Research on Aerodynamic and Strength Performance of Last Stage in High-Pressure Cylinder of Steam Turbine Under Variable Working Conditions

doi:10.12096/j.2096-4528.pgt.21105

Abstract

Abstract:

Using the one-way fluid-structure interaction method, the aerodynamic and strength performance of the last stages in high-pressure cylinder of a steam turbine were numerically investigated at four extraction percentages (0%, 8%, 15% and 20% of the total mass flow rate in stages). The aerodynamic efficiency of last stages, as well as the aerodynamic loads on the blades, was obtained under design and off-design conditions. With the computed aerodynamic loads, the strength performance of the last rotor blade was analyzed, and the maximum stress and deformation in rotor blade at various conditions were derived. The results show that the power output of last two stages is nearly linearly decreased with the increase of extraction percentage. If the extraction percentage equals to 20%, the power output is reduced by 44% as compared with the design case. As the extraction percentage increases, the total temperature at last stage outlet is gradually increased. With 20% extraction rate, the total temperature at last stage outlet is increased by about 10 ℃ compared with the design case. The extraction rate has a significant influence on the leakage performance in the tip and hub labyrinth seals of last stage, resulting in the variations of total-total isentropic efficiency, reaction degree and outlet flow angle distributions along the spanwise direction in the off-design conditions. The influence region in the last stage is mainly existed within 30% blade span near hubs due to varied extractions. Compared with the original design case, the total-total isentropic efficiency, reaction degree and outlet flow angle in the last stage are varied by 3.8%, 1.6% and 2.4° at most as the extraction percentage varies from 0 to 20%. With the centrifugal and aerodynamic forces, the maximum stress in the last stage rotor blade is occurred at the upstream side bottom fillet of T-shape root, and the maximum displacement in blade tip is 0.443 mm. As the extraction percentage increases, the maximum stress and maximum displacement in last stage rotor blade are almost linearly decreased.

Key words: steam turbine, aerodynamic performance, blade strength, high-pressure cylinder

CLC Number:

TK 262

Honghui SHI, Haibo WANG, Rongxiu CAO, Li YAO, Xin YAN. Research on Aerodynamic and Strength Performance of Last Stage in High-Pressure Cylinder of Steam Turbine Under Variable Working Conditions[J]. Power Generation Technology, 2022, 43(6): 959-969.

Figures/Tables 24

Fig. 1 CFD computational model for the last two stages in high pressure cylinder

Tab. 1 Main geometrical parameters for blades and seals

叶栅	叶片数	叶高/mm	弦长/mm	汽封间隙/mm
S11	80	106.5	38	0.8
R11	64	110.5	50	0.8
S12	80	114.6	42	0.9
R12	64	118.3	59	0.9

Fig. 2 Computational meshes for blades and seals

Fig. 3 Meridian view of CFD computational model

Tab. 2 Boundary conditions of CFD computational model

边界	设置(设计工况)
进口总压P_in/MPa	9.834
进口总温T_in/K	708.05
出口静压P_out/MPa	7.76
动、静叶栅交界面(1)(2)(3)	冻结转子
汽封-主通道交界面(4)(6)(8)(10)	一般连接
汽封-主通道交界面(5)(7)(9)(11)	冻结转子

Tab. 3 Independency analysis of the first mesh layer distance near wall

y_wall/mm	近壁面平均y⁺	$η i t$	$m ˙$ /(kg·s^-1)	相对偏差/%
0.01	70.6	0.905 8	747.08	2.037
0.005	33.1	0.904 9	746.06	1.897
0.0025	16.9	0.905 2	742.11	1.358
0.001	7.8	0.904 4	734.49	0.317
0.000 5	3.6	0.904 2	732.17	—

Tab. 3 Independency analysis of the first mesh layer distance near wall

y_wall/mm	近壁面平均y⁺	$η i t$	$m ˙$ /(kg·s^-1)	相对偏差/%
0.01	70.6	0.905 8	747.08	2.037
0.005	33.1	0.904 9	746.06	1.897
0.0025	16.9	0.905 2	742.11	1.358
0.001	7.8	0.904 4	734.49	0.317
0.000 5	3.6	0.904 2	732.17	—

Tab. 4 Independency analysis for grid density of blades

节点数/万	y_wall/mm	$η i t$	$m ˙$ /(kg·s^-1)	相对偏差/%
490	0.001	0.902 3	734.87	0.204
710	0.001	0.904 4	734.49	0.152
1 049	0.001	0.904 9	733.95	0.079

Tab. 4 Independency analysis for grid density of blades

节点数/万	y_wall/mm	$η i t$	$m ˙$ /(kg·s^-1)	相对偏差/%
490	0.001	0.902 3	734.87	0.204
710	0.001	0.904 4	734.49	0.152
1 049	0.001	0.904 9	733.95	0.079

Tab. 5 Independency analysis for grid density of seals

节点数/万	y_wall/mm	$η i t$	$m ˙$ /(kg·s^-1)	相对偏差/%
238	0.001	0.904 9	734.51	0.016
479	0.001	0.904 4	734.49	0.015
958	0.001	0.904 4	734.45	0.010

Tab. 5 Independency analysis for grid density of seals

节点数/万	y_wall/mm	$η i t$	$m ˙$ /(kg·s^-1)	相对偏差/%
238	0.001	0.904 9	734.51	0.016
479	0.001	0.904 4	734.49	0.015
958	0.001	0.904 4	734.45	0.010

Fig. 4 FEA computational model for the last stage rotor blade-disk in high pressure cylinder

Tab. 6 Main mechanical property parameters of 2Cr13 at 400 ℃

参数

弹性模量/

MPa

泊松比

密度/

(kg·s^-3)

屈服强度

σ 0.2

Tab. 6 Main mechanical property parameters of 2Cr13 at 400 ℃

参数

弹性模量/

MPa

泊松比

密度/

(kg·s^-3)

屈服强度

σ 0.2

/MPa

数值

1.99×10⁵

0.337

7 750

735

Fig. 5 FEA computational meshes for blade-disk

Fig. 6 Boundary conditions and loads for the FEA computational model

Tab. 7 Overall parameters of final two stage variable conditions of high-pressure cylinder

工况	P_in/MPa	T_out/K	$m ˙$ /(kg·s^-1)	$P ˙$ /MW	功率占比/%
设计工况	9.834	673.44	738.93	45.36	100
8%抽汽	9.549	676.82	680.18	36.95	81.46
15%抽汽	9.305	680.63	628.22	30.05	66.24
20%抽汽	9.135	683.42	591.30	25.45	56.11

Tab. 7 Overall parameters of final two stage variable conditions of high-pressure cylinder

工况	P_in/MPa	T_out/K	$m ˙$ /(kg·s^-1)	$P ˙$ /MW	功率占比/%
设计工况	9.834	673.44	738.93	45.36	100
8%抽汽	9.549	676.82	680.18	36.95	81.46
15%抽汽	9.305	680.63	628.22	30.05	66.24
20%抽汽	9.135	683.42	591.30	25.45	56.11

Fig. 7 Secondary flow meridian streamlines caused by steam steal leakage under 20% extraction condition

Fig. 8 Total-total isentropic efficiency distributions along spanwise direction

Fig. 9 Reaction degree distributions along the spanwise direction

Fig. 10 Blade outlet flow angle distributions along the spanwise direction

Fig. 11 Stress distributions in blade and disk with only centrifugal force

Fig. 12 Parameter distributions on the interface between FEA and CFD domain under design condition

Fig. 13 Stress distributions in blade and disk with both centrifugal force and aerodynamic force

Fig. 14 Deformation displacement distributions of blade before and after loading aerodynamic force (magnify 50 times)

Fig. 15 Position and number of high stress area in blade and disk

Tab. 8 Stress of key parts of blade and disk under variable conditions

工况	位置①	位置②	位置③	位置④	位置⑤	位置⑥
设计工况	236.8	289.1	391.4	214.2	420.7	379.5
8%抽汽	238.7	283.0	375.2	207.7	408.7	374.4
15%抽汽	240.1	278.9	361.2	202.1	398.4	370.0
20%抽汽	240.9	276.2	351.2	198.1	390.9	366.8

Tab. 9 Maximum deformation displacement of blade tip under variable conditions

工况	径向	切向	轴向	总位移
设计工况	0.212	0.029	0.400	0.443
8%抽汽	0.206	0.028	0.363	0.408
15%抽汽	0.200	0.027	0.331	0.379
20%抽汽	0.196	0.027	0.308	0.358

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