Research Papers

Blade Loading and Its Application in the Mean-Line Design of Low Pressure Turbines

[+] Author and Article Information
John D. Coull

e-mail: jdc38@cam.ac.uk

Howard P. Hodson

e-mail: hph1000@cam.ac.ukWhittle Laboratory,
University of Cambridge,
1 J.J. Thomson Ave,
Cambridge CB3 0DY, UK

For a high speed datum turbine, this effect is slightly magnified due to the high Mach numbers in this region of the Smith chart.

Note that these designs have low flow turning, so for a constant circulation they must have a high pitch-to-chord ratio.

It should be noted that Ainley and Mathieson account for the machine hub-to-tip ratio rather than the aspect ratio.

1Corresponding author.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received August 24, 2011; final manuscript received October 6, 2011; published online November 8, 2012. Editor: David Wisler.

J. Turbomach 135(2), 021032 (Nov 08, 2012) (12 pages) Paper No: TURBO-11-1192; doi: 10.1115/1.4006588 History: Received August 24, 2011; Revised October 06, 2011

In order to minimize the number of iterations to a turbine design, reasonable choices of the key parameters must be made at the preliminary design stage. The choice of blade loading is of particular concern in the low pressure (LP) turbine of civil aero engines, where the use of high-lift blades is widespread. This paper considers how blade loading should be measured, compares the performance of various loss correlations, and explores the impact of blade lift on performance and lapse rates. To these ends, an analytical design study is presented for a repeating-stage, axial-flow LP turbine. It is demonstrated that the long-established Zweifel lift coefficient (Zweifel, 1945, “The Spacing of Turbomachine Blading, Especially with Large Angular Deflection” Brown Boveri Rev., 32(1), pp. 436–444) is flawed because it does not account for the blade camber. As a result the Zweifel coefficient is only meaningful for a fixed set of flow angles and cannot be used as an absolute measure of blade loading. A lift coefficient based on circulation is instead proposed that accounts for the blade curvature and is independent of the flow angles. Various existing profile and secondary loss correlations are examined for their suitability to preliminary design. A largely qualitative comparison demonstrates that the loss correlations based on Ainley and Mathieson (Ainley and Mathieson, 1957, “A Method of Performance Estimation for Axial-Flow Turbines,” ARC Reports and Memoranda No. 2974; Dunham and Came, 1970, “Improvements to the Ainley-Mathieson Method of Turbine Performance Prediction,” Trans. ASME: J. Eng. Gas Turbines Power, July, pp. 252–256; Kacker and Okapuu, 1982, “A Mean Line Performance Method for Axial Flow Turbine Efficiency,” J. Eng. Power, 104, pp. 111–119). are not realistic, while the profile loss model of Coull and Hodson (Coull and Hodson, 2011, “Predicting the Profile Loss of High-Lift Low Pressure Turbines,” J. Turbomach., 134(2), pp. 021002) and the secondary loss model of (Traupel, W, 1977, Thermische Turbomaschinen, Springer-Verlag, Berlin) are arguably the most reasonable. A quantitative comparison with multistage rig data indicates that, together, these methods over-predict lapse rates by around 30%, highlighting the need for improved loss models and a better understanding of the multistage environment. By examining the influence of blade lift across the Smith efficiency chart, the analysis demonstrates that designs with higher flow turning will tend to be less sensitive to increases in blade loading.

Copyright © 2013 by ASME
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Fig. 1

Turbine stage efficiency normalized for zero tip gap, 50% reaction designs, Smith [8]

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Fig. 2

Velocity triangles and angle conventions

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Fig. 3

Calculated flow and geometry parameters across the design space: (a) stator exit velocity; (b) mean span; (c) ratio of S0/Cx; (d) Reynolds number

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Fig. 4

Geometry estimation using a parabolic camberline

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Fig. 5

Sample surface velocity distributions

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Fig. 6

Low speed definition of: (a) Zweifel lift coefficient Zw (Eq. (19)); (b) Circulation coefficient Co (Eq. (21))

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Fig. 7

Predicted efficiency for constant Zw=1.10 using the models of Refs. [6] and [7]

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Fig. 8

Diffusion factor for constant Zw=1.10 using the models of Refs. [6] and [7]

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Fig. 9

Predicted stage efficiency for constant circulation coefficient Co=0.70 using the models of Refs. [6] and [7]

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Fig. 10

Predicted lost efficiency due to profile loss for Co=0.70: (a) Denton [13]; (b) Coull and Hodson [6]; (c) Ainley and Mathieson [3]; (d) Dunham and Came [4]; (e) Kacker and Okapuu [5]; (f) Craig and Cox [7]

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Fig. 11

Predicted lost efficiency due to secondary loss for Co=0.70, according to: (a) Craig and Cox [6]; (b) Ainley and Mathieson [3]; (c) Dunham and Came [4]; (d) Kacker and Okapuu [5]; (e) Traupel [7]; (f) Benner et al. [17]

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Fig. 12

Predicted lost efficiency with increasing lift for the datum flow angles (φ=0.9, ψ=2).: (a) Profile Loss; (b) Secondary Loss

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Fig. 13

Predicted lost efficiency with varying Reynolds number for the datum turbine: (a) profile loss; (b) secondary loss

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Fig. 14

Reynolds number lapse for varying lift, showing efficiency when considering profile loss alone [6], secondary loss alone [8] and the overall efficiency; datum flow angles (φ=0.9, ψ=2)

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Fig. 15

Comparison of experimental and predicted efficiency lapse rates using the profile loss model of Coull and Hodson [6] Traupel [7] secondary loss model

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Fig. 16

Efficiency contours for three lift coefficients (Co=0.70, 0.75 0.80), using the profile loss model of Coull and Hodson [6] and secondary model of Traupel [7]




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