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.

1.
Ainley
,
D. G.
, and
Mathieson
,
G. C. R.
, 1957, “
A Method of Performance Estimation for Axial-Flow Turbines
,” ARC Reports and Memoranda No. 2974.
2.
Dunham
,
J.
, and
Came
,
P. M.
, 1970, “
Improvements to the Ainley–Mathieson Method of Turbine Performance Prediction
,”
ASME J. Eng. Power
0022-0825,
A92
, pp.
252
256
.
3.
Craig
,
H. R. M.
, and
Cox
,
H. J. A.
, 1971, “
Performance Estimation of Axial Flow Turbines
,”
Proc. Inst. Mech. Eng.
0020-3483,
185
, pp.
407
424
.
4.
Smith
,
S. F.
, 1965, “
A Simple Correlation of Turbine Efficiency
,”
J. R. Aeronaut. Soc.
0368-3931,
69
, pp.
367
370
.
5.
Hourmouziadis
,
J.
, 1987, “
Aerodynamic Design of Low Pressure Turbines
,”
AGARD Lecture Series No. 167
.
6.
Vázquez
,
R.
,
Cadrecha
,
D.
, and
Torre
,
D.
, 2003, “
High Stage Loading Low Pressure Turbines. A New Proposal for an Efficiency Chart
,”
ASME
Paper No. GT2003-38374.
7.
Coull
,
J. D.
,
Thomas
,
R. L.
, and
Hodson
,
H. P.
, 2010, “
Velocity Distributions for Low Pressure Turbines
,”
ASME J. Turbomach.
0889-504X,
132
(
4
), p.
041006
.
8.
Halstead
,
D. E.
,
Wisler
,
D. C.
,
Okiishi
,
T. H.
,
Walker
,
G. J.
,
Hodson
,
H. P.
, and
Shin
,
H. W.
, 1997, “
Boundary Layer Development in Axial Compressors and Turbines: Part 3 of 4: LP Turbines
,”
ASME J. Turbomach.
0889-504X,
119
(
2
), pp.
225
237
.
9.
Praisner
,
T. J.
,
Grover
,
E. A.
,
Knezevici
,
D. C.
,
Popovic
,
I.
,
Sjolander
,
S. A.
,
Clarke
,
J. P.
, and
Sondergaard
,
R.
, 2008, “
Towards the Expansion of Low-Pressure-Turbine Airfoil Design Space
,”
ASME
Paper No. GT2008-50898.
10.
Gier
,
J.
,
Franke
,
M.
,
Hübner
,
N.
, and
Schröder
,
T.
, 2008, “
Designing LP Turbines for Optimized Airfoil Lift
,”
ASME
Paper No. GT2008-51101.
11.
Denton
,
J. D.
, 1993, “
Loss Mechanisms in Turbomachines
,”
ASME J. Turbomach.
0889-504X,
115
(
4
), pp.
621
656
.
12.
Roberts
,
Q. D. H.
, 1998, “
The Trailing Edge Loss of Subsonic Turbine Blades
,” Ph.D. thesis, Cambridge University.
13.
Curtis
,
E. M.
,
Hodson
,
H. P.
,
Banieghbal
,
M. R.
,
Howell
,
R. J.
, and
Harvey
,
N. W.
, 1997, “
Development of Blade Profiles for Low-Pressure Turbine Applications
,”
ASME J. Turbomach.
0889-504X,
119
(
3
), pp.
531
538
.
14.
Coull
,
J. D.
, 2009, “
Wake Induced Transition in Low Pressure Turbines
,” Ph.D. thesis, Cambridge University.
15.
Hodson
,
H. P.
, 1990, “
Modelling Unsteady Transition and Its Effects on Profile Loss
,”
ASME J. Turbomach.
0889-504X,
112
(
4
), pp.
691
701
.
16.
Opoka
,
M. M.
, 2007, “
The Effect of Upstream and Downstream Bladerows on Transition in Low Pressure Turbines
,” Ph.D. thesis, University of Cambridge.
17.
Himmel
,
C.
, and
Hodson
,
H. P.
, 2009, “
Modifying Ultra-High Lift Low Pressure Turbine Blades for Low Reynolds Number Applications
,”
ISUAAAT 12
, Imperial College, London, Sep. 1–4.
18.
Thwaites
,
B.
, 1949, “
Approximate Calculation of the Laminar Boundary Layer
,”
Aeronaut. Q.
0001-9259,
1
, pp.
245
280
.
19.
White
,
F. M.
, 1991,
Viscous Fluid Flow
,
2nd ed.
,
McGraw-Hill
,
New York
.
20.
Youngren
,
H.
, and
Drela
,
M.
, 1991, “
Viscous/Inviscid Method for Preliminary Design of Transonic Cascades
,”
AIAA, SAE, ASME, and ASEE, Joint Propulsion Conference, 27th
, Sacramento, CA, Jun. 24–26.
21.
Stratford
,
B. S.
, 1954, Flow in the Laminar Boundary Layer Near Separation, Ministry of Supply, Aeronautical Research Council, London, No. 3002.
22.
Stieger
,
R. D.
, and
Hodson
,
H. P.
, 2004, “
The Transition Mechanism of Highly Loaded Low-Pressure Turbine Blades
,”
ASME J. Turbomach.
0889-504X,
126
(
2
), pp.
388
394
.
23.
Zhang
,
X. F.
, 2005, “
Separation and Transition Control on Ultra-High-Lift Low Pressure Turbines
,” Ph.D. thesis, University of Cambridge.
24.
Howell
,
R. J.
,
Ramesh
,
O. N.
,
Hodson
,
H. P.
,
Harvey
,
N. W.
, and
Schulte
,
V.
, 2001, “
High Lift and Aft-Loaded Pressure Profiles for Low-Pressure Turbines
,”
ASME J. Turbomach.
0889-504X,
123
(
2
), pp.
181
188
.
25.
Vera
,
M.
,
Hodson
,
H. P.
, and
Vazquez
,
R.
, 2003, “
The Effect of Mach Number on LP Turbine Wake-Blade Interaction
,”
Ninth ISUAAAT
, Lyon, France, Sept. 4–8.
26.
Vera
,
M.
,
Zhang
,
X. F.
,
Hodson
,
H. P.
, and
Harvey
,
N.
, 2005, “
Separation and Transition Control on Aft-Loaded Ultra-High-Lift LP Turbine Blade at Low Reynolds Numbers: High-Speed Validation
,”
ASME
Paper No. GT2005-68893.
27.
Rosenhead
,
L.
, ed., 1963,
Laminar Boundary Layers
,
Oxford University Press
,
UK
.
28.
Pohlhausen
,
K.
, 1921, “
Zur näherungsweisen Integration der Differentialgleichung der laminaren Grenzschicht
,”
Z. Angew. Math. Mech.
0044-2267,
1
, pp.
252
290
.
29.
Timman
,
R.
, 1949, “
A One-Parameter Method for the Calculation of Laminar Boundary Layers
,” Rep. Trans. Nat. LuchtvLab. No. 15 F29-45, Amsterdam.
30.
Walz
,
A.
, 1941, “
Ein neuer Ansatz für das Geschwindigkeitsprofil der laminaren Reibungsschicht
,”
Ber. Lilienthal-Ges. Luftfahrf
,
141
, pp.
8
12
.
31.
Curle
,
N.
, and
Skan
,
S. W.
, 1957, “
Approximate Methods for Predicting Separation Properties of Laminar Boundary Layers
,”
Aeronaut. Q.
0001-9259,
8
, pp.
257
268
.
32.
Howell
,
R. J.
, 1999, “
Wake-Separation Bubble Interactions in Low Reynolds Number Turbomachinery
,” Ph.D. thesis, Cambridge University.
33.
Corke
,
T. C.
, and
Thomas
,
F. O.
, 2003, “
Enhanced Design of Turbo-Jet LPT by Separation Control Using Phased Plasma Actuators
,” Report No. NASA/CR-2003-212294.
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