This contribution presents an alternative to classical data reduction techniques to measure the heat transfer using thin-film gauges. A finite-element model of the two-dimensional unsteady heat conduction equation is solved in the cross-sectional area of a metallic airfoil bounded with a polyamide sheet on which thermal sensors are deposited. This novel methodology allows capturing all 2D heat conduction effects that are irremediably neglected with the 1D data reduction technique. The application of this technique in a compression tube facility allows an exact evaluation of the initial wall heat flux into cooled rotor blades. During the spinning-up period, the rotor is spun up to nearly its nominal speed (from 0 rpm to 6200 rpm) resulting in preheating due to drag losses. The long duration of this experiment (450s) and the magnitude of the wall temperature increase result in significant 2D conduction effects that are not accounted for using the 1D approach. In addition, short-duration experiments confirm the existence of 2D effects at smaller time scales (0.5s), as well as the influence of the initial nonuniform temperature distribution in the rotor blade. The resulting flux with such an initial condition appears to be the superposition of the wall heat flux at the end of the spinning up before the test and the flux due to the blow-down itself.

1.
Arts
,
T.
, and
Lambert de Rouvroit
,
M.
, 1992, “
Aero-Thermal Performance of a Two-Dimensional Highly Loaded Transonic Turbine Nozzle Guide Vane: A Test Case for Inviscid and Viscous Flow Computations
,”
ASME J. Turbomach.
0889-504X,
114
, pp.
147
154
.
2.
Dunn
,
M. G.
, 1985, “
Measurement of Heat Flux and Pressure in a Turbine Stage
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
107
, pp.
76
83
.
3.
Dénos
,
R.
, 1996, “
Aerothermal Investigation of the Unsteady Flow in the Rotor of a Transonic Turbine Stage
,” Ph.D. thesis, University of Poitiers, France.
4.
Didier
,
F.
,
Dénos
,
R.
, and
Arts
,
T.
, 2002, “
Unsteady Rotor Heat Transfer in a Transonic Turbine Stage
,”
ASME J. Turbomach.
0889-504X,
124
(
4
), pp.
614
622
.
5.
Epstein
,
A. H.
,
Guenette
,
G. R.
,
Norton
,
R. J. G.
, and
Yuzhang
,
C.
, 1986, “
High-Frequency Response Heat-Flux Gauge
,”
Rev. Sci. Instrum.
0034-6748,
57
(
4
), pp.
639
649
.
6.
Doorly
,
J. E.
, and
Oldfield
,
M. L. G.
, 1986, “
New Heat Transfer Gages for Use on Multilayered Substrates
,”
ASME J. Turbomach.
0889-504X,
108
, pp.
153
160
.
7.
Iliopoulou
,
V.
,
Dénos
,
R.
,
Billiard
,
N.
, and
Arts
,
T.
, 2004, “
Time-Averaged and Time-Resolved Heat Flux Measurements on a Turbine Stator Blade Using Two-Layered Thin-Film Gauges
,”
ASME J. Turbomach.
0889-504X,
126
, pp.
570
577
.
8.
Piccini
,
E.
,
Guo
,
S. M.
, and
Jones
,
T. V.
, 2000, “
The Development of a New Direct-Heat-Flux Gauge for Heat-Transfer Facilities
,”
Meas. Sci. Technol.
0957-0233,
11
, pp.
342
349
.
9.
Schultz
,
D. L.
, and
Jones
,
T. V.
, 1973, “
Heat Transfer Measurements in Short Duration Facilities
,” AGARDograph Report No. 165.
10.
Doorly
,
J. E.
, and
Oldfield
,
M. L. G.
, 1987, “
The Theory of Advanced Multi-Layer Thin Film Heat Transfer Gauges
,”
Int. J. Heat Mass Transfer
0017-9310,
30
(
6
), pp.
1159
1168
.
11.
Billiard
,
N.
,
Iliopoulou
,
V.
,
Ferrara
,
F.
, and
Dénos
,
R.
, 2002, “
Data Reduction and Thermal Product Determination for Single and Multi-Layered Substrates Thin-Film Gauges
,”
Proceedings of the 16th Symposium on Measuring Techniques
, Cambridge, UK.
12.
Smith
,
M.
, and
Kuethe
,
A.
, 1966, “
Effects of Turbulence on Laminar Skin Friction and Heat Transfer
,”
Phys. Fluids
0031-9171,
9
, pp.
2337
2344
.
13.
Kestin
,
J.
, and
Wood
,
R.
, 1971, “
The Influence of Turbulence on Mass Transfer From Cylinders
,”
Trans. ASME, Ser. C: J. Heat Transfer
0022-1481,
93
, pp.
321
327
.
14.
Lowery
,
G. W.
, and
Vachon
,
R. I.
, 1975, “
The Effect of Turbulence on Heat Transfer From Heated Cylinders
,”
Int. J. Heat Mass Transfer
0017-9310,
18
, pp.
1229
1242
.
15.
Buttsworth
,
D. R.
, and
Jones
,
T. V.
, 1997, “
Radial Conduction Effects in Transient Heat Transfer Experiments
,”
Aeronaut. J.
0001-9240,
101
, pp.
209
212
.
16.
Traupel
,
W.
, 1958,
Thermische Turbomaschinen
, Vol.
1
,
Springer
,
Göttingen, Heidelberg
.
17.
Dénos
,
R.
,
Paniagua
,
G.
,
Yasa
,
T.
, and
Fortugno
,
E.
, 2006, “
Determination of the Efficiency of a Cooled HP Turbine in a Blow-Down Facility
,” ASME Paper No. GT-2006-9046.
18.
Paniagua
,
G.
,
Dénos
,
R.
, and
Oropesa
,
M.
, 2002, “
Thermocouple Probes for Accurate Temperature Measurements in Short Duration Facilities
,” ASME Paper No. GT-2002-30043.
19.
Rao
,
S. S.
, 1989,
The Finite Element Method in Engineering
,
2nd ed.
,
Pergamon
,
New York
.
20.
Incropera
,
F. P.
, and
DeWitt
,
D. P.
, 2002,
Introduction to Heat Transfer
,
4th ed.
,
Wiley
,
New York
.
21.
Saad
,
Y.
, and
Schultz
,
M. H.
, 1986, “
GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
,”
SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput.
0196-5204,
7
, pp.
856
869
.
You do not currently have access to this content.