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Research Papers

Endwall Loss in Turbine Cascades

[+] Author and Article Information
John D. Coull

Whittle Laboratory,
University of Cambridge,
Cambridge CB3 0DY, UK
e-mail: jdc38@cam.ac.uk

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received October 24, 2016; final manuscript received December 16, 2016; published online March 15, 2017. Editor: Kenneth Hall.

J. Turbomach 139(8), 081004 (Mar 15, 2017) (12 pages) Paper No: TURBO-16-1281; doi: 10.1115/1.4035663 History: Received October 24, 2016; Revised December 16, 2016

Prior to the detailed design of components, turbomachinery engineers must guide a mean-line or throughflow design toward an optimum configuration. This process requires a combination of informed judgement and low-order correlations for the principle sources of loss. With these requirements in mind, this paper examines the impact of key design parameters on endwall loss in turbines, a problem which remains poorly understood. This paper presents a parametric study of linear cascades, which represent a simplified model of real-engine flow. The designs are nominally representative of the low-pressure turbine blades of an aero-engine, with varying flow angles, blade thickness, and suction surface lift styles. Reynolds-averaged Navier–Stokes (RANS) calculations are performed for a single aspect ratio (AR) and constant inlet boundary layer thickness. To characterize the cascades studied, the two-dimensional design space is examined before studying endwall losses in detail. It is demonstrated that endwall loss can be decomposed into two components: one due to the dissipation associated with the endwall boundary layer and another induced by the secondary flows. This secondary-flow-induced loss is found to scale with a measure of streamwise vorticity predicted by classical secondary flow theory.

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Figures

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Fig. 1

Secondary flow in a turbine cascade

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Fig. 2

Designs with varying flow angles, see Table 1

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Fig. 3

Mises Cp distributions for the designs in Fig. 2: (a) relative to outlet pressure and (b) relative to trailing edge pressure

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Fig. 4

Typical CFD domain

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Fig. 5

Mesh sensitivity for a single design (α1 = 30 deg, α2=−65 deg, and Tmax/Cx  = 0.15)

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Fig. 6

CFD and experimental endwall losses [27,28]

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Fig. 7

Geometric parameters for the designs in Fig. 2: (a) suction surface length versus axial chord, (b) pitch versus axial chord, (c) pitch versus suction surface length, and (d) suction surface length versus effective throat

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Fig. 8

(a) Zweifel lift coefficient [29] and breakdown (a) Zweifel lift coefficient [29] and breakdown: pressure-side integral ((b), (c)) and suction-side integral ((d), (e))

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Fig. 9

Mises Cp versus x/Cx for the designs in Fig. 2: (a) relative to outlet pressure and (b) relative to trailing edge pressure

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Fig. 10

(a) Circulation lift coefficient [14] and breakdown: pressure-side integral ((b), (c)) and suction-side integral ((d), (e))

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Fig. 11

(a) Leading edge incidence (difference between the inlet flow and metal angles) and (b) deviation (Mises)

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Fig. 12

(a) Trailing edge Mach number (Mises); (b) uncovered turning angle; (c) codependence

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Fig. 13

Definition of uncovered turning angle

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Fig. 14

Fully turbulent profile loss for the designs shown in Fig. 2: (a) RANS; (b) Mises; (c) Eq. (7) for Mises

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Fig. 15

Breakdown of loss contributions in Eq. (7) for fully turbulent Mises calculations: (a) momentum deficit; (b) blockage; (c) base pressure

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Fig. 16

Endwall entropy loss coefficients

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Fig. 17

Estimated background dissipation loss: (a) ratio of endwall and exit flow area; (b) midspan velocity ratio; (c) simple estimate; (d) integrated estimate

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Fig. 18

(a) Estimated contributions from secondary-flow-induced loss and (b) the SKE factor of Ref. [34] (Eq. (12))

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Fig. 19

Vorticity amplification factors, after Hawthorne [2]: (a) passage vortex, (b) counter vortex, (c) shed vorticity, and (d) total

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Fig. 20

Vorticity amplification factors, after Marsh [35]: (a) passage vortex, (b) counter vortex, (c) shed vorticity, and (d) total

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Fig. 21

Comparison of estimated secondary-flow-induced loss and the summed amplification factor of Hawthorne [2]

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Fig. 22

Comparison of estimated secondary-flow-induced loss and the summed amplification factor of Marsh [35]

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Fig. 25

Free-vortex model for the covered turning region: (a) geometric approximation, (b) free-vortex, and (c) pressure distribution

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Fig. 26

Free-vortex model of CP−PS for the thin (a) and thick (b) sets of blades

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Fig. 27

Pressure-side circulation integral for the thin (a) and thick (b) sets of blades, from Mises design calculations

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Fig. 24

Endwall loss: simple model versus CFD

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Fig. 23

Mises Cp distributions for the thinner designs: (a) relative to outlet pressure and (b) relative to trailing edge pressure

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