# Thermal Hydraulic Analysis of a Passive Residual Heat Removal System for an Integral Pressurized Water Reactor

Authors: Junli Gou; Suizheng Qiu; Guanghui Su; Douna Jia
Journal: Science and Technology of Nuclear Installations
 (2009)

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## Abstract

A theoretical investigation on the thermal hydraulic characteristics of a new type of passive residual heat removal system (PRHRS), which is connected to the reactor coolant system via the secondary side of the steam generator, for an integral pressurized water reactor is presented in this paper. Three-interknited natural circulation loops are adopted by this PRHRS to remove the residual heat of the reactor core after a reactor trip. Based on the one-dimensional model and a simulation code (SCPRHRS), the transient behaviors of the PRHRS as well as the effects of the height difference between the steam generator and the heat exchanger and the heat transfer area of the heat exchanger are studied in detail. Through the calculation analysis, it is found that the calculated parameter variation trends are reasonable. The higher height difference between the steam generator and the residual heat exchanger and the larger heat transfer area of the residual heat exchanger are favorable to the passive residual heat removal system.


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## Body

## 1. Introduction

Integral  pressurized water reactor (IPWR) is being considered as one of
the next-generation advanced  nuclear reactors designed to be inherently safe by
naturally and physically passive mechanisms. The primary coolant system
components of the IPWRs, composed of the core, the
pressurizer, the main coolant pumps (MCPs), and the once-through steam generators  (OTSGs), are housed in the reactor
pressure vessel (RPV). The adoption of the special in-vessel layout eliminates
the pipe connection between those components, and thus the occurrence of large
break loss-of-coolant accidents (LBLOCAs) is essentially excluded by the new design. In addition,
one of the very important design features of the IPWRs is the simplifications and improvements in the safety systems. Especially, such passive safety systems as passive
residual heat removal system (PRHRS) are employed to accomplish the
inherent safety functions and mitigate the consequences of the postulated
accidents. PRHRS is expected to safely remove the core decay heat, only through
natural circulation, in case of both station blackout accident and long-term
cooling for repair or refueling.A literature survey reveals that there have been many
experimental and numerical investigations on the characteristics of different
PRHRSs. The Westinghouse advanced passive PWRs,
AP-600, AP-1000, and EP-1000 (IAEA-TECDOC-1391, 2004;  Adomaitis et al. [1]; Reyes and Hochreiter [2]; Zhang
et al. [3]) adopt passive core cooling
system (PXS) to protect the plant against reactor coolant system (RCS) leaks
and ruptures of various sizes and locations. The PXS includes a 100% capacity
passive  residual heat removal heat exchanger (PRHR HX), which satisfies the
safety criteria for loss of feedwater, feedwater and steam line breaks. The
PRHR HX, immersed in the in-containment refueling water storage tank (IRWST),
is connected through the cold leg and hot leg to the core. The IRWST water
volume is sufficient to absorb decay heat for more than 1 hour before the water
begins to boil. Once boiling starts in the IRWST, the steam passes to the containment
and condenses on the inner surface of the steel containment vessel, and then drains
by gravity back into the IRWST. The PRHR HX and the passive containment cooling
system (PCCS) provide indefinite decay heat removal capability with no operator
action required. The theoretical and experimental investigations on the PXS
characteristics of AP600 indicate that the design of the PRHRS is feasible and
rational.The PRHRSs via the secondary side of the
steam generators for WWER-1000/V-392 and WWER-640/V-407 plants (Hyvärinen  [4]; IAEA-TECDOC-1391, [5]; Krepper [6]; Mousavian et al. [7]) are intended to remove decay heat from the reactor in a case of a station blackout with intact
primary and secondary circuits, and to depressurize the RCS under a small break
LOCA. The PRHRS of V-392 consists of four independent
trains, each of which has pipelines for steam supply and removal of condensate,
valves, and an air-cooled heat exchanger installed outside the containment. The
steam generated in the steam generators due to the heat released in the reactor
condenses in the air-cooled heat exchanger and rejects its heat to the ambient
air. The motion of the cooling medium
takes place in natural circulation. While in the
V-407 design, the PRHRS removes the heat to the heat exchangers immersed to the
emergency heat removal tanks, which are installed outside the containment. The
water inventory in the tanks is sufficient for the long-term heat removal (at
least 24 hours) and can be replenished if necessary. The experimental
investigation and calculation analyses show that the PRHRS for WWER can safely remove the
decay heat in case of the station blackout accident and enhance the inherent
safety of the plant. The experimental investigations
have confirmed the design function of the passive safety means proposed and
also created the necessary experimental database for modeling by the system
thermohydraulic codes. Further investigations are being planned for additional
verification of the passive safety systems and for the  optimization of their
design.The PRHRS (Su et al. [8, 9], Qiu et
al.  [10], Zejun et al. [11]) for Chinese
advanced PWR (AC-600) is used to remove the decay heat
in the event of a station blackout by natural circulation. It may also be effective
in a main steam pipe rupture or loss of feedwater event. The system consists of
two independent trains, each of them being connected to the reactor coolant
loops via the secondary side of the respective steam generator. Each train has
a feedwater tank, an air cooler located in a chimney outside the containment,
and piping (and valves) for steam and condensate circulation. The air cooler
with the help of chimney rejects the core decay heat transferred from the steam
generators into the atmosphere. Based on the experimental investigations,
semiempirical theoretical
model related to height between heat resource and heat sink has been
established which can be applied to the system arrangement design for the PRHRS
of Chinese advanced PWR. Transient experiment also provides the basis for the startup
mode of the PRHRS. Furthermore, a way to avoid potential water hammer in the
feedwater tank has been identified. Computer code MISAP2.0 has been developed
with self-reliance copyright, which is a useful tool for the PRHRS design.The PRHRS for SMART (Chang et al.
[12]; Chung et al. [13]; Chung et al. [14]; Chung et al. [15]), a small modular integral-type pressurized
water reactor developed by KAERI, is also a steam
generator secondary side decay heat removal system. Two of the four independent PRHRS trains are sufficient to remove the
decay heat. Each train is composed of a compensating tank pressurized by
nitrogen, a heat exchanger immersed in an in-containment refueling water tank, valves and piping for steam and condensate. The compensating
tank makes up the water volume change in the passive residual heat removal system
and holds the water inventory for the filling system pipelines during a
cooldown transient. The check valves are installed on the pipelines between the
compensating tank and the heat exchanger outlet to keep the water from leaving
the compensating tank in the first instants of a cooldown, which would prevent
a natural circulation from being developed. The refueling water tank is located
high enough above the steam generator to remove the heat transferred from the
primary side in the steam generator by a natural convection when the secondary
system loses its heat removal capability. The water in the refueling water tank
is heated, boiled, and eventually evaporated into the atmosphere. The water inventory
in the refueling water tank can remove the heat for 36 hours at least without
any operator actions to respond to the design basis events. The heat transfer characteristics and the natural circulation performance
of the PRHRS for the SMART have been experimentally investigated in the VISTA facility, and the experimental results have been
analyzed using a best-estimated system analysis code, MARS. The
comparison of the experimental data and the theoretical prediction shows good agreement accept for some parameters, such as the fluid temperature
in the PRHRS condensate line. It seems that it is due to an insufficient heat
transfer modeling in the pool such as the refueling water tank in the MARS calculation. Besides, PRHRSs for other reactors have been
developed in the last decade (Iwamura et al. [16]; Samoilov et
al.  [17]; Peng et al. [18]; Jinling and Yujun  [19]; Kusunoki et al. [20]; Xinian et al.
[21]; Carelli et al. [22]).A detailed review of the related
literatures indicates that the PRHRSs are quite different from one another in
design for different PWRs. The merits and demerits of different PRHRSs are very
difficult to be evaluated. Both the test facilities for the corresponding
PRHRSs and the commercial analysis codes (like Relap, Retran, etc.) have their
own limitations. It is evident that due to the complexity of the thermal hydraulic process
involved in the PRHRSs with their small inherent natural driving forces (i.e.,
gravity, natural circulation, etc.), experimental and theoretical
investigations have to be performed for each specific design. Validated
computer codes must be developed to support the expected operational
performance. Consequently, considering the design features and operation
performances of a new type of PRHRS, systematic analyses on the thermal
hydraulic characteristics of it should be performed in detail at the conceptual design stage from both experimental and
analytical points of view.In the present paper, a theoretical investigation on the
thermal hydraulic characteristics of a new type of PRHRS, which is connected to
the reactor system via the secondary side of the steam generator, for an
integral pressurized water reactor is conducted. With three-interknited natural
coolant circulation loops, the core decay heat should be safely removed to an
ultimate heat sink, a water pool (WP) with a large enough size. In order to
estimate the thermal hydraulic characteristics and evaluate the heat removal
capacity of the PRHRS, a one-dimensional two-phase flow model and a simulation
code (SCPRHRS) are developed. The model is based on the fundamental
conservation principles, namely, the mass, momentum, and energy conservation
equations. System component models are included according to the special design
features of it. All possible flow and heat transfer conditions are considered and
the corresponding optional models are supplied in the simulation code. Using the
code, the analyses results of the PRHRS transient behavior are presented in this
paper.


## 2. System Description

The layout of the primary coolant system components
and the PRHRS of this IPWR are shown in Figure1(a). The primary coolant system
components, including a core, a pressurizer, 2 main coolant pumps (MCPs), and
12 once-through steam generators (OTSGs), are contained in the reactor pressure
vessel (RPV). The reactor core is located at the bottom of the RPV. The MCPs
and the OTSGs are installed symmetrically in the annular space between the
reactor barrel and the RPV. This configuration results in an integral and
compact system. There is a long riser on the top of the core outlet to enhance
the natural circulation capacity. At the same time, a natural circulation
by-pass valve, installed between the inlet and the outlet of each MCP, is
designed to reduce the natural circulation form loss.Schematic diagram of the PRHRS and OTSG heat transfer
tubes.
(a)(b)Under forced circulation conditions, the natural
circulation by-pass valve is kept closed and the primary coolant is driven by
the MCPs to circulate along the primary circuit. The primary coolant enters the
core from the lower plenum. After being heated, the coolant flows out of the core and upwards
through the riser. Then, the coolant is pumped by the MCPs, located at the exit
of the riser, and flows through the annular cavity on top of the primary entry
of the OTSGs. Subsequently, it flows downwards through the primary side of the
OTSGs, cooled by the secondary coolant and the downcomer until reaching the
lower plenum. Finally, it flows back into the core and recirculates continually
along the flow path. The heat transfer element of the OTSGs has a straight
annular channel, composed of two concentric circular tubes with different
diameters (see Figure1(b)). In the steam generator, the secondary coolant
flows upwards in the annular channel and is bilaterally heated by the primary
coolant, which flows downwards in the shell-side of the annular channel outer
tube and the inner tube of the annular channel, respectively.There are
two sets of independent residual heat removal system with identical
characteristics. They are installed outside the reactor pressure vessel and
connected to the secondary circuit loops (Figure1(a)). The residual heat
exchanger, which has a straight tubular bundle type, is immerged in a water
pool with very large size. Under normal operating conditions, the heat
exchanger is filled with water and isolated by a check valve and an isolation
valve. The PRHRS removes the core decay heat by natural circulation under
station blackout accident as well as in the case of long-term cooling for
repair or refueling. After a reactor trip, the PRHRS will start to work
automatically without any active operation. The shutdown signal from the
reactor control system makes the turbine tripped, the main steam valves and the
feed water valves closed. The forced circulation in the primary loop turns into
natural circulation. At the same time, the check and isolation valves open
automatically and the water in the heat exchanger enters the secondary side of
the OTSGs by gravity. After exiting the steam generator as superheated or
saturated fluid, the secondary coolant enters the residual heat exchanger and
flows downwards in the tube-inside, where it is cooled by the shell-side water
in the water pool and condensed to subcooled water. Finally, the condensate
flows back to the steam generator. Also, the natural circulation will establish
in the water pool because of the continual heating from the secondary coolant.
Consequently, the residual decay heat of the core is passively removed to the
ultimate heat sink through three-interknited natural circulation loops, namely,
(1) the primary circulation loop composed of the core, the primary side of the
OTSGs, and the connecting plenums; (2) the secondary circulation loop including
the secondary side of the OTSGs, the tube-inside of the heat exchangers, and
the connecting pipes and plenums; (3) the third circulation loop in the water
pool.


## 3. Theoretical Model

The basic
field model is based on the fundamental conservation principles: the mass,
momentum, and energy conservation equations. With the assumption of
one-dimensional flow, these equations, including single-phase and two-phase
conservative equations, can be easily found in the reference (Collier and Thome [23]). The characteristics of the theoretical model are introduced in the
following in detail.


### 3.1. Core Power

The core power is calculated
using the decay heat equation and point neutron kinetics equation with six groups
of delayed neutron (Pingan et al. [24]). Each group has its own yield and decay
constant. The reactivity feedback caused by the temperature change of the
moderator and the fuel is specially considered. The axial power distribution is
specified by a profile supplied. At the same time, the power distribution in
the radial direction is assumed to be uniform.


### 3.2. System Components Model

#### 3.2.1. Mass Flow Rate of the Primary Loop

By integrating the momentum conservative equation
along the primary loop, the mass flow rate equation is given by(1)∂WP∂τ∮1Adz=−∮∂P∂Zdz−∮1A∂∂z(WP2ρA)dz−∮ρgdz−WP2∑i=1n(c2ρA2)i−WP2∮f12DeρA2dz. In fact,
the second terms on the right hand of (1) can be  eliminated. By introducing
natural circulation driving head BP,
(1) is simplified as follows:(2)∂WP∂τ=(Ppump+BP−ΔPlocP−ΔPfP)∮(dz/A), where ΔPlocP  and ΔPfp are the local pressure drop and the friction
pressure drop along the primary loop, respectively; Ppump is the pressure  head of the MCP. BP, ΔPlocP,
and ΔPfp are defined by (3)Ppump=ρgHpump,BP=−∮ρgdz,ΔPlocP=WP2∑i=1n(c2ρA2)i,ΔPfP=WP2∮f12DeρA2dz.The pressure head of the MCP during the transient
process is a very important parameter to calculate the mass flow rate of the
primary loop. However, the pressure head of the MCPs reduces rapidly to zero
due to the small inertia rotation after a reactor trip. Moreover, as mentioned
above, the MCPs stop and the by-pass valves are opened to enhance the natural
circulation under natural circulation conditions. Because the local form loss
coefficient of the by-pass valve is much less than that of the MCP, most of the
primary coolant flows through the by-pass valve. The relationship between the
local pressure drop of the MCP and the by-pass valve is expressed by(4)Δppump=Δpv. That is, (5)12cpumpWpump2Apump2ρ=12cvWv2Av2ρ. While (6)Wp=Wpump+Wv.
Substituting (5) and (6) into (4), the local pressure drop of the
MCP is (7)Δppump=12cpumpW2(1+Avcpump/cv/Apump)2Apump2ρ.


#### 3.2.2. Mass Flow Rate of the Secondary Loop

Similarly, by integrating the momentum conservative
equation along the secondary loop, the mass flow rate equation is given by(8)∂Ws∂τ=(Bs−ΔPlocs−ΔPfs)∮(dz/A), where Bs, ΔPlocs,
and ΔPfs are expressed by (9)Bs=−∮ρgdz,ΔPlocs=Ws2∑i=1n(c2ρA2)i,ΔPfs=Ws2∮f12DeρA2dz.


#### 3.2.3. Mass Flow Rate of the Third Loop

Because the size of the water pool is large enough, an
assumption, that the change of the pool water temperature can be neglected, is
rational. Similarly, by applying the momentum conservative equation, the mass
flow rate of the third loop is written as(10)∂Wt∂τ=(Bt−ΔPloct−ΔPft)∑i=1k(Δz/A)i, where Bt, ΔPloct,
and ΔPft are defined as follows: (11)Bt=ρpgL−∑j=1k(ρgΔz)j,ΔPloct=Wt2∑i=1n(c2ρA2)i,ΔPft=Wt2∑j=1k(fΔz2DeρA2)j.It is noted that the
equations for mass flow rate calculation of the three loops are simplified
equations with an assumption of constant flow rate along the circuit. This
simplification may cause inaccuracy especially in case of two-phase flow. However,
this simplified model has been successfully adopted in our previous
investigations (Su and Guo [8], Qiu et al. [10], Zejun et
al.  [11], Tian et al. [25, 26]). The comparisons of our results with those of RETRAN-02 and RELAP/MOD3
gave good agreements. So, using the simplified model in this calculation is still
believed to be feasible for the conceptual design of the PRHRS.


#### 3.2.4. Pressure of the Secondary Loop

Under normal operation condition with rated core
power, the spatial variation of the pressure in the secondary loop cannot be neglected
because of the large pressure drop from the inlet to the outlet of the OTSG
secondary side (about 1.5 MPa). However, in case of natural circulation, the
spatial pressure difference of the secondary loop becomes very small as a
result of the loss of feed water pump head. Thus, an assumption, that the
spatial variation of the pressure in the secondary loop is negligible, can be
made. Consequently, by integrating the mass continuity equation along the
secondary loop, the pressure equation of the secondary loop can be written as(12)∑i=1n[(∂ρ∂h∂h∂τ+∂ρ∂p∂p∂τ)A⋅ΔZ]i=−∮∂W∂zdz. Practically,
the right-hand side of (12) equals zero. Thus, (12) is simplified as (13)∂p∂τ=−∑i=1n(ρ2A⋅ΔZ(∂υ/∂h)(∂h/∂τ))i∑i=1n(ρ2A⋅ΔZ(∂υ/∂p))i.


#### 3.2.5. Tube Wall Heat Transfer

Because of the very small thickness of the tube wall,
lumped parameter method is used to calculate the wall heat transfer. Ignoring
the axial conduction heat transfer, the tube wall heat transfer equation is
expressed by(14)mCp∂Tw∂τ=H1A1(T1−Tw)−H2A2⋅(Tw−T2), where Tw is the average temperature of the tube wall; H1 and H2 are heat transfer coefficients of the two surfaces of the wall,
respectively; A1 and A2 are heat transfer area of the two surfaces of the wall,
respectively; T1 and T2 are the fluid temperatures, respectively.


#### 3.2.6. Pipe and Plenum

In the PRHRS, there are pipes and plenums to connect
the major components. With an assumption of thermal isolation, the energy
conservative equation of them can be expressed by(15)Mdhdτ=W(hin−h).


#### 3.2.7. Heat Transfer and Frictional Coefficient Correlations

The dominant heat transfer of the primary loop and the
third loop is single-phase mode, and the modes of the secondary loop are
single-phase and boiling heat transfer in the OTSG and condensation and
single-phase heat transfer in the heat exchanger. According to the
corresponding flow regimes, appropriate heat transfer and frictional
coefficient correlations are selected. Two-phase
frictional multiplier is used to calculate the two-phase flow pressure drop,
that is,(16)ftp=flo⋅Φtp2.The involved heat transfer and frictional coefficient
correlations are listed in Tables1 and 2, respectively.Table 1
Heat transfer correlations.
Flow
regimeCorrelationReferenceSingle-phase
waterLaminarCollier[27]TransitionInterpolationTurbulentSieder-Tate[28]Subcooled
boilingJens and
Lottes[23]Saturated
boilingChen[23]Transition/film
boilingGroeneveld[29]Superheated
vaporSieder-Tate[28]CondensationShaha[30]Table 2
Frictional coefficient correlations.
Flow
regimeCorrelationReferenceSingle
phaseLaminar flowDarcy[24]Transition flow0.048Turbulent flowBlasiusTwo phaseHomogeneous model[31]Drift flux modelChisholm[32]


### 3.3. Nodalization of the PRHRS

In order to numerically simulate the thermal hydraulic
characteristics of the PRHRS, the whole system shown in Figure1 is divided
into many control volumes and junctions according to the different geometrical
and heat transfer conditions. Figure 2 schematically shows the nodalization of
the PRHRS. The primary circuit model used in the thermal hydraulic analysis
consists of a core, a steam generator, a pump, a pressurizer, a downcomer, and
plenums. The modeling of the PRHRS is composed of a steam generator, a heat
exchanger, a water pool, pipes, plenums, and valves. In the core, the steam
generator and the heat exchanger, fine control volume division is used to
properly predict the heat transfer phenomena. The number of the control volume
can be easily changed for different calculation requirements.Figure 2
SCPRHRS nodalization for the PRHRS.


## 3.1. Core Power

The core power is calculated
using the decay heat equation and point neutron kinetics equation with six groups
of delayed neutron (Pingan et al. [24]). Each group has its own yield and decay
constant. The reactivity feedback caused by the temperature change of the
moderator and the fuel is specially considered. The axial power distribution is
specified by a profile supplied. At the same time, the power distribution in
the radial direction is assumed to be uniform.


## 3.2. System Components Model

### 3.2.1. Mass Flow Rate of the Primary Loop

By integrating the momentum conservative equation
along the primary loop, the mass flow rate equation is given by(1)∂WP∂τ∮1Adz=−∮∂P∂Zdz−∮1A∂∂z(WP2ρA)dz−∮ρgdz−WP2∑i=1n(c2ρA2)i−WP2∮f12DeρA2dz. In fact,
the second terms on the right hand of (1) can be  eliminated. By introducing
natural circulation driving head BP,
(1) is simplified as follows:(2)∂WP∂τ=(Ppump+BP−ΔPlocP−ΔPfP)∮(dz/A), where ΔPlocP  and ΔPfp are the local pressure drop and the friction
pressure drop along the primary loop, respectively; Ppump is the pressure  head of the MCP. BP, ΔPlocP,
and ΔPfp are defined by (3)Ppump=ρgHpump,BP=−∮ρgdz,ΔPlocP=WP2∑i=1n(c2ρA2)i,ΔPfP=WP2∮f12DeρA2dz.The pressure head of the MCP during the transient
process is a very important parameter to calculate the mass flow rate of the
primary loop. However, the pressure head of the MCPs reduces rapidly to zero
due to the small inertia rotation after a reactor trip. Moreover, as mentioned
above, the MCPs stop and the by-pass valves are opened to enhance the natural
circulation under natural circulation conditions. Because the local form loss
coefficient of the by-pass valve is much less than that of the MCP, most of the
primary coolant flows through the by-pass valve. The relationship between the
local pressure drop of the MCP and the by-pass valve is expressed by(4)Δppump=Δpv. That is, (5)12cpumpWpump2Apump2ρ=12cvWv2Av2ρ. While (6)Wp=Wpump+Wv.
Substituting (5) and (6) into (4), the local pressure drop of the
MCP is (7)Δppump=12cpumpW2(1+Avcpump/cv/Apump)2Apump2ρ.


### 3.2.2. Mass Flow Rate of the Secondary Loop

Similarly, by integrating the momentum conservative
equation along the secondary loop, the mass flow rate equation is given by(8)∂Ws∂τ=(Bs−ΔPlocs−ΔPfs)∮(dz/A), where Bs, ΔPlocs,
and ΔPfs are expressed by (9)Bs=−∮ρgdz,ΔPlocs=Ws2∑i=1n(c2ρA2)i,ΔPfs=Ws2∮f12DeρA2dz.


### 3.2.3. Mass Flow Rate of the Third Loop

Because the size of the water pool is large enough, an
assumption, that the change of the pool water temperature can be neglected, is
rational. Similarly, by applying the momentum conservative equation, the mass
flow rate of the third loop is written as(10)∂Wt∂τ=(Bt−ΔPloct−ΔPft)∑i=1k(Δz/A)i, where Bt, ΔPloct,
and ΔPft are defined as follows: (11)Bt=ρpgL−∑j=1k(ρgΔz)j,ΔPloct=Wt2∑i=1n(c2ρA2)i,ΔPft=Wt2∑j=1k(fΔz2DeρA2)j.It is noted that the
equations for mass flow rate calculation of the three loops are simplified
equations with an assumption of constant flow rate along the circuit. This
simplification may cause inaccuracy especially in case of two-phase flow. However,
this simplified model has been successfully adopted in our previous
investigations (Su and Guo [8], Qiu et al. [10], Zejun et
al.  [11], Tian et al. [25, 26]). The comparisons of our results with those of RETRAN-02 and RELAP/MOD3
gave good agreements. So, using the simplified model in this calculation is still
believed to be feasible for the conceptual design of the PRHRS.


### 3.2.4. Pressure of the Secondary Loop

Under normal operation condition with rated core
power, the spatial variation of the pressure in the secondary loop cannot be neglected
because of the large pressure drop from the inlet to the outlet of the OTSG
secondary side (about 1.5 MPa). However, in case of natural circulation, the
spatial pressure difference of the secondary loop becomes very small as a
result of the loss of feed water pump head. Thus, an assumption, that the
spatial variation of the pressure in the secondary loop is negligible, can be
made. Consequently, by integrating the mass continuity equation along the
secondary loop, the pressure equation of the secondary loop can be written as(12)∑i=1n[(∂ρ∂h∂h∂τ+∂ρ∂p∂p∂τ)A⋅ΔZ]i=−∮∂W∂zdz. Practically,
the right-hand side of (12) equals zero. Thus, (12) is simplified as (13)∂p∂τ=−∑i=1n(ρ2A⋅ΔZ(∂υ/∂h)(∂h/∂τ))i∑i=1n(ρ2A⋅ΔZ(∂υ/∂p))i.


### 3.2.5. Tube Wall Heat Transfer

Because of the very small thickness of the tube wall,
lumped parameter method is used to calculate the wall heat transfer. Ignoring
the axial conduction heat transfer, the tube wall heat transfer equation is
expressed by(14)mCp∂Tw∂τ=H1A1(T1−Tw)−H2A2⋅(Tw−T2), where Tw is the average temperature of the tube wall; H1 and H2 are heat transfer coefficients of the two surfaces of the wall,
respectively; A1 and A2 are heat transfer area of the two surfaces of the wall,
respectively; T1 and T2 are the fluid temperatures, respectively.


### 3.2.6. Pipe and Plenum

In the PRHRS, there are pipes and plenums to connect
the major components. With an assumption of thermal isolation, the energy
conservative equation of them can be expressed by(15)Mdhdτ=W(hin−h).


### 3.2.7. Heat Transfer and Frictional Coefficient Correlations

The dominant heat transfer of the primary loop and the
third loop is single-phase mode, and the modes of the secondary loop are
single-phase and boiling heat transfer in the OTSG and condensation and
single-phase heat transfer in the heat exchanger. According to the
corresponding flow regimes, appropriate heat transfer and frictional
coefficient correlations are selected. Two-phase
frictional multiplier is used to calculate the two-phase flow pressure drop,
that is,(16)ftp=flo⋅Φtp2.The involved heat transfer and frictional coefficient
correlations are listed in Tables1 and 2, respectively.Table 1
Heat transfer correlations.
Flow
regimeCorrelationReferenceSingle-phase
waterLaminarCollier[27]TransitionInterpolationTurbulentSieder-Tate[28]Subcooled
boilingJens and
Lottes[23]Saturated
boilingChen[23]Transition/film
boilingGroeneveld[29]Superheated
vaporSieder-Tate[28]CondensationShaha[30]Table 2
Frictional coefficient correlations.
Flow
regimeCorrelationReferenceSingle
phaseLaminar flowDarcy[24]Transition flow0.048Turbulent flowBlasiusTwo phaseHomogeneous model[31]Drift flux modelChisholm[32]


## 3.2.1. Mass Flow Rate of the Primary Loop

By integrating the momentum conservative equation
along the primary loop, the mass flow rate equation is given by(1)∂WP∂τ∮1Adz=−∮∂P∂Zdz−∮1A∂∂z(WP2ρA)dz−∮ρgdz−WP2∑i=1n(c2ρA2)i−WP2∮f12DeρA2dz. In fact,
the second terms on the right hand of (1) can be  eliminated. By introducing
natural circulation driving head BP,
(1) is simplified as follows:(2)∂WP∂τ=(Ppump+BP−ΔPlocP−ΔPfP)∮(dz/A), where ΔPlocP  and ΔPfp are the local pressure drop and the friction
pressure drop along the primary loop, respectively; Ppump is the pressure  head of the MCP. BP, ΔPlocP,
and ΔPfp are defined by (3)Ppump=ρgHpump,BP=−∮ρgdz,ΔPlocP=WP2∑i=1n(c2ρA2)i,ΔPfP=WP2∮f12DeρA2dz.The pressure head of the MCP during the transient
process is a very important parameter to calculate the mass flow rate of the
primary loop. However, the pressure head of the MCPs reduces rapidly to zero
due to the small inertia rotation after a reactor trip. Moreover, as mentioned
above, the MCPs stop and the by-pass valves are opened to enhance the natural
circulation under natural circulation conditions. Because the local form loss
coefficient of the by-pass valve is much less than that of the MCP, most of the
primary coolant flows through the by-pass valve. The relationship between the
local pressure drop of the MCP and the by-pass valve is expressed by(4)Δppump=Δpv. That is, (5)12cpumpWpump2Apump2ρ=12cvWv2Av2ρ. While (6)Wp=Wpump+Wv.
Substituting (5) and (6) into (4), the local pressure drop of the
MCP is (7)Δppump=12cpumpW2(1+Avcpump/cv/Apump)2Apump2ρ.


## 3.2.2. Mass Flow Rate of the Secondary Loop

Similarly, by integrating the momentum conservative
equation along the secondary loop, the mass flow rate equation is given by(8)∂Ws∂τ=(Bs−ΔPlocs−ΔPfs)∮(dz/A), where Bs, ΔPlocs,
and ΔPfs are expressed by (9)Bs=−∮ρgdz,ΔPlocs=Ws2∑i=1n(c2ρA2)i,ΔPfs=Ws2∮f12DeρA2dz.


## 3.2.3. Mass Flow Rate of the Third Loop

Because the size of the water pool is large enough, an
assumption, that the change of the pool water temperature can be neglected, is
rational. Similarly, by applying the momentum conservative equation, the mass
flow rate of the third loop is written as(10)∂Wt∂τ=(Bt−ΔPloct−ΔPft)∑i=1k(Δz/A)i, where Bt, ΔPloct,
and ΔPft are defined as follows: (11)Bt=ρpgL−∑j=1k(ρgΔz)j,ΔPloct=Wt2∑i=1n(c2ρA2)i,ΔPft=Wt2∑j=1k(fΔz2DeρA2)j.It is noted that the
equations for mass flow rate calculation of the three loops are simplified
equations with an assumption of constant flow rate along the circuit. This
simplification may cause inaccuracy especially in case of two-phase flow. However,
this simplified model has been successfully adopted in our previous
investigations (Su and Guo [8], Qiu et al. [10], Zejun et
al.  [11], Tian et al. [25, 26]). The comparisons of our results with those of RETRAN-02 and RELAP/MOD3
gave good agreements. So, using the simplified model in this calculation is still
believed to be feasible for the conceptual design of the PRHRS.


## 3.2.4. Pressure of the Secondary Loop

Under normal operation condition with rated core
power, the spatial variation of the pressure in the secondary loop cannot be neglected
because of the large pressure drop from the inlet to the outlet of the OTSG
secondary side (about 1.5 MPa). However, in case of natural circulation, the
spatial pressure difference of the secondary loop becomes very small as a
result of the loss of feed water pump head. Thus, an assumption, that the
spatial variation of the pressure in the secondary loop is negligible, can be
made. Consequently, by integrating the mass continuity equation along the
secondary loop, the pressure equation of the secondary loop can be written as(12)∑i=1n[(∂ρ∂h∂h∂τ+∂ρ∂p∂p∂τ)A⋅ΔZ]i=−∮∂W∂zdz. Practically,
the right-hand side of (12) equals zero. Thus, (12) is simplified as (13)∂p∂τ=−∑i=1n(ρ2A⋅ΔZ(∂υ/∂h)(∂h/∂τ))i∑i=1n(ρ2A⋅ΔZ(∂υ/∂p))i.


## 3.2.5. Tube Wall Heat Transfer

Because of the very small thickness of the tube wall,
lumped parameter method is used to calculate the wall heat transfer. Ignoring
the axial conduction heat transfer, the tube wall heat transfer equation is
expressed by(14)mCp∂Tw∂τ=H1A1(T1−Tw)−H2A2⋅(Tw−T2), where Tw is the average temperature of the tube wall; H1 and H2 are heat transfer coefficients of the two surfaces of the wall,
respectively; A1 and A2 are heat transfer area of the two surfaces of the wall,
respectively; T1 and T2 are the fluid temperatures, respectively.


## 3.2.6. Pipe and Plenum

In the PRHRS, there are pipes and plenums to connect
the major components. With an assumption of thermal isolation, the energy
conservative equation of them can be expressed by(15)Mdhdτ=W(hin−h).


## 3.2.7. Heat Transfer and Frictional Coefficient Correlations

The dominant heat transfer of the primary loop and the
third loop is single-phase mode, and the modes of the secondary loop are
single-phase and boiling heat transfer in the OTSG and condensation and
single-phase heat transfer in the heat exchanger. According to the
corresponding flow regimes, appropriate heat transfer and frictional
coefficient correlations are selected. Two-phase
frictional multiplier is used to calculate the two-phase flow pressure drop,
that is,(16)ftp=flo⋅Φtp2.The involved heat transfer and frictional coefficient
correlations are listed in Tables1 and 2, respectively.Table 1
Heat transfer correlations.
Flow
regimeCorrelationReferenceSingle-phase
waterLaminarCollier[27]TransitionInterpolationTurbulentSieder-Tate[28]Subcooled
boilingJens and
Lottes[23]Saturated
boilingChen[23]Transition/film
boilingGroeneveld[29]Superheated
vaporSieder-Tate[28]CondensationShaha[30]Table 2
Frictional coefficient correlations.
Flow
regimeCorrelationReferenceSingle
phaseLaminar flowDarcy[24]Transition flow0.048Turbulent flowBlasiusTwo phaseHomogeneous model[31]Drift flux modelChisholm[32]


## 3.3. Nodalization of the PRHRS

In order to numerically simulate the thermal hydraulic
characteristics of the PRHRS, the whole system shown in Figure1 is divided
into many control volumes and junctions according to the different geometrical
and heat transfer conditions. Figure 2 schematically shows the nodalization of
the PRHRS. The primary circuit model used in the thermal hydraulic analysis
consists of a core, a steam generator, a pump, a pressurizer, a downcomer, and
plenums. The modeling of the PRHRS is composed of a steam generator, a heat
exchanger, a water pool, pipes, plenums, and valves. In the core, the steam
generator and the heat exchanger, fine control volume division is used to
properly predict the heat transfer phenomena. The number of the control volume
can be easily changed for different calculation requirements.Figure 2
SCPRHRS nodalization for the PRHRS.


## 4. Numerical Method and Code Description

In order to theoretically analyze the thermal
hydraulic characteristics of the PRHRS, the above equations need to be
numerically solved. Through discretizing the spatial terms of the above
differential equations, they have a form in common as follows:(17)dy⇀dτ=f⇀(t,y⇀,y⇀′),y⇀(τ0)=y⇀0.It is noted that numeric
solution of these equations is an initial value problem of nonlinear
first-order ordinary differential equations with variable coefficients. These
differential equations used to describe the reactor system usually have large
stiffness. It is shown that, using the traditional algorithm such as the Runge-Kutta
algorithm to solve the stiff differential equations may result in failure in
some cases. In the present paper, Gear algorithm (Yuan Zhaoding  [33]; Su et
al.  [34]; Tian et al. [25]; Yun et al. [35]), which is a backward
difference implicit algorithm and especially suitable for solving stiff
differential equations, is adopted to solve the above equations.Base on the theoretical model and solution method, a simulation code, SCPRHRS,
is developed. The code is in Fortran 90 format and can be maintained in the
PC/Windows environment. For convenient maintenance and readability of the code,
modular programing
techniques are adopted. The main function modules are data input module,
initialization module, transient module, derivative module, numerical method
module, auxiliary module, thermophysical property module, output module, and so
forth. All involved
heat transfer and friction coefficient correlations are supplied in the auxiliary
module.
Derivative module is used to calculate the right-hand side of the differential
equations (like (17)). Modification of these modules or addition of new
modules can be easily done for different calculation requirements. The calling
relationship of these modules and the N-S flowchart of SCPRHRS are shown in Figures
3 and 4, respectively.Figure 3
Calling
relationships of the modules.Figure 4
N-S flowchart of
the code.


## 5. Initial Conditions

The major structural and initial parameters used for
the theoretical analysis are shown in Table3. There are two sets of PRHRS,
each of which has the same characteristics and is connected with four OTSGs,
respectively. In the calculation, because of the large heat capacity of the
water pool, an assumption, that the inlet temperature of the third loop is
constant, is made. Before the PRHRS starts up, the reactor is under a normal
operating steady state, and the PRHRS and the third loop do not work.Table 3
Main parameters of SG and PRHRS.
ParameterValueInitial
core power160 MWSteam
generatorPrimary
operation pressure15.5 MPaPrimary mass flow rate980 kg /sPrimary
inlet temperature295°CPrimary outlet temperature265°CSecondary mass flow rate60 kg /sSecondary
inlet temperature60°CSecondary
outlet temperature270°CSecondary pressure3.0 MPaDiameter of inner tube8×1mmDiameter of outer tube12×1mmLength of the tube2.0 mPassive
heat removal systemSecondary initial temperature30°CSecondary initial pressure3.0 MPaDiameter of tube25×2.5 mmLength of the tube2.0 mWater temperature of WP30°CWP pressure0.1 MPa


## 6. Results
and Discussion

### 6.1. Transient Thermal Hydraulic Characteristics of PRHRS

Figure5 shows the core power, the heat transferred to
secondary side of the steam generator, and the heat transferred to the WP after
the reactor is shut down. It can be seen that the core power and the heat
transferred to the secondary side of the steam generator decrease rapidly at
the initial stage and at about 20 seconds they begin to decrease slowly. The
heat transferred to the WP is under a very low level at the beginning of the
transient process. With the establishment of the natural circulation in the
PRHRS, the heat transferred to the WP increases gradually, and at about 150 seconds
it becomes higher than that transferred to the secondary side of the steam
generator. At about 300 seconds, the heat transferred to the secondary side of
the steam generator is higher than the core power. It can be assumed that after
this point the decay heat can be removed safely.Figure 5
Decay
power and heat transferred in the SG and PRHRS.After the reactor is shut down, the control system
makes the MCPs stopped, the forced circulation of the primary loop transits to
natural circulation. The mass flow rate of the primary loop is shown in Figure6.
Because of the rapid decrease of the core power, the pressure and the water
level of the pressurizer decrease immediately at the initial stage. On the
other hand, with the increase of the secondary loop pressure (see Figure 7),
the saturated temperature of the secondary loop increases  correspondingly. The
temperature difference of the two sides of the steam generator becomes smaller,
which leads to the degradation of the heat transfer of the steam generator.
Consequently, the pressure and the water  level of the pressurizer have a slight
increase. Subsequently, with the farther decrease of the core power and the establishment
of the natural circulation of the three loops, they begin to decrease slowly.Figure 6
Mass flow
rate of the primary loop, pressure, and water level of the pressurizer.Figure 7
Mass flow rate and pressure of the secondary loop, mass flow rate and outlet temperature of
the third loop.At the initial transient stage, the sudden closure of
the main steam valves as well as the higher heat transferred to the secondary
side of the steam generator than that removed by the residual heat exchanger
(see Figure5) causes a rapid increase of the secondary loop pressure as shown
in Figure 7. With the establishment of the natural circulation of the three
loops, it begins to decrease slowly. It is noted that the peak value of the
secondary loop pressure is very high without considering the overpressure
protection. Thus, a pressure protection measure should be included to prevent
the secondary loop pressure exceeding the acceptable value. The mass flow rate
of the secondary loop is also shown in Figure 7. After the PRHRS starts up, the
water in it immediately enters into the steam generators, which causes a rapid
increase of the mass flow rates in the heat exchanger. The cold water in the
shell-side of the heat exchanger is heated gradually after the high-temperature
fluid from the steam generator enters the tube-inside of the heat exchanger. At
about 40 seconds, the outlet fluid temperature of the third loop reaches its
maximum value as shown in Figure 7. Correspondingly, the transient behavior of
the third loop mass flow rate is similar to the outlet fluid temperature of the
third loop (see Figure 7). Figure 7 also shows that the establishment of the
natural circulation in the third loop needs a period of time (about 40 seconds).
After reaching their peak values, they start to decrease slowly with the decrease
of the heat transferred to the third loop.


### 6.2. Effect of Parameter on the Characteristics of PRHRS

Height difference, between the steam generator and the
heat exchanger, and the heat transfer area of the heat exchanger are the two
main parameters affecting the thermal hydraulic characteristics of the PRHRS.
The effects of these two factors are investigated in this paper. The variation
of the heat transfer area of the heat exchanger is carried out through changing
the number of the heat transfer tube without changing their length.The mass
flow rates of the third loop with different height difference and heat transfer
area are shown in Figure8. F is the heat transfer area of the heat exchanger,
while H is the height difference between the steam generator and the heat
exchanger in Figure 8. It shows that the higher the height difference between
the steam generator and the heat exchanger, the easier the establishment of the
natural circulation in the water pool and the larger the peak value of the mass
flow rate. The initial capacity of the cold water in the tube-inside of the
heat exchanger increases with the increase of the heat transfer area of the
heat exchanger, which leads that the time when the fluid with high temperature
from the steam generator replaces the initial cold water is longer with larger
heat transfer area (see Figure 9). Correspondingly, the smaller the heat
transfer area of the heat exchanger, the earlier the outlet fluid temperature
of the third loop reaching its maximum value as shown in Figure 10. Therefore,
with the decrease of the heat transfer area, the establishment of the natural
circulation in the water pool becomes earlier (see Figure 8).Figure 8
Mass flow
rates of the third loop with different height differences and heat transfer
areas.Figure 9
Outlet fluid temperature in the heat exchanger of the
secondary loop with different height differences
and heat transfer areas.Figure 10
Outlet
fluid temperature of the third loop with different height differences and heat
transfer areas.The pressure of the secondary loop and the pressurizer
are shown in Figures11 and 12, respectively. The peak value of the secondary
loop pressure decreases with the increase of the height difference between the
steam generator and the heat exchanger, and increases with the increase of the
heat transfer area of the heat exchanger. Figure 11 also indicates that the
effects of the height difference between the steam generator and the heat exchanger
on the pressure of the secondary loop is larger than that of the heat transfer
area of the heat exchanger. For the pressure of the pressurizer, the higher the
height difference between the steam generator and the heat exchanger and the
larger the transfer area of the heat exchanger, the quicker the decrease of it
(see Figure 12). Consequently, the higher height difference between the steam
generator and the residual heat exchanger and the larger heat transfer area of
the residual heat exchanger are favorable to the passive residual heat removal
system.Figure 11
Pressure
of the secondary loop with different height differences and heat transfer areas.Figure 12
Pressure
of pressurizer with different height differences and heat transfer areas.


## 6.1. Transient Thermal Hydraulic Characteristics of PRHRS

Figure5 shows the core power, the heat transferred to
secondary side of the steam generator, and the heat transferred to the WP after
the reactor is shut down. It can be seen that the core power and the heat
transferred to the secondary side of the steam generator decrease rapidly at
the initial stage and at about 20 seconds they begin to decrease slowly. The
heat transferred to the WP is under a very low level at the beginning of the
transient process. With the establishment of the natural circulation in the
PRHRS, the heat transferred to the WP increases gradually, and at about 150 seconds
it becomes higher than that transferred to the secondary side of the steam
generator. At about 300 seconds, the heat transferred to the secondary side of
the steam generator is higher than the core power. It can be assumed that after
this point the decay heat can be removed safely.Figure 5
Decay
power and heat transferred in the SG and PRHRS.After the reactor is shut down, the control system
makes the MCPs stopped, the forced circulation of the primary loop transits to
natural circulation. The mass flow rate of the primary loop is shown in Figure6.
Because of the rapid decrease of the core power, the pressure and the water
level of the pressurizer decrease immediately at the initial stage. On the
other hand, with the increase of the secondary loop pressure (see Figure 7),
the saturated temperature of the secondary loop increases  correspondingly. The
temperature difference of the two sides of the steam generator becomes smaller,
which leads to the degradation of the heat transfer of the steam generator.
Consequently, the pressure and the water  level of the pressurizer have a slight
increase. Subsequently, with the farther decrease of the core power and the establishment
of the natural circulation of the three loops, they begin to decrease slowly.Figure 6
Mass flow
rate of the primary loop, pressure, and water level of the pressurizer.Figure 7
Mass flow rate and pressure of the secondary loop, mass flow rate and outlet temperature of
the third loop.At the initial transient stage, the sudden closure of
the main steam valves as well as the higher heat transferred to the secondary
side of the steam generator than that removed by the residual heat exchanger
(see Figure5) causes a rapid increase of the secondary loop pressure as shown
in Figure 7. With the establishment of the natural circulation of the three
loops, it begins to decrease slowly. It is noted that the peak value of the
secondary loop pressure is very high without considering the overpressure
protection. Thus, a pressure protection measure should be included to prevent
the secondary loop pressure exceeding the acceptable value. The mass flow rate
of the secondary loop is also shown in Figure 7. After the PRHRS starts up, the
water in it immediately enters into the steam generators, which causes a rapid
increase of the mass flow rates in the heat exchanger. The cold water in the
shell-side of the heat exchanger is heated gradually after the high-temperature
fluid from the steam generator enters the tube-inside of the heat exchanger. At
about 40 seconds, the outlet fluid temperature of the third loop reaches its
maximum value as shown in Figure 7. Correspondingly, the transient behavior of
the third loop mass flow rate is similar to the outlet fluid temperature of the
third loop (see Figure 7). Figure 7 also shows that the establishment of the
natural circulation in the third loop needs a period of time (about 40 seconds).
After reaching their peak values, they start to decrease slowly with the decrease
of the heat transferred to the third loop.


## 6.2. Effect of Parameter on the Characteristics of PRHRS

Height difference, between the steam generator and the
heat exchanger, and the heat transfer area of the heat exchanger are the two
main parameters affecting the thermal hydraulic characteristics of the PRHRS.
The effects of these two factors are investigated in this paper. The variation
of the heat transfer area of the heat exchanger is carried out through changing
the number of the heat transfer tube without changing their length.The mass
flow rates of the third loop with different height difference and heat transfer
area are shown in Figure8. F is the heat transfer area of the heat exchanger,
while H is the height difference between the steam generator and the heat
exchanger in Figure 8. It shows that the higher the height difference between
the steam generator and the heat exchanger, the easier the establishment of the
natural circulation in the water pool and the larger the peak value of the mass
flow rate. The initial capacity of the cold water in the tube-inside of the
heat exchanger increases with the increase of the heat transfer area of the
heat exchanger, which leads that the time when the fluid with high temperature
from the steam generator replaces the initial cold water is longer with larger
heat transfer area (see Figure 9). Correspondingly, the smaller the heat
transfer area of the heat exchanger, the earlier the outlet fluid temperature
of the third loop reaching its maximum value as shown in Figure 10. Therefore,
with the decrease of the heat transfer area, the establishment of the natural
circulation in the water pool becomes earlier (see Figure 8).Figure 8
Mass flow
rates of the third loop with different height differences and heat transfer
areas.Figure 9
Outlet fluid temperature in the heat exchanger of the
secondary loop with different height differences
and heat transfer areas.Figure 10
Outlet
fluid temperature of the third loop with different height differences and heat
transfer areas.The pressure of the secondary loop and the pressurizer
are shown in Figures11 and 12, respectively. The peak value of the secondary
loop pressure decreases with the increase of the height difference between the
steam generator and the heat exchanger, and increases with the increase of the
heat transfer area of the heat exchanger. Figure 11 also indicates that the
effects of the height difference between the steam generator and the heat exchanger
on the pressure of the secondary loop is larger than that of the heat transfer
area of the heat exchanger. For the pressure of the pressurizer, the higher the
height difference between the steam generator and the heat exchanger and the
larger the transfer area of the heat exchanger, the quicker the decrease of it
(see Figure 12). Consequently, the higher height difference between the steam
generator and the residual heat exchanger and the larger heat transfer area of
the residual heat exchanger are favorable to the passive residual heat removal
system.Figure 11
Pressure
of the secondary loop with different height differences and heat transfer areas.Figure 12
Pressure
of pressurizer with different height differences and heat transfer areas.


## 7. Conclusions

A theoretical one-dimensional model and a simulation
code (SCPRHRS) are developed to investigate the thermal hydraulic
characteristics of a new type of PRHRS, connected to the reactor coolant system
via the secondary side of the steam generators, for an integral PWR. The model
is based on the fundamental conservation principles: the mass, momentum, and
energy conservation equations. System component models are included according
to the special design features of it. All possible flow and heat transfer conditions are
considered and the corresponding optional models are supplied in the code.The transient behavior of the PRHRS and the effects of
parameters such as the height difference between the steam generator and the
heat exchanger and the heat transfer area of the heat exchanger are studied in
detail. It is found that the calculated parameter variation trends are
reasonable. The decay heat can be safely removed by the PRHRS. The higher
height difference between the steam generator and the residual heat exchanger
and the larger heat transfer area of the residual heat exchanger are favorable
to the passive residual heat removal system. It is noted that the peak value of
the secondary loop pressure is very high without considering the overpressure
protection. Thus, a pressure protection should be included to prevent the
secondary loop pressure exceeding the acceptable value. Also, experimental
verification of the code as well as the model improvement is expected to be
going on in the future since there is no experimental data can be adopted
currently.



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*Source: 473795-2009-03-18.xml*