An increasingly common experimental method allows determination of the overall effectiveness of a film cooled turbine component. This method requires the Biot number of the experimental model to match that of the engine component such that the nondimensional surface temperature, ϕ, is matched to that of the engine component. The matched Biot number requirement effectively places a requirement on the thermal conductivity of the model and the traditional implementation places no requirement on the model's density or specific heat. However, such is not the case if such a model is exposed to unsteadiness in the flow such as with film cooling unsteadiness. In this paper, we develop an additional nondimensional parameter that must also be theoretically matched to conduct overall effectiveness experiments with unsteady film cooling. Since finding suitable materials with an acceptable combination of thermodynamic properties for a typical low temperature experiment can be difficult, simulations were conducted to determine the impact of imperfectly matched parameters achievable with common materials. Because the disparity between the diffusion and the unsteadiness time scales can hinder numerical simulation, a novel analytical solution to the heat equation with relevant unsteady Robin type boundary conditions is developed. Particular solutions are examined to determine the sensitivity of the temperature response of a turbine blade (or a model of one) to its material properties and the form of the unsteady variation in the convection parameters. It is shown that it is possible to obtain useful experimental results even with imperfectly matched parameters.

References

References
1.
Williams
,
R. P.
,
Dyson
,
T. E.
,
Bogard
,
D. G.
, and
Bradshaw
,
S. D.
,
2014
, “
Sensitivity of the Overall Effectiveness to Film Cooling and Internal Cooling on a Turbine Vane Suction Side
,”
ASME J. Turbomach.
,
136
(
3
), p.
031006
.
2.
Albert
,
J. E.
,
Bogard
,
D. G.
, and
Cunha
,
F.
,
2004
, “
Adiabatic and Overall Effectiveness for a Film Cooled Blade
,”
ASME
Paper No. GT2004-53998.
3.
Polanka
,
M. D.
,
Rutledge
,
J. L.
,
Bogard
,
D. G.
, and
Anthony
,
R. J.
,
2017
, “
Determination of Cooling Parameters for a High Speed, True Scale, Metallic Turbine Vane
,”
ASME J. Turbomach.
,
139
(
1
), p.
011001
.
4.
Rutledge
,
J. L.
,
Polanka
,
M. D.
, and
Greiner
,
N. J.
,
2017
, “
Computational Fluid Dynamics Evaluations of Film Cooling Flow Scaling Between Engine and Experimental Conditions
,”
ASME J. Turbomach.
,
139
(
2
), p.
021004
.
5.
Abhari
,
R. S.
,
1996
, “
Impact of Rotor-Stator Interaction on Turbine Blade Film Cooling
,”
ASME J. Turbomach.
,
118
(
1
), pp.
123
133
.
6.
Haldeman
,
C. W.
,
Mathison
,
R. M.
,
Dunn
,
M. G.
,
Harral
,
J. W.
, and
Heltland
,
G.
,
2008
, “
Aerodynamic and Heat Flux Measurements in a Single-Stage Fully Cooled Turbine—Part II: Experimental Results
,”
ASME J. Turbomach.
,
130
(
2
), p.
021016
.
7.
Rutledge
,
J. L.
,
King
,
P. I.
, and
Rivir
,
R.
,
2010
, “
Time Averaged Net Heat Flux Reduction for Unsteady Film Cooling
,”
ASME J. Eng. Gas Turbines Power
,
132
(
12
), p.
121601
.
8.
Sen
,
B.
,
Schmidt
,
D. L.
, and
Bogard
,
D. G.
,
1996
, “
Film Cooling With Compound Angle Holes: Heat Transfer
,”
ASME J. Turbomach.
,
118
(
4
), pp.
800
806
.
9.
Rutledge
,
J. L.
, and
McCall
,
J. F.
,
2013
, “
Determination of Time Resolved Heat Transfer Coefficient and Adiabatic Effectiveness Waveforms With Unsteady Film
,”
ASME J. Turbomach.
,
135
(
2
), p.
021021
.
10.
Rutledge
,
J. L.
, and
Polanka
,
M. D.
,
2015
, “
Waveforms of Time-Resolved Film Cooling Parameters on a Leading Edge Model
,”
J. Propul. Power
,
31
(
1
), pp.
253
264
.
11.
Rutledge
,
J. L.
,
Rathsack
,
T. C.
,
Van Voorhis
,
M.
, and
Polanka
,
M. D.
,
2016
, “
Film Cooling Parameter Waveforms on a Film Cooled Turbine Blade Leading Edge With Oscillating Stagnation Line
,”
ASME J. Turbomach.
,
138
(
7
), p.
071005
.
12.
DuPont
,
2015
, “
DuPont Corian Performance Properties
,” E.I. du Pont de Nemours and Company, Wilmington, DE.
13.
Stewart
,
W. R.
, and
Dyson
,
T. E.
,
2017
, “
Conjugate Heat Transfer Scaling for Inconel 718
,”
ASME
Paper No. GT2017-64873.
14.
Dyson
,
T. E.
,
Bogard
,
D. G.
,
Piggush
,
J. D.
, and
Kohli
,
A.
,
2013
, “
Overall Effectiveness for a Film Cooled Turbine Blade Leading Edge With Varying Hole Pitch
,”
ASME J. Turbomach.
,
135
(
3
), p.
031011
.
You do not currently have access to this content.