The effect of the upstream wake on the time averaged rotor blade heat transfer was numerically investigated. The geometry and flow conditions of the first stage turbine blade of GE’s $E3$ engine with a tip clearance equal to 2% of the span were utilized. The upstream wake had both a total pressure and temperature deficit. The rotor inlet conditions were determined from a steady analysis of the cooled upstream vane. Comparisons between the time average of the unsteady rotor blade heat transfer and the steady analysis, which used the average inlet conditions of unsteady cases, are made to illuminate the differences between the steady and unsteady calculations. To help in the understanding of the differences between steady and unsteady results on one hand and to evaluate the effect of the total temperature wake on the other, separate calculations were performed to obtain the rotor heat transfer and adiabatic wall temperatures. It was found that the Nusselt number distribution for the time average of unsteady heat transfer is invariant if normalized by the difference in the adiabatic and wall temperatures. It appeared though that near the endwalls the Nusselt number distribution did depend on the thermal wake strength. Differences between steady and time averaged unsteady heat transfer results of up to 20% were seen on the blade surface. Differences were less on the blade tip surface.

1.
Rao
,
K. V.
,
Delaney
,
R. A.
, and
Dunn
,
M. G.
, 1994, “
Vane-Blade Interaction in a Transonic Turbine, II—Heat Transfer
,”
J. Propul. Power
0748-4658,
10
(
3
), pp.
312
317
.
2.
Dunn
,
M. G.
,
Haldeman
,
C. W.
,
Abhari
,
R. S.
, and
McMillan
,
M. L.
, “
Influence of Vane/Blade Spacing on the Heat Flux for a Transonic Turbine
,” ASME Paper No. 2000-GT-0206.
3.
Michelassi
,
V.
,
Martelli
,
F.
,
Deons
,
R.
,
Arts
,
T.
, and
Sieverding
,
C. H.
, 1999, “
Unsteady Heat Transfer in Stator-Rotor Interaction by Two-Equation Turbulence Mode
,”
ASME J. Turbomach.
0889-504X,
121
, pp.
436
447
.
4.
Abhari
,
R. S.
,
Guenette
,
G. R.
,
Epstein
,
A. H.
, and
Giles
,
M. B.
, 1992, “
Comparison of Time-Resolved Turbine Rotor Blade Heat Transfer Measurements and Numerical Calculations
,”
ASME J. Turbomach.
0889-504X,
114
(
4
), pp.
818
827
.
5.
Ameri
,
A. A.
,
Rigby
,
D.
,
Heidmann
,
J.
,
,
E.
, and
Fabian
,
J.
, 2006, “
Effects of Unsteadiness Due to Wake Passing on Rotor Blade Heat Transfer
,” AIAA Paper No. AIAA-2006-3263.
6.
Hodson
,
H. P.
, and
Dawes
,
W. N.
, 1998, “
On the Interpretation of Measured Profile Losses in Unsteady Wake-Turbine Blade Interaction Studies
,”
ASME J. Turbomach.
0889-504X,
120
, pp.
276
284
.
7.
Denos
,
R.
,
Sieverding
,
C. H.
,
Arts
,
T.
,
Brouckaert
,
J.
,
Paniagua
,
G.
, and
Michelassi
,
V.
, 1999, “
Experimental Investigation of the Unsteady Rotor Aerodynamics of a Transonic Turbine Stage
,”
Third European Conference in Turbomachinery, Fluid Dynamics and Thermodynamics (IACA Programme)
.
8.
Chana
,
K. S.
,
Hilditch
,
M. A.
, and
Anderson
,
J. A.
, 2005, “
An Investigation of the Effects of Film Cooling in a High-Pressure Aeroengine Turbine Stage
,” ASME Paper No. GT-2005-68564.
9.
Ameri
,
A. A.
,
Rigby
,
D. L.
,
,
E.
,
Heidmann
,
J.
, and
Fabian
,
J. C.
, 2007, “
Numerical Simulation of Unsteady Turbine Blade and Tip Heat Transfer Due to Wake Passing
,” ASME Paper No. GT2007-27550.
10.
Wilcox
,
D. C.
, 1994,
Turbulence Modeling for CFD
,
DCW Industries, Inc.
,
.
11.
Ameri
,
A. A.
,
,
E.
, and
Rigby
,
D.
, 1998, “
Effect of Squealer Tips on Rotor Heat Transfer and Efficiency
,”
ASME J. Turbomach.
0889-504X,
120
(
4
), pp.
753
759
.
12.
Halila
,
E. E.
and
Lenahan
,
D. T.
, and
Thomas
,
L. L.
, 1982, “
Energy Efficient Engine, High Pressure Turbine Test Hardware Detailed Design Report
,”
NASA
Report No. CR-167955.
13.
Ameri
,
A. A.
,
,
E.
, and
Rigby
,
D.
, 1999, “
Effect of Tip Clearance and Casing Recess on Heat Transfer and Stage Efficiency in Axial Turbines
,”
ASME J. Turbomach.
0889-504X,
121
(
4
), pp.
683
693
.
14.
Ameri
,
A. A.
, and
Bunker
,
R. S.
, 2000, “
Heat Transfer and Flow in the First Stage Blade Tip of a Power Generation Gas Turbine, Part 2: Analytical Results
,”
ASME J. Turbomach.
0889-504X,
122
, pp.
272
277
.
15.
Ameri
A. A.
, 2001, “
Heat Transfer and Flow on the Blade Tip of a Gas Turbine Equipped With a Mean-Camberline Strip
,”
ASME J. Turbomach.
0889-504X,
123
(
4
), pp.
704
708
.
16.
Mumic
,
F.
,
Eriksson
,
D.
, and
Sunden
,
B.
, 2004, “
On Prediction of Tip Leakage Flow and Heat Transfer in Gas Turbines
,” ASME Paper No. GT2004-53448.
17.
Yang
,
D. -L.
, and
Feng
,
Z. -P.
, 2007, “
Tip Leakage Flow and Heat Transfer Predictions for Turbine Blade
,” ASME Paper No. GT2007-27728.
18.
Dorney
,
D. J.
,
Davis
,
R. L.
,
Edwards
R. L.
, and
N. K.
, 1992, “
Unsteady Analysis of Hot Streak Migration in a Turbine Stage
,”
J. Propul. Power
0748-4658,
8
(
2
), pp.
520
529
.
19.
Kerrebrock
,
J. L.
, and
Mikolajczak
,
A. A.
, 1970, “
Intra-Stator Transport of Rotor Wakes and Its Effect on Compressor Performance
,”
ASME J. Eng. Power
0022-0825,
92
(
4
), pp.
359
368
.
20.
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
.