and entropy variation for ten steps along the cooled nozzle-blade chord (last column refers to trailing edge discharge)

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Figure 9

Stagnation and static enthalpy for ten steps along the cooled nozzle-blade chord (showing enthalpy at the mean blade channel line and at the blade pressure and suction surfaces for the mainstream gas flow)

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Figure 10

Mainstream gas flow velocity for ten steps along the cooled nozzle-blade chord (showing velocity at the mean blade channel line and at the blade pressure and suction surfaces).

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Figure 11

Enthalpy-entropy diagrams for uncooled and cooled rotating rows (showing both relative stagnation and static enthalpy for the mainstream gas flow)

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Figure 12

Enthalpy-entropy diagrams for cooled nozzle guide vane row (showing both stagnation and static enthalpy for the mainstream gas flow). Expansion evaluated by the stepped approach is the same as in Fig. 4. Expansion evaluated by the whole-blade-chord approach is overwritten on the diagram, for comparison.

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Figure 13

Enthalpy-entropy diagrams for cooled rotating row (showing both relative stagnation and static enthalpy for the mainstream gas flow). Expansion evaluated by the stepped approach is the same as in Fig. 1. Expansion evaluated by the whole-blade-chord approach is overwritten on the diagram, for comparison.

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