Two extended models for the calculation of rough wall transitional boundary layers with heat transfer are presented. Both models comprise a new transition onset correlation, which accounts for the effects of roughness height and density, turbulence intensity, and wall curvature. In the transition region, an intermittency equation suitable for rough wall boundary layers is used to blend between the laminar and fully turbulent states. Finally, two different submodels for the fully turbulent boundary layer complete the two models. In the first model, termed KS-TLK-T in this paper, a sand roughness approach from (Durbin, et al., 2001, “Rough Wall Modification of Two-Layer k-ε ,” ASME J. Fluids Eng., 123, pp. 16–21), which builds on a two-layer k-ε-turbulence model, is used for this purpose. The second model, the so-called DEM-TLV-T model, makes use of the discrete-element roughness approach, which was recently combined with a two-layer k-ε-turbulence model by the present authors. The discrete-element model will be formulated in a new way suitable for randomly rough topographies. Part I of this paper will provide detailed model formulations as well as a description of the database used for developing the new transition onset correlation. Part II contains a comprehensive validation of the two models, using a variety of test cases with transitional and fully turbulent boundary layers. The validation focuses on heat transfer calculations on both the suction and the pressure side of modern turbine airfoils. Test cases include extensive experimental investigations on a high pressure turbine vane with varying surface roughness and turbulence intensity, recently published by the current authors, as well as new experimental data from a low pressure turbine vane. In the majority of cases, the predictions from both models are in good agreement with the experimental data.

1.
Stripf
,
M.
,
Schulz
,
A.
,
Bauer
,
H.-J.
, and
Wittig
,
S.
, 2009, “
Extended Models for Transitional Rough Wall Boundary Layers With Heat Transfer—Part I: Model Formulations
,”
ASME J. Turbomach.
0889-504X,
131
, p.
031016
.
2.
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
.
3.
Patankar
,
S. V.
, and
Spalding
,
D. B.
, 1970,
Heat and Mass Transfer in Boundary Layers
,
2nd ed.
,
International Textbook
,
London
.
4.
Hosni
,
M. H.
, 1989, “
Measurement and Calculation of Surface Roughness Effects on Turbulent Flow and Heat Transfer
,” Ph.D. thesis, Mississippi State University, Starkville, MS.
5.
Hosni
,
M. H.
,
Coleman
,
H. W.
, and
Taylor
,
R. P.
, 1991, “
Heat Transfer Measurements and Calculations in Transitionally Rough Flow
,”
ASME J. Turbomach.
0889-504X,
113
, pp.
404
411
.
6.
Chakroun
,
W.
, 1992, “
Experimental Investigation of the Effects of Acceleration on Flow and Heat Transfer in the Turbulent Rough-Wall Boundary Layer
,” Ph.D. thesis, Mississippi State University, Starkville, MS.
7.
Chakroun
,
W.
, and
Taylor
,
R. P.
, 1993, “
The Effects of Moderately Strong Acceleration on Heat Transfer in the Turbulent Rough-Wall Boundary Layer
,”
ASME J. Heat Transfer
0022-1481,
115
, pp.
782
785
.
8.
Waigh
,
D. R.
, and
Kind
,
R. J.
, 1998, “
Improved Aerodynamic Characterization of Regular Three-Dimensional Roughness
,”
AIAA J.
,
36
, pp.
1117
1119
. 0001-1452
9.
Healzer
,
J. M.
, 1974, “
The Turbulent Boundary Layer on a Rough, Porous Plate: Experimental Heat Transfer With Uniform Blowing
,” Ph.D. thesis, Stanford University, Palo Alto, CA.
10.
Coleman
,
H. W.
,
Moffat
,
R. J.
, and
Kays
,
W. M.
, 1976, “
Momentum and Energy Transport in the Accelerated Fully Rough Turbulent Boundary Layer
,”
Stanford University
, Report No. HMT-24.
11.
Coleman
,
H. W.
,
Moffat
,
R. J.
, and
Kays
,
W. M.
, 1977, “
The Accelerated Fully Rough Turbulent Boundary Layer
,”
J. Fluid Mech.
0022-1120,
82
, pp.
507
528
.
12.
Coleman
,
H. W.
,
Moffat
,
R. J.
, and
Kays
,
W. M.
, 1981, “
Heat Transfer in the Accelerated Fully Rough Turbulent Boundary Layer
,”
ASME J. Heat Transfer
,
103
, pp.
153
158
. 0022-1481
13.
Bons
,
J. P.
,
Taylor
,
R. T.
,
McClain
,
S. T.
, and
Rivir
,
R. B.
, 2001, “
The Many Faces of Turbine Surface Roughness
,”
ASME J. Turbomach.
0889-504X,
123
, pp.
739
748
.
14.
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
,”
Proceedings of the FEDSM 03
, Paper No. FEDSM2003-45411.
15.
McClain
,
S. T.
, 2002, “
A Discrete-Element Model for Turbulent Flow Over Randomly-Rough Surfaces
,” Ph.D. thesis, Mississippi State University, Starkville, MS.
16.
Bons
,
J. P.
, 2002, “
St and cf Augmentation for Real Turbine Roughness With Elevated Freestream Turbulence
,”
ASME J. Turbomach.
0889-504X,
124
, pp.
632
644
.
17.
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
.
18.
Stripf
,
M.
,
Schulz
,
A.
, and
Bauer
,
H.-J.
, 2007, “
Roughness and Secondary Flow Effects on Turbine Vane External Heat Transfer
,”
J. Propul. Power
0748-4658,
23
(
2
), pp.
283
291
.
19.
Stripf
,
M.
, 2007, “
Einfluss der Oberflächenrauigkeit auf die Transitionale Grenzschicht an Gasturbinenschaufeln
,” doctoral thesis, Universität Karlsruhe, Germany.
20.
Smith
,
M. C.
, and
Kuethe
,
A. M.
, 1966, “
Effects of Turbulence on Laminar Skin Friction and Heat Transfer
,”
Phys. Fluids
,
9
, pp.
2337
2344
. 1070-6631
21.
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.