A series of computational predictions generated using FINE/TURBO are compared with data to investigate implementation techniques available for predicting temperature migration through a turbine stage. The experimental results used for comparison are from a one-and-one-half stage turbine operating at design-corrected conditions in a short-duration facility. Measurements of the boundary conditions are used to set up the computational models, and the predicted temperatures are compared with measured fluid temperatures at the blade leading edge and just above the blade platform. Fluid temperature measurements have not previously been available for these locations in a transonic turbine operating at design-corrected conditions, so this represents a novel comparison. Accurate predictions for this short-duration turbine experiment require use of the isothermal wall boundary condition instead of an adiabatic boundary condition and accurate specification of the inlet temperature profile all the way to the wall. Predictions using the harmonic method agree with the temperatures measured for the blade leading edge from 65% to 95% span to within 1% normalized temperature data. Agreement over much of the rest of the leading edge is within 5% of the measured value. Comparisons at 5–10% span and for the blade platform show larger differences up to 10%, which indicates that the flow in this region is not fully captured by the prediction. This is not surprising since the purge cavity and platform leading-edge features present in the experiment are treated as a smooth hub wall in the current simulation. This work represents a step toward the larger goal of accurately predicting surface heat-flux for the complicated environment of an operational engine as it is reproduced in a laboratory setting. The experiment upon which these computations are based includes realistic complications such as one-dimensional and two-dimensional inlet temperature profiles, a heavily film-cooled vane, and purge cooling. While the ultimate goal is to accurately handle all of these features, the current model focuses on the treatment of a subset of experiments performed for a one-dimensional radial inlet temperature profile and no cooling.

1.
Tallman
,
J. A.
,
Haldeman
,
C. W.
,
Dunn
,
M. G.
,
Tolpadi
,
A. K.
, and
Bergholz
,
R. F.
, 2009, “
Heat Transfer Measurements and Predictions for a Modern, High-Pressure, Transonic Turbine, Including Endwalls
,”
ASME J. Turbomach.
0889-504X,
131
(
2
), p.
021001
.
2.
Haldeman
,
C. W.
,
Dunn
,
M. G.
,
Southworth
,
S. A.
,
Chen
,
J. -P.
,
Heitland
,
G.
, and
Liu
,
J.
, 2009, “
Time-Accurate Predictions for a Fully Cooled High-Pressure Turbine Stage—Part II: Methodology for Quantifications of Prediction Quality
,”
ASME J. Turbomach.
0889-504X,
131
, p.
031004
.
3.
Haldeman
,
C. W.
,
Mathison
,
R. M.
,
Dunn
,
M. G.
,
Southworth
,
S.
,
Harral
,
J. W.
, and
Heitland
,
G.
, 2008, “
Aerodynamic and Heat Flux Measurements in a Single Stage Fully Cooled Turbine—Part I: Experimental Approach
,”
ASME J. Turbomach.
0889-504X,
130
, p.
021015
.
4.
Haldeman
,
C. W.
,
Mathison
,
R. M.
,
Dunn
,
M. G.
,
Southworth
,
S.
,
Harral
,
J. W.
, and
Heitland
,
G.
, 2008, “
Aerodynamic and Heat Flux Measurements in a Single Stage Fully Cooled Turbine—Part II: Experimental Results and CFD Comparison
,”
ASME J. Turbomach.
0889-504X,
130
, p.
021016
.
5.
Crosh
,
E.
, 2008, “
Time-Accurate Predictions for the Aerodynamics of a 1 and 1/2 Stage HP Transonic Turbine
,” MS thesis, The Ohio State University, Columbus, OH.
6.
Southworth
,
S. A.
,
Dunn
,
M. G.
,
Haldeman
,
C. W.
,
Chen
,
J. -P.
,
Heitland
,
G.
, and
Liu
,
J.
, 2009, “
Time-Accurate Predictions for a Fully Cooled High-Pressure Turbine Stage—Part I: Comparison of Predictions With Data
,”
ASME J. Turbomach.
0889-504X,
131
, p.
031003
.
7.
Rai
,
M. M.
, and
Dring
,
R. P.
, 1990, “
Navier–Stokes Analyses of the Redistribution of Inlet Temperature Distortions in a Turbine
,”
J. Propul. Power
0748-4658,
6
(
3
), pp.
276
282
.
8.
Rai
,
M. M.
, 1987, “
Navier–Stokes Simulations of Rotor-Interaction Using Patched and Overlaid Grids
,”
J. Propul. Power
0748-4658,
3
(
5
), pp.
387
396
.
9.
Dorney
,
D. J.
,
Davis
,
R. L.
,
Edwards
,
D. D.
, and
Madavan
,
N. K.
, 1992, “
Unsteady Analysis of Hot Streak Migration in a Turbine Stage
,”
J. Propul. Power
0748-4658,
8
(
2
), pp.
520
529
.
10.
Krouthen
,
B.
, and
Giles
,
M. B.
, 1990, “
Numerical Investigation of Hot Streaks in Turbines
,”
J. Propul. Power
0748-4658,
6
(
6
), pp.
769
776
.
11.
Takahashi
,
R. K.
, and
Ni
,
R. H.
, 1990, “
Unsteady Euler Analysis of the Redistribution of an Inlet Temperature Distortion in a Turbine
,”
The 26th Joint Propulsion Conference
, Orlando, FL, Paper No. AIAA 90-2262.
12.
Sharma
,
O. P.
,
Pickett
,
G. F.
, and
Ni
,
R. H.
, 1990, “
Assessment of Unsteady Flows in Turbines
,”
ASME
Paper No. 90-GT-150.
13.
Ni
,
R. H.
, and
Sharma
,
O. P.
, 1990, “
Using 3-D Euler Flow Simulations to Assess Effects of Periodic Unsteady Flow Through Turbines
,” Paper No. AIAA 90-2357.
14.
Saxer
,
A. P.
, and
Giles
,
M. B.
, 1994, “
Predictions of Three-Dimensional Steady and Unsteady Inviscid Transonic Stator/Rotor Interaction With Inlet Radial Temperature Nonuniformity
,”
ASME J. Turbomach.
0889-504X,
116
, pp.
347
357
.
15.
Shang
,
T.
, and
Epstein
,
A. H.
, 1997, “
Analysis of Hot Streak Effects on Turbine Rotor Heat Load
,”
ASME J. Turbomach.
0889-504X,
119
, pp.
544
553
.
16.
Dorney
,
D. J.
, and
Schwab
,
J. R.
, 1996, “
Unsteady Numerical Simulations of Radial Temperature Profile Redistribution in a Single-Stage Turbine
,”
ASME J. Turbomach.
0889-504X,
118
, pp.
783
791
.
17.
Dorney
,
D. J.
, and
Sondak
,
D. L.
, 2000, “
Effects of Tip Clearance on Hot Streak Migration in a High-Subsonic Single-Stage Turbine
,”
ASME J. Turbomach.
0889-504X,
122
, pp.
613
620
.
18.
Ong
,
J.
, and
Miller
,
R. J.
, 2008, “
Hot Streak and Vane Coolant Migration in a Downstream Rotor
,”
ASME
Paper No. GT2008-50971.
19.
Pau
,
M.
,
Paniagua
,
G.
,
Delhaye
,
D.
,
de la Loma
,
A.
, and
Ginibre
,
P.
, 2008, “
Aerothermal Impact of Stator-Rim Purge Flow and Rotor-Platform Film Cooling on a Transonic Turbine Stage
,”
ASME
Paper No. GT2008-51295.
20.
Martelli
,
F.
,
Adami
,
P.
,
Salvadori
,
S.
,
Chana
,
K. S.
, and
Castillon
,
L.
, 2008, “
Aero-Thermal Study of the Unsteady Flow Field in a Transonic Gas Turbine With Inlet Temperature Distortions
,”
ASME
Paper No. GT2008-50628.
21.
Dunn
,
M. G.
, 2001, “
Convective Heat Transfer and Aerodynamics in Axial Flow Turbines
,”
ASME
Paper No. 2001-GT-0506.
22.
Dunn
,
M. G.
,
Bennett
,
W.
,
Delaney
,
R. A.
, and
Rao
,
K. V.
, 1990, “
Investigation of Unsteady Flow Through a Transonic Turbine Stage: Part II—Data/Prediction Comparison for Time-Averaged and Phase-Resolved Pressure Data
,”
The AIAA/SAE/ASME/ASEE 26TH Joint Propulsion Conference
, Orlando, FL, Paper No. AIAA-90-2409.
23.
Erdos
,
J. I.
,
Alzner
,
E.
, and
McNally
,
W.
, 1977, “
Numerical Solution of Periodic Transonic Flow Through a Fan Stage
,”
AIAA J.
0001-1452,
15
(
11
), pp.
1559
1568
.
24.
Giles
,
M.
, and
Haimes
,
R.
, 1993, “
Validation of a Numerical Method for Unsteady Flow Calculations
,”
ASME J. Turbomach.
0889-504X,
115
, pp.
110
117
.
25.
Dawes
,
W. N.
, 1992, “
The Simulation of Three-Dimensional Viscous Flow in Turbomachinery Geometries Using a Solution-Adaptive Unstructured Mesh Methodology
,”
ASME J. Turbomach.
0889-504X,
114
(
3
), pp.
528
537
.
26.
Rao
,
K. V.
,
Delaney
,
R. A.
, and
Dunn
,
M. G.
, 1990, “
Investigation of Unsteady Flow Through Transonic Turbine Stage Part I: Analysis
,”
The AIAA/SAE/ASME/ASEE 26th Joint Propulsion Conference
, Orlando, FL, Paper No. AIAA-90-2408.
27.
Dunn
,
M. G.
,
Bennett
,
W. A.
,
Delaney
,
R. A.
, and
Rao
,
K. V.
, 1992, “
Investigation of Unsteady Flow Through a Transonic Turbine Stage: Data/Prediction Comparison for Time-Averaged and Phase-Resolved Pressure Data
,”
ASME J. Turbomach.
0889-504X,
114
, pp.
91
99
.
28.
Rao
,
K. V.
,
Delaney
,
R. A.
, and
Dunn
,
M. G.
, 1994, “
Vane-Blade Interaction in a Transonic Turbine, Part I: Aerodynamics
,”
J. Propul. Power
0748-4658,
10
(
3
), pp.
305
311
.
29.
Rao
,
K. V.
,
Delaney
,
R. A.
, and
Dunn
,
M. G.
, 1994, “
Vane-Blade Interaction in a Transonic Turbine, Part II: Heat Transfer
,”
J. Propul. Power
0748-4658,
10
(
3
), pp.
312
317
.
30.
Abhari
,
R. S.
,
Guenette
,
G. R.
,
Epstein
,
A. H.
, and
Giles
,
M.
, 1991, “
Comparison of Time-Resolved Turbine Rotor Blade Heat Transfer Measurements and Numerical Calculations
,”
ASME
Paper No. 91-GT-190.
31.
Abhari
,
R. S.
, 1996, “
Impact of Rotor-Stator Interaction on Turbine Blade Film Cooling
,”
ASME J. Turbomach.
0889-504X,
118
, pp.
123
133
.
32.
Dunn
,
M. G.
,
Haldeman
,
C. W.
, and
Abhari
,
R. S.
, 2000, “
Influence of Vane/Blade Spacing on the Heat Flux for a Transonic Turbine
,”
Turbo Expo
, Munich, Germany.
33.
Haldeman
,
C. W.
,
Dunn
,
M. G.
,
Barter
,
J. W.
,
Green
,
B. R.
, and
Bergholz
,
R. F.
, 2004, “
Aerodynamic and Heat-Flux Measurements With Predictions on a Modern One and 1/2 Stage High Pressure Transonic Turbine
,”
ASME
Paper No. GT2004-53478.
34.
Venable
,
B. L.
,
Delaney
,
R. A.
,
Busby
,
J. A.
,
Davis
,
R. L.
,
Dorney
,
D. J.
,
Dunn
,
M. G.
,
Haldeman
,
C. W.
, and
Abhari
,
R. S.
, 1999, “
Influence of Vane-Blade Spacing on Transonic Turbine Stage Aerodynamics: Part I: Time Resolved Data and Analysis
,”
ASME J. Turbomach.
0889-504X,
121
, pp.
663
672
.
35.
Busby
,
J. A.
,
Davis
,
R. L.
,
Dorney
,
D. J.
,
Dunn
,
M. G.
,
Haldeman
,
C. W.
,
Abhari
,
R. S.
,
Venable
,
B. L.
, and
Delaney
,
R. A.
, 1999, “
Influence of Vane-Blade Spacing on Transonic Turbine Stage Aerodynamics: Part II: Time Resolved Data and Analysis
,”
ASME J. Turbomach.
0889-504X,
121
, pp.
673
682
.
36.
Barter
,
J. W.
,
Vitt
,
P. H.
, and
Chen
,
J. P.
, 2000, “
Interaction Effects in a Transonic Turbine Stage
,”
ASME
Paper No. 2000-GT-0376.
37.
Adamczyk
,
J. J.
, 1985, “
Model Equations for Simulating Flows in Multistage Turbomachinery
,”
NASA Lewis Research Center
, Cleveland, OH, Report No. NASA-TM-86869.
38.
Verdon
,
J. M.
, and
Caspar
,
J. R.
, 1982, “
Development of a Linear Unsteady Aerodynamic Analysis for Finite-Deflection Subsonic Cascades
,”
AIAA J.
0001-1452,
20
(
9
), pp.
1259
1267
.
39.
Verdon
,
J. M.
, and
Caspar
,
J. R.
, 1984, “
A Linearized Unsteady Aerodynamic Analysis for Transonic Cascades
,”
J. Fluid Mech.
0022-1120,
149
, pp.
403
429
.
40.
Hall
,
K. C.
, and
Crawley
,
E. F.
, 1989, “
Calculation of Unsteady Flows in Turbomachinery Using the Linear Euler Equations
,”
AIAA J.
0001-1452,
27
(
6
), pp.
777
787
.
41.
Hall
,
K. C.
,
Clark
,
W. S.
, and
Lorence
,
C. B.
, 1994, “
A Linearized Euler Analysis of Unsteady Transonic Flows in Turbomachinery
,”
ASME J. Turbomach.
0889-504X,
116
(
3
), pp.
477
488
.
42.
Ning
,
W.
, and
He
,
L.
, 1998, “
Computation of Unsteady Flows Around Oscillating Blades Using Linear and Nonlinear Harmonic Euler Methods
,”
ASME J. Turbomach.
0889-504X,
120
, pp.
508
514
.
43.
He
,
L.
, and
Ning
,
W.
, 1998, “
Efficient Approach for Analysis of Unsteady Viscous Flows in Turbomachines
,”
AIAA J.
0001-1452,
36
(
11
), pp.
2005
2012
.
44.
Chen
,
T.
,
Vasanthakumar
,
P.
, and
He
,
L.
, 2001, “
Analysis of Unsteady Blade Row Interaction Using Nonlinear Harmonic Approach
,”
J. Propul. Power
0748-4658,
17
(
3
), pp.
651
658
.
45.
Fritsch
,
G.
, and
Giles
,
M. B.
, 1995, “
An Asymptotic Analysis of Mixing Loss
,”
ASME J. Turbomach.
0889-504X,
117
, pp.
367
374
.
46.
Aube
,
M.
, and
Hirsch
,
C.
, 2001, “
Numerical Investigation of a 1–1/2 Axial Turbine Stage at Quasi-Steady and Fully Unsteady Conditions
,”
ASME
Paper No. 2001-GT-0309.
47.
Vilmin
,
S.
,
Lorrain
,
E.
,
Hirsch
,
C.
, and
Swoboda
,
M.
, 2006, “
Unsteady Flow Modeling Across the Rotor/Stator Interface Using the Nonlinear Harmonic Method
,”
ASME
Paper No. GT2006-90210.
48.
Gerolymos
,
G. A.
,
Michon
,
G. J.
, and
Neubauer
,
J.
, 2002, “
Analysis and Application of Chorochronic Periodicity in Turbomachinery Rotor/Stator Interaction Computations
,”
J. Propul. Power
0748-4658,
18
(
6
), pp.
1139
1152
.
49.
Crosh
,
E. A.
,
Haldeman
,
C. W.
,
Dunn
,
M. G.
,
Holmes
,
D. G.
, and
Mitchell
,
B. D.
, 2009, “
Investigation of Turbine Shroud Distortions on the Aerodynamics of a One and One-Half Stage High-Pressure Turbine
,”
ASME
Paper No. GT2009-59562.
50.
Mathison
,
R. M.
,
Haldeman
,
C. W.
, and
Dunn
,
M. G.
, 2010, “
Aerodynamics and Heat Transfer for a Cooled One and One-Half Stage High-Pressure Turbine–Part I: Vane Inlet Temperature Profile Generation and Migration
,”
ASME
Paper No. GT2010-22716.
51.
Mathison
,
R. M.
,
Haldeman
,
C. W.
, and
Dunn
,
M. G.
, 2010, “
Aerodynamics and Heat Transfer for a Cooled One and One-Half Stage High-Pressure Turbine—Part II: Influence of Inlet Temperature Profile on Blade Heat Flux
,”
ASME
Paper No. GT2010-22718.
52.
Mathison
,
R. M.
,
Haldeman
,
C. W.
, and
Dunn
,
M. G.
, 2010, “
Heat Transfer for the Blade of a Cooled Stage and One-Half High-Pressure Turbine, Part I: Influence of Vane Cooling and Disk Cavity Purge Flow
,”
ASME
Paper No. GT2010-22713.
53.
Mathison
,
R. M.
,
Haldeman
,
C. W.
, and
Dunn
,
M. G.
, 2010, “
Heat Transfer for the Blade of a Cooled One and One-Half Stage High-Pressure Turbine, Part II: Influence of Purge Cooling Variation
,”
ASME
Paper No. GT2010-22715.
You do not currently have access to this content.