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Research Papers

# Predicting the Profile Loss of High-Lift Low Pressure Turbines

[+] Author and Article Information
John D. Coull

Whittle Laboratory, University of Cambridge, Cambridge CB3 0DY, UKjdc28@cam.ac.uk

Howard P. Hodson

Whittle Laboratory, University of Cambridge, Cambridge CB3 0DY, UKhph1000@cam.ac.uk

This parameter is also fundamental in the Falkner–Skan similar boundary layer profiles $U=constant×Sm$, where $m=(dU/U)/(dS/S)$.

It is also possible to use a velocity parameter of similar scaling but this pressure parameter allowed a slightly better fit to the flat plate distributions.

A reasonable estimate of the circulation may also be obtained by assuming a linear deceleration, such that this contribution is simply $(1+0.5DF)(1−Speak/S0)$.

A similar performance is also predicted for designs between {1} and {3}, suggesting significant freedom in the design space.

J. Turbomach 134(2), 021002 (Jun 21, 2011) (14 pages) doi:10.1115/1.4002961 History: Received June 21, 2010; Revised July 02, 2010; Published June 21, 2011; Online June 21, 2011

## Abstract

The overall efficiency of low pressure turbines is largely determined by the two-dimensional profile loss, which is dominated by the contribution of the suction surface boundary layer. This boundary layer typically features a laminar separation bubble and is subjected to an inherently unsteady disturbance environment. The complexity of the flow behavior makes it difficult to numerically predict the profile loss. To address this problem, an empirical method is proposed for predicting the boundary layer integral parameters at the suction surface trailing edge, allowing the profile loss to be estimated. Extensive measurements have been conducted on a flat plate simulation of the suction surface boundary layer. The disturbance environment of real machines was modeled using a moving bar wake generator and a turbulence grid. From this data set, empirically based methods have been formulated using physical principles for the prediction of the momentum thickness and shape factor at the suction surface trailing edge. The predictions of these methods may be used to estimate the profile loss of a given cascade, which achieves reasonable agreement with the available data. By parameterizing the shape of the suction surface velocity distribution, the method is recast as a preliminary design tool. Powerfully, this may be used to guide the selection of the key design parameters (such as the blade loading and velocity distribution shape) and enables a reasonable estimation of the unsteady profile loss to be made at a very early stage of design. To illustrate the capabilities of the preliminary design tool, different styles of velocity distribution are evaluated for fixed blade loading and flow angles. The predictions suggest that relatively “flat-top” designs will have the lowest profile loss but good performance can also be achieved with front-loaded “peaky” distributions. The latter designs are more likely to have acceptable incidence tolerance.

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## Figures

Figure 1

Schematic of the flat plate experiment

Figure 2

Isentropic velocity distributions for designs B, D, and G at ReC≈200,000, fr=0.84 alongside the assumed pressure surface distribution

Figure 3

Measured θTE/S0: designs B, C, and E, fr=0.84

Figure 4

The growth of momentum thickness downstream of separation (θTE/θsep), fr=0.84

Figure 5

Comparison between measured θTE/S0 and tripped MISES calculation for design B, fr=0.42

Figure 6

Difference between the measurements and the tripped MISES calculations for all designs, fr=0.42

Figure 7

Breakdown of the terms of the θTE/S0 correlation for design B, fr=0.84

Figure 8

Comparison of θTE/S0 from the correlation with the flat plate data (around 200 measurements in total)

Figure 9

Comparison of θTE/S0 from the correlation with the flat plate data for designs C, D, and E, fr=0.84

Figure 10

Comparison of cascade measurements of θTE/S0(13,16,24) with the current predictions

Figure 11

Comparison of HTE from the correlation in Eq. 20 with the flat plate data

Figure 12

Comparison of measured profile losses (17,24,32) to the predictions using the boundary layer correlations and Eq. 2

Figure 13

The influence of the leading edge integral

Figure 14

The variation of UTE/U2 with the ratio of pitch to suction surface length (13,16-17,23-24,32)

Figure 15

Comparison of measured profile loss (17,24,32) with the preliminary design tool predictions

Figure 16

Four candidate suction surface designs with the same circulation as design D

Figure 17

Estimated profile loss coefficients for each of the candidate designs, fr=0.84

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