Conjugate heat transfer is gaining acceptance for predicting the thermal loading in high pressure nozzles. Despite the accuracy nowadays of numerical solvers, it is not clear how to include the uncertainties associated to the turbulence level, the temperature distribution, or the thermal barrier coating thickness in the numerical simulations. All these parameters are stochastic even if their value is commonly assumed to be deterministic. For the first time, in this work a stochastic analysis is used to predict the metal temperature in a real high-pressure nozzle. The domain simulated is the high pressure nozzle of an F-type Mitsubishi Heavy Industries gas turbine. The complete coolant system is included: impingement, film, and trailing edge cooling. The stochastic variations are included by coupling uncertainty quantification methods and conjugate heat transfer. Two uncertainty quantification methods have been compared: a probabilistic collocation method (PCM) and a stochastic collocation method (SCM). The stochastic distribution of thermal barrier coating thickness, used in the simulations, has been measured at the midspan. A Gaussian distribution for the turbulence intensity and hot core location has been assumed. By using PCM and SCM, the probability to obtain a specific metal temperature at midspan is evaluated. The two methods predict the same distribution of temperature with a maximum difference of 0.6%, and the results are compared with the experimental data measured in the real engine. The experimental data are inside the uncertainty band associated to the CFD predictions. This work shows that one of the most important parameters affecting the metal temperature uncertainty is the pitch-wise location of the hot core. Assuming a probability distribution for this location, with a standard deviation of 1.7 deg, the metal temperature at midspan can change up to 30%. The impact of turbulence level and thermal barrier coating thickness is 1 order of magnitude less important.

References

References
1.
Fadlun
,
E. A.
,
Michelizzi
,
I.
, and
De Iaco
,
M.
,
2008
, “
Measurement Error Influence on Gas Turbine Operability for Condition-Based Maintenance and Reliability/Availability Improvement
,”
Proceedings of the ASME Turbo Expo 2008
,
Berlin, Germany
, June 9–13,
ASME
Paper No. GT2008-50749. 10.1115/GT2008-50749
2.
Spieler
,
S.
,
Staudacher
,
S.
,
Fiola
,
R.
,
Sahm
,
P.
, and
Weißschuh
,
M.
,
2008
, “
Probabilistic Engine Performance Scatter and Deterioration Modeling
,”
ASME J. Eng. Gas Turbines Power
,
130
, p.
042507
.10.1115/1.2800351
3.
Bunker
,
R. S.
,
2009
, “
The Effect of Manufacturing Tolerances on Gas Turbine Cooling
,”
ASME J. Turbomach.
,
131
, p.
041018
.10.1115/1.3072494
4.
Salvadori
,
S.
,
Montomoli
,
F.
,
Martelli
,
F.
,
Adami
,
P.
,
Chana
,
K.
, and
Castillon
,
L.
,
2011
, “
Aero-Thermal Study of the Unsteady Flow Field in a Transonic Gas Turbine With Inlet Temperature Distortions
,”
ASME J. Turbomach.
,
133
, p.
031030
.10.1115/1.4002421
5.
Montomoli
,
F.
,
Massini
,
M.
, and
Salvadori
,
S.
,
2011
, “
Geometrical Uncertainty in Turbomachinery
,”
Comput. Fluids
,
46
, pp.
362
368
.10.1016/j.compfluid.2010.11.031
6.
Ames
,
F. E.
, and
Moffat
,
R. J.
,
1990
, “
Effects of Simulated Combustor Turbulence on Boundary Layer Heat Transfer
,”
Proceedings of the AIAA/ASME Joint Thermophysics and Heat Transfer Conference
,
Turbulent Flows Session
,
Seattle, WA
, June 18–20, Paper No. HTD 138.
7.
Krishnamoorthy
,
V.
, and
Sukhatme
,
S. P.
,
1989
, “
The Effect of Free-Stream Turbulence on Gas Turbine Blade Heat Transfer
,”
ASME J. Turbomach.
,
111
, pp.
497
501
.10.1115/1.3262299
8.
Mehendale
,
A. B.
,
Han
,
J. C.
, and
Ou
,
S.
,
1991
, “
Influence of High Mainstream Turbulence on Leading Edge Heat Transfer
,”
ASME J. Heat Transfer
,
113
, pp.
843
850
.10.1115/1.2911212
9.
Langtry
,
R. B.
, and
Menter
,
F. R.
,
2005
, “
Transition Modeling for General CFD Applications in Aeronautics
,” AIAA Paper No. 2005-522.
10.
Montomoli
,
F.
,
Adami
,
P.
, and
Martelli
,
F.
,
2009
, “
A Finite Volume Method for the Conjugate Heat Transfer in Film Cooling Devices
,”
Proc. Inst. Mech. Eng., Part A
,
223
(
A2
), pp.
191
200
.10.1243/09576509JPE640
11.
Mitsubishi Heavy Industries, Ltd
.,
2003
, “
Mitsubishi Gas Turbine M501F/M701F
,”
product brochure
.
12.
Montomoli
,
F.
,
Massini
,
M.
,
Yang
,
H.
, and
Han
,
J.-C.
,
2012
, “
The Benefit of High-Conductivity Materials in Film Cooled Turbine Nozzles
,”
Int. J. Heat Fluid Flow
,
34
, pp.
107
116
.10.1016/j.ijheatfluidflow.2011.12.005
13.
Ong
,
J.
, and
Miller
,
R.
,
2012
, “
Hot Streak and Vane Coolant Migration in a Downstream Rotor
,”
ASME J. Turbomach.
,
134
, p.
051002
.10.1115/1.4003832
14.
Wilcox
,
D.
,
2006
,
Turbulence Modeling for CFD
,
3rd ed.
,
DCW Industries
,
La Canada, CA
.
15.
Harrison
,
K. L.
, and
Bogard
,
D. G.
,
2008
, “
Comparison of RANS Turbulence Models for Prediction of Film Cooling Performance
,”
Proceedings of the ASME Turbo Expo
,
ASME
Paper No. GT2008-51423
.10.1115/GT2008-51423
16.
Wiener
,
N.
,
1938
, “
The Homogenous Chaos
,”
Am. J. Math.
,
60
, pp.
897
936
.10.2307/2371268
17.
Xiu
,
D.
,
2010
,
Numerical Methods for Stochastic Computations A Spectral Method Approach
,
Princeton Press
,
Princeton, NJ
.
18.
Isukapalli
,
S. S.
,
Roy
,
A.
, and
Georgopoulos
,
P. G.
,
1998
, “
Stochastic Response Surface Methods (SRSMs) for Uncertainty Propagation: Application to Environmental and Biological Systems
,”
Risk Anal.
,
18
(
3
), pp.
351
363
.10.1111/j.1539-6924.1998.tb01301.x
19.
Eldred
,
M. S.
, and
Burkardt
,
J.
,
2009
, “
Comparison of Non-Intrusive Polynomial Chos and Stochastic Collocation Methods for Uncertainty Quantification
,” AIAA Paper No. 2009-0976.
20.
Hosder
,
S.
,
Walters
,
R. W.
, and
Perez
,
R.
,
2006
, “
A Non-Intrusive Polynomial Chaos Method for Uncertainty Propagation in CFD Simulations
,” AIAA Paper No. 2006-891.
21.
Eldred
,
M. S.
,
2009
, “
Recent Advances in Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Analysis and Design
,” AIAA Paper No. 2009-2274.
22.
Gil
,
A.
,
Segura
,
J.
, and
Temme
,
N. M.
,
2007
,“
Numerical Methods for Special Functions
,”
SIAM
,
Philadelphia, PA
.
23.
Radomsky
,
R.
, and
Thole
,
K. A.
,
2000
, “
Highly Turbulent Flowfield Measurements Around a Stator Vane
,”
ASME J. Turbomach.
,
122
, pp.
255
262
.10.1115/1.555442
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