A new model for predicting heat transfer in the transitional boundary layer of rough turbine airfoils is presented. The new model makes use of extensive experimental work recently published by the current authors. For the computation of the turbulent boundary layer, a discrete element roughness model is combined with a two-layer model of turbulence. The transition region is modeled using an intermittency equation that blends between the laminar and turbulent boundary layer. Several intermittency functions are evaluated in respect of their applicability to rough-wall transition. To predict the onset of transition, a new correlation is presented, accounting for the influence of freestream turbulence and surface roughness. Finally, the new model is tested against transitional rough-wall boundary layer flows on high-pressure and low-pressure turbine airfoils.

1.
Bogard
,
D. G.
,
Schmidt
,
D. L.
, and
Tabbita
,
M.
, 1998, “
Characterization and Laboratory Simulation of Turbine Airfoil Surface Roughness and Associated Heat Transfer
,”
ASME J. Turbomach.
0889-504X,
120
, pp.
337
342
.
2.
Bons
,
J. P.
,
Taylor
,
R. P.
,
McClain
,
S. T.
, and
Rivir
,
R. B.
, 2001, “
The Many Faces of Turbine Surface Roughness
,”
ASME J. Turbomach.
0889-504X,
123
, pp.
739
748
.
3.
Turner
,
A. B.
,
Tarada
,
F. H. A.
, and
Bayley
,
F. J.
, 1985, “
Effects of Surface Roughness on Heat Transfer to Gas Turbine Blades
,” AGARD-CP-390, Paper No. 9.
4.
Hoffs
,
A.
,
Drost
,
U.
, and
Bõlcs
,
A.
, 1996, “
Heat Transfer Measurements on a Turbine Airfoil at Various Reynolds Numbers and Turbulence Intensities Including Effects of Surface Roughness
,” ASME Paper No. 96-GT-169.
5.
Abuaf
,
N.
,
Bunker
,
R. S.
, and
Lee
,
C. P.
, 1997, “
Effects of Surface Roughness on Heat Transfer and Aerodynamic Performance of Turbine Airfoils
,” ASME Paper No. 97-GT-10.
6.
Bunker
,
R. S.
, 1997, “
Separate and Combined Effects of Surface Roughness and Turbulence Intensity on Vane Heat Transfer
,” ASME Paper No. 97-GT-135.
7.
Boyle
,
R. J.
,
Spuckler
,
C. M.
,
Lucci
,
B. L.
, and
Camperchioli
,
W. P.
, 2000, “
Infrared Low Temperature Turbine Vane Rough Surface Heat Transfer Measurements
,” ASME Paper No. 2000-GT-0216.
8.
Blair
,
M. F.
, 1994, “
An Experimental Study of Heat Transfer in a Large-Scale Turbine Rotor Passage
,”
ASME J. Turbomach.
0889-504X,
116
, pp.
1
13
.
9.
Stripf
,
M.
,
Schulz
,
A.
, and
Wittig
,
S.
, 2005, “
Surface Roughness Effects on External Heat Transfer of a HP Turbine Vane
,”
ASME J. Turbomach.
0889-504X,
127
, pp.
200
208
.
10.
Stripf
,
M.
,
Schulz
,
A.
, and
Bauer
,
H.-J.
, 2005, “
Surface Roughness and Secondary Flow Effects on External Heat Transfer of a HP Turbine Vane
,” ISABE Paper No. 2005-1116.
11.
Dvorak
,
F. A.
, 1972, “
Calculation of Compressible Turbulent Boundary Layers With Roughness and Heat Transfer
,”
AIAA J.
0001-1452,
10
, pp.
1447
1451
.
12.
Dirling
,
R. B.
, 1973, “
A Method for Computing Rough Wall Heat Transfer Rates on Reentry Nosetips
,” AIAA Paper No. 73-763.
13.
Rotta
,
J. C.
, 1962, “
Turbulent Boundary Layers in Incompressible Flow
,”
Progress in Aeronautical Sciences
,
Pergamon
, London, Vol.
2
, pp.
1
120
.
14.
Cebeci
,
T.
, and
Chang
,
K. C.
, 1978, “
Calculation of Incompressible Rough-Wall Boundary-Layer Flows
,”
AIAA J.
0001-1452,
16
, pp.
730
735
.
15.
Feiereisen
,
W. J.
, and
Acharya
,
M.
, 1986, “
Modeling of Transition and Surface Roughness Effects in Boundary-Layer Flows
,”
AIAA J.
0001-1452,
24
, pp.
1642
1649
.
16.
Granville
,
P. S.
, 1985, “
Mixing-Length Formulations for Turbulent Boundary Layers Over Arbitrarily Rough Surfaces
,”
J. Ship Res.
0022-4502,
29
, pp.
223
233
.
17.
Krogstad
,
P.
, 1990, “
Modification of the van Driest Damping Function to Include the Effects of Surface Roughness
,”
AIAA J.
0001-1452,
29
, pp.
888
894
.
18.
Guo
,
S. M.
,
Jones
,
T. V.
,
Lock
,
G. D.
, and
Dancer
,
S. N.
, 1998, “
Computational Prediction of Heat Transfer to Gas Turbine Nozzle Guide Vanes With Roughened Surfaces
,”
ASME J. Turbomach.
0889-504X,
120
, pp.
343
350
.
19.
Jouini
,
D. B.
,
Bergenblock
,
T. C.
, and
Sjolander
,
S. A.
, 1997, “
Computation of the Aerodynamic Performance of Axial-Turbine Blades With Surface Roughness
,” ISABE Paper No. 97-7041.
20.
Lee
,
J.
, and
Paynter
,
G. C.
, 1996, “
Modified Spalart-Allmaras One-Equation Turbulence Model for Rough Wall Boundary Layers
,”
J. Propul. Power
0748-4658,
12
(
4
), pp.
809
812
.
21.
Wilcox
,
D. C.
, 1993,
Turbulence Modeling for CFD
,
DCW Industries Inc.
, La Cañada, CA.
22.
Hellsten
,
A.
, and
Laine
,
S.
, 1998, “
Extension of k-ω Shear-Stress Transport Model for Rough-Wall Flows
,”
AIAA J.
0001-1452,
36
(
9
), pp.
1728
1729
.
23.
Durbin
,
P. A.
,
Medic
,
G.
,
Seo
,
J.
,
Eaton
,
J. K.
, and
Song
,
J.
, 2001, “
Rough Wall Modification of Two-Layer k-ε
,”
ASME J. Fluids Eng.
0098-2202,
123
, pp.
16
21
.
24.
Schlichting
,
H.
, 1936, “
Experimentelle Untersuchungen zum Rauhigkeitsproblem
,”
Ing.-Arch.
0020-1154,
7
, pp.
1
34
.
25.
Finson
,
M. L.
, and
Wu
,
P. K. S.
, 1979, “
Analysis of Rough Wall Turbulent Heating With Application to Blunted Flight Vehicles
,” AIAA Paper No. 79-0008.
26.
Christoph
,
G. H.
, and
Pletcher
,
R. H.
, 1983, “
Prediction of Rough-Wall Skin Friction and Heat Transfer
,”
AIAA J.
0001-1452,
21
(
4
), pp.
509
515
.
27.
Taylor
,
R. P.
,
Coleman
,
H. W.
, and
Hodge
,
B. K.
, 1984, “
A Discrete Element Prediction Approach for Turbulent Flow Over Rough Surfaces
,” Mississippi State University, Report No. TFD-84-1.
28.
Lin
,
T. C.
, and
Bywater
,
R. J.
, 1982, “
Turbulence Models for High-Speed, Rough-Wall Boundary Layers
,”
AIAA J.
0001-1452,
20
(
3
), pp.
325
333
.
29.
Tarada
,
F. H. A.
, 1987, “
Heat Transfer to Rough Turbine Blading
,” Ph.D. thesis, University of Sussex, England.
30.
Hosni
,
M. H.
,
Coleman
,
H. W.
, and
Taylor
,
R. P.
, 1991, “
Measurements and Calculations of Rough-Wall Heat Transfer in the Turbulent Boundary Layer
,”
Int. J. Heat Mass Transfer
0017-9310,
34
, pp.
1067
1082
.
31.
McClain
,
S. T.
, 2002, “
A Discrete-Element Model for Turbulent Flow Over Randomly-Rough Surfaces
,” Ph.D. thesis, Mississippi State University.
32.
Mayle
,
R. E.
, 1991, “
The Role of Laminar-Turbulent Transition in Gas Turbine Engines
,”
ASME J. Turbomach.
0889-504X,
113
, pp.
509
537
.
33.
Sieger
,
K.
,
Schulz
,
A.
,
Crawford
,
M. E.
, and
Wittig
,
S.
, 1993, “
An Evaluation of Low-Reynolds Number k-e Turbulence Models for Predicting Transition Under the Influence of Free-Stream Turbulence and Pressure Gradient
,”
Engineering Turbulence Modelling and Measurements
, Vol.
2
,
Elsevier
, New York, pp.
593
602
.
34.
Schmidt
,
R. C.
, and
Patankar
,
S. V.
, 1991, “
Simulating Boundary Layer Transition With Low-Reynolds-Number k-ε Turbulence Models—Part 2: An Approach to Improving the Predictions
,”
ASME J. Turbomach.
0889-504X,
113
, pp.
18
26
.
35.
Lam
,
C. K. G.
, and
Bremhorst
,
K.
, 1981, “
A Modified Form of the k-ε Model for Predicting Wall Turbulence
,”
ASME J. Fluids Eng.
0098-2202,
103
, pp.
456
460
.
36.
Launder
,
B. E.
, and
Sharma
,
B. I.
, 1974, “
Application of the Energy-Dissipation Model of Turbulence to the Calculation of Flow Near a Spinning Disc
,”
Lett. Heat Mass Transfer
0094-4548,
1
, pp.
131
138
.
37.
Emmons
,
H.
, 1951, “
The Laminar-Turbulent Transition in a Boundary Layer—Part I
,”
J. Aeronaut. Sci.
0095-9812,
18
, pp.
490
498
.
38.
Narasimha
,
R.
, 1957, “
On the Distribution of Intermittency in the Transition Region of a Boundary Layer
,”
J. Aeronaut. Sci.
0095-9812,
24
(
9
), pp.
711
712
.
39.
Solomon
,
W. J.
,
Walker
,
G. J.
, and
Gostelow
,
J. P.
, 1996, “
Transition Length Prediction for Flows With Rapidly Changing Pressure Gradients
,”
ASME J. Turbomach.
0889-504X,
118
, pp.
744
751
.
40.
Byvaltsev
,
P. M.
, and
Kawaike
,
K.
, 2005, “
A Comparative Study of Two Transition Zone Models in Heat Transfer Predictions
,”
ASME J. Turbomach.
0889-504X,
127
, pp.
230
239
.
41.
Gostelow
,
J. P.
,
Melwani
,
N.
, and
Walker
,
G. J.
, 1996, “
Effects of Streamwise Pressure Gradient on Turbulent Spot Development
,”
ASME J. Turbomach.
0889-504X,
118
, pp.
737
743
.
42.
D’Ovidio
,
A.
,
Harkins
,
J. A.
, and
Gostelow
,
J. P.
, 2001, “
Turbulent Spots in Strong Adverse Pressure Gradients: Part 2 – Spot Propagation and Spreading Rates
,” ASME Paper No. 2001-GT-0406.
43.
Fraser
,
C. J.
,
Higazy
,
M. G.
, and
Milne
,
J. S.
, 1994, “
End-Stage Boundary Layer Transition Models for Engineering Calculations
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
0954-4062,
208
, pp.
47
58
.
44.
Roberts
,
S. K.
, and
Yaras
,
M. I.
, 2004, “
Modeling of Boundary-Layer Transition
,” ASME Paper No. GT2004-53664.
45.
Sieger
,
K.
,
Schiele
,
R.
,
Kaufmann
,
F.
,
Wittig
,
S.
, and
Rodi
,
W.
, 1995, “
A Two-Layer Turbulence Model for the Calculation of Transitional Boundary-Layers
,” ERCOFTAC Bull., pp.
21
25
.
46.
Rodi
,
W.
,
Mansour
,
N. N.
, and
Michelassi
,
V.
, 1993, “
One-Equation Near-Wall Turbulence Modeling With the Aid of Direct Simulation Data
,”
ASME J. Fluids Eng.
0098-2202,
115
, pp.
196
205
.
47.
Schiele
,
R.
, 1999, “
Die transitionale Grenzschicht an Gasturbinenschaufeln: Experimentelle Untersuchungen und Entwicklung eine neuen Verfahrens zur numerischen Beschreibung des laminar-turbulenten Umschlags
,” dissertation, Universität Karlsruhe, Germany.
48.
Tarada
,
F. H. A.
, 1990, “
Prediction of Rough-Wall Boundary Layers Using a Low Reynolds Number k-ε Model
,”
Int. J. Heat Fluid Flow
0142-727X,
11
(
4
), pp.
331
345
.
49.
McClain
,
S. T.
,
Hodge
,
B. K.
, and
Bons
,
J. P.
, 2003, “
Predicting Skin Friction for Turbulent Flow Over Randomly-Rough Surfaces Using the Discrete-Element Method: Part I—Surface Characterization
,” ASME Paper No. FEDSM2003-45411.
50.
Finson
,
M. L.
, and
Clarke
,
A. S.
, 1980, “
The Effect of Surface Roughness Character on Turbulent Reentry Heating
,” AIAA Paper No. 80-1459.
51.
Patankar
,
S. V.
, and
Spalding
,
D. B.
, 1970,
Heat and Mass Transfer in Boundary-Layers
,
2nd ed.
,
Intertext
, London.
52.
Abu-Ghannam
,
B. J.
, and
Shaw
,
R.
, 1980, “
Natural Transition of Boundary-Layers—The Effects of Turbulence, Pressure Gradient and Flow History
,”
J. Mech. Eng. Sci.
0022-2542,
22
, pp.
213
228
.
53.
Menter
,
F. R.
,
Langtry
,
R. B.
,
Likki
,
S. R.
,
Suzen
,
Y. B.
,
Huang
,
P. G.
, and
Völker
,
S.
, 2004, “
A Correlation-Based Transition Model Using Local Variables: Part I—Model Formulation
,” ASME Paper No. GT2004-53452.
54.
Gibbings
,
J. C.
, and
Al-Shukri
,
S. M.
, 1997, “
Effect of Sandpaper Roughness and Stream Turbulence on the Laminar Layer and its Transition
,”
Aeronaut. J.
0001-9240,
101
, pp.
17
24
.
55.
Arts
,
T.
, and
De Rouvroit
,
M. L.
, 1992, “
Aero-Thermal Performance of a Two Dimensional Highly Loaded Transonic Turbine Nozzle Guide Vane
,”
ASME J. Turbomach.
0889-504X,
114
, pp.
147
154
.
56.
Daniels
,
L.
, 1978, “
Film-Cooling of Gas Turbine Blades
,” Ph.D. thesis, University of Oxford, England.
57.
Schulz
,
A.
, 1986, “
Zum Einfluß hoher Freistromturbulenz, intensiver Kühlung und einer Nachlaufströmung auf den Wärmeübergang einer konvektiv gekühlten Gasturbinenschaufel
,” dissertation, Universität Karlsruhe, Germany.
58.
Blair
,
M. F.
, and
Werle
,
M. J.
, 1981, “
Combined Influence of Freestream Turbulence and Favorable Pressure Gradients on Boundary Layer Transition and Heat Transfer
,” United Technologies Research Center, East Hartford, CT, Report-No. R81-914388-17.
59.
Coupland
,
J.
, 1993, personal communication, ERCOFTAC Special Interest Group on Transition Test Cases.
60.
Rüd
,
K.
, and
Wittig
,
S.
, 1986, “
Laminar and Transitional Boundary Layer Structures in Accelerating Flow With Heat Transfer
,”
ASME J. Turbomach.
0889-504X,
108
, pp.
116
123
.
61.
Smith
,
M. C.
, and
Kuethe
,
A. M.
, 1966, “
Effects of Turbulence on Laminar Skin Friction and Heat Transfer
,”
Phys. Fluids
0031-9171,
9
(
12
), pp.
2337
2344
.
62.
Byvaltsev
,
P. M.
, and
Nagashima
,
T.
, 1998, “
Correlation of Numerical and Experimental Heat Transfer Data at the Turbine Blade Surface
,”
JSME Int. J., Ser. B
1340-8054,
41
, pp.
191
199
.
You do not currently have access to this content.