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Frontiers in Energy

Front. Energy    2016, Vol. 10 Issue (1) : 57-64
Effect of heat transfer coefficient of steam turbine rotor on thermal stress field under off-design condition
Jie GUO,Danmei XIE(),Hengliang ZHANG,Wei JIANG,Yan ZHOU
School of Power and Mechanical Engineering, Wuhan University, Wuhan 430072, China
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The precise calculation of temperature and thermal stress field of steam turbine rotor under off-design conditions is of paramount significance for safe and economic operation, in which an accurate calculation of heat transfer (HT) coefficient plays a decisive role. HT coefficient changes dramatically along with working conditions. First, a finite element analysis of rotor model, applied with ordinary rotor materials, has been conducted to investigate the temperature and thermal stress difference along with the change of HT coefficient from 20 W/(m2·°C) to 20000 W/(m2·°C). Next, the differentiation between existing empirical formulas has been analyzed from the aspect of physical significance of non-dimension parameters. Finally, a verifying case of the cold startup of a 1000MW unit has been proceeded. The result shows that the accuracy of coefficient calculation when steam parameters are low has a greater influence on that of rotor temperature and thermal stress, which means a precise empirical HT coefficient formula, like the Sarkar formula is strongly recommended. When steam parameters are high and HT coefficient is larger than 104 W/(m2·°C), there will be barely any influence on the calculation of thermal stress. This research plays a constructive role in the calculation and analysis of thermal stress.

Keywords steam turbine      rotor      thermal stress      heat transfer coefficient      empirical formula     
Corresponding Authors: Danmei XIE   
Online First Date: 04 November 2015    Issue Date: 29 February 2016
 Cite this article:   
Jie GUO,Danmei XIE,Hengliang ZHANG, et al. Effect of heat transfer coefficient of steam turbine rotor on thermal stress field under off-design condition[J]. Front. Energy, 2016, 10(1): 57-64.
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Fig.1  Meshing of single stage rotor
T/°C D/ kg•m−3 C/ J•(kg•K)−1 λ/ W•(m•K)−1 α/106•K−1 E/GPa γ
100 7820 516 47.7 12.47 213 0.286
200 7820 599 47.7 13.05 209 0.288
300 7820 611 44.0 13.56 205 0.288
400 7820 657 41.0 14.00 199 0.293
500 7820 716 38.1 14.35 181 0.281
600 7820 779 35.6 14.64 177 0.295
Tab.1  Physical parameters of rotor material
Case HT coefficient (W/(m2•°C)
1 20
2 200
3 2000
4 20000
5 500
6 750
7 1000
8 1250
9 1500
10 1750
Tab.2  HT coefficients in all cases
Fig.2  Results of Cases 1, 2, 3, 4

(a) Temperature-time curves; (b) thermal stress-time curves

HT coefficient/(W·(m2·°C)−1) Maximal temp./°C Increment Maximal stress/MPa Increment/%
20 162 83
200 416 156.79% 177 113.25
2000 556 33.65% 355 100.56
20000 585 5.22% 393 10.70
Tab.3  Values of maximal temperature and thermal stress of Cases 1 to 4
Fig.3  Results of Cases 5 to 10

(a) Temperature-time curves; (b) thermal stress-time curves

HT coefficient/(W·(m2·°C)−1) Maximal temp./°C Increment/% Maximal stress/MPa Increment/%
500 494 274
750 518 4.86 305 11.31
1000 532 2.70 324 6.23
1250 541 1.69 335 3.40
1500 547 1.11 344 2.69
1750 552 0.91 350 1.74
2000 556 0.72 355 1.43
Tab.4  Values of maximal temperature and thermal stress of Cases 5 to 10
Fig.4  1000 MW HP rotor model
Fig.5  Refinement in impeller root
Case HT coefficient calculation formula
A SU&HTC formula
B Sarkar formula
C Westinghouse formula
Tab.5  Cases of cold startup
Fig.6  Cold startup curves
Fig.7  HT coefficients by different formula
Fig.8  Temperature distribution at the end of startup (°C)
Fig.9  Thermal stress distribution at the end of startup (MPa)
Fig.10  Temperature-time curves of all cases
Fig.11  Thermal stress-time curves of all cases
Fig.12  Mean error curves
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