The emerging renewable energy market calls for more advanced prediction tools for turbine transient operations in fast startup/shutdown cycles. Reliable numerical analysis of such transient cycles is complicated by the disparity in time scales of the thermal responses in fluid and solid domains. Obtaining fully coupled time-accurate unsteady conjugate heat transfer (CHT) results under these conditions would require to march in both domains using the time-step dictated by the fluid domain: typically, several orders of magnitude smaller than the one required by the solid. This requirement has strong impact on the computational cost of the simulation as well as being potentially detrimental to the accuracy of the solution due to accumulation of round-off errors in the solid. A novel loosely coupled CHT methodology has been recently proposed, and successfully applied to both natural and forced convection cases that remove these requirements through a source-term based modeling (STM) approach of the physical time derivative terms in the relevant equations. The method has been shown to be numerically stable for very large time steps with adequate accuracy. The present effort is aimed at further exploiting the potential of the methodology through a new adaptive time stepping approach. The proposed method allows for automatic time-step adjustment based on estimating the magnitude of the truncation error of the time discretization. The developed automatic time stepping strategy is applied to natural convection cases under long (2000 s) transients: relevant to the prediction of turbine thermal loads during fast startups/shutdowns. The results of the method are compared with fully coupled unsteady simulations showing comparable accuracy with a significant reduction of the computational costs.

References

References
1.
Greis
,
J.
,
Gobrecht
,
E.
, and
Wendt
,
S.
,
2012
, “
Flexible and Economical Operation of Power Plants: 25 Years of Expertise
,”
ASME
Paper No. GT2012-68716.
2.
Topel
,
M.
,
Genrup
,
M.
,
Jöcker
,
M.
,
Spelling
,
J.
, and
Laumert
,
B.
,
2015
, “
Operational Improvements for Startup Time Reduction in Solar Steam Turbines
,”
ASME. J. Eng. Gas Turbines Power
,
137
(
4
), p.
042604
.
3.
Stein
,
P.
,
Marinescu
,
G.
,
Born
,
D.
, and
Lerch
,
M.
,
2014
, “
Thermal Modeling and Mechanical Integrity Based Design of a Heat Shield on a High Pressure Module Solar Steam Turbine Inner Casing With Focus on Lifetime
,”
ASME
Paper No. GT2014-25846.
4.
Vogt
,
J.
,
Schaaf
,
T.
, and
Helbig
,
K.
,
2013
, “
Optimizing Lifetime Consumption and Increasing Flexibility Using Enhanced Lifetime Assessment Methods With Automated Stress Calculation From Long-Term Operation Data
,”
ASME
Paper No. GT2013-95068.
5.
Marinescu
,
G.
,
Sell
,
M.
,
Ehrsam
,
A.
, and
Brunner
,
P. B.
,
2013
, “
Experimental Investigation Into Thermal Behavior of Steam Turbine Components—Part 3: Startup and the Impact on LCF Life
,”
ASME
Paper No. GT2013-94356.
6.
Topel
,
M.
,
Jöcker
,
M.
,
Paul
,
S.
, and
Laumert
,
B.
,
2016
, “
Differential Expansion Sensitivity Studies During Steam Turbine Startup
,”
ASME J. Eng. Gas Turbines Power
,
138
(
6
), p.
062102
.
7.
Marinescu
,
G.
,
Stein
,
P.
, and
Sell
,
M.
,
2015
, “
Natural Cooling and Startup of Steam Turbines: Validity of the Over-Conductivity Function
,”
ASME J. Eng. Gas Turbines Power
,
137
(
11
), p.
112601
.
8.
Marinescu
,
G.
,
Mohr
,
W. F.
,
Ehrsam
,
A.
,
Ruffino
,
P.
, and
Sell
,
M.
,
2014
, “
Experimental Investigation Into Thermal Behavior of Steam Turbine Components—Temperature Measurements With Optical Probes and Natural Cooling Analysis
,”
ASME J. Eng. Gas Turbines Power
,
136
(
2
), p.
021602
.
9.
Marinescu
,
G.
, and
Ehrsam
,
A.
, “
Experimental Investigation Into Thermal Behavior of Steam Turbine Components—Part 2: Natural Cooling of Steam Turbines and the Impact on LCF Life
,”
ASME
Paper No. GT2012-68759.
10.
Born
,
D.
,
Stein
,
P.
,
Marinescu
,
G.
,
Koch
,
S.
, and
Schumacher
,
D.
,
2017
, “
Thermal Modeling of an Intermediate Pressure Steam Turbine by Means of Conjugate Heat Transfer—Simulation and Validation
,”
ASME J. Eng. Gas Turbines Power
,
139
(
3
), p.
031903
.
11.
Maffulli
,
R.
, and
He
,
L.
,
2014
, “
Wall Temperature Effects on Heat Transfer Coefficient for High-Pressure Turbines
,”
J. Propul. Power
,
30
(
4
), pp.
1080
1090
.
12.
Maffulli
,
R.
, and
He
,
L.
,
2017
, “
Impact of Wall Temperature on Heat Transfer Coefficient and Aerodynamics for Three-Dimensional Turbine Blade Passage
,”
J. Therm. Sci. Eng. Appl.
,
9
(
4
), p.
041002
.
13.
Zhang
,
Q.
, and
He
,
L.
,
2014
, “
Impact of Wall Temperature on Turbine Blade Tip Aerothermal Performance
,”
ASME J. Eng. Gas Turbines Power
,
136
(
5
), p.
052602
.
14.
He
,
L.
, and
Oldfield
,
M. L. G.
,
2011
, “
Unsteady Conjugate Heat Transfer Modeling
,”
ASME J. Turbomach.
,
133
(
3
), p.
031022
.
15.
Cless
,
C. M.
, and
Prescott
,
P. J.
,
1996
, “
Effect of Time Marching Schemes on Predictions of Oscillatory Natural Convection in Fluids of Low Prandtl Number
,”
Numer. Heat Transfer, Part A
,
29
(
6
), pp.
575
597
.
16.
Sun
,
Z.
,
Chew
,
J. W.
,
Hills
,
N. J.
,
Volkov
,
K. N.
, and
Barnes
,
C. J.
,
2010
, “
Efficient Finite Element Analysis/Computational Fluid Dynamics Thermal Coupling for Engineering Applications
,”
ASME J. Turbomach.
,
132
(
3
), p.
031016
.
17.
Errera
,
M. P.
, and
Baqué
,
B.
,
2013
, “
A Quasi‐Dynamic Procedure for Coupled Thermal Simulations
,”
Int. J. Numer. Methods Fluids
,
72
(
11
), pp.
1183
1206
.
18.
Wang
,
Z.
,
Corral
,
R.
,
Chaquet
,
J. M.
, and
Pastor
,
G.
,
2013
, “
Analysis and Improvement of a Loosely Coupled Fluid-Solid Heat Transfer Method
,”
ASME
Paper No. GT2013-94332.
19.
Altaç
,
Z.
, and
Uğurlubilek
,
N.
,
2016
, “
Assessment of Turbulence Models in Natural Convection From Two- and Three-Dimensional Rectangular Enclosures
,”
Int. J. Therm. Sci.
,
107
, pp.
237
246
.
20.
Ma
,
J.
, and
Xu
,
F.
,
2015
, “
Transient Flows Around a Fin at Different Positions
,”
Procedia Eng.
,
126
, pp.
393
398
.
21.
He
,
L.
, and
Fadl
,
M.
,
2017
, “
Multi‐Scale Time Integration for Transient Conjugate Heat Transfer
,”
Int. J. Numer. Methods Fluids
,
83
(
12
), pp.
887
904
.
22.
Fadl
,
M.
,
He
,
L.
,
Stein
,
P.
, and
Marinescu
,
G.
,
2018
, “
Assessment of Unsteadiness Modeling for Transient Natural Convection
,”
ASME J. Eng. Gas Turbines Power
,
140
(
1
), p.
012605
.
23.
Perelman
,
T. L.
,
1961
, “
On Conjugated Problems of Heat Transfer
,”
Int. J. Heat Mass Transfer
,
3
(
4
), pp.
293
303
.
24.
Giles
,
M. B.
,
1997
, “
Stability Analysis of Numerical Interface Conditions in Fluid–Structure Thermal Analysis
,”
Int. J. Numer. Methods Fluids
,
25
(
4
), pp.
421
436
.
25.
Xiaa
,
J. L.
,
Smith
,
B. L.
,
Yadigaroglu
,
G.
,
Gantner
,
U.
, and
Sigg
,
B.
,
1998
, “
Numerical and Experimental Study of Transient Turbulent Natural Convection in a Horizontal Cylindrical Container
,”
Int. J. Heat Mass Transfer
,
41
(
22
), pp.
3635
3645
.
26.
Tome
,
M. F.
, and
McKee
,
S.
,
1994
, “
GENSMAC: A Computational Marker and Cell Method for Free Surface Flows in General Domains
,”
J. Comput. Phys.
,
110
(
1
), pp.
1
186
.
27.
Gresho
,
P. M.
,
Lee
,
R. L.
, and
Sani
,
R. L.
,
1980
, “
On the Time-Dependent Solution of the Incompressible Navier-Stokes Equations in Two and Three Dimensions
,”
Recent Adv. Numer. Methods Fluids
,
1
, pp.
27
79
. http://www.iaea.org/inis/collection/NCLCollectionStore/_Public/10/426/10426723.pdf
28.
Shampine
,
L. F.
,
1985
, “
Local Error Estimation by Doubling
,”
Computing
,
34
(
2
), pp.
179
190
.
29.
Shampine
,
L. F.
,
2005
, “
Error Estimation and Control for ODEs
,”
J. Sci. Comput.
,
25
(
1–2
), pp.
3
16
.
30.
Kuehn
,
T. H.
, and
Goldstein
,
R. J.
,
1978
, “
An Experimental Study of Natural Convection Heat Transfer in Concentric and Eccentric Horizontal Cylindrical Annuli
,”
ASME J. Heat Transfer
,
100
(
4
), pp.
635
640
.
You do not currently have access to this content.