THERMODYNAMIC CONSIDERATIONS FOR SCW NPP CYCLES
Pioro, I., Naidin, M. and Zirn*, U.
Faculty of Energy Systems and Nuclear Science,
University of Ontario Institute of Technology
2000 Simcoe Str. North, Oshawa, Ontario, L1H 7K4 Canada
E-mail: igor.pioro@uoit.ca and maria.naidin@mycampus.uoit.ca
*
Hitachi Power Systems America, Ltd., 645 Martinsville Road, Basking Ridge, NJ 07920 USA
E-mail: udo.zirn@hal.hitachi.com
ABSTRACT
Currently, there are a number of Generation IV SuperCritical Water-cooled nuclear Reactor (SCWR)
concepts under development worldwide. The main objectives for developing and utilizing SCWRs are: 1)
Increase gross thermal efficiency of current Nuclear Power Plants (NPPs) from 30 – 35% to approximately 45 –
50%, and 2) Decrease capital and operational costs and, in doing so, decrease electrical-energy costs.
SCW NPPs will have much higher operating parameters compared to current NPPs (i.e., steam pressures of
about 25 MPa and steam outlet temperatures up to 625°C). Additionally, SCWRs will have a simplified flow
circuit in which steam generators, steam dryers, steam separators, etc. will be eliminated. Furthermore, SCWRs
operating at higher temperatures can facilitate an economical co-generation of hydrogen through thermochemical cycles (particularly, the copper-chlorine cycle) or direct high-temperature electrolysis.
To decrease significantly the development costs of a SCW NPP, to increase its reliability, and to achieve
similar high thermal efficiencies as the advanced fossil steam cycles, it should be determined whether SCW
NPPs can be designed with a steam-cycle arrangement that closely matches that of mature SuperCritical (SC)
fossil-fired thermal power plants (including their SC-turbine technology). The state-of-the-art SC-steam cycles
at fossil-fired power plants are designed with a single-steam reheat and regenerative feedwater heating. Due to
that, they reach thermal steam-cycle efficiencies up to 54% (i.e., net plant efficiencies of up to 43% on a Higher
Heating Value (HHV) Basis).
This paper consists of three parts. The first part analyzes main parameters and performance in terms of
thermal efficiency of a SCW NPP concept based on a direct single-reheat regenerative cycle. The cycle is
comprised of: an SCWR, a SC turbine (consisting of one High-Pressure (HP) cylinder, one IntermediatePressure (IP) cylinder and two Low-Pressure (LP) cylinders), one deaerator, ten feedwater heaters, and pumps.
Since this option includes a “nuclear” steam-reheat stage, the SCWR is based on a pressure-tube design. A
thermal-performance simulation reveals that the overall thermal efficiency is approximately 50%. Previous
studies have shown that direct cycles, with no-reheat and single-reheat configurations are the best choice for the
SCWR concept. However, the single-reheat cycle requires a nuclear steam-reheat, thus increasing the
complexity of the reactor core design.
The second part analyzes the main parameters and performance in terms of thermal efficiency of a SCW
NPP based on a no-reheat, direct cycle with heat regeneration. When compared to the single-reheat cycle, the
no-reheat
configuration
has
a
more
simplified
design:
the Intermediate-Pressure
(IP) turbine section is eliminated and the exhaust from the High-Pressure (HP) turbine is directly routed to the
inlet of the Low-Pressure (LP) turbines. The cycle also consists of a condenser, nine feedwater heaters, a
topping de-superheater, associated pumps, and the nuclear source of energy, i.e., the SCWR. In general, the
major technical challenge associated with a SC no-reheat turbine is the high moisture content in the LP turbine
exhaust. A thermal-performance simulation reveals that the steam quality at the exhaust from the LP turbine is
approximately 81%. However, the moisture can be reduced by implementation of contoured channels in the
inner casing for draining water and moisture removal stages. The overall thermal efficiency of the cycle was
determined to be about 50% (assumptions are made to account for turbine and pump efficiency losses).
Furthermore, the third part presents important safety parameters such as bulk-fluid temperature, sheath
temperature and fuel-centerline temperature profiles along the heated bundle-string length, which were
calculated for a non-uniform cosine Axial Heat Flux Profile (AHFP) along a generic fuel channel of the noreheat SCWR concept.
1. INTRODUCTION
Currently, there are a number of Generation IV SCWR concepts under development worldwide (Pioro and
Duffey, 2007). The main objectives for developing and utilizing SCWRs are: 1) Increase the thermal efficiency
of current NPPs from 30 – 35% to approximately 45 – 50%, and 2) Decrease capital and operational costs and,
in doing so, decrease electrical-energy costs.
SCW NPPs will have much higher operating parameters compared to current NPPs (i.e., pressures of about
25 MPa and outlet temperatures up to 625°C) (see Figure 1). Additionally, SCWRs will have a simplified flow
circuit in which steam generators, steam dryers, steam separators, etc., will be eliminated. Furthermore,
SCWRs operating at higher temperatures can facilitate an economical production of hydrogen through thermochemical cycles or direct high-temperature electrolysis (Naidin et al., 2008; Naterer et al., 2009).
Table 1. Major parameters of SCW CANDU®
and KP-SKD nuclear reactors concepts (Pioro
and Duffey, 2007).
Parameters
Reactor type
Reactor spectrum
Coolant
Moderator
Electric power, MW
Pressure, MPa
Inlet temperature, C
Outlet temperature, C
No. of fuel elements in bundle
Length of bundle string, m
Max. cladding temperature, C
SCW
KPCANDU SKD
PT
Thermal
Light water
Heavy water
1220
850
25
25
350
270
625
545
43
18
6
–
850
700
Fig. 1: Pressure-Temperature Diagram of Water
for Typical Operating Conditions of SCWRs,
PWRs, CANDU-6 Reactors and BWRs.
The SCWR concepts (Duffey et al., 2008a; Pioro and Duffey, 2007) follow two main types: (a) A large
reactor pressure vessel (PV) with a wall thickness of about 0.5 m to contain the reactor core (fuelled) heat
source, analogous to conventional Light Water Reactors (LWRs); or (b) Distributed pressure tubes (PTs)
analogous to conventional Heavy Water Reactors (HWRs).
Within those two main classes, PT reactors are more flexible to flow, flux and density changes than PV
reactors. This makes it possible to use the experimentally confirmed, better solutions developed for these
reactors. The main ones are fuel re-loading and channel-specific flow-rate adjustments or regulations. A design
whose basic element is a channel or tube, which carries a high pressure, has an inherent advantage of greater
safety than large vessel structures at supercritical pressures.
AECL (Atomic Energy of Canada Limited) and RDIPE (Research and Development Institute of Power
Engineering, Moscow, Russia) are currently developing concepts of PT SCWRs (see Table 1).
To decrease significantly the development costs of a SCW NPP and to increase its reliability, it should be
determined whether SCW NPPs can be designed with a steam-cycle arrangement that closely matches that of
SC fossil-fired power plants (including their SC-turbine technology) that have been used extensively at existing
thermal power plants for the last 50 years.
Previous publications have been mainly devoted to a general development of SCWR concepts (Pioro and
Duffey, 2007). However, very few publications were dedicated to development of a general steam-cycle
arrangement of a SCW NPP (Duffey et al., 2008b; Naidin et al., 2008; Duffey and Pioro, 2006).
2. GENERAL CONSIDERATIONS REGARDING SCW NPP CYCLE
2.1. Review of SC Turbines
SC-“steam” turbines of medium and large capacities (450 – 1200 MWe) (Duffey et al., 2008b; Naidin et al.,
2008; Pioro and Duffey, 2007) have been used very successfully at many fossil power plants worldwide for
more than fifty years. Their steam-cycle thermal efficiencies have reached nearly 54%, which is equivalent to a
net-plant efficiency of approximately 40 – 43% on a Higher-Heating Value (HHV) basis.
Table 2 lists selected current and upcoming SC turbines manufactured by Hitachi for reference purposes.
Table 2: Major Parameters of Selected Current and Upcoming Hitachi SC Plants.
First Year of Operation
Power Rating (MWe)
P (MPa)
Tmain / Treheat (°C)
2011
495
677
809
790
677
600
1000
870
870
1000
870
24.6
25.5
25.4
26.4
25.5
25.5
24.9
24.7
24.7
24.9
25.3
566/566
566/566
579/579
600/620
566/566
600/620
600/600
566/593
566/593
600/600
566/593
2010
2009
2008
2007
It should be noted that the absolute leaders among large-scale power plants in terms of thermal efficiencies
are combined-cycle (i.e., tandem arrangement of gas turbine and subcritical-pressure steam turbine) gas-fired
power plants with about 60% net plant efficiency on a Lower-Heating Value (LHV) basis or net-plant
efficiencies of up to 54% on a HHV basis.
An analysis of SC-turbine data (Duffey et al., 2008b; Naidin et al., 2008; Pioro and Duffey, 2007) showed
that:
 The vast majority of the modern and upcoming SC turbines are single-reheat-cycle turbines;
 Major “steam” inlet parameters of these turbines are: main or primary SC “steam” – P = 24 – 25 MPa and
T = 540 – 600°C; and the reheat or secondary subcritical-pressure steam – P = 3 – 5 MPa and T = 540 –
620°C.
 Usually, the main “steam” and reheat-steam temperatures are the same or very close (for example,
566/566°C; 579/579; 600/600°C; 566/593; 600/620°C).
 Only very few double-reheat-cycle turbines were manufactured. The market demand for double-reheat
turbines disappeared due to economic reasons after the first few units were built.
2.2 Direct, Indirect and Dual Cycle Options
Since the steam parameters of a SCW NPP are much higher than those of current NPPs, several conceptual
designs have been investigated to determine the optimum configuration. As such, direct, indirect and dual
cycles have been considered.
In a direct cycle, SC “steam” from the nuclear reactor is fed directly to a SC turbine, as illustrated in a
previously proposed cycle shown in Figure 2 (Duffey et al., 2008b). This concept eliminates the need for
complex and expensive equipment such as steam generators. From a thermodynamic perspective, this allows
for high steam pressures and temperatures, and results in the highest cycle efficiency for the given parameters.
Current Boiling Water Reactor (BWR) NPPs are based on this concept.
620kPa
0.978x
25MPa, 625°C
RB
HPT
596kPa, 249°C
MSR
LPT
IPT
5kPa
Reactor
CND
CEP
HTP
315°C
HP Heaters
LP Heaters
Figure 2: Schematic of Direct Steam Cycle with Moisture Separator Reheater (MSR)
in SCWR Plant (Duffey et al., 2008b).
Reactor Building
Turbine Building
6.3MPa, 625°C
500kPa, 250°C
25MPa, 625°C
IPT
HPT
Reactor
7MPa
419°C
LPT
5kPa
620kPa
288°C
SG
CND
Dea
121°C
315°C
HP Heaters
LP Heaters
Drain
Pump
HTP
CEP
FWP
Figure 3: Schematic of Dual-Cycle with Reheat in SCWR Plant (Duffey et al., 2008b).
The indirect and dual cycles utilize heat exchangers (steam generators) to transfer heat from the reactor
coolant to the turbine. They are currently used in Pressurized Water Reactors (PWRs) and CANDU power
plants. The indirect cycle has the safety benefit of containing the potential radioactive particles inside the
primary coolant. However, the heat-transfer process through heat exchangers reduces the maximum
temperature of the secondary-loop coolant, thus lowering the efficiency of the cycle. A schematic of a
previously proposed dual cycle is shown in Figure 3 (Duffey et al., 2008b).
Since increasing the thermal efficiency is one of the main objectives in the development of SCW NPPs, the
direct cycle is further investigated in this paper.
2.3 Reheating Options for SCW NPP
A preliminary investigation of SCW NPP reheat options (Naidin et al., 2008) revealed the following:
 The no-reheat cycle offers a simplified SCW NPP layout, contributing to lower capital costs. However, the
efficiency of this cycle was the lowest of all the considered configurations.
 The single-reheat cycle has the advantage of high thermal efficiency (compared to that of the no-reheat
cycle) and reduced development costs due to a wide variety of single-reheat SC turbines manufactured by
companies worldwide. The major disadvantage was the increased design complexity associated with the
introduction of steam-reheat channels to the reactor core.
 While the double-reheat cycle had the highest thermal efficiency, it was deemed that the complicated
nuclear-steam reheat configuration would significantly increase the design and construction costs of such a
facility.
In conclusion, the double-reheat configuration is no longer considered of interest, while the most viable
options are the no-reheat and single-reheat SCW NPP.
2.4 Regenerative Cycle
Another way of increasing the average temperature during heat addition is to increase the temperature of
feedwater entering the SCWR. Since the reactor inlet temperature is approximately 350°C, it is obvious that a
regenerative cycle needs to be implemented to increase the feedwater temperature from the condenser outlet
(about 40ºC) to the reactor inlet conditions (350ºC).
In practice, regeneration is accomplished through feedwater heaters. Steam extracted from the turbine at
various points is used to heat the feedwater to the desired temperature. The regeneration process does not only
improve the cycle efficiency, but also improves the quality of the feedwater system by removing air and other
non-condensable gases.
2.5 Turbine Options
Since the no-reheat and single-reheat cycles were deemed to be viable, a suitable turbine arrangement must
be chosen as well. In a single-reheat configuration, the supercritical “steam” coming from the reactor flows to
the HP turbine, where it expands and is exhausted back to the subcritical-pressure steam-reheat channels. Here,
the steam temperature is increased to superheated conditions and the steam is allowed to expand through an
Intermediate-Pressure (IP) turbine. Furthermore, the steam is carried through a cross-over pipe to the LowPressure (LP) turbine and exhausted to a condenser.
However, for a no-reheat cycle, the IP turbine is eliminated and the steam is transferred directly from the HP
Turbine to the LP Turbines.
The LP turbines have large exhaust areas, because the steam is expanded to very low pressures for the
purpose of extracting as much of the useful energy as reasonably possible. Due to the large volume of steam,
the LP turbines have a double-flow configuration. The single-reheat cycle IP turbine is also a double-flow since
the expected flow rate of steam is quite high.
From a shaft orientation perspective, the turbine-generator module can be classified as a tandem compound
or cross compound. Generally, the cross-compound configuration consists of the HP and IP turbines located on
the same shaft and driving one generator, while the LP turbines are on a different shaft, driving a separate
generator. The speed of the HP and IP turbine shaft is generally 3600 rpm, while that of the LP turbine shaft is
1800 rpm (in a 60 Hz electrical grid). The slower speed of the LP turbine allows the implementation of longer
last-turbine blades with expansion to higher moisture percentages and less exhaust losses, thus increasing the
overall cycle efficiency (Black and Veatch, 1995). Due to this, the proposed turbine arrangement for the SCW
NPP single-reheat cycle is the cross-compound option. However, it is to be noted that there is a higher cost
associated with cross-compound turbine arrangements.
2.6 Assumptions and Constraints
For the purpose of simplifying the calculations presented in Sections 3 and 4 of this paper, the Gland-Steam
System and auxiliary-steam consumers are neglected. Also, the following performance losses are neglected:
 Mechanical Losses (Bearing Losses)
 Turbine-Packing Leakage
 Generator Losses
 Pump Losses and Power Consumption
 Piping-Pressure Drop.
System parameters such as mass flowrates, power outputs, etc., are calculated for a NPP power output of
1200 MWe. The assumed efficiencies of pumps and turbines used in the thermal-performance simulations are
presented in Table 3.
Table 3: Assumed Efficiencies for Turbines and Pumps in SCW NPP.
Component
HP Turbine
IP Turbine
LP Turbine
CEP
RFP
Efficiency (%)
89
92
92
84
84
To be able to model the system performance, it is assumed that all processes are steady-state and steadyflow with negligible potential and kinetic effects and no chemical reactions. Also, the heat transfer to the
system and work transfer to the system are considered positive values.
3. SINGLE-REHEAT CYCLE SYSTEM ANALYSIS
3.1 Single-Reheat Cycle System Description
The proposed cycle layout for a single-reheat SCW NPP is illustrated in Figure 4. As per the previous
sections, the cycle has a direct, regenerative configuration. As such, the SC “steam” exiting the reactor is
expanded through a single-flow HP turbine. From here, the steam is sent back to the reheater (steam channels
inside the reactor), where the temperature is raised to superheated conditions. Furthermore, the subcriticalpressure superheated steam is expanded in the IP turbine and transferred, through a cross-over pipe, to the LP
turbines. Since the volume of the steam at the exhaust of the IP turbine is quite high, two LP turbines are being
utilized. The turbine-generator arrangement is a cross-compound: the HP and IP turbines are located on the
same shaft, while the LP turbines are located on a separate shaft.
The steam is exhausted from the turbine to the condenser, suffering exhaust losses, which depend on the
exhaust area and the steam velocity. The exhaust losses are added to the Expansion Line End Point (ELEP)
enthalpy to determine the actual enthalpy of the steam leaving the LP turbine, also known as Used Energy End
Point (UEEP) (Black and Veatch, 1995). ELEP is the value used to calculate the isentropic efficiency of the LP
turbine. It should be noted that the values used in this paper have not been corrected for the moisture content in
the LP exhaust.
The saturated steam undergoes a phase change and is condensed at a constant pressure and temperature by a
cooling medium inside the condenser. The Condensate Extraction Pump (CEP) is taking its suction from the
condenser outlet. It pumps the condensate from the hotwell through a series of 5 LP feedwater heaters (LP HTR
1 to 5) to the deaerator. The feedwater temperature differentials across the LP heaters are assumed
approximately the same. The LP heaters are tube-in-shell, closed type heat exchangers. On the steam side, they
contain condensing and subcooling zones.
The deaerator is an open-type feedwater heater, where the feedwater, extraction steam and drains of the HP
heaters come into a direct contact. The feedwater is heated (at constant pressure) to the saturation temperature,
and leaves the deaerator as saturated liquid. The Reactor Feedwater Pump (RFP) takes its suction from the
deaerator and raises the feedwater pressure to the required value at the reactor inlet.
Figure 4: Single-Reheat Cycle for SCW NPP.
Furthermore, the feedwater is passed through 3 HP heaters (HP HTR 7 to 9) and a topping de-superheater
(HP HTR 10). The HP heaters are tube-in-shell, closed-type heat exchangers with de-superheating, condensing
and subcooling zones.
3.2 Single-Reheat Cycle Parameters
The T-s diagram associated with the proposed single-reheat SCW NPP cycle is illustrated in Figure 5, while
the process data is shown in Table 4. It is interesting to observe that for all LP-feedwater heaters, the inlet and
outlet parameters follow those of the saturation curve, with zero quality.
The exhausts of the HP and IP turbines remain in the superheated region, while that of the LP turbine falls
into the saturated line, having a steam quality of 87% at the condenser inlet.
The thermal efficiency of the cycle was determined to be approximately 51%, when heat contributions from
the pumps are included. The value is much higher than that of current NPPs. This makes the SCWR design a
viable choice for Generation IV reactors from a thermodynamic perspective.
Table 4: Process data for proposed single-reheat SCW NPP cycle.
System Component
Flow (kg/s) Power (MW)
Reactor
1005
1956
HP Turbine*
915
-280
Reheater
844
362
IP Turbine*
755
-272
LP Turbine*
533
-648
Condenser*
716
-1127
LP Heater 1
716
96
LP Heater 2
716
97
LP Heater 3
716
98
LP Heater 4
716
99
LP Heater 5
716
102
Deaerator *
1005
395
HP Heater 7
1005
152
HP Heater 8
1005
162
HP Heater 9
1005
181
HP Heater 10
1005
97
*flow through system component shown at outlet.
Figure 5: T-s diagram of Single-Reheat SCW NPP.
4. NO-REHEAT CYCLE SYSTEM ANALYSIS
The single-reheat cycle introduces nuclear steam-reheat channels, thus increasing the complexity of the
reactor core. The less complex core configuration associated with a no-reheat steam cycle might prove to be a
major factor when selecting the most suitable design. In conclusion, it is worth analyzing the possibility of a
no-reheat SCW NPP cycle such as the one proposed in this paper.
4.1 No-Reheat Cycle System Description
The proposed no-reheat SCW cycle consists of five Low-Pressure (LP) feedwater heaters, one deaerator,
three High-Pressure (HP) feedwater heaters and one topping de-superheater (for details, see Figure 6). The
cycle has a direct, no-reheat, regenerative configuration. As such, the SC “steam” exiting the reactor is
expanded through a double-flow HP turbine to superheated conditions. Since the volume of the steam at the
exhaust of the HP turbine is quite high, two LP turbines are being utilized. Furthermore, the steam is exhausted
from the LP turbine to the condenser. The saturated steam undergoes a phase change and is condensed at
constant pressure and temperature by a cooling medium inside a condenser.
Fig. 6: No-Reheat Cycle for SCW NPP.
The Condensate-Extraction Pump (CEP) is taking its suction from the condenser hotwell. It pumps the
condensate through a series of five LP feedwater heaters (LP HTR 1 to 5) to the deaerator. The feedwater
temperature differentials across the LP and HP feedwater heaters are approximately the same. The LP heaters
are tube-in-shell, closed-type heat exchangers. Typical values for the Drain-Cooler Approach (DCA) and
Terminal-Temperature Difference (TTD) parameters for each LP Heater are listed in Table 5 (Black and Veatch,
1996), while the steam extraction points can be observed in Figure 6.
Table 5: Feedwater Heaters Parameters.
Heater identifier Heat exchanger type
HTR 1
LP, Closed
HTR 2
LP, Closed
HTR 3
LP, Closed
HTR 4
LP, Closed
HTR 5
LP, Closed
Deaerator
Open
HTR 7
HP, Closed
HTR 8
HP, Closed
HTR 9
HP, Closed
HTR 10
HP, Closed
DCA (°C)
5.6
5.6
5.6
5.6
5.6
5.6
5.6
5.6
-
TTD (°C)
2.8
2.8
2.8
2.8
2.8
1.5
0
-1.6
-
The deaerator is an open-type feedwater heater, where the feedwater, extracted steam and drains of the HP
heaters come into a direct contact. The feedwater is heated at constant pressure, and leaves the deaerator as
saturated liquid. A Reactor Feedwater Pump (RFP) takes its suction from the deaerator and raises the feedwater
pressure to the required value at the reactor inlet (25 MPa).
Furthermore, the feedwater is passed through three HP heaters (HP HTR 7 to 9) and a topping desuperheater (HP HTR 10).
4.2 No-Reheat Cycle Parameters
The T-s diagram associated with the proposed no-reheat SCW NPP cycle is illustrated in Figure 7. The
exhaust of the HP turbine is situated in the superheated region, while that of the LP turbine falls in the saturated
region. The moisture content at the outlet of the LP turbine is calculated to be 19%. This could be a major
technical challenge for the SCW NPP based on a no-reheat cycle. However, the moisture can be reduced by
implementing contoured channels in the inner casing for draining the water and moisture removal stages.
The overall thermal efficiency of the cycle was determined to be approximately 50%. Table 6 illustrates the
process data resulted from the thermal performance simulation.
Fig. 7: T-s diagram of No-Reheat SCW NPP Cycle.
Table 6: Process data for No-Reheat SCW NPP cycle.
System Component
Reactor
HP Turbine *
LP Turbine *
Condenser *
CEP
LP Heater 1
LP Heater 2
LP Heater 3
LP Heater 4
LP Heater 5
Deaerator *
RFP
HP Heater 7
HP Heater 8
HP Heater 9
HP Heater 10
Flow (kg/s)
1201
1093
596
830
830
830
830
830
830
830
1201
1201
1201
1201
1201
1201
Power (MW)
2336
-334
-866
-1159
3
112
112
113
115
118
493
39
181
193
216
115
5. NO-REHEAT CYCLE FUEL CHANNEL CALCULATIONS
A safety analysis associated with the design and operation of any NPP has to prove that the fuel-centerline
temperature will not exceed the fuel melting temperature at any operating conditions. At the same time the
sheath temperature has to remain well below the temperature limit of the sheath material. These two safety
limits have been established to ensure fuel integrity and thus containment of radioactive particles, for the
purpose of staff, public, and environment protection.
To be able to calculate the fuel-centerline temperature, the heat transfer coefficient (HTC) and
thermophysical properties profiles along the heated length of a fuel channel have to be well understood. The
sheath temperature must be below the design limit of 850°C (Khartabil et al., 2005), while the fuel-centerline
temperature should be below the industry accepted limit of about 1850°C.
In previous studies (Pioro et al., 2008a), a preliminary analysis of heat-transfer to supercritical water in
pressure tubes, as well as a computation of fuel-centerline temperature have been completed. A linear, average
heat flux was used along the heated fuel channel. The temperature of the fuel along the heated channel was
obtained using the original Bishop et al. correlation (Bishop et al., 1964). To obtain the fuel-centerline
temperature of the fuel, a constant value for thermal conductivity of the fuel and the cladding was used. The
values used for conductivities were chosen to be the lowest possible, as part of a conservative approach. The
obtained results gave an over-estimation of the fuel-centerline temperature, providing a basis for future
comparisons. However, the Axial Heat Flux Profile (AHFP) was considered to be uniform, which is not the
actual case. In general, heat-flux profiles are close to a cosine-type shape.
In the current work, coolant, sheath and fuel-centerline temperatures were calculated for three non-uniform
AHFPs: cosine-shaped, upstream skewed and downstream skewed (Figure 8). The nominal channel power is
8.5 MW.
Fig. 8: Axial Heat Flux Profiles used in fuel channel heat-transfer calculations.
The thermal conductivities of Inconel-718 fuel cladding and uranium dioxide (UO2) fuel vary with
temperature (Special Metals, 2007). The determination of fuel-cladding and fuel-centerline temperatures relies
heavily on an accurate estimation of the heat transfer coefficient. The heat-transfer correlation used in the fuelchannel calculations is based on the updated Bishop et al. correlation using the latest data available (Pioro et al.,
2008b):
Nu  0.0056 Re
0.91
Pr
0.64
 ρw 
 
 ρb 
0.50
(1)
The correlation uses an averaged Prandtl number, which requires an averaged specific heat. The use of
averaged values is required due to significant bulk-fluid temperature variations in a cross-section. It is
important to note that the correlation is determined based on experiments in bare tubes.
Pr 
μb  c p ,
(2)
kb
where μb , c p and kb denote a viscosity, average specific heat, and thermal conductivity, respectively.
H  Hb
,
cp  w
Tw  Tb
where Hw and Hb refer to the enthalpy at the channel wall and bulk-fluid enthalpy, respectively.
Parameters used in the heat-transfer calculations are listed in Table 7.
Table 7: Fuel-Channel Major Parameters used in Calculations
Parameter, (Unit)
Bundle
No. of Elements
No. of Elements per Ring
Value
43
Center
Inner
Intermed.
Outer
42
1
11.5
23.6
10.72
481
No. of Fuelled Elements
Center Rod with Low Heat Flux
Fuelled Element OD, (mm)
Center Rod OD, (mm)
Fuel Pellet OD, (mm)
Heated Length, (mm)
Bundle String
No. of Bundles
Heated Length, (m)
Pressure-Tube
Pressure Tube ID, (mm)
Flow Cross-Sectional Area, (mm2)
Hydraulic-Equivalent Diameter,
(mm)
Other Parameters
12
5.772
103.38
3594
7.5
1
7
14
21
(3)
Mass Flow Rate, (kg/s)
4.36
(a)
(a)
(b)
(b)
(c)
(c)
Fig. 9: Thermophysical properties variations along Fig. 10: Temperature and HTC profiles along
SCWR fuel channel for: a) cosine-shaped AHFP; b) SCWR fuel channel for: a) cosine-shaped AHFP;
upstream-skewed AHFP; and c) downstream- b) upstream-skewed AHFP; and c) downstreamskewed AHFP.
skewed AHFP.
A comparison of selected thermophysical-properties profiles for the coolant, along the fuel-channel heated
length, at non-uniform cosine-shaped, upstream and downstream skewed heat-flux profiles is shown in Figure 9
(a, b, and c). These figures are drawn for the specified non-uniform axial heat-flux profiles at a pressure of 25
MPa.
In general, all thermophysical properties undergo significant variations near the critical and pseudocritical
points. These variations are dramatic near the critical point. However, within a pseudocritical region and with
an increase in pressure, these variations become less distinct. For the upstream-skewed AHFP the
pseudocritical region occurs within Bundle 4, for the cosine-shaped AHFP - between Bundle 4 and 5, while for
the downstream-skewed AHFP the same region occurs within Bundle 6. These significant differences are
caused with the different linear local heat flux applied in each of the three cases.
It can be observed in Figure 9 that properties such as density, thermal conductivity, and dynamic viscosity
undergo a significant drop along the heated channel. Dynamic viscosity has a minimum value, beyond which, it
is slightly increasing. Specific heat, thermal conductivity, and Prandtl number all have peaks near the
pseudocritical point (Figure 9). The magnitude of these peaks decreases very quickly with an increase in
pressure (Pioro and Duffey, 2007).
The HTC profiles in Figure 10 appear to have two distinctive peaks. It has been determined that the first
peak appears as a result of the averaged Prandtl number, while the second peak corresponds to the peak in
thermal conductivity observed in Figure 9. Although the second peak is smaller than the first one, it is
interesting to note that it occurs in the pseudocritical region.
The temperature profiles illustrated in Figure 11 represent the inner-sheath and fuel-centerline temperatures
for the chosen non-uniform AHFPs. The maximum sheath temperature is obviously obtained on the inner
surface of the cladding. It is important to observe that, for all three heat-flux profiles analyzed, the sheath
temperature remains below the conservatively established sheath-temperature limit of 850°C (Figure 11). This
has a huge impact upon the safety of the SCWR concept since the fuel cladding integrity is maintained.
However, the maximum sheath temperature occurs within Bundle 7 for the upstream-skewed AHFP and is
significantly lower than that of the downstream-skewed AHFP, which occurs within Bundle 10.
In all three cases, the fuel-centerline temperature exceeds the industry accepted limit of 1850°C. However,
the temperature remains well below the fuel (UO2) melting temperature for all three non-uniform profiles. The
maximum fuel temperature (approximately 2200°C) occurs within Bundles 5 and 6 for the upstream-skewed
profile. At the same time, for the downstream-skewed AHFP maximum fuel temperature (2330°C) occurs
within Bundles 8 and 9. The cosine-shaped AHFP causes the lowest fuel-centerline temperature, at
approximately 2100°C. It is obvious that, due to a lower fuel-centerline temperature, the cosine-shaped AHFP
would be the preferred choice.
Since the literature survey did not yield any heat-transfer correlations for supercritical water flowing inside
fuel bundles, as a preliminary approach, the correlation used for bare tubes (1) can be applied. It should be
noted that this is a conservative approach, because the end plates and other appendages associated with the fuel
bundle will actually increase the flow turbulence and thus the heat transfer.
(a)
(b)
(c)
Fig. 11: Fuel-centerline temperature profiles along
SCWR fuel channel for: a) cosine-shaped AHFP; b)
upstream-skewed AHFP; and c) downstreamskewed AHFP.
5. CONCLUSIONS
The following conclusions can be made:
1. The vast majority of modern SC turbines are single-reheat-cycle turbines. Just a few double-reheat-cycle
SC turbines have been manufactured and put into operation. However, despite their efficiency benefit,
double-reheat-turbines have not been considered economical.
2. Major inlet parameters of the current and upcoming single-reheat-cycle SC turbines are: the main or primary
SC “steam” – pressure of 24 – 25 MPa and temperature of 540 – 600°C; and the reheat or secondary
subcritical-pressure steam – P = 3 – 5 MPa and T = 540 – 620°C.
3. Usually, inlet temperatures of the main SC “steam” and the reheat subcritical-pressure steam are the same or
very close (for example, 566/566°C; 579/579; 600/600°C; 566/593; 600/620°C).
4. In order to maximize the thermal-cycle efficiency of the SCW NPPs it would be beneficial to include
nuclear steam reheat. Advantages of a single-reheat cycle in application to SCW NPPs are:
(a) High thermal efficiency (45 – 50%), which is the current level for SC thermal power plants and close to
the maximum thermal efficiency achieved in the power industry at combined-cycle power plants (up to
60%).
(b) High reliability through proven state-of-the-art turbine technology; and
(c) Reduced development costs accounting on wide variety of SC turbines manufactured by companies
worldwide.
5. The major disadvantage of a single-reheat cycle implementation in SCW NPPs is the requirement for
significant changes to the reactor-core design due to the addition of the nuclear-steam reheat at subcritical
pressures.
6. The thermal-performance simulation of the proposed no-reheat SCW NPP cycle showed that the overall
thermal efficiency of the system is approximately 50%. This value makes the SCW NPP concept
competitive on the energy market. As expected, the moisture content at the outlet of the LP turbine is
approximately 19%, which is quite high. However, moisture removal stages can be implemented to reduce
the damage to the turbine blades.
7. The axial heat-flux profile has a significant impact on fuel-centerline temperature. The sheath temperature
remained well below the practical limit of 850°C for the upstream and downstream-skewed AHFPs. The
fuel-centerline temperature exceeded the conservative limit of 1850°C for all non-uniform AHFPs.
However, all temperatures stayed well below the fuel melting temperature.
ACKNOWLEDGEMENT
Financial supports from the NSERC Discovery Grant and NSERC/NRCan/AECL Generation IV Energy
Technologies Program (NNAPJ) are gratefully acknowledged.
NOMENCLATURE
Hb
Hw
kb
m
Nu
P
Q
average specific heat, J/kg K
bulk-fluid enthalpy, J/kg
fluid enthalpy at wall temperature, J/kg
bulk-fluid thermal conductivity, W/m K
mass-flow rate, kg/s
Nusselt number
pressure, Pa
power or heat-transfer rate, W
Pr
Re
T
Tb
Tpc
Tw
Prandtl number
Reynolds number
temperature, °C
bulk-fluid temperature, ºC
pseudocritical temperature, °C
wall temperature, ºC
Greek symbols
∆
difference
µb
bulk-fluid viscosity, Pa s
ρb
bulk-fluid density, kg/m3
ρw
fluid density at wall temperature, kg/m3
Subscripts
e
th
electrical
thermal
Acronyms
AECL
AHFP
BWR
CANDU
CEP
DCA
Gen IV
HHV
HP
HTC
HTR
HWR
HX
IP
KP-SKD
LHV
LP
LWR
Mix Ch
MSR
NPP
PT
PV
PWR
RDIPE
RFP
SC
Atomic Energy of Canada Limited
Axial Heat Flux Profile
Boiling Water Reactor
CANada Deuterium Uranium (reactor)
Condenser-Extraction Pump
Drain Cooler Approach
Generation IV Reactor Concepts
Higher-Heating Value
High Pressure
Heat Transfer Coefficient
Heater
Heavy Water Reactor
Heat eXchanger
Intermediate Pressure
Channel Reactor of Supercritical Pressure (in Russian abbreviations)
Lower-Heating Value
Low Pressure
Light Water Reactors
Mixing Chamber (deaerator)
Molten Salt Reactor
Nuclear Power Plant
Pressure Tube (reactor)
Pressure Vessel (reactor)
Pressurized Water Reactor
Research and Development Institute of Power Engineering (Moscow, Russia)
Reactor Feed Pump
SuperCritical
SCW
SCWR
TTD
UOIT
VHTR
SuperCritical Water
SuperCritical Water Reactor
Terminal Temperature Difference
University of Ontario Institute of Technology
Very High Temperature Reactor
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