Research Papers

Analytical Modeling of Turbine Cascade Leading Edge Heat Transfer Using Skin Friction and Pressure Measurements

[+] Author and Article Information
Brian M. Holley

Department of Mechanical Engineering, University of Connecticut, 191 Auditorium Road, Storrs, CT 06269-3139bmholley@engr.uconn.edu

Lee S. Langston

Department of Mechanical Engineering, University of Connecticut, 191 Auditorium Road, Storrs, CT 06269-3139langston@engr.uconn.edu

J. Turbomach 130(2), 021001 (Feb 12, 2008) (9 pages) doi:10.1115/1.2812328 History: Received May 30, 2007; Revised June 26, 2007; Published February 12, 2008

The flow near the leading edge stagnation line of a plane turbine cascade airfoil is analyzed using measurements, analytical modeling, and computational fluid dynamics modeling. New measurements of skin friction and pressure are used to show that the aerodynamics of the leading edge, within what we call the stagnation region, are well described by an exact analytical solution for laminar stagnation-point or Hiemenz flow. The skin friction measurements indicate the extent of the stagnation region. The same parameters that characterize Hiemenz flow also characterize stagnation-point potential flow. The thermal resistance of the laminar momentum boundary layer in Hiemenz flow is absent in the inviscid solution. Consequently, the heat transfer in stagnation-point potential flow is greater than the heat transfer in Hiemenz flow. Based on measurements from an earlier study, the highest heat transfer levels in the cascade occur along the leading edge stagnation line. Stagnation-point potential flow provides a close, upper bound for the measured heat transfer at this small but critical location within the stagnation region. This paper describes how to apply the analytical model for predicting cascade stagnation-line heat transfer using only surface pressure calculations.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 3

Cascade coordinate system with stagnation streamline and lengths scaled by axial chord. Stagnation line measured at x=0.036, y=0.571, where s=0 is prescribed.

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Figure 4

This interferogram is from OFI applied to a 50μm thick nickel foil substrate wrapped around the leading edge of a plane turbine cascade airfoil at midspan

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Figure 5

Midspan static pressure measurements for Airfoils 2 and 3, and potential flow solution

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Figure 6

Hiemenz flow, or plane stagnation-point flow, following Schlichting (4)

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Figure 7

Qualitative representation of velocity scaled by Uo and length scaled by bx along a stagnation streamline for plane stagnation-point potential flow, Hiemenz flow, and cascade wind tunnel flow

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Figure 1

Schematic of the large-scale airfoil cascade used for measurements of skin friction, static pressure, and heat transfer. The inlet boundary layer measurement location also serves as a reference location for total and static pressures.

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Figure 2

Arclength and normal coordinate definitions for airfoil leading edge, with arclength and leading edge radius scaled by axial chord. The extent of the stagnation region is about −0.06<s<0.02.

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Figure 9

Skin friction measurements from 15% to 60% span with CFD calculations and a Hiemenz analytical solution fit to measurements. The extent of the stagnation region is about −0.06<s<0.02.

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Figure 10

Measured and calculated midspan static pressure with Hiemenz flow analytical values

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Figure 11

Measured (3) and calculated midspan Stanton number along with Hiemenz flow and plane stagnation-point potential flow analytical values. The extent of the stagnation region is about −0.06<s<0.02.

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Figure 12

Airfoil shapes considered for comparison to leading edge heat transfer model (Eq. 11)

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Figure 13

Cascade heat transfer data from four studies of five airfoils, with all Reynolds numbers based on cascade inlet velocity (choice of length scale does not affect the result)

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Figure 8

Momentum and thermal boundary layers in Hiemenz flow and plane stagnation-point potential flow



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