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ORIGINAL RESEARCH
published: 26 November 2018
doi: 10.3389/fenrg.2018.00127
Frontiers in Energy Research | www.frontiersin.org 1November 2018 | Volume 6 | Article 127
Edited by:
Jun Wang,
University of Wisconsin-Madison,
United States
Reviewed by:
Yacine Addad,
Khalifa University,
United Arab Emirates
Claudio Tenreiro,
University of Talca, Chile
Hui Cheng,
City University of Hong Kong,
Hong Kong
*Correspondence:
Yuan Yuan
yuanyuan5@mail.sysu.edu.cn
Specialty section:
This article was submitted to
Nuclear Energy,
a section of the journal
Frontiers in Energy Research
Received: 08 September 2018
Accepted: 07 November 2018
Published: 26 November 2018
Citation:
Yuan Y, Shan J, Wang L, Wang D and
Zhang X (2018) Startup Thermal
Analysis of a Supercritical-Pressure
Light Water-Cooled Reactor
CSR1000. Front. Energy Res. 6:127.
doi: 10.3389/fenrg.2018.00127
Startup Thermal Analysis of a
Supercritical-Pressure Light
Water-Cooled Reactor CSR1000
Yuan Yuan1
*, Jianqiang Shan 2, Li Wang 1, Dongqing Wang 1and Xiaoying Zhang 1
1Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-sen University, Zhuhai, China, 2School of Nuclear
Science and Technology, Xi’an Jiaotong University, Xi’an, China
Supercritical-pressure light water-cooled reactors (SCWR) are the only water cooled
reactor types in Generation IV nuclear energy systems. Startup systems, and their
associated startup characteristic analyses, are important components of the SCWR
design. To analyze the entire startup system, we propose a wall heat transfer model
in a paper, based on the results from a supercritical transient analysis code named
SCTRAN developed by Xi’an Jiao tong University. In this work, we propose a new
heat transfer mode selection process. Additionally, the most appropriate heat transfer
coefficient selection method is chosen from existing state-of-the-art methods. Within the
model development section of the work, we solve the problem of discontinuous heat
transfer coefficients in the logic transformation step. When the pressure is greater than
19 Mpa, a look-up table method is used to obtain the heat transfer coefficients with the
best prediction accuracy across the critical region. Then, we describe a control strategy
for the startup process that includes a description of the control objects for coolant flow
rate, heat-exchange outlet temperature, system pressure, core thermal power, steam
drum water-level and the once-through direct cycle loop inlet temperature. Different
control schemes are set-up according to different control objectives of the startup
phases. Based on CSR1000 reactor, an analytical model, which includes a circulation
loop and once-through direct cycle loop is established, and four startup processes, with
control systems, are proposed. The calculation results show that the thermal parameters
of the circulation loop and the once-through direct cycle meets all expectations. The
maximum cladding surface temperature remains below the limit temperature of 650◦C.
The feasibility of the startup scheme and the security of the startup process are verified.
Keywords: Supercritical Water Reactor, SCTRAN, heat transfer coefficient, control system, startup
INTRODUCTION
Supercritical Water Reactor (SCWR) is the only water cooled reactor type in Generation IV
nuclear energy systems. SCWR is an innovative system which is aimed for high thermal efficiency
and economy. SCWR works at a high pressure, 25 MPa, with a core outlet temperature up to
500◦C. Moreover, Canada’s pressure vessel-type reactor outlet temperature even up to 625◦C.
So the cladding temperature can reach 650◦C, far beyond the current pressurized water reactor.
Supercritical water properties rapid changes at the trans-critical region, and neutron moderating
ability would be weakened. The University of Tokyo was the first to study the startup procedure of
Yuan et al. Startup Thermal Analysis of CSR1000
FIGURE 3 | Relationship between the heat transfer coefficient, enthalpy and
pressure from a low-pressure to high-pressure region.
SCWR. Since the startup procedure involves the process of
cooling a reactor from a subcritical to supercritical state,
analyzing SCWR-based startup thermo-hydraulic characteristics
becomes an important consideration (Oka and Koshizuka, 2001).
There exist two main startup strategies for SCWRs. One is
constant pressure startup, and the other one is sliding pressure
startup (Yi et al., 2004). During constant pressure startup
procedure, the reactor starts at a supercritical pressure. This
procedure is that there is no need to concern about critical heat
flux or two-phase instability in two-phase flow. The disadvantage
is that large pumping power is needed to make the system
operate. During sliding pressure startup procedure, the reactor
starts at a subcritical pressure. Using the traditional variable
pressure startup system, it must be assured that the maximum
cladding surface temperature is below the criterion and flow
instability is avoided during startup at subcritical pressures. To
avoid the above issues, Ishiwatari et al proposed e recirculation
system, instead of a bypass system (Oka, 2013). The recirculation
system was separated from the main line of once-through direct-
cycle. Compared with the constant pressure startup procedure,
the advantage of the sliding pressure startup system is that
the pumping power consumption is decreased, which results
in a higher efficiency during low load operations. Therefore,
the recirculation system startup procedure is applied in this
paper. The past investigation of startup was carried out by
several researchers. Yi et al analyzed detailed thermal behavior
for a high-temperature supercritical-pressure light water-cooled
thermal reactor Super LWR (SCLWR-H) (Yi et al., 2004) and
a Super FR with downward-upward two-pass coolant flow (Cai
et al., 2009). A sliding pressure startup scheme of recirculation
system for SCWRs was proposed to provide a pressurization
system which was raised independently from the power (Yamada
and Ishiwatari, 2009). With the modified ATHLET-SC code,
which realizes the simulation of trans-critical transients using
two-phase model the thermal-hydraulic dynamic behavior of the
mixed SCWR core during the startup process is simulated (Fu
et al., 2011). It can be concluded that the focus of previous work
are mainly on the thermal hydraulics behavior of SCWR during
startup to validate the limiting criteria, but there are few work on
the control system design to achieve startup procedure.
The SCWR coolant loop is a once-through direct cycle that
is very sensitive to disturbances. The startup procedure needs
to be operated by the control system. Yuki et al. designed
a control system of the SCLWR-H under steady state. The
turbine inlet pressure is controlled by the turbine control valves.
The main steam temperature is controlled by the feedwater
flow rate. The core power is controlled by the control rods
(Ishiwatari et al., 2003). Wang et al. sing FORTRAN program
to make code, when perturbation happens such as pressure set-
point changes, feed-water temperature drop, reactor parameters
changes with time were researched at the control rod, steam
turbine control valves and there actor coolant pumps as the
plant control system (Wang et al., 2012). To analyze the control
characteristics of SCWRs, Ishiwatari et al. (2003); (Ishwatari
et al., 2010) optimized the SCR control parameters, modified
the feed water control system of Super LWRs and improved
the delay problem of the temperature control system. Sun and
Jiang (2012) studied the control system of Canadian SCWRs
and obtained the control system linearization equations via
the solution of a complete nonlinear dynamic equations. Dong
et al. (2016) proposed a Moving Boundary Method to control
the steam temperature. To meet the startup requirements of
the entire system, and based on the three typical PID control
systems designed by Nakatsuka et al. (1997), control systems are
proposed that have controls for coolant flow rate, heat exchanger
outlet temperature, system pressure, core thermal power, steam
drum water level and the once-through direct cycle loop inlet
temperature. By adjusting the control parameters, the startup
procedure of the SCWR can be operated according to the starting
curve.
The SCWR startup procedure must ensure that the Maximum
fuel cladding surface temperature (MCST) does not exceed
the limit 650◦C. Accordingly, the heat transfer coefficient
value is very important for the calculation of the cladding
temperature. A complete set of heat transfer coefficients is
needed to meet the wall heat transfer requirements for a smooth
transition between the subcritical and supercritical heat transfer
coefficients. Ishiwatari et al. (2005) used the “oka-koshizuka
correlation” (or “Kitoh correlation”) to calculate the heat transfer
deterioration under supercritical region of SCWR. oka-koshizuka
correlation was developed on the basis of the typical single-
phase turbulence model, which is in good agreement with
the experimental data of Yamagata (Yamagata et al., 1972;
Koshizuka et al., 1995). However, the calculated values of heat
transfer coefficient of oka-koshizuka correlation is larger than
Watts correlation and Bishop correlation in the deteriorating
area (Ishiwatari et al., 2005). SPRAT-DOWN code which
is developed by Ishiwatrai adopts oka-koshizuka correlation
in rated, transient and accident conditions. Thermophysical
properties and transport properties of coolant change greatly
during subcritical pressure to supercritical pressure under
SCWR startup procedure. It needs a wall heat transfer model
with wide-scope parameter which can satisfy the heat transfer
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Yuan et al. Startup Thermal Analysis of CSR1000
coefficient smooth transition requirements from subcritical
and supercritical region. By summarizing a large number of
supercritical regional databases and literature, Zahlan et al.
(2015) proposed a look-up table to calculate trans-critical
heat transfer in water-cooled tubes. The SCTRAN code is
chosen to analyze the SCWR startup control characteristics.
This choice is made because SCTRAN (Wu et al., 2013) can
smoothly calculate the physical properties of water in the cross-
critical region. The wall heat transfer model of the existing
SCTRAN code has a heat transfer coefficient that changes
drastically near the critical point and the heat transfer coefficient
jump in supercritical regions. The paper puts forward the
new wall heat transfer model. The new wall heat transfer
model proposes a new logic for the selection of the heat
transfer modes and the most appropriate model from the
literature is chosen to determine the heat transfer coefficient.
Moreover, the discontinuous heat transfer coefficients in the
logic transformation are removed. The purpose of this paper is
to design a control system for the SCWR’s circulation sliding
pressure startup process based on an improved SCTRAN code.
This work is the foundation of a complete and reliable startup
analysis system.
FIGURE 4 | Relationship between the heat transfer coefficient, enthalpy and pressure in a high-pressure region.
TABLE 1 | The heat transfer correlations used in SCTRAN.
Application SCTRAN (Zahlan et al., 2015) Wall heat transfer model with a wide-scope
parameter (Gou et al., 2012)
Single-phase
liquid
Collier correlation
Dittus-Boelter correlation
Sellars correlation
Dittus-Boelter correlation
Nucleate boiling Thom correlation Chen correlation
Vaporization Schrock-Grossman correlation
Transition boiling Mcdonongh, Milich and King correlation Chen-Sundaram-Ozkaynak correlation
Weisman correlation
Film boiling Groeneveld correlation
Dougall-Rohsenow correlation
Berenson correlation
Bromley correlation
Groeneveld-Leung PDO look-up table Bromely
correlation
Clare-Fairbairn correlation
Single phase vapor Collier correlation
Dittus-Boelter correlation
Lahey correlation
Condensation Collier correlation Nusselt correlation
Chato correlation
Shah correlation
Supercritical water Jackson-Hall correlation Look-up table for trans-critical region
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Yuan et al. Startup Thermal Analysis of CSR1000
IMPROVEMENT AND VERIFICATION
SCTRAN
SCTRAN was developed in Xi′an Jiao Tong University. It is
a one-dimensional safety analysis code for SCWRs (Wu et al.,
2013). SCTRAN code has been verified by relap5 and other codes.
Typical accidents such as LOCA, LOFA and so on of CANDU-
SCWR, CGNPC-SCWR and CSR1000 are calculated (Gou et al.,
2012). A homogenous equilibrium mixture model with an
optional phasic slip formulation was applied in code SCTRAN.
TABLE 2 | Sliding pressure startup procedure.
Pressure/MPa Pre-start state I. The raising of feed water
temperature
II. Pressurization III. Switching from the
recirculation line to the
once-through line
IV. Power-raising
Pressure/MPa 0.1 0.1→6.5 6.5→25.0 25.0 25.0
Power/% 0.1 0.1→0.1 0.1→9.0 9.0→25.1 25.1→100
Outlet temperature/◦C 80 80→280 280→374.5 375→500 500
inlet temperature/◦C 80 80→280 280 280 280
Flow rate/% 25 25 25 25 25→100
TABLE 3 | SCWR control system.
Control system Control method Equation
Heat exchanger outlet temperature control The temperature is kept constant by regulating the
secondary side flow of the heat exchanger or the
condenser.
u(s)
1T(s)=hKP+KI
s×1+T1s
(1+T2s)Tset i·KT
Power control The change of thermal power is sensitive to insertion
reactivity.
vρ=
vρmaxe/b(|e|<b)
vρmax (|e|≥b),ρ=
t
R
0
vρdt
Pressure control The pressure is kept constant by regulating the opening
of the control valves
1V(s)
1P(s)=K1×1+T1s
1+T2s+K2×1
s
Steam drum water level control The water level is kept constant by regulating the flow
rate discharge from the steam drum.
1m(s)
1H(s)=K1×1+T1s
1+T2s+K2×1
s·1
ρmix ·kppb2−4ac
Once-through direct-cycle loop
inlet-temperature control
The extraction steam flow rate is sensitive to new steam
entering the heater.
1V(s)
1T(s)=KP+KI
s×1+T1s
(1+T2s)Tset
Coolant flow rate control The coolant flow rate is kept constant by regulating the
opening of the control valves.
1V(s)
1m(s)=K1×1+T1s
1+T2s+K2×1
s
FIGURE 5 | Control system strategies for SCWR sliding pressure startups with circulation loop.
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Yuan et al. Startup Thermal Analysis of CSR1000
TABLE 4 | Experimental conditions.
Experiment Pressure/MPa Mass flow rate/
kg·m−2·s−1
Average heat flux
/W·m−2
Inlet sub-cooling
/kJ·kg−1
Bailey-A 1257 18.1 4150.1 1,889,600 370.3
Bailey-A 1272 18.0 2766.7 1,072,561 227.7
Bailey-A 1305 18.1 2237.8 712,938 75.9
Bailey-A 1313 17.9 2224.3 971,614 269.4
Bailey-A 1332 18.0 4177. 2 1,580,450 231.0
Bailey-A 1341 18.1 3621.1 1,403,793 145.1
Bailey-A 1342 17.9 3621.1 1,406,950 80.9
Subbotin 1.001 4.9 350 321,646 −0.08
FIGURE 6 | Variation of the Wall Temperature in Bailey Experiment.
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Yuan et al. Startup Thermal Analysis of CSR1000
TABLE 5 | The disturbance conditions of control system.
Control system Control method Disturbance Control goal
Heat exchanger outlet
temperature control
Regulating secondary side flowrate of
heat exchanger
The core power increases linearly
at 1% per second at 10 s
Heat exchanger outlet
temperature
System pressure control Regulating the opening of the control
valves.
Pressure increases linearly by
10% at 10 s
System pressure
Thermal power control Regulating withdrawn and insertion of
control rods
Thermal power increases linearly
by 10% at 10 s
Thermal power
Steam drum water level control Charging and letdown of steam drum Coolant flow increased linearly
by 10% at 10 s
steam drum water level
Coolant flow rate control Regulating the opening of the control
valves.
Coolant flow increases linearly by
10% at 10 s
Coolant flow rate
Once-through direct cycle loop
inlet temperature control
Regulating the opening of the control
valves.
Thermal power increases linearly
by 10% at 10 s
Inlet temperature control
FIGURE 7 | Variation of the Wall Temperature in Subbotin Experiment.
The homogenous model made the following assumptions: (1)
the velocities of gas and liquid were the same; (2) gas and liquid
were in thermodynamic equilibrium. Here the basic equations of
homogenous equilibrium mixture model are summarized.
Mass conservation equation
∂
∂tρA+∂
∂zW=0 (1)
where:
ρ=αgρg+αlρl(2)
W=Wg+Wl=αgρgvg+αlρlvl(3)
Momentum conservation equation
∂
∂tW+∂
∂zWv = −A∂p
∂z−2Aρv|v|
Dh
ftp +ρAgz(4)
Energy conservation equation
d
dt U= − 1
2
L
A
d
dt W2
ρ
−X
jWghg+Wlhl+1
2Wgvgvg+Wlvlvl
+Wgz−zj+Q(5)
In numerical calculation, SCTRAN code adopts the staggered
grid in fluid space discretization and adopts the control volume
balance method to discrete fluid basic equations.
The SCTRAN module call diagram is shown in Figure 1.
SCTRAN code mainly includes the following several modules:
input module, output module, conservation equation module,
pressure calculation module, thermal power calculation
module, structure temperature calculation module, heat transfer
coefficient and heat flux calculation module, subcritical region
and supercritical region fluid physical parameters calculation
module. The calculation flow chart of SCTRAN is shown in
Figure 2. The iterative calculation mainly determines judges
whether the change speed of internal energy 1U/U is convergent
and whether it reaches the end time of calculation.
Wall Heat Transfer Model With a
Wide-Scope Parameter
The wall heat transfer model mainly includes three parts: heat
transfer modes, selection procedures of heat transfer modes
(logic) and heat transfer correlations. To analyze the wall heat
transfer characteristics of the SCTRAN code, a simulation of
a pipe was made. The pipe fluid inlet temperature is 100◦C,
the outlet temperature is 500◦C, the fixed flow rate per unit
area is 500 kg·m−2·s−1, and the pipe is uniformly heated along
the axial direction; the pressure varies from 1 to 28 MPa. The
curves of the heat transfer coefficient are associated with pressure
and enthalpy; they are shown in Figures 3,4. There are some
problems with the SCTRAN calculations of the heat transfer
coefficient. They include: (1) SCTRAN adopts Jackson heat
transfer correlation for supercritical regions, which leads to a
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Yuan et al. Startup Thermal Analysis of CSR1000
FIGURE 8 | Control capability of control systems under disturbance conditions.
large error. (2) The wall heat transfer model is not comprehensive
for all modes. (3) The heat transfer coefficient drastically changes
near the critical point and the mode transition region. To solve
these problems, the project introduces a new wall heat transfer
model that can be calculated from the subcritical to supercritical
region. The model selects the appropriate heat transfer
correlation and a lookup table (Zahlan et al., 2015) to improve
the accuracy of the calculation (Table 1). In the sub-critical
region, since the heat transfer coefficient of the convection
term of the Chen correlation is calculated by using the DB
correlation for hmac, after the heat transfer mode is converted,
the DB relational expression can be smoothly transferred to
the Chen correlation. Then the values of qCHF and TCHF are
the results of the iterative calculation of the table and Chen
correlation, so the nucleate boiling correlation can be smoothly
transitioned to transition boiling. While the rest of the relations
are transformed by linear interpolation. In the supercritical
region, only the look-up table for trans-critical region
is used.
Control System Design
Per the SCWR startup sequence (Table 2), the startup procedure
is divided into four phases: raising of feed water temperature,
pressurization, switching from recirculation line to once-through
line and power-raising. The control of the SCWR circulation
startup system should be able to meet the control requirements
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Yuan et al. Startup Thermal Analysis of CSR1000
FIGURE 9 | Transient performance of the startup procedure. (A) Transient performance of thermal power and feed water flow rate. (B) Transient performance of the
core reactivity. (C) Transient performance of the steam drum water level and its average quality. (D) Transient performance of the coolant temperature and pressure.
(E) Transient performance of the maximum cladding surface temperature for SCWR. (F) Transient performance of core average quality. (G) Transient performance of
the first process flow rate. (H) Transient performance of the second process flow rate.
needed for the pressure, thermal power, temperature, steam
drum water level and coolant flow rate. Therefore, we designed
six different control systems for the SCWR startup procedure
(Table 3). The basic control methods and equations can be
introduced by reference (Nakatsuka et al., 1997; Ishiwatari et al.,
2003). Based on the HPLWR thermal cycle, SCWR circulation
loop, CSR1000 design parameters and the control method
proposed in this paper, a complete CSR1000 control system
(Figure 5) is designed.
Verification of the Wall Heat Transfer Model
Bailey experiment and Subbotin experiment (Wu et al., 2016)
were selected to validate the calculation accuracy of the wall heat
transfer model with wide-scope parameter. The inner diameter
and wall thickness of Bailey and Subbotin experiment are
12.7762 mm and 2.3368 mm, respectively. The heated length of
the test section of Bailey and Subbotin experiment are 3.048 and
6.000 m, respectively. The experimental conditions are shown
in Table 4. By comparing the wall temperature obtained by the
codes with the experiment data, we can verify the modified
model.
The CHF calculation correlation used in the new wall
heat transfer model is the Groeneveld CHF look-up table
developed in 2006 (Groeneveld et al., 2007). From the validation
results of Bailey experiment (Figure 6) and Subbotin experiment
(Figure 7), we can see that the modified model better predicted
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Yuan et al. Startup Thermal Analysis of CSR1000
the wall temperature during film boiling under all cases, and it got
the relatively good results of the locations where CHF occurred in
most cases. In the prediction of the CHF occurrence location, the
SCTRAN new calculation results were early, which was caused
by the inherent error of the CHF look-up table. The low heat
transfer coefficient value obtained from the look-up table leads
to a higher wall temperature and makes the CHF occurrence
location in advance.
Verification of the Control System
Based on the various disturbances, this part demonstrates
the steady ability of control system. The introduced linear
perturbations include main steam temperature, system pressure,
core power, coolant flow, and so on (Table 5).
When subjected to various disturbances, under the
control of the control system, each control system can effectively
controls the control target quickly and steadily (Figure 8). It
shows that the control system designed in this thesis is fast
and effective. Response of the main steam temperature control
system.
ANALYSIS OF RECIRCULATION SLIDING
PRESSURE STARTUP SYSTEM
Typical startup schemes use a sliding startup system that includes
a circulation loop for startup and a once-through direct loop
(Figure 5). The whole startup procedure needs to be completed
in approximately 61.59 h. The variation of thermodynamic
parameters is shown in Figure 9. During the startup procedure,
with the thermal power control system and the flow control
system controlling, the core power and the flow rate operates
according to the requirements (Figures 9A,B). The doppler
reactivity, void fraction reactivity and reactivity inserted by the
control rod can be seen in Figure 9B. At the beginning of the
fourth stage, the flow rate of the water rod in the second process
is negative, and the coolant is counter-current. At about 41.2 h,
the flow rate of the water rod in the second process becomes
positive, and the coolant flows normally. At this time, the power
and flow rate is about 59%.With the rise of the coolant flow,
the buoyancy resistance is not enough to resist the pressure
drop increase with the driving force, caused the second process
water rod flow rate from the larger negative value changes into
larger positive value. It makes the value of void fraction reactivity
dramatic changes in this place. The water level can be controlled,
up to a height of about 3 m (Figure 9C), via the steam drum
water level control system. The steam drum water level control
system is deactivated at 20 MPa (15.6 h). Under the control of
the once-through direct-cycle loop-inlet control system, the core-
inlet coolant temperature can be maintained at 280◦C. The outlet
coolant temperature gradually increases with time until the rated
operating temperature is 500◦C (Figure 9D). The MCST does not
exceed the limit temperature of 650◦C throughout the startup
procedure (Figure 9E). The lower plenum will not generate
steam during the entire startup procedure and the supercritical
steam occurs only in the lower plenum after the supercritical
pressure has been achieved. Thus, the coolant remains in a single-
phase state and there is no boiling crisis or flow instability
problem within the core (Figure 9F). Because the buoyancy is
greater than the driving force, during the lowering of the water
in the second process, the coolant reverses from the subcritical
region to the supercritical region (Figures 9G,H). The mass flow
rate greatly affects the surface temperature of the cladding and the
value of the reactivity feedback. The abrupt flow generally causes
avoid reactivity great changes (Figure 9A).
CONCLUSION
A new wall heat transfer model is developed for SCTRAN
applications to analyze the SCWR startup characteristics. In the
model, drastic changes to the heat transfer coefficient (calculated
by the SCTRAN) near the critical region is resolved and the heat
transfer coefficient from a subcritical to supercritical pressure is
forecast precisely and smoothly.
Because the thermo-physical properties and transport
properties of coolant change significantly from a subcritical to
supercritical pressure, a control system is required to adjust the
parameter changes during the startup procedure. Under the
control strategy of the startup procedure, the system pressure,
temperature, thermal power and flow rate can be regulated
according to the startup objectives. The calculation results show
that the thermal parameters of the circulation loop and the
once-through direct cycle meet the requirement and the MCST
remains below the limit temperature of 650◦C.
AUTHOR CONTRIBUTIONS
YY wrote the manuscript. JS guided this research. LW, DW, and
XZ critical revised the article.
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Conflict of Interest Statement: The authors declare that the research was
conducted in the absence of any commercial or financial relationships that could
be construed as a potential conflict of interest.
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Frontiers in Energy Research | www.frontiersin.org 11 November 2018 | Volume 6 | Article 127
Yuan et al. Startup Thermal Analysis of CSR1000
NOMENCLATURE
A: flow area/m2
e(t): main steam temperature deviation from set point, %
Dh: Hydraulic equivalent diameter, m
ftp: friction coefficient
g: gravitational acceleration, m·s–2
h: enthalpy, J·kg–1
K1: lead-lag coefficient
K2: integral coefficient
KP: proportional gain
KI: integral gain
L: length, m
T1: lead time, s
T2: lag time, s
Tmean: measured temperature by the thermometer, ◦C
Tset: main steam temperature set point, ◦C
Tstream: main steam real temperature, ◦C
t: time, t
U: internal energy, J·kg–1
u(t): feed water flow rate signal, kg/s
1V: valve opening relative to initial time
v: fluid velocity, m·s–1
W: flow rate, kg·s–1
z: distance, m
vρ: insertion reactivity speed, cent/s
vρmax: the maximum insertion reactivity speed, cent/s
ρmix: mixture density, kg/m3
Frontiers in Energy Research | www.frontiersin.org 12 November 2018 | Volume 6 | Article 127
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