﻿ 立式自然循环蒸汽发生器机理建模与仿真研究
 舰船科学技术  2017, Vol. 39 Issue (3): 113-117 PDF

Study of mechanism modeling and simulation of natural circulation steam generator
ZOU Hai, LI Liang, ZHENG Wei, YAN Bing
Wuhan Second Ship Design and Research Institute, Wuhan 430064, China
Abstract: According to the vertical natural circulation steam generator, a mathmatic model is build by modularized mechanism modeling method. The mathmatic model includes 16 control volumes. According to the control volumes the mathmatic model with 12 state variables is created and deduced by lumped parameter method. The mathematical model of vertical natural circulation steam generator is resolved by Runge-Kutta method. The model is verified by simulation test. The mathmatic model can be used to analyze the dynamic characteristics of steam generator,and design the controller. It has a definite application value.
Key words: dynamic characteristics     simulation     steam generator     mathematical model
0 引　言

1 蒸汽发生器简介

2 蒸汽发生器数学模型 2.1 蒸汽发生器数学模型模块划分

 图 1 蒸汽发生器建模结构 Fig. 1 The model structure of steam generator
2.2 蒸汽发生器数学模型建模假设

2.3 蒸汽发生器一次侧数学模型

 ${(MC)_{sgci}}\frac{{{\rm d}{T_{sgci}}}}{{\rm{d}\tau }} = \frac{1}{2}{G_{sgc}}{C_{sgc}}({T_{sgci}} - {T_{sgc1}}) \text{；}$ (1)

 $\begin{array}{l}\displaystyle{(MC)_{sgc1}}\frac{{{\rm d}{T_{sgc1}}}}{{{\rm d}\tau }} = \frac{1}{2}{G_{sgc}}{C_{sgc}}({T_{sgci}} - {T_{sgc1}}) - \\[5pt]{(UF)_{sgc1}}({T_{sgc1}} - {T_{sgm1}})\text{，}\\[5pt]\displaystyle {(MC)_{sgm1}}\frac{{{\rm d}{T_{sgm1}}}}{{{\rm d}\tau }} = {(UF)_{sgc1}}({T_{sgc1}} - {T_{sgm1}}) - \\[5pt]{(UF)_{sgp1}}({T_{sgm1}} - {T_{sgpa}}) - {(UF)_{sgs1}}({T_{sgm1}} - {T_s})\text{；}\end{array}$ (2)

 ${(MC)_{sgc2}}\frac{{ {\rm d}}{T_{sgcmo}}}{{{\rm d}\tau }} = \frac{1}{2}{G_{sgc}}{C_{sgc}}({T_{sgc1o}} - {T_{sgcmo}}) \text{；}$ (3)

 $\begin{array}{l}\displaystyle{(MC)_{sgc2}}\frac{{{\rm d}{T_{sgc2}}}}{{\rm{d}\tau }} = \frac{1}{2}{G_{sgc}}{C_{sgc}}({T_{sgcmo}} - {T_{sgc2}}) - \\[5pt] \displaystyle {(UF)_{sgc2}}({T_{sgc2}} - {T_{sgm2}})\text{，}\\[5pt]\displaystyle{(MC)_{sgm2}}\frac{{{\rm d}{T_{sgm2}}}}{{{\rm d}\tau }} = {(UF)_{sgc2}}({T_{sgc2}} - {T_{sgm2}}) - \\[5pt]\displaystyle {(UF)_{sgp2}}({T_{sgm2}} - {T_{sgpa}}) - {(UF)_{sgs2}}({T_{sgm2}} - {T_s}) \text{；} \end{array}$ (4)

 ${(MC)_{sgco}}\frac{{{\rm d}{T_{sgco}}}}{{\rm{d}\tau }} = \frac{1}{2}{G_{sgc}}{C_{sgc}}({T_{sgc2o}} - {T_{sgco}}) \text{。}$ (5)

 ${T_{sgc2o}}{\rm{ = }}2{T_{sgc2}} - {T_{sgcmo}},{T_{sgc1o}} = 2{T_{sgc1}} - {T_{sgc{i}}}\text{。}$ (6)
 图 2 一回路冷却剂温度示意图 Fig. 2 Schematic diagram of primary system coolant temperatures
2.4 蒸汽发生器二次侧数学模型

 $\begin{array}{l}\displaystyle \frac{{{\rm d}{M_{fwv}}}}{{{\rm d}\tau }} = {G_{fw}} + \left( {1 - {x_0}} \right){G_{bvo}} - {G_{wd}}\text{，}\\[5pt]\displaystyle L = {L_{wd}} + {M_{fwv}}/({\rho _{fwv}}{F_{fwv}})\frac{{\rm d}}{{{\rm d}\tau }}\left( {{M_{fwv}}{h_{fwv}}} \right) = \\[5pt]{G_{fw}}{h_{fw}} + (1 - {x_0}){G_{bvo}}h' - {G_{wd}}{h_{fwv}}\text{；}\end{array}$ (7)

 $\begin{array}{l}\displaystyle \frac{{\rm d}}{{{\rm d}\tau }}\left( {{M_{wd}}{h_{wdo}}} \right) = {G_{wd}}({h_{fwv}} - {h_{wdo}})\text{，}\\[5pt]{M_{wd}} = {V_{wd}}{\rho _{wd}} \text{；}\end{array}$ (8)

 $\begin{array}{l}\displaystyle\frac{{\rm d}}{{{\rm d}\tau }}\left( {{L_{ph}}{F_r}{\rho _{ph}}{h_{ph}}} \right) = {G_{wd}}\left( {{h_{wdo}} - h'} \right) + {Q_{ph}}{Q_{ph}} = \\[5pt]{(UF)_{sgp1}}({T_{sgm1}} \!-\! {T_{sgma}})\! +\! {(UF)_{sgp2}}({T_{sgm2}}\!\! -\! {T_{sgpa}}) \text{；}\!\!\end{array}$ (9)

 $\begin{array}{l}\displaystyle \frac{{\rm d}}{{{\rm d}\tau }}\left( {{V_{bv}}{\rho _{bv}}} \right) = {G_{wd}} - {G_{bvo}}\text{，}\\[5pt]{V_{bv}} \!=\! ({L_h} - {L_{ph}}){F_r}\text{，}\\[5pt]\displaystyle {V_{bv}}\frac{{\rm d}}{{{\rm d}\tau }}\left( {{\rho _{bv}}{h_{bv}}} \right)\! =\! {G_{wd}}h' - {G_{bvo}}{h_{bvo}} + {Q_{bh}}\text{，}\\[5pt]{Q_{bh}}\!\! =\! \!{(UF)_{sgs1}}({T_{sgm1}}\! - \!{T\!_s}) \!\!+\! {(UF)_{sgs2}}({T_{sgm2}} \!-\! {T_s}) \text{；}\!\!\end{array}$ (10)

 $\begin{array}{l}\displaystyle \frac{{\rm d}}{{{\rm d}\tau }}\left( {{V_{SGS}}\rho ''} \right) = {G_{bvo}} - {G_s}/2 - (1 - {x_0}) \cdot {G_{bvo}}\text{，}\\[5pt]{V_{sgs}} = {V_{sgs0}} + ({L_0} - L) \cdot {F_{fwv}} \text{；}\end{array}$ (11)

 $\begin{array}{l}\displaystyle \left[ {{\zeta _d}\left( {\frac{1}{{F_{wd}^2{\rho _{wd}}}} + \frac{1}{{F_{fwv}^2{\rho _{fwv}}}}} \right) + {\zeta _{ph}}\left( {\frac{1}{{F_r^2{\rho _{ph}}}}} \right)} \right]\frac{{G_{wd}^2}}{{2g}} + \\[8pt]\displaystyle \left( {{\zeta _{bv}}\frac{1}{{F_r^2{\rho _{bv}}}} + {\zeta _{se}}\frac{1}{{F_{se}^2{\rho _{bvo}}}}} \right)\frac{{G_{bvo}^2}}{{2g}} + \left( {\frac{{L - {L_{wd}}}}{{{F_{fwv}}g}} + \frac{{{L_{wd}}}}{{{F_{wd}}g}} + \frac{{{L_{ph}}}}{{{F_r}g}}} \right)\\[8pt]\displaystyle \frac{{{\rm d}{G_{wd}}}}{{{\rm d}\tau }} + \left( {\frac{{{L_{bh}}}}{{{F_r}g}} + \frac{{{L_{se}}}}{{{F_{se}}g}}} \right)\frac{{{\rm d}{G_{bvo}}}}{{{\rm d}\tau }} = \left( {L - {L_{wd}}} \right){\rho _{fwv}} + \\[8pt]{L_{wd}}{\rho _{wd}} - {L_{ph}}{\rho _{ph}} - {L_{bh}}{\rho _{bh}} - {L_{se}}{\rho _{bvo}}\text{。}\qquad\qquad\qquad (12)\end{array}$ (12)
3 蒸汽发生器数学模型解算 3.1 模型推导

 $\displaystyle re = 1 + \frac{{\rho '}}{{\rho ''}}{x_0}, {\rho _{bv}} = \frac{{\rho ''}}{{{x_0}}}\ln re, {\rho _{bvo}} = \frac{{\rho ''}} {\displaystyle {{1 + {x_0}\frac{{\rho '}}{{\rho ''}}}}}\text{，}$ (13)

 $\frac{{{\rm d}{\rho _{bv}}}}{{{\rm d}\tau }} = (\frac{{re{\rho _{bv}} - \rho '}}{{re\rho ''}})\frac{{{\rm d}\rho ''}}{{{\rm d}\tau }} + (\frac{{\rho ' - re{\rho _{bv}}}}{{{x_0}re}})\frac{{{\rm d}{x_0}}}{{{\rm d}\tau }}\text{，}$ (14)

 $\begin{array}{l}{h_{bv}} = \frac{1}{2}\left( {h' + {x_0}h'' + (1 - {x_0})h'} \right)\text{，}\\[5pt] \displaystyle \frac{{{\rm d}{h_{bv}}}}{{{\rm d}\tau }} = \frac{{{\rm d}h'}}{{{\rm d}\tau }} + \frac{{{x_0}}}{2}\left( {\frac{{{\rm d}h''}}{{{\rm d}\tau }} - \frac{{{\rm d}h'}}{{{\rm d}\tau }}} \right) + \frac{{h'' - h'}}{2}\frac{{{\rm d}{x_0}}}{{{\rm d}\tau }}\text{。}\end{array}$ (15)

 $\begin{split}\\[-14pt]& \displaystyle \left( {{\rho _{fwv}} + \frac{{1 - {x_0}}}{{{x_0}}}\rho ''} \right){F_{fwv}}\frac{{{\rm d}L}}{{{\rm d}\tau }} - \frac{{1 - {x_0}}}{{{x_0}}} \cdot {V_{SGS}} \cdot \\& \quad\quad\quad \displaystyle \frac{{{\rm d}\rho ''}}{{{\rm d}{p_s}}} \cdot \frac{{{\rm d}{p_s}}}{{{\rm d}\tau }} = {G_{fw}} + \frac{{1 - {x_0}}}{{2{x_0}}}{G_s} - {G_{wd}}\text{，}\\& \displaystyle \left( {{V_{bv}}(\frac{{re{\rho _{bv}} - \rho '}}{{re\rho ''}}) + \frac{{{V_{SGS}}}}{{{x_0}}}} \right) \cdot \frac{{{\rm d}\rho ''}}{{{\rm d}{p_s}}} \cdot \frac{{{\rm d}{p_s}}}{{{\rm d}\tau }} - \frac{{{F_{fwv}}\rho ''}}{{{x_0}}} \times \\ & \quad\quad \displaystyle \frac{{{\rm d}L}} {{{\rm d}\tau }}+ {V_{bv}}(\frac{{\rho ' - re{\rho _{bv}}}}{{{x_0}re}})\frac{{{\rm d}{x_0}}}{{{\rm d}\tau }} = {G_{wd}} - \frac{1}{{2{x_0}}}{G_s}\text{。}\end{split}$ (16)
 $\begin{split}\\[-12pt]\displaystyle {F\!_{fwv}}& \left( {{\rho _{fwv}} \cdot {h_{fwv}} \!+\! \frac{{1 \!-\! {x_0}}}{{{x_0}}}\rho ''h'} \right)\frac{{{\rm d}L}}{{{\rm d}\tau }} \!\!-\! \frac{{1 - {x_0}}}{{{x_0}}}{V_{SGS}}\\& \displaystyle h'\frac{{{\rm d}\rho ''}}{{{\rm d}{p_s}}} \cdot \frac{{\rm{d}{p_s}}}{{{\rm d}\tau }} + {\rho _{fwv}} \cdot {F_{fwv}}\left( {L - {L_{wd}}} \right)\frac{{{\rm d}{h_{fwv}}}}{{{\rm d}\tau }} = \\& \displaystyle {G_{fwv}}{h_{fwv}} + \frac{{1 - {x_0}}}{{2{x_0}}}{G_s}h' - {G_{wd}}{h_{fwv}}\\& \displaystyle {M_{wd}}\frac{{{\rm d}{h_{wd0}}}}{{{\rm d}\tau }} = {G_{wd}}\left( {{h_{fwv}} - {h_{wd0}}} \right)\text{。}\end{split}$ (17)
 $\begin{split}& \left\{ \begin{array}{l}\displaystyle\!\! {\!\!V_{bv}}{\rho _{bv}}\left[ {\frac{{{\rm d}h'}}{{{\rm d}{p_s}}}\!\!+\!\! \frac{{{x_0}}}{2}\left( {\frac{{{\rm d}h''}}{{{\rm d}{p_s}}}\! -\! \frac{{{\rm d}h'}}{{{\rm d}{p_s}}}} \right)}\! \right] \!+\! \frac{1}{2}{l_{ph}}{F_r}{\rho _{ph}}\frac{{{\rm d}h'}}{{{\rm d}{p_s}}}\!\!\\\displaystyle +\left[ {{V_{bv}}{h_{bv}}(\frac{{re{\rho _{bv}} - \rho '}}{{re\rho ''}}) + \frac{{{V_{SGS}}}}{{{x_0}}}{h_{bvo}}} \right] \cdot \frac{{{\rm d}\rho ''}}{{{\rm d}{p_s}}}\end{array} \right\} \cdot \\& \quad\quad\displaystyle \frac{{{\rm d}{p_s}}}{{{\rm d}\tau }} - \frac{{\rho ''{F_{fwv}}}}{{{x_0}}}{h_{bvo}}\frac{{{\rm d}L}}{{{\rm d}\tau }} + \frac{1}{2}{L_{ph}}{F_r}{\rho _{ph}}\frac{{{\rm d}{h_{wdo}}}}{{{\rm d}\tau }} + \\& \quad\quad \displaystyle {V_{bv}}\left[ {{h_{bv}}(\frac{{\rho ' - re{\rho _{bv}}}}{{{x_0}re}}) + \frac{1}{2}{\rho _{bv}}\left( {h'' - h'} \right)} \right]\frac{{{\rm d}{x_0}}}{{{\rm d}\tau }} = \\& \quad\quad \displaystyle {G_{wd}}{h_{wdo}} - \frac{1}{{2{x_0}}}{G_s}{h_{bvo}} + Q\text{。}\end{split}\!\!\!\!$ (18)

 $Nu = A\mathop {Pr}\limits_f^{{n_1}} P_e^{{n_2}}K_p^{{n_3}}K_t^{{n_4}}\text{，}$ (19)

 \begin{aligned}& \displaystyle Nu = \frac{\alpha }{{{\lambda _f}}}\sqrt {\frac{\sigma }{{g\left( {{\rho _f} - {\rho _g}} \right)}}} \text{，}\\& \displaystyle {P_e} = \frac{q}{{{h_{fg}}{\rho _g}{\alpha _f}}}\sqrt {\frac{\sigma }{{g\left( {{\rho _f} - {\rho _g}} \right)}}} \text{，}\\& \displaystyle {K_p} = \frac{p}{{\sqrt {\sigma \rho \left( {{\rho _f} - {\rho _g}} \right)} }}\text{，}\\& \displaystyle {K_t} = \frac{{{{\left( {{h_{fg}}{\rho _g}} \right)}^2}}}{{{\rho _f}{c_{p,f}}{T_s}\sqrt {\sigma \rho \left( {{\rho _f} - {\rho _g}} \right)} }}\text{。}\end{aligned} (20)

3.2 模型计算

 $\begin{array}{l}X = ({T_{sgci}},{T_{sgc1}},{T_{sgm1}},{T_{sgcmo}},{T_{sgc2}},\\[5pt]{T_{sgm2}},{T_{sgco}},{p_s},L,{x_0},{h_{fwv}},{h_{wdo}}{)^{\rm{T}}}\text{，}\\[5pt]\displaystyle \frac{{{\rm d}X}}{{{\rm d}\tau }} = (\frac{{{\rm d}{T_{sgci}}}}{{{\rm d}\tau }},\frac{{{\rm d}{T_{sgc1}}}}{{{\rm d}\tau }},\frac{{{\rm d}{T_{sgm1}}}}{{{\rm d}\tau }},\frac{{{\rm d}{T_{sgcmo}}}}{{{\rm d}\tau }},\frac{{{\rm d}{T_{sgc2}}}}{{{\rm d}\tau }},\\[10pt]\displaystyle \frac{{{\rm d}{T_{sgm2}}}}{{{\rm d}\tau }},\frac{{{\rm d}{T_{sgco}}}}{{{\rm d}\tau }},\frac{{{\rm d}{p_s}}}{{{\rm d}\tau }},\frac{{{\rm d}L}}{{{\rm d}\tau }},\frac{{{\rm d}{x_0}}}{{{\rm d}\tau }},\frac{{{\rm d}{h_{fwv}}}}{{{\rm d}\tau }},\frac{{{\rm d}{h_{wdo}}}}{{{\rm d}\tau }}{)^{{\rm d}}}\text{，}\end{array}$ (21)

 $A = \left[ {\frac{{\begin{array}{*{20}{l}}{{E_{11}}} & 0 & 0 & 0 & 0 & 0 & 0\\0 & {{E_{22}}} & 0 & 0 & 0 & 0 & 0\\0 & 0 & {{E_{33}}} & 0 & 0 & 0 & 0\\0 & 0 & 0 & {{E_{44}}} & 0 & 0 & 0\\0 & 0 & 0 & 0 & {{E_{55}}} & 0 & 0\\0 & 0 & 0 & 0 & 0 & {{E_{66}}} & 0\\0 & 0 & 0 & 0 & 0 & 0 & {{E_{77}}}\end{array}}}{{\begin{array}{*{20}{l}}0 & \: \: 0 & \: \: 0 & \: \: 0 & \: \: 0 & \: \: 0 & \: \: 0 & \\0 & \: \: 0 & \: \: 0 & \: \: 0 & \: \: 0 & \: \: 0 & \: \: 0 & \\0 & \: \: 0 & \: \: 0 & \: \: 0 & \: \: 0 & \: \: 0 & \: \: 0 & \\0 & \: \: 0 & \: \: 0 & \: \: 0 & \: \: 0 & \: \: 0 & \: \: 0 & \\0 & \: \: 0 & \: \: 0 & \: \: 0 & \: \: 0 & \: \: 0 & \: \: 0 & \end{array}}}\left| {\frac{{\begin{array}{*{20}{l}}0 & \: \: 0 & \: \: 0 & \: \: 0 & \: \: 0 & \: \: \\0 & \: \: 0 & \: \: 0 & \: \: 0 & \: \: 0 & \\0 & \: \: 0 & \: \: 0 & \: \: 0 & \: \: 0 & \\0 & \: \: 0 & \: \: 0 & \: \: 0 & \: \: 0 & \\0 & \: \: 0 & \: \: 0 & \: \: 0 & \: \: 0 & \\0 & \: \: 0 & \: \: 0 & \: \: 0 & \: \: 0 & \\0 & \: \: 0 & \: \: 0 & \: \: 0 & \: \: 0\end{array}}}{{\begin{array}{*{20}{l}}{{C_{11}}} & {{C_{12}}} & 0 & 0 & 0\\{{C_{21}}} & {{C_{22}}} & {{C_{23}}} & 0 & 0\\{{C_{31}}} & {{C_{32}}} & 0 & {{C_{34}}} & 0\\0 & 0 & 0 & 0 & {{C_{45}}}\\{{C_{51}}} & {{C_{52}}} & {{C_{53}}} & 0 & {{C_{55}}} \text{，}\end{array}}}} \right.} \right]\text{。}$ (22)

 $\begin{array}{l}\! {E_{11}}\!\! = \!\!{(MC)_{sgci}}, {E_{22}} \!\!=\!\! {(MC)_{sgc1}}, {E_{33}} \!\!=\!\! {(MC)_{sgm1}}\text{，}\!\!\\[5pt]\! {E_{44}} \!\!=\!\! {(MC)_{sgcmo}}\text{，}\!\!\!\!\!{E_{55}}\!\! =\!\! {(MC)_{sgc2}}\text{，}\!\!\!\!\!\!{E_{66}}\!\! =\! {(MC)_{sgm2}}\text{，}\\[5pt]\! {E_{77}} = {(MC)_{sgco}},\end{array}$ (23)
 $\begin{split}\\[-12pt]& \displaystyle{C_{11}} = - \frac{{1 - {x_0}}}{{{x_0}}} \cdot {V_{SGS}} \cdot \frac{{\rm{d}\rho ''}}{{\rm{d}{p_s}}}\text{，}\\[-1pt]& \displaystyle{C_{12}} = {K_{z12}} = \left( {{\rho _{fwv}} + \frac{{1 - {x_0}}}{{{x_0}}}\rho ''} \right){F_{fwv}}\text{，}\\[-1pt]& \displaystyle{C_{21}} = \left( {{V_{bv}}(\frac{{re{\rho _{bv}} - \rho '}}{{re\rho ''}}) + \frac{{{V_{SGS}}}}{{{x_0}}}} \right) \cdot \frac{{\rm{d}\rho ''}}{{\rm{d}{p_s}}} {C_{22}} = - \frac{{{F_{fwv}}\rho ''}}{{{x_0}}}\text{，}\\[-1pt]& \displaystyle {C_{23}} = {V_{bv}}(\frac{{\rho ' - re{\rho _{bv}}}}{{{x_0}re}}), {C_{31}} = - \frac{{1 - {x_0}}}{{{x_0}}}{V_{SGS}}h'\frac{{\rm{d}\rho ''}}{{\rm{d}{p_s}}}\text{，}\\[-1pt]& \displaystyle {C_{32}} = {F_{fwv}}\left( {{\rho _{fwv}} \cdot {h_{fwv}} + \frac{{1 - {x_0}}}{{{x_0}}}\rho ''h'} \right)\text{，}\\[-1pt]& \displaystyle {C_{34}} = {\rho _{fwv}} \cdot {F_{fwv}}\left( {L - {L_{wd}}} \right), {C_{45}} = {M_{wd}}\text{，}\qquad\qquad\quad\:\:(24)\end{split}$ (24)
 \begin{aligned}& {C_{51}}\!\! =\!\! \left\{ \begin{array}{l}\displaystyle {V_{bv}}{\rho _{bv}}\left [ {\frac{{{\rm d}h'}}{{{\rm d}{p_s}}} + \frac{{{x_0}}}{2}\left( {\frac{{{\rm d}h''}}{{{\rm d}{p_s}}} - \frac{{{\rm d}h'}}{{{\rm d}{p_s}}}} \right)} \right]\!\!\\ + \left[ \begin{array}{l}\displaystyle {V_{bv}}{h_{bv}}(\frac{{re{\rho _{bv}} - \rho '}}{{re\rho ''}})\!\!\\ \displaystyle + \frac{{{V_{SGS}}}}{{{x_0}}}{h_{bvo}}\end{array} \right] \displaystyle \cdot \frac{{{\rm d}\rho ''}}{{{\rm d}{p_s}}}\!\!\\ \displaystyle + \frac{1}{2}{l_{ph}}{F_r}{\rho _{ph}}\frac{{{\rm d}h'}}{{{\rm d}{p_s}}}\end{array} \right\}\displaystyle \cdot \frac{{{\rm d}{p_s}}}{{{\rm d}\tau }}\text{，}\\& \displaystyle {C_{52}} = - \frac{{\rho ''{F_{fwv}}}}{{{x_0}}}{h_{bvo}}\text{，} \displaystyle {C_{55}} = \frac{1}{2}{L_{ph}}{F_r}{\rho _{ph}}\text{，}\\& \displaystyle {C_{53}} = {V_{bv}}\left[ {{h_{bv}}(\frac{{\rho ' - re{\rho _{bv}}}}{{{x_0}re}}) + \frac{1}{2}{\rho _{bv}}\left( {h'' - h'} \right)} \right]\text{，}\quad\qquad(25)\end{aligned} (25)

B 为时变矩阵，包含参变量的非线性项。 ${B} = \left[ {\begin{array}{*{20}{c}} {{{B}_1}}\\ {{{B}_2}} \end{array}} \right]$ ，其中：

 \begin{aligned}& {B_1} \!=\! \left[ \!\!{\begin{array}{*{20}{c}}\displaystyle {\frac{1}{2}{G_{sgc}}{C_{sgc}}({T_{sgci}} - {T_{sgc1}})}\\[8pt] \displaystyle \!\!\!{\frac{1}{2}{G_{sgc}}{C_{sgc}}({T_{sgci}} - {T_{sgc1}}) - {{(UF)}_{sgc1}}({T_{sgc1}} - {T_{sgm1}})}\\[8pt] \displaystyle \begin{array}{l}\displaystyle {(MC)_{sgm1}}\frac{{d{T_{sgm1}}}}{{{\rm d}\tau }} = {(UF)_{sgc1}}({T_{sgc1}} - {T_{sgm1}}) - \\[8pt]\displaystyle {(UF)_{sgp1}}({T_{sgm1}} - {T_{sgpa}}) - {(UF)_{sgs1}}({T_{sgm1}} - {T_s})\end{array}\\[8pt]\displaystyle {\frac{1}{2}{G_{sgc}}{C_{sgc}}({T_{sgc1o}} - {T_{sgcmo}})}\\[8pt]\displaystyle {\frac{1}{2}{G_{sgc}}{C_{sgc}}({T_{sgcmo}} - {T_{sgc2}}) - {{(UF)}_{sgc2}}({T_{sgc2}} - {T_{sgm2}})}\\[8pt]\begin{array}{l}\displaystyle {(UF)_{sgc2}}({T_{sgc2}} - {T_{sgm2}}) - {(UF)_{sgp2}}({T_{sgm2}} - {T_{sgpa}})\\[8pt]\displaystyle - {(UF)_{sgs2}}({T_{sgm2}} - {T_s})\end{array}\\[8pt]\displaystyle \!\!{\frac{1}{2}{G_{sgc}}{C_{sgc}}({T_{sgc2o}} - {T_{sgco}})}\end{array}}\!\! \right]\text{，}\\[8pt]& {B_2} = \left[ \displaystyle {\begin{array}{*{20}{c}}\displaystyle {{G_{fw}} + \frac{{1 - {x_0}}}{{2{x_0}}}{G_s} - {G_{wd}}}\\[8pt]\displaystyle {{G_{wd}} - \frac{1}{{2{x_0}}}{G_s}}\\[8pt]\displaystyle {{G_{fwv}}{h_{fwv}} + \frac{{1 - {x_0}}}{{2{x_0}}}{G_s}h' - {G_{wd}}{h_{fwv}}}\\[8pt]\displaystyle {{G_{wd}}\left( {{h_{fwv}} - {h_{wd0}}} \right)}\\[8pt]\displaystyle {{G_{wd}}{h_{wdo}} - \frac{1}{{2{x_0}}}{G_s}{h_{bvo}} + Q}\end{array}} \right]\text{。}\quad\quad\quad\quad\quad(26) \end{aligned} (26)

4 仿真试验

为了验证立式自然循环蒸汽发生器模型的正确性，对该模型进行仿真验证试验。蒸汽发生器在稳态时对负荷加入 10% 扰动。蒸汽发生器水位不采用自动控制，对蒸汽发生器水位、蒸汽比焓、一回路冷却剂温度、给水比焓、饱和蒸汽干度等变量进行仿真，结果如图 3图 7 所示。随着给水流量的增加蒸汽发生器水位逐渐增加、一次侧温度随之降低，由于温度的变化使得蒸汽与给水的比焓降低。饱和蒸汽干度上升。

 图 3 蒸汽发生器水位 Fig. 3 Water level of steam generator

 图 4 蒸汽发生器蒸汽比焓 Fig. 4 Steam enthalpy of steam generator

 图 5 一回路冷却剂温度 Fig. 5 Primary system coolant temperatures

 图 6 蒸汽发生器给水比焓 Fig. 6 Feedwater enthalpy of steam generator

 图 7 蒸汽发生器饱和蒸汽干度 Fig. 7 Saturated steam dryness of steam generator
5 结　语

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