A three-equation model has been applied to the prediction of separation-induced transition in high-lift low-Reynolds-number cascade flows. Classical turbulence models fail to predict accurately laminar separation and turbulent reattachment, and usually overpredict the separation length, the main reason for this being the slow rise of the turbulent kinetic energy in the early stage of the separation process. The proposed approach is based on solving an additional transport equation for the so-called laminar kinetic energy, which allows the increase in the nonturbulent fluctuations in the pretransitional and transitional region to be taken into account. The model is derived from that of Lardeau et al. (2004, “Modelling Bypass Transition With Low-Reynolds-Number Non-Linear Eddy-Viscosity Closure,” Flow, Turbul. Combust., 73, pp. 49–76), which was originally formulated to predict bypass transition for attached flows, subject to a wide range of freestream turbulence intensity. A new production term is proposed, based on the mean shear and a laminar eddy-viscosity concept. After a validation of the model for a flat-plate boundary layer, subjected to an adverse pressure gradient, the T106 and T2 cascades, recently tested at the von Kármán Institute, are selected as test cases to assess the ability of the model to predict the flow around high-lift cascades in conditions representative of those in low-pressure turbines. Good agreement with experimental data, in terms of blade-load distributions, separation onset, reattachment locations, and losses, is found over a wide range of Reynolds-number values.

1.
Cobley
,
K.
,
Coleman
,
N.
,
Siden
,
G.
, and
Arndt
,
N.
, 1997, “
Design of New Three Stage Low Pressure Turbine for the BMW Rolls-Royce BR715 Turbofan Engine
,”
ASME
Paper No. 97-GT-419.
2.
Curtis
,
E. M.
,
Hodson
,
H. P.
,
Banieghbal
,
M. R.
,
Denton
,
J. D.
,
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
.
3.
Haselbach
,
F.
,
Schiffer
,
H. P.
,
Horsman
,
M.
,
Dressen
,
S.
,
Harvey
,
N. W.
, and
Read
,
S.
, 2002, “
The Application of Ultra High Lift Blading in the BR715 LP Turbine
,”
ASME J. Turbomach.
0889-504X,
124
(
1
), pp.
45
51
.
4.
Howell
,
R. J.
,
Hodson
,
H. P.
,
Schulte
,
V.
,
Stieger
,
R. D.
,
Schiffer
,
H. P.
,
Haselbach
,
F.
, and
Harvey
,
N. W.
, 2002, “
Boundary Layer Development in the BR710 and BR715 LP Turbines—The Implementation of High-Lift and Ultra-High-Lift Concepts
,”
ASME J. Turbomach.
0889-504X,
124
(
3
), pp.
385
392
.
5.
Schulte
,
V.
, and
Hodson
,
H. P.
, 1998, “
Unsteady Wake–Induced Boundary Layer Transition in High Lift HP Turbines
,”
ASME J. Turbomach.
0889-504X,
120
(
1
), pp.
28
35
.
6.
Stieger
,
R. D.
, and
Hodson
,
H. P.
, 2004, “
The Transition Mechanism of Highly Loaded Low-Pressure Turbine Blades
,”
ASME J. Turbomach.
0889-504X,
126
(
4
), pp.
536
543
.
7.
Zhang
,
F. H.
,
Vera
,
M.
,
Hodson
,
H. P.
, and
Harvey
,
N.
, 2006, “
Separation and Transition Control on an Aft-Loaded Ultra-High-Lift LP Turbine Blade at Low Reynolds Numbers: Low-Speed Investigation
,”
ASME J. Turbomach.
0889-504X,
128
(
3
), pp.
517
527
.
8.
Rumsey
,
C. L.
,
Gatski
,
T. B.
,
Sellers
,
W. L.
, III
,
Vatsa
,
V. N.
, and
Viken
,
S. A.
, 2006, “
Summary of the 2004 Computational Fluid Dynamics Validation Workshop on Synthetic Jets
,”
AIAA J.
0001-1452,
44
(
2
), pp.
194
207
.
9.
Gaster
,
M.
, 1969, “
The Structure and Behaviour of Laminar Separation Bubbles
,” Aeronautical Research Council R&M 3595.
10.
Lou
,
W.
, and
Hourmouziadis
,
J.
, 2000, “
Separation Bubbles Under Steady and Periodic-Unsteady Main Flow Conditions
,”
ASME J. Turbomach.
0889-504X,
122
(
4
), pp.
634
643
.
11.
Hatman
,
A.
, and
Wang
,
T.
, 1999, “
A Prediction Model for Separated-Flow Transition
,”
ASME J. Turbomach.
0889-504X,
121
(
3
), pp.
594
602
.
12.
McAuliffe
,
B. R.
and
Yaras
,
M. I.
, 2005, “
Separation-Bubble-Transition Measurements on a Low-Re Airfoil Using Particle Image Velocimetry
,”
ASME
Paper No. GT2005-68663.
13.
Menter
,
F. R.
,
Langtry
,
R. B.
,
Likki
,
S. R.
,
Suzen
,
Y. B.
,
Huang
,
P. G.
, and
Völker
,
S.
, 2006, “
A Correlation-Based Transition Model Using Local Variables –Part I: Model Formulation
,”
ASME J. Turbomach.
0889-504X,
128
(
3
), pp.
413
422
.
14.
Langtry
,
R. B.
,
Menter
,
F. R.
,
Likki
,
S. R.
,
Suzen
,
Y. B.
,
Huang
,
P. G.
, and
Völker
,
S.
, 2006, “
A Correlation-Based Transition Model Using Local Variables–Part II: Test Cases and Industrial Applications
,”
ASME J. Turbomach.
0889-504X,
128
(
3
), pp.
423
434
.
15.
Kožulović
,
D.
,
Röber
,
T.
, and
Nürnberger
,
D.
, 2007, “
Application of a Multimode Transition Model to Turbomachinery Flows
,”
Proceedings of the Seventh European Turbomachinery Conference
, Athens, Greece.
16.
Suzen
,
Y. B.
,
Huang
,
P. G.
,
Ashpis
,
D. E.
,
Volino
,
R. J.
,
Corke
,
T. C.
,
Thomas
,
F. O.
,
Huang
,
J.
,
Lake
,
J. P.
, and
King
,
P. I.
, 2007, “
A Computational Fluid Dynamics Study of Transitional Flows in Low-Pressure Turbines Under a Wide Range of Operating Conditions
,”
ASME J. Turbomach.
0889-504X,
129
(
3
), pp.
527
541
.
17.
Walters
,
D. K.
, and
Leylek
,
J. H.
, 2005, “
Computational Fluid Dynamics Study of Wake-Induced Transition on a Compressor-Like Flat Plate
,”
ASME J. Turbomach.
0889-504X,
127
(
1
), pp.
52
63
.
18.
Walters
,
D. K.
, and
Leylek
,
J. H.
, 2004, “
A New Model for Boundary Layer Transition Using a Single-Point RANS Approach
,”
ASME J. Turbomach.
0889-504X,
126
(
1
), pp.
193
202
.
19.
Lardeau
,
S.
,
Leschziner
,
M. A.
, and
Li
,
N.
, 2004, “
Modelling Bypass Transition With Low-Reynolds-Number Non-Linear Eddy-Viscosity Closure
,”
Flow, Turbul. Combust.
1386-6184,
73
, pp.
49
76
.
20.
Mayle
,
R. E.
, and
Schulz
,
A.
, 1997, “
The Path to Predicting Bypass Transition
,”
ASME J. Turbomach.
0889-504X,
119
(
3
), pp.
405
411
.
21.
Cutrone
,
L.
,
De Palma
,
P.
,
Pascazio
,
G.
, and
Napolitano
,
M.
, 2007, “
An Evaluation of Bypass Transition Models for Turbomachinery Flows
,”
Int. J. Heat Fluid Flow
0142-727X,
28
, pp.
161
177
.
22.
Lardeau
,
S.
, and
Leschziner
,
M. A.
, 2006, “
Modelling of Wake-Induced Transition in Low-Pressure Turbine Cascades
,”
AIAA J.
0001-1452,
44
(
8
), pp.
1854
1865
.
23.
Wilcox
,
D. C.
, 1998,
Turbulence Modeling for CFD
,
2nd ed.
,
DCW Industries Inc.
,
La Cañada, CA
.
24.
Abe
,
K.
,
Jang
,
Y. -J.
, and
Leschziner
,
M. A.
, 2003, “
An Investigation of Wall-Anisotropy Expressions and Length-Scale Equations for Non-Linear Eddy-Viscosity Models
,”
Int. J. Heat Fluid Flow
0142-727X,
24
, pp.
181
198
.
25.
Wissink
,
J. G.
, and
Rodi
,
W.
, 2006, “
Direct Numerical Simulations of Transitional Flow in Turbomachinery
,”
ASME J. Turbomach.
0889-504X,
128
(
4
), pp.
668
678
.
26.
Lardeau
,
S.
,
Li
,
N.
, and
Leschziner
,
M. A.
, 2007, “
Large Eddy Simulations of Transitional Boundary Layers at High Free-Stream Turbulence Intensity and Implications for RANS Modeling
,”
ASME J. Turbomach.
0889-504X,
129
(
2
), pp.
311
317
.
27.
Arnone
,
A.
,
Liou
,
M. S.
, and
Povinelli
,
L. A.
, 1992, “
Navier–Stokes Solution of Transonic Cascade Flow Using Non–Periodic C–Type Grids
,”
J. Propul. Power
0748-4658,
8
(
2
), pp.
410
417
.
28.
Arnone
,
A.
, and
Pacciani
,
R.
, 1996, “
Rotor-Stator Interaction Analysis Using the Navier-Stokes Equations and a Multigrid Method
,”
ASME J. Turbomach.
0889-504X,
118
(
4
), pp.
679
689
.
29.
Jameson
,
A.
, 1991, “
Time Dependent Calculations Using Multigrid With Applications to Unsteady Flows Past Airfoils and Wings
,” AIAA Paper No. 91-1596.
30.
Marconcini
,
M.
and
Pacciani
,
R.
, 2003, “
Numerical Investigation of Wake–Shock Interactions and Clocking in a Transonic HP Turbine
,”
ASME
Paper No. 2003-GT-38401.
31.
Schmitt
,
S.
,
Eulitz
,
F.
,
Wallscheid
,
L.
,
Arnone
,
A.
, and
Marconcini
,
M.
, 2001, “
Evaluation of Unsteady CFD Methods by Their Application to a Transonic Propfan Stage
,”
ASME
Paper No. 2001-GT-310.
32.
Arnone
,
A.
,
Marconcini
,
M.
,
Pacciani
,
R.
,
Schipani
,
C.
, and
Spano
,
E.
, 2002, “
Numerical Investigation of Airfoil Clocking in a Three-Stage Low Pressure Turbine
,”
ASME J. Turbomach.
0889-504X,
124
(
1
), pp.
61
68
.
33.
Talan
,
M.
, and
Hourmouziadis
,
J.
, 2002, “
Characteristic Regimes of Transitional Separation Bubbles in Unsteady Flow
,”
Flow, Turbul. Combust.
1386-6184,
69
, pp.
207
227
.
34.
Hoheisel
,
H.
, 1990, “
Test Case E/CA-6, Subsonic Turbine Cascade T106, Test Cases for Computation of Internal Flows in Aero Engine Components
,” Paper No. AGARD-AR-275.
35.
Pacciani
,
R.
and
Spano
,
E.
, 2006, “
Numerical Investigation of the Effect of Roughness and Passing Wakes on LP Turbine Blades Performance
,”
ASME
Paper No. GT2006-90221.
36.
Horton
,
H.
, 1969, “
A Semi-Empirical Theory for the Growth and Bursting of Laminar Separation Bubbles
,” Aeronautical Research Council CP 1073.
You do not currently have access to this content.