The effect of a Mach number correction on a model for predicting the length of transition was investigated. The transition length decreases as the turbulent spot production rate increases. Many of the data for predicting the spot production rate come from low-speed flow experiments. Recent data and analysis showed that the spot production rate is affected by Mach number. The degree of agreement between analysis and data for turbine blade heat transfer without film cooling is strongly dependent on accurately predicting the length of transition. Consequently, turbine blade heat transfer data sets were used to validate a transition length turbulence model. A method for modifying models for the length of transition to account for Mach number effects is presented. The modification was made to two transition length models. The modified models were incorporated into the two-dimensional Navier–Stokes code, RVCQ3D. Comparisons were made between predicted and measured midspan surface heat transfer for stator and rotor turbine blades. The results showed that accounting for Mach number effects significantly improved the agreement with the experimental data.

1.
Ameri, A. A., and Arnone, A., 1992, “Navier–Stokes Heat Transfer Predictions Using Two-Equation Turbulence Closures,” AIAA Paper No. 92-3067.
2.
Arnone
A.
,
Liou
M.-S.
, and
Povinelli
L. A.
,
1992
, “
Navier–Stokes Solution of Transonic Cascade Flows Using Non-Periodic C-Type Grids
,”
AIAA Journal of Propulsion and Power
, Vol.
8
, No.
2
, pp.
410
417
.
3.
Arts, T., Lambert de Rouvroit, M., and Rutherford, A.W., 1990, “Aero-Thermal Investigation of a Highly Loaded Transonic Linear Turbine Guide Vane Cascade,” VKI Technical Note 174.
4.
Arts
T.
,
Duboue
J.-M.
, and
Rollin
G.
,
1998
, “
Aero-Thermal Performance Measurements and Analysis of a Two-Dimensional High Turning Rotor Blade
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
120
, pp.
494
499
.
5.
Baldwin, B. S., and Lomax, H., 1978, “Thin-Layer Approximation and Algebraic Model for Separated Turbulent Flows,” Paper No. AIAA-78-257.
6.
Boyle
R. J.
,
1991
, “
Navier–Stokes Analysis of Turbine Blade Heat Transfer
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
113
, pp.
392
403
.
7.
Boyle
R. J.
, and
Ameri
A. A.
,
1997
, “
Grid Orthogonality Effects on Predicted Turbine Midspan Heat Transfer and Performance
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
119
, pp.
31
38
.
8.
Chen
K. K.
, and
Thyson
N. A.
,
1971
, “
Extension of Emmons’ Spot Theory to Flows on Blunt Bodies
,”
AIAA Journal of Propulsion and Power
, Vol.
9
, No.
5
, pp.
821
825
.
9.
Chima
R. V.
,
1987
, “
Explicit Multigrid Algorithm for Quasi-Three-Dimensional Flows in Turbomachinery
.”
AIAA Journal of Propulsion and Power
, Vol.
3
, No.
5
, pp.
397
405
.
10.
Chima, R. V., and Yokota, J. W., 1988, “Numerical Analysis of Three-Dimensional Viscous Internal Flows,” AIAA Paper No. 88-3522; NASA TM-100878.
11.
Chima, R. V., Giel, P. W., and Boyle, R. J., 1993, “An Algebraic Turbulence Model for Three-Dimensional Viscous Flows,” AAIA Paper No. 93-0083; NASA TM-105931.
12.
Chima
R. V.
,
1996
, “
Application of the k–ω Turbulence Model to Quasi-Three-Dimensional Turbomachinery Flows
,”
AIAA Journal of Propulsion and Power
, Vol.
12
, No.
6
, pp.
1176
1179
.
13.
Clark, J. P., 1993, “A Study of Turbulent Spot Propagation in Turbine Representative Flows,” Ph.D. Thesis, St. Catherine’s College, University of Oxford.
14.
Clark
J. P.
,
Jones
T. V.
, and
LaGraff
J. E.
,
1994
, “
On the Propagation of Naturally Occurring Turbulent Spots
,”
Journal of Engineering Mathematics
, Vol.
28
, pp.
1
19
.
15.
Crawford, M. E., and Kays, W. M., 1976, “STAN5 — A Program for Numerical Computation of Two-Dimensional Internal and External Boundary Layer Flows,” NASA CR-2742.
16.
Dey, J., and Narasimha, R., 1985, “Spot Formation Rates in High Speed Flows,” Report 85 FM 11, Dept. Aero. Eng., Indian Inst. Sci.
17.
Dullenkopf
K.
, and
Mayle
R. E.
,
1994
, “
The Effects of Incident Turbulence and Moving Wakes on Laminar Heat Transfer in Gas Turbines
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
116
, pp.
23
28
.
18.
Emmons
H. W.
,
1951
, “
The Laminar-Turbulent Transition in a Boundary Layer — Part I
,”
Journal of Aerospace Sciences
, Vol.
18
, No.
7
, pp.
490
498
.
19.
Fraser
C. J.
,
Higazy
M. G.
, and
Milne
J. S.
,
1994
, “
End-Stage Boundary Layer Transition Models for Engineering Calculations
,”
Proc. Institution of Mechanical Engineers
, Part C, Vol.
208
, pp.
47
58
.
20.
Gostelow
J. P.
,
Blunden
A. R.
,
Walker
G. J.
,
1994
, “
Effects of Free-Stream Turbulence and Adverse Pressure Gradients on Boundary Layer Transition
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
116
, pp.
392
404
.
21.
Gostelow
J. P.
,
Melwani
N.
, and
Walker
G. J.
,
1996
, “
Effects of a Streamwise Pressure Gradient on Turbulent Spot Development
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
118
, pp.
737
743
.
22.
Hylton, L. D., Mihelc, M. S., Turner, E. R., Nealy, D. A., and York, R. F., 1983, “Analytical and Experimental Evaluation of the Heat Transfer Distribution Over the Surfaces of Turbine Vanes,” NASA CR-168015.
23.
Kays, W. M., and Crawford, M. E., 1980, Convective Heat and Mass Transfer, 2nd ed., McGraw-Hill, New York
24.
Mack, L. M., 1969, “Boundary Layer Stability Theory,” Document 900-277, Rev. A, Jet Propulsion Laboratory, Pasadena, CA.
25.
Mayle
R. E.
,
1991
, “
The Role of Laminar–Turbulent Transition in Gas Turbine Engines
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
113
, pp.
509
537
.
26.
McCormick
M. E.
,
1968
, “
An Analysis of the Formation of Turbulent Patches in the Transition Boundary Layer
,”
ASME Journal of Applied Mechanics
, Vol.
35
, pp.
216
219
.
27.
Narasimha
R.
,
1957
, “
On the Distribution of Intermittency in the Transition Region of a Boundary Layer
,”
Journal of Aerospace Sciences
, Vol.
24
, No.
9
, pp.
711
712
.
28.
Narasimha
R.
,
1985
, “
The Laminar–Turbulent Transition Zone in the Boundary Layer
,”
Journal of Aerospace Sciences
, Vol.
22
, pp.
29
80
.
29.
Owen
F. K.
, and
Horstman
C. C.
,
1972
, “
Hypersonic Transitional Boundary Layers
,”
AIAA Journal
, Vol.
8
pp.
769
775
.
30.
Sharma, O. P., 1987, “Momentum and Thermal Boundary Layer Development on Turbine Airfoil Suction Surfaces,” AIAA Paper No. 87-1918.
31.
Simon
F. F.
,
1995
, “
The Use of Transition Region Characteristics to Improve the Numerical Simulation of Heat Transfer in Bypass Transitional Flows
,”
International Journal of Rotating Machinery
, Vol.
2
, No.
2
pp.
93
102
; also NASA TM 106445.
32.
Simon, F. F., and Ashpis, D. E., 1996, “Progress in Modeling of Laminar to Turbulent Transition on Turbine Vanes and Blades,” presented at the Int. Conf. on Turbulent Heat Transfer, Mar. 10–15, San Diego, CA; also NASA TM 107180.
33.
Smith
M. C.
, and
Kuethe
A. M.
,
1966
, “
Effects of Turbulence on Laminar Skin Friction and Heat Transfer
,”
The Physics of Fluids
, Vol.
9
, No.
12
, pp.
2337
2344
.
34.
Solomon
W. J.
,
Walker
G. J.
, and
Gostelow
J. P.
,
1996
, “
Transition Length Prediction for Flows With Rapidly Changing Pressure Gradients
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
118
, pp.
744
753
.
35.
Sorenson, R. L., 1980, “A Computer Program to Generate Two-Dimensional Grids About Airfoils and Other Shapes by the Use of Poisson’s Equation,” NASA TM 81198.
36.
Walker
G. J.
,
1989
, “
Transitional Flow on Axial Turbomachine Blading
,”
AIAA Journal
, Vol.
27
, No.
5
, pp.
595
602
.
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