Dynamic response characteristics of once-through steam generator secondary side under valve disturbances

doi:10.11949/0438-1157.20250465

Abstract

Abstract:

The flexible and stable regulation of small module reactors is of great significance for the safe operation, and the dynamic characteristics of once-through steam generators with valve regulations in small modular reactors is extremely important for the regulation strategy. In this study, a dynamic model of the secondary loop was developed using the vPower platform. And the behaviors of the secondary side of the OTSG under step disturbances of the inlet and outlet valves were investigated, focusing on the main steam parameters at the outlet of the OTSG and the local heat transfer characteristics in the OTSG. Initially, disturbances in the inlet valve have a greater impact on the main steam parameters compared to the outlet valve. When subjected to a step disturbance of ±10%, ±15%, ±20%, the fluctuations in main steam mass flow rate, pressure, and temperature caused by the inlet valve are 2.09 to 14.09 times, 1.78 to 6.67 times, and -1.67 to -14.38 times larger than those caused by the outlet valve, respectively. Additionally, the buffering effect of the compressible volume in the OTSG on the flow rate and pressure was discovered, which limits the overshoot caused by valve disturbance to the vicinity of the valve. Furthermore, under inlet and outlet valve disturbances, the local pressure drop ratios and internal enthalpy rise rates of the steam generator vary, resulting in opposite trends in the impact of inlet and outlet valve disturbances on internal pressure and main steam temperature. The results have significant guiding significance for the operation control strategy of the OTSG in the secondary circuit.

Key words: small modular reactor, once-through steam generator, dynamic simulation, heat transfer, transient response

摘要：

小型反应堆的灵活稳定调控对于其安全运行具有重要意义，其中直流蒸汽发生器二次侧进出口阀门开度调节是二回路系统调控的重要途径之一，对阀门扰动引起的套管式蒸汽发生器动态特性进行研究对于优化阀门调控策略具有重要意义。基于vPower系统动态仿真平台搭建了一、二回路耦合换热的小型反应堆二回路动态模型，研究了套管式直流蒸汽发生器二次侧在入口与出口阀门阶跃扰动工况下主蒸汽参数及轴向参数的动态响应特性及机制。研究结果表明：入口阀门扰动对主蒸汽参数的影响显著大于出口阀门，在±10%、±15%和±20%开度扰动范围内，入口阀门对主蒸汽流量、压力、温度的影响幅度分别为出口阀门的2.09~14.09倍、1.78~6.67倍、-1.67~-14.38倍；同时，发现了蒸汽发生器内部两相流及蒸汽区对流量和压力的明显缓冲作用，进出口阀门在阶跃扰动时由于压力和流量响应速度不同导致超调，而OTSG的缓冲作用导致该超调仅发生在阀门附近；此外，进出口阀门扰动下，各设备局部压降占比及蒸汽发生器内部焓升速率的变化规律不同，导致入口阀门和出口阀门扰动对蒸汽发生器内部压力和主蒸汽温度的影响规律呈现相反趋势。研究成果对于蒸汽发生器二回路运行调控策略具有重要指导意义。

关键词: 小型反应堆, 直流蒸汽发生器, 动态仿真, 传热, 瞬态响应

CLC Number:

TK 212

Yuhan LIU, Chuangchuang WANG, Lin XIAN, Kai ZHAO, Daotong CHONG, Quanbin ZHAO. Dynamic response characteristics of once-through steam generator secondary side under valve disturbances[J]. CIESC Journal, 2025, 76(11): 5739-5752.

刘雨晗, 王创创, 鲜麟, 赵凯, 种道彤, 赵全斌. 套管式直流蒸汽发生器二次侧阀门扰动下的动态特性研究[J]. 化工学报, 2025, 76(11): 5739-5752.

Figures/Tables 19

Fig.1 Secondary loop thermodynamic system model established through vPower

Table 1 Design parameters of the casing OTSG

参数	数值	参数	数值
管束数量/根	665	一次侧冷却剂流量/(kg·s^-1)	126.2
换热段有效长度/m	2.15	冷却剂入口温度/℃	319.5
外管外径/mm	13	冷却剂出口温度/℃	286.5
外管内径/mm	10	一次侧压力/MPa	15.0
内管外径/mm	8	给水流量/(kg·s^-1)	10.3
内管内径/mm	6	给水温度/℃	140.0
管束排列节距/mm	13.8	蒸汽温度/℃	285.0
总换热功率/MW	24.1	蒸汽压力/MPa	4.01

Fig.2 Schematic diagram of the single-tube cross-section and the flow regime of secondary side

Table 2 Boundary criterion of flow region and heat transfer coefficient correlation of the secondary side

区域	起始判据	传热系数计算关联式
预热区	—	$k = 0.023 λ f D e R e f 0.8 P r f 0.4$ ^[28]
过冷沸腾区	$Δ T s, O N B = 0.556 q 1082 p 1.156 0.463 p 0.0234$ ^[29]	$Δ T s = 25 q 106 0.25 e - p 6.2$ ^[30]
饱和沸腾区	$x > 0$	$k = k n u c + k c o n v$ ^[31] $k n u c = 0.00122 λ l 0.79 c p l 0.45 ρ l 0.49 g 0.25 σ 0.5 μ l 0.29 i 0.24 ρ g 0.24 Δ T s 0.24 Δ p s 0.75 S$ ^[31] $k c o n v = 0.023 R e l 0.8 P r l 0.4 λ l D e F$ ^[31]
缺液区	$x c 1 D e 1 0.15 = 1.4244 x c D e 0.15$ ^[32] $x c = 0.3 + 0.7 e - 45 ω$ ^[32] $ω = m ˙ μ l σ ρ l (ρ l ρ g) 13$ ^[32]	$N u = 0.052 R e g x + ρ g ρ l 1 - x 0.683 P r g 1.26 Y - 1.06$ ^[33] $Y = m a x 1 - 0.1 1 - x 0.4 ρ l ρ g - 1 0.4, 0.1$ ^[33]
过热区	$x > 1$	$k = 0.023 λ f D e R e f 0.8 P r f 0.4$ ^[28]

Table 2 Boundary criterion of flow region and heat transfer coefficient correlation of the secondary side

区域	起始判据	传热系数计算关联式
预热区	—	$k = 0.023 λ f D e R e f 0.8 P r f 0.4$ ^[28]
过冷沸腾区	$Δ T s, O N B = 0.556 q 1082 p 1.156 0.463 p 0.0234$ ^[29]	$Δ T s = 25 q 106 0.25 e - p 6.2$ ^[30]
饱和沸腾区	$x > 0$	$k = k n u c + k c o n v$ ^[31] $k n u c = 0.00122 λ l 0.79 c p l 0.45 ρ l 0.49 g 0.25 σ 0.5 μ l 0.29 i 0.24 ρ g 0.24 Δ T s 0.24 Δ p s 0.75 S$ ^[31] $k c o n v = 0.023 R e l 0.8 P r l 0.4 λ l D e F$ ^[31]
缺液区	$x c 1 D e 1 0.15 = 1.4244 x c D e 0.15$ ^[32] $x c = 0.3 + 0.7 e - 45 ω$ ^[32] $ω = m ˙ μ l σ ρ l (ρ l ρ g) 13$ ^[32]	$N u = 0.052 R e g x + ρ g ρ l 1 - x 0.683 P r g 1.26 Y - 1.06$ ^[33] $Y = m a x 1 - 0.1 1 - x 0.4 ρ l ρ g - 1 0.4, 0.1$ ^[33]
过热区	$x > 1$	$k = 0.023 λ f D e R e f 0.8 P r f 0.4$ ^[28]

Fig.3 Flow and heat transfer model of the primary and secondary sides of casing OTSG with 20 nodes

Fig.4 Schematic diagram and flowchart of wall coupling heat transfer calculation of OTSG

Fig.5 Effect of node number on accuracy of OTSG model

Table 3 Simulation error of the secondary loop thermodynamic system

二回路系统参数	设计值	计算值	误差
主汽压/MPa	4.01	4.01	0.00%
主汽温/℃	288.00	288.06	0.02%
给水流量/(kg∙s^-1)	165.77	166.52	0.45%
给水温度/℃	139.90	138.99	0.65%
热功率/MW	385.30	388.12	0.73%
汽机功率/MW	127.52	126.64	0.69%

Fig.6 Dynamic characteristics of main steam pressure under ±10%， ±15%， ±20% step disturbance of inlet and outlet valves

Table 4 The overshoot of the main steam mass flow rate， pressure and temperature under the inlet valve and outlet valve disturbance by ±10%， ±15% and ±20%

阀门扰动	流量	压力	温度
入口阀+10%	+0.12%	+0.04%	0
入口阀+15%	+0.03%	+1.97%	-0.05%
入口阀+20%	+0.04%	+1.42%	-0.07%
入口阀-10%	-0.11%	-0.01%	+0.01%
入口阀-15%	-0.25%	-0.03%	0
入口阀-20%	-0.22%	-0.09%	+0.01%
出口阀+10%	+0.80%	+0.59%	+0.03%
出口阀+15%	+0.61%	+0.12%	+0.04%
出口阀+20%	+0.62%	+0.11%	+0.04%
出口阀-10%	-0.84%	-0.53%	-0.10%
出口阀-15%	-5.51%	-4.31%	-0.03%
出口阀-20%	-2.76%	-2.05%	-0.06%

Fig.7 Dynamic characteristics of main steam mass flow rate under ±10%， ±15%， ±20% step disturbance of inlet and outlet valves

Fig.8 Dynamic characteristics of main steam temperature under ±10%， ±15%， ±20% step disturbance of inlet and outlet valves

Fig.9 Dynamic characteristics of pressure drop of secondary loop under ±15% step disturbance of the inlet and outlet valves

Table 5 Pressure drop of inlet valve， OTSG， and outlet valve under the ±10%， ±15%， ±20% disturbance of inlet and outlet valves

工况	总压降/MPa	入口给水阀压降/MPa	入口给水阀压降占比/%	OTSG 压降/MPa	OTSG压降占比/%	出口主汽阀压降/MPa	出口主汽阀压降占比/%
初始工况	3.27	3.04	92.86	16.65×10^-3	0.51	0.22	6.63
入口阀+10%	2.95	2.71	91.96	16.46×10^-3	0.56	0.22	7.42
入口阀+15%	2.87	2.62	91.39	17.29×10^-3	0.60	0.23	8.01
入口阀+20%	2.75	2.51	91.13	17.17×10^-3	0.62	0.23	8.19
入口阀-10%	3.69	3.46	93.92	15.71×10^-3	0.43	0.21	5.61
入口阀-15%	3.94	3.73	94.64	15.75×10^-3	0.40	0.20	4.96
入口阀-20%	4.22	4.02	95.27	14.72×10^-3	0.35	0.18	4.35
出口阀+10%	3.24	3.10	95.69	16.43×10^-3	0.51	0.12	3.76
出口阀+15%	3.22	3.11	96.38	16.82×10^-3	0.52	0.10	3.09
出口阀+20%	3.22	3.12	96.85	16.53×10^-3	0.51	0.08	2.58
出口阀-10%	3.41	2.90	84.87	15.52×10^-3	0.45	0.50	14.63
出口阀-15%	3.56	2.73	76.68	15.41×10^-3	0.43	0.81	22.88
出口阀-20%	3.81	2.42	63.48	13.68×10^-3	0.36	1.38	36.12

Fig.10 Dynamic characteristics of local mass flow rate of OTSG under ±15% step disturbance of the inlet and outlet valves

Fig.11 Dynamic and statistic characteristics of local fluid temperature of OTSG under step disturbance of the inlet and outlet valves

Fig.12 Dynamic and statistic characteristics of local vapor quality of OTSG under step disturbance of the inlet and outlet valves

Fig.13 Dynamic and statistic characteristics of local heat load of OTSG under step disturbance of the inlet and outlet valves

Table 6 Relative difference of average heat load for different flow regions under the ±10%， ±15%， ±20% disturbance of inlet and outlet valves

阀门开度	平均局部换热功率稳态相对变化量
	入口阀门			出口阀门
	单相液	两相区	单相气	单相液	两相区	单相气
+10%	+5.45%	-13.72%	—	+0.39%	+1.77%	-2.22%
+15%	+8.79%	-17.17%	—	+0.46%	+2.21%	-2.86%
+20%	+11.79%	-19.41%	—	+0.54%	+2.47%	-2.95%
-10%	-6.32%	+24.23%	-62.26%	-1.16%	-4.81%	+6.49%
-15%	-8.03%	+41.77%	-82.32%	-2.41%	-9.87%	+12.51%
-20%	-11.49%	+61.83%	-94.64%	-5.69%	-18.64%	+3.03%

References 37

[1]	王鑫, 赵钢, 曲新鹤, 等. 某小型模块化反应堆核电站二回路系统变工况特性[J]. 清华大学学报(自然科学版), 2024, 64(1): 155-163.
	Wang X, Zhao G, Qu X H, et al. Investigating the off-design performance of the secondary circuit system in a small modular reactor nuclear power plant[J]. Journal of Tsinghua University (Science and Technology), 2024, 64(1): 155-163.
[2]	孔夏明, 王苇, 孟海波, 等. 直流蒸汽发生器启动系统动态特性仿真[J]. 舰船科学技术, 2013, 35(10): 56-59.
	Kong X M, Wang W, Meng H B, et al. Simulation study of dynamic characteristic of start-up system for once-through steam generator[J]. Ship Science and Technology, 2013, 35(10): 56-59.
[3]	朱一虎. 螺旋管式直流蒸汽发生器建模与控制策略研究[D]. 哈尔滨: 哈尔滨工程大学, 2023.
	Zhu Y H. Modeling and control strategy research of helical tube once-through steam generator[D]. Harbin: Harbin Engineering University, 2023.
[4]	彭敏俊. 船舶核动力装置[M]. 北京: 原子能出版社, 2009.
	Peng M J. Ship Nuclear Power Plant[M]. Beijing: Atomic Press, 2009.
[5]	丁训慎. 核电厂蒸汽发生器设计中的安全问题[J]. 核安全, 2005, 4(2): 1-6, 15.
	Ding X S. The design safety of steam generators in NPP[J]. Nuclear Safety, 2005, 4(2): 1-6, 15.
[6]	熊扬恒. 核电站蒸汽发生器研究设计中的几个问题[J]. 核动力工程, 1994, 15(4): 319-322, 333.
	Xiong Y H. Several problems in the research and design to the steam generator of the nuclear power plant[J]. Nuclear Power Engineering, 1994, 15(4): 319-322, 333.
[7]	戴饶棋, 段天英, 刘勇, 等. 钠冷快堆直流蒸汽发生器建模与仿真研究[J]. 节能技术, 2023, 41(4): 362-366.
	Dai R Q, Duan T Y, Liu Y, et al. Study on modeling and simulation of once-through steam generator in sodium-cooled fast reactors[J]. Energy Conservation Technology, 2023, 41(4): 362-366.
[8]	王寒雨. 套管式直流蒸汽发生器建模与特性分析[D]. 南京: 东南大学, 2022.
	Wang H Y. Modeling and characteristic analysis of casing once-through steam generator[D]. Nanjing: Southeast University, 2022.
[9]	王楠. 基于隐式差分格式的直流蒸汽发生器动态性能研究[D]. 哈尔滨: 哈尔滨工程大学, 2022.
	Wang N. Research on dynamic performance of once through steam generator based on implicit scheme[D]. Harbin: Harbin Engineering University, 2022.
[10]	许余, 皇甫泽玉, 胥建群, 等. 直流蒸汽发生器动态特性与小破口故障仿真研究[J]. 核动力工程, 2021, 42(2): 161-167.
	Xu Y, Huangfu Z Y, Xu J Q, et al. Simulation research on dynamic characteristics and small break fault of once-through steam generator[J]. Nuclear Power Engineering, 2021, 42(2): 161-167.
[11]	许余, 皇甫泽玉, 胥建群, 等. 直流蒸汽发生器建模与仿真研究[J]. 核动力工程, 2021, 42(1): 154-160.
	Xu Y, Huangfu Z Y, Xu J Q, et al. Research on modeling and simulation of once-through steam generator[J]. Nuclear Power Engineering, 2021, 42(1): 154-160.
[12]	魏巍. 600 MW钠冷快堆蒸汽发生器仿真研究[D]. 哈尔滨: 哈尔滨工程大学, 2019.
	Wei W. Simulation of 600 MW sodium-cooled fast reactor steam generator[D]. Harbin: Harbin Engineering University, 2019.
[13]	丁宏达. 考虑流动阻力的直流蒸汽发生器换热性能仿真[D]. 哈尔滨: 哈尔滨工程大学, 2018.
	Ding H D. Simulation of heat transfer performance of once-through steam generator with flow resistance is considered[D]. Harbin: Harbin Engineering University, 2018.
[14]	薄琳, 孙宝芝, 干依燃, 等. 一次扰动下直流蒸汽发生器动态换热性能仿真[J]. 化工学报, 2018, 69(S1): 64-71.
	Bo L, Sun B Z, Gan Y R, et al. Simulation of heat transfer performance of once-through steam generator under primary side disturbance[J]. CIESC Journal, 2018, 69(S1): 64-71.
[15]	张羽, 孙宝芝, 童铁峰. 运行条件对蒸汽发生器热工参数影响的仿真研究[J]. 原子能科学技术, 2015, 49(12): 2157-2163.
	Zhang Y, Sun B Z, Tong T F. Simulation research of impact of operating condition on thermal parameters in steam generator[J]. Atomic Energy Science and Technology, 2015, 49(12): 2157-2163.
[16]	Zhang G L, Zhang Y, Yang Y L, et al. Dynamic heat transfer performance study of steam generator based on distributed parameter method[J]. Annals of Nuclear Energy, 2014, 63: 658-664.
[17]	Zhu J Y, Guo Y, Zhang Z J. Dynamic simulation of once-through steam generator with concentric annuli tube[J]. Annals of Nuclear Energy, 2012, 50: 185-198.
[18]	朱景艳, 张志俭, 郭赟. 套管式直流蒸汽发生器动态实时仿真研究[J]. 原子能科学技术, 2011, 45(8): 937-940, 942.
	Zhu J Y, Zhang Z J, Guo Y. Dynamic real-time simulation research on once-through steam generator with concentric annuli tube[J]. Atomic Energy Science and Technology, 2011, 45(8): 937-940, 942.
[19]	刘建阁, 彭敏俊, 张志俭, 等. 套管式直流蒸汽发生器负荷跟随动态特性分析[J]. 原子能科学技术, 2010, 44(2): 175-182.
	Liu J G, Peng M J, Zhang Z J, et al. Load following dynamic characteristic analysis of casing once-through steam generator[J]. Atomic Energy Science and Technology, 2010, 44(2): 175-182.
[20]	李海鹏, 黄晓津, 张良驹. 螺旋管式直流蒸汽发生器的集总参数动态模型[J]. 原子能科学技术, 2008, 42(8): 729-733.
	Li H P, Huang X J, Zhang L J. Lumped parameter dynamic model of helical coiled once-through steam generator[J]. Atomic Energy Science and Technology, 2008, 42(8): 729-733.
[21]	黄晓津, 冯元琨, 郭人俊. HTR-10螺旋管式直流蒸汽发生器的动态数学模型[J]. 高技术通讯, 2001, 11(1): 96-99, 93.
	Huang X J, Feng Y K, Guo R J. Dynamic mathematical model of helical coils of steam generator of HTR-10[J]. High Technology Letters, 2001, 11(1): 96-99, 93.
[22]	郭海红. 蒸汽发生器工作过程动态仿真[D]. 哈尔滨: 哈尔滨工程大学, 2007.
	Guo H H. Working process dynamic simulation of steam generator[D]. Harbin: Harbin Engineering University, 2007.
[23]	张伟, 边信黔, 夏国清. 套管式直流蒸汽发生器动态特性仿真研究[J]. 核科学与工程, 2006, 26(2): 103-107.
	Zhang W, Bian X Q, Xia G Q. Simulation study of dynamic characteristic of once-through steam generator in annuli tube[J]. Chinese Journal of Nuclear Science and Engineering, 2006, 26(2): 103-107.
[24]	Bai X, Wei Y Z, Zhang R, et al. Operation Scheme analysis of a multipurpose small modular reactor under cogeneration condition based on a once-through steam generator dynamic model[J]. Applied Thermal Engineering, 2024, 257: 124264.
[25]	Wan J S, Xie J Y, Wang P F, et al. Control system design for the once-through steam generator of lead-bismuth cooled reactor based on classical control theory[J]. Annals of Nuclear Energy, 2022, 175: 109214.
[26]	Li C, Yu R, Yu W M, et al. Pressure control of once-through steam generator using proximal policy optimization algorithm[J]. Annals of Nuclear Energy, 2022, 175: 109232.
[27]	Tao M, Ke Z W, Li X L, et al. The research of the model-free adaptive control method of once-through steam generator in nuclear power[C]//2017 25th International Conference on Nuclear Engineering. Shanghai, China, 2017.
[28]	陶文铨. 传热学[M]. 5版. 北京: 高等教育出版社, 2019.
	Tao W Q. Heat Transfer[M]. 5th ed. Beijing: Higher Education Press, 2019.
[29]	Bergles A E, Rohsenow W M. The determination of forced-convection surface-boiling heat transfer[J]. Journal of Heat Transfer, 1964, 86(3): 365-372.
[30]	Jens W H, Lottes P A. Analysis of heat transfer, burnout, pressure drop and density data for high pressure water[R]. Chicago: Argonne National Laboratory, 1951.
[31]	Chen J C. Correlation for boiling heat transfer to saturated fluids in convective flow[J]. Industrial & Engineering Chemistry Process Design and Development, 1966, 5(3): 322-329.
[32]	吴鸽平, 吴埃敏, 郭贇, 等. 环形窄缝通道内流动沸腾干涸点的研究[J]. 西安交通大学学报, 2004, 38(7): 686-689, 697.
	Wu G P, Wu A M, Guo Y, et al. Experimental research on dryout point of flow boiling in narrow annular channel[J]. Journal of Xi'an Jiaotong University, 2004, 38(7): 686-689, 697.
[33]	Groeneveld D C, Delorme G G J. Prediction of thermal non-equilibrium in the post-dryout regime[J]. Nuclear Engineering and Design, 1976, 36(1): 17-26.
[34]	The Babcock & Wilcox Company. Steam: Its Generation and Use[M]. Akron: The Babcock & Wilcox Company, 2011.
[35]	孔夏明, 王苇, 孟海波, 等. 负荷扰动下直流蒸汽发生器蒸汽压力控制仿真[J]. 舰船科学技术, 2013, 35(2): 68-71.
	Kong X M, Wang W, Meng H B, et al. Simulation research on pressure control of main steam in once through steam generator load disturbance[J]. Ship Science and Technology, 2013, 35(2): 68-71.
[36]	Li H P, Huang X J, Zhang L J. A lumped parameter dynamic model of the helical coiled once-through steam generator with movable boundaries[J]. Nuclear Engineering and Design, 2008, 238(7): 1657-1663.
[37]	吴青阳, 李根, 刘明, 等. 核能水电联产系统的变负荷动态特性与灵活运行控制策略优化研究[J]. 动力工程学报, 2025, 45(4): 582-591.
	Wu Q Y, Li G, Liu M, et al. Research on dynamic characteristics and flexible operation control strategy optimization of nuclear power and water cogeneration system[J]. Journal of Chinese Society of Power Engineering, 2025, 45(4): 582-591.