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Comparison of Two Models for a Pebble Bed Modular Reactor Core

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					2nd International Topical Meeting on HIGH TEMPERATURE REACTOR TECHNOLOGY
Beijing, CHINA, September 22-24, 2004                                                       #Paper D08




        Comparison of Two Models for a Pebble Bed Modular Reactor Core
                          Coupled to a Brayton Cycle

                              Ayelet Walter, Alexander Schulz, Günter Lohnert
                        Institute of Nuclear Technology and Energy Systems (IKE),
                    University of Stuttgart, Pfaffenwaldring 31, 70569 Stuttgart, Germany
          Tel: +49-(0)711-6852145 ; Fax: +49-(0)711-6852010; e-mail: walter@ike.uni-stuttgart.de

                                                Abstract

The Pebble Bed Modular Reactor (PBMR) plant is a promising concept for inherently safe nuclear
power generation. This paper presents two dynamic models for the core of a High Temperature
Reactor (HTR) power plant with a helium gas turbine. Both the PBMR and its power conversion unit
(PCU) based on a three-shaft, closed cycle, recuperative, inter-cooled Brayton cycle have been
modeled with the network simulation code Flownex.

One model utilizes a core simulation already incorporated in the Flownex software package, and the
other a core simulation based on multi-dimensional neutronics and thermal-hydraulics. The reactor
core modeled in Flownex is a simplified model, based on a zero-dimensional point-kinetics approach,
whereas the other model represents a state-of-the-art approach for the solution of the neutron diffusion
equations coupled to a thermal-hydraulic part describing realistic fuel temperatures during fast
transients. Both reactor models were integrated into a complete cycle, which includes a PCU modeled
in Flownex.

Flownex is a thermal-hydraulic network analysis code that can calculate both steady-state and transient
flows. An interesting feature of the code is its ability to allow the integration of an external program
into Flownex by means of a memory map file.

The total plant models are compared with each other by calculating representative transient cases
demonstrating that the coupling with external models works sufficiently. To demonstrate the features
of the external program a hypothetical fast increase of reactivity was simulated.


1      Introduction

Substantial interest has emerged in advanced reactors over the last few years. This interest has been
motivated by the view of new nuclear power reactors that will be needed to provide low carbon
generation electricity and possibly hydrogen to support the future growth in demand of both of these
commodities [1]. Some governments feel that substantially different designs will be needed to satisfy
the desires for public perception, improved safety, proliferation resistance, reduced waste and
competitive economics. This has motivated the creation of the Generation IV Nuclear Energy Systems
program in which ten countries have agreed on a framework for international cooperation in research
for advanced reactors. Six designs have been selected for continued evaluation with the objective of
deployment by 2030. One of these designs is the Very High Temperature Reactor (VHTR), which is a
thermal neutron spectrum system with a helium-cooled graphite moderated core.

The pebble bed modular reactor (PBMR), being currently developed in South Africa as a world wide
international association between Eskom the national utility, and other industrial partners, will
represent a key milestone on the way to achievement of a new generation of High Temperature
Reactor design objectives.


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COMPARISON OF TWO MODELS FOR A PEBBLE BED MODULAR REACTOR CORE COUPLED TO A BRAYTON CYCLE            #D08


This high temperature gas cooled reactor is based on the recuperative inter-cooled closed loop Brayton
cycle using helium as coolant (see in figure 1) [2]. Starting at 1, helium at a relatively low pressure
and temperature (1) is compressed by a low-pressure compressor (LPC) to an intermediate pressure (2)
after which it is cooled in an inter-cooler to state 3. A high pressure compressor (HPC) then
compresses the helium to state 4. From 4 to 5 the helium is preheated in the recuperator before
entering the reactor, which heats the helium to state 6. After the reactor the hot high pressure helium is
expanded in a high pressure turbine (HPT) to state 7 after which it is further expanded in a low
pressure turbine (LPT) to state 8. The high pressure turbine drives the high pressure compressor while
the low pressure turbine drives the low pressure compressor. After the low pressure turbine the heated
helium is further expanded in the power turbine, which drives the generator, to the pressure 9, which is
approximately the same pressure at 10 and 1. From 9 to 10 the still hot helium is cooled in the
recuperator after which it is further cooled in the pre-cooler to state 1. This completes the cycle. The
heat rejected from 9 to 10 is equal to the heat transferred to the helium from 4 to 5.
                                               4                  6
                              HPC                                         HPT
                                      3                                          Reactor

                                               Inter-
                                               cooler             7
                                                2

                              LPC                                         LPT
                                      1                                   8
                             Pre-
                                                        Power
                             cooler
                                                        turbine
                                                                                Generator
                              BPV         10                          9

                                                              5
                                Recuperator

    Figure 1. Schematic diagram of the PBMR high temperature gas cooled reactor Brayton cycle [2].

The complexity associated with the thermal-flow design of the cycle requires the use of a variety of
analysis techniques and simulation tools. These range from simple one-dimensional models that do not
capture all the significant physical phenomena to large-scale three-dimensional CFD codes that, for
practical reasons, can not simulate the entire plant as a single integrated model [3]. Furthermore, the
treatment of the coupled neutronics and thermal-hydraulics in the reactor core coupled to the PCU
network is a complex part which requires a realistic connection of a detailed core model with the
network model.
One of the most prominent codes that provide a suitable compromise, is the thermal-flow network
simulation code Flownex.


2    Description of Flownex

Flownex is a network simulation code, which encompasses the ability to perform detailed analysis and
design of complex thermal-fluid systems such as power plants. Flownex solver, described elsewhere
[4], is based on the implicit pressure correction method (IPCM) that solves the momentum equation at
each element and the continuity and energy equations at each node in large arbitrary structured
networks for both steady state and dynamic flow. The solver can deal with both fast and slow
transients. Fast simulation speeds, on standard desktop computers, allow for real time simulations to
be performed. The code has been validated against other codes as well as with experimental data.

With the network approach, a complex thermal-fluid system is represented as a network of one-
dimensional elements connected at common nodes (see figure 2). In this figure, elements are denoted
by cycles and nodes are denoted by squares. Elements represent components such as pipes,
compressors, turbines, heat exchangers, control valves or the pebble bed reactor core.



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HTR 2004                                                                            Beijing, CHINA, 2004.9




                    1        1     2      2    3        3   4      4     5



                                               5            6     13     7


                                               6        8   7      9     8



                                               10           11          12


                                               9            10          11


                        Figure 2. Example of Flownex network representation [5]

The code features the ability to simultaneously solve multiple gas and liquid networks that are
connected through heat exchangers. It also enables the user to construct re-usable models of complex
components or sub-systems such as gas-cooled nuclear reactors and heat exchangers. The reactor and
the heat exchangers are not treated as lumped systems but as distributed systems. The code can also
deal with conductive heat transfer through solid structures.
Advanced rotating model allows for stage-by-stage modeling of compressors and turbines. Other
features of the code are its ability to design PID controllers and control systems.
The software can be directly linked with other external computational codes, which can be externally
coupled to it.


3   Characterization of the Flownex core model

The pebble bed reactor core is made up of fuel spheres and passive graphite spheres [6], such as the
one shown schematically in figure 3. Each of the fuel spheres that make up the core consists of an
inner fuel region with a 50 mm outer diameter made up of coated Uranium dioxide (UO2) particles
imbedded in a graphite matrix. A fuel-free graphite protective layer with an outer diameter of 60 mm
covers the fuel region.




                         Figure 3. Schematic representation of a fuel sphere [2].




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COMPARISON OF TWO MODELS FOR A PEBBLE BED MODULAR REACTOR CORE COUPLED TO A BRAYTON CYCLE           #D08




    Figure 4. Schematic two-dimensional representation of the core of the pebble bed reactor [2].

A schematic two-dimensional representation of the geometry of the reactor core is shown in figure 4.
The inner core region contains passive graphite spheres while the outer active core region is filled with
fuel spheres. Helium gas enters the top of the reactor core at approximately 500°C. The gas is heated
primarily through the active core region where heat is generated inside the fuel spheres. Upon leaving
the core at the bottom the hot gas is mixed with gas from the passive region to obtain a fully mixed
exit temperature of approximately 900°C.




    Figure 5. Graphical representation of the thermal-hydraulic network for the reactor core [2].

The existing model consists of three main parts [7]:
• Heat transfer and fluid flow of the gas within the core. The model is based on a discretised two
   dimensional axi-symetric network, which consists of any number of control volumes in the axial
   and/or radial directions as demonstrated in figure 5. The model includes the convective heat
   transfer between the gas and the surface of a representative sphere in each of the control volumes.
   However, it only allows for the simulation of the core itself, excluding all core structures, and is
   based on a core layout with a homogeneous graphite pebble region at the center and a
   homogeneous fuel pebble region in the annulus without a solid central reflector column. Also, it
   does not allow for the addition or extraction of leak flows from the inner or outer perimeter of the
   core and the gas inlet and outlet is assumed to be from voids at the very top and the very bottom of
   the core.




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HTR 2004                                                                              Beijing, CHINA, 2004.9



•   Heat conduction within the pebbles. Each of the core control volumes contains a representative
    pebble for which the heat conduction is modeled in a one-dimensional spherical frame of reference
    together with the convection heat transfer between the gas and the surface of the sphere. The
    sphere consists of an outer graphite layer and the inner fuel matrix region, both of which can be
    discretised into any number of spherical `onion ring shaped´ control volumes. This allows for the
    calculation of the temperature distribution within the pebbles in any region of the core. The
    nuclear power generated in the core is distributed with the fuel matrix region only in the form of a
    source term in the heat conduction equation.
•   Nuclear power and decay heat generation. The model is based on a zero-dimensional point-
    kinetics approach and calculates a single normalized power level for the core as a whole based on
    reactivity feedback equations taking into account the average fuel and moderator temperatures,
    xenon concentration and the control rod settings. The total reactor power is distributed among the
    axial layers of the core based on a fixed normalized power distribution profile. However, it does
    not account for any radial power distribution profile on each of the different axial levels. Figure 6
    shows a schematic representation of the interaction between the three models mentioned.




           Figure 6. Schematic illustration of the interaction between the three models [2].

The purpose of this model was not to do detailed reactor design, but rather to allow for the integrated
simulation of the reactor together with the PCU within acceptable computer simulation times. Hence,
the requirement for this existing model was to provide quick results of the main flow and heat transfer
phenomena in the core only, in order to obtain boundary values for the simulation of the rest of the
PCU [7].
The phenomena that cannot be simulated in the existing model include the following:
• The presence of a central reflector column that implies that the core itself has an annular rather
    than a cylindrical shape.
• The addition and extraction of gas via purpose provided channels and/or leak paths along the inner
    or outer perimeters of the core.
• The simulation of heat transfer and fluid flow through porous and solid core structures
    surrounding the core.
• The simulation of fluid flow and heat transfer, including radiation and natural convection, in
    purpose provided cavities between core structures with a two-dimensional rather than one-
    dimensional nature.
• The ability to take into account variations in porosity throughout the core.
• The ability to specify normalized radial power distribution profiles within the different axial layers
    in the core.
• The ability to account for heat generation that may occur in any of the core structures.

Therefore, a need exists for the development of a more comprehensive pebble bed reactor model that
can still provide with integrated plant simulations, but includes the phenomena listed above.




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COMPARISON OF TWO MODELS FOR A PEBBLE BED MODULAR REACTOR CORE COUPLED TO A BRAYTON CYCLE          #D08


4   Description of an alternative (WKIND) core model

The core model built in into Flownex describes the reactor mainly like a point without detailed
consideration of changes in power distribution during reactivity transients (e. g. by control rod
movement, strong temperature changes or spatial changes in xenon distribution). These effects can
only be regarded by solving the space dependent neutron diffusion equation together with an adequate
model for calculating the temperatures of active core and reflector zones. Furthermore, it is very
important to model the detailed heat transfer from fuel zone in the coated particle to the graphite
matrix and finally to the coolant gas since the fuel temperature is mainly responsible for the negative
reactivity feedback and a homogeneous model under-estimates the fuel temperature and
correspondingly over-estimates the power increase for fast reactivity transients.

As several verified core models for coupled neutronics and thermal-hydraulics exist, it is obviously
needed to couple such stand alone core models with a corresponding network for the PCU to get the
realistic boundary conditions and core-PCU interaction for the simulation of operational and
accidental transients. Presently at IKE two programs for core models are available: WKIND and
RZKIND [8].

 WKIND is a one-dimensional neutronics thermal-hydraulics code which solves the one group neutron
diffusion equation in axial direction based on a set of prepared cross sections which regard spectrum
effects from fuel, moderator, reflector (via bucklings), control rods, small absorber spheres (SAS) and
xenon. The thermal-hydraulics part regards the average axial fuel, moderator and gas temperature
distribution in the core as well as the reflector temperature distribution. An important feature is the
detailed model for the heat transport from fuel in the coated particle to the moderator. For fast
transient this is very important since the relaxation time for heat transport from the graphite is
dominant for the fuel temperature and is therefore responsible for a fast negative feedback via the
Doppler effect. The cross section sets used in WKIND will be prepared by the stationary HTR
neutronics and thermal-hydraulics system WKIND [9] developed by Framatome ANP GmbH.

RZKIND is the two-dimensional (R,Z) version of WKIND, but with a different solver for the
neutronics and the thermal-hydraulics equations. The thermal-hydraulics equations can be solved
alternatively to the original version of RZKIND also by the 2D THERMIX/KNOVEK code . At the
moment the detailed fuel temperature model of WKIND is not yet implemented into RZKIND but it
will be done in future. With the core models available several transients can be treated with sufficient
accuracy by the 1D-method WKIND. For a more detailed transient analysis with significant changes
in radial and axial power distributions the 2D version RZKIND and if necessary in future also a 3D
version will be available.

The coupling with the PCU network will be done via an interface with Flownex in order to simulate
the realistic boundary conditions for the core mass flow and the temperature and pressure at the inlet
node. The results of the neutronics thermal-hydraulics model serve as the transferred energy from core
to the coolant and the pressure drop.

Both codes were validated against theoretical and experimental results especially for the German AVR
Reactor and reviewed by German licensing authorities for the HTR-Modul concept.

The codes WKIND and RZKIND allow for the following quasi stationary and transient simulations:

•   Slow transients due to load changes, start up, shut down;
•   Analysis of slow xenon transients after load changes;
•   Slow transients after restart from a hot stand-by;
•   Slow transients due to recriticality after core heat-up accidents;
•   Fast transients due to changes of control rod position, SAS position or loss of absorbing
    substances;




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HTR 2004                                                                                 Beijing, CHINA, 2004.9



•   Fast transients due to changes of coolant mass flow;
•   Fast transients due to changes of coolant inlet temperature;
•   Fast transients due to ingress of moderating substances (e. g. water);
•   Fast transients due to reactivity increase because of compression of the pebble bed.

Once these codes are coupled with a network model, the parameters: coolant inlet temperature and
coolant mass flow through the core are not specified in the WKIND or RZKIND input, but are given
from Flownex. The time dependant control rod or SAS absorber position (or any other external
reactivity event) will be specified in the core model input description. The outlet temperature and
power of the core will be transmitted to the Flownex model. If there are actions initiated by the reactor
protection system, they can be formulated by the core model input description (e. g. scram by too high
reactor power or exceeding of maximum outlet temperature) or by the interface core model – Flownex
or by the input data tables of diverse Flownex elements (e. g. predefined set of time points for opening
valves etc.). With these features a realistic simulation of diverse operational and accidental transients
can be formulated and executed by the coupled Flownex-WKIND (RZKIND) model. Pre-condition for
a successful coupled calculation is a consistency of the core parameters and the network parameters
for the initial conditions of the transient and a synchronous solving of the core model and network
equations.


5   Coupling of Flownex Power Conversion Unit model with an alternative core model

A system code consisting of the dynamic systems code Flownex and the neutron kinetic/dynamic code
WKIND has been created through the use of an independent software component. The main goal of
the design of this coupling component was to develop a software solution, which enables a coupling
between the two before mentioned applications as well as having the opportunity to couple arbitrary
components with Flownex.

The basic coupling technique is a time step based data exchange. After the initialization sequence the
two applications alternately calculate the results for a distinct time step. Each application is interrupted
after one time step, so that the data can be read from the coupling component. Hereafter the data is
processed and transferred to the second application, which is now able to calculate the next time step.
As long as the calculation proceeds, the data is transferred back to the first application.

In order to enable such a time step based data exchange, the participating applications have to provide
suitable interfaces, that can be used within a software component. Flownex and WKIND provide
different interfaces, which are described more in details as following:

•   Flownex: Flownex and an external component interact by means of a memory map file. Methods
    for the usage and handling of such a memory map file are provided by the so called Windows®
    API (application programming interface). The Windows® API is an inherent part of the
    Windows® operating system. In order to enable the interaction of two applications by means of a
    memory map file, the Windows® API provides a global access point for the file. The input and
    output variables stored in that file are defined within Flownex.

•   WKIND: The interface for data exchange provided by WKIND is a file based mechanism. When
    WKIND is initialized a file is created. This file contains the time step size, the inlet temperature,
    the relative coolant mass flow, the control rod position and the power. A character at the beginning
    of the file indicates whether WKIND or Flownex is the active application.

As Flownex provides only with the access to the variables of a model, it was still necessary to find a
proper substitute for the reactor core. In this case a pipe was used, to replace the reactor core within
the Flownex model. The pressure drop of the pipe was adapted according to the reactor model. The
inlet temperature and the mass flow at the pipe entry are used for generating the input for WKIND.




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COMPARISON OF TWO MODELS FOR A PEBBLE BED MODULAR REACTOR CORE COUPLED TO A BRAYTON CYCLE              #D08


It simulates the heat up of the coolant as in the core model for the actual time step. The transient
simulation of the coupled system begins with starting the Flownex transient until the initial stationary
conditions are reached. In parallel the WKIND program which calculates also the stationary initial
conditions is started. Afterwards both programs solve their equations for the next time step alternately.
The time step size is determined by the WKIND time step specification.


6 Results

The following section will present results generated with the Flownex PCU network coupled with the
Flownex integrated pebble bed core, compared to corresponding results generated using the same
Flownex PCU network but coupled with the WKIND core model. Furthermore coupled Flownex-
WKIND simulations will be presented for a fast reactivity transient by rapid withdrawing all control
rods without shutdown and a reactivity transient due to withdrawing of control rods and shutdown
(control rod insertion and load rejection after scram signal).

The cases are presented as following: first, a short description of the problem that was modeled is
given. Second, the main interesting results are presented and compared to results obtained with the
alternative core model for the first example and discussed for all examples.


6.1 Load rejection

Description
In the first transient a load rejection case is simulated. Full load rejection due to the loss of grid power
is one of the most severe load control scenarios for a power plant [1]. Initially the plant operates at
maximum power and in less than one second the generator load is instantaneously reduced to zero.
The shaft directly goes into over speed, and thus it is necessary to quickly reduce the power output of
the power turbine to prevent the generator from over speeding. The generator speed is therefore
controlled by opening the Gas Cycle Bypass Valve (GCBV). This valve connects the points of the
highest and lowest pressure within the system and reduces the overall system pressure ratio and thus
also the power output. The GCBV is a quick acting, open-close valve. After the power output has been
reduced, the GCBV is closed again to maintain stable operation.
In the load rejection of the design configuration simulated here, the grid power is reduced from full
load (=111.578 MW) to 10 MW.

Results
Figure 7 shows the increase in power turbine speed up to 51.5 Hz.
                                52.0
                                                                                  FLOWNEX
                                51.5                                              WKIND

                                51.0
                   Speed [Hz]




                                50.5

                                50.0

                                49.5

                                49.0

                                48.5
                                       0.0   2.5    5.0    7.5     10.0   12.5   15.0   17.5   20.0
                                                                 Time [s]
                                        Figure 7. Power turbine speed during load rejection.




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HTR 2004                                                                                                              Beijing, CHINA, 2004.9




From figure 7 it can be seen that the controller managed successfully to reduce the power turbine over
speed to 1.5 Hz in both models. Both models reach the same degree of over speed. In the system
utilizing a Flownex pebble bed reactor model, the shaft reaches the nominal value of the rotational
velocity (50 Hz) after 7.5 seconds, whereas in the alternative model, the speed returns to operate at its
nominal value after 12.9 seconds after load rejection.

Figure 8 and figure 9 show the variation in the recuperator inlet and outlet temperature after the event.


                                                900.0
                                                800.0
                 Recuperator temperature [°c]




                                                700.0
                                                600.0                                     FLOWNEX LP Inlet
                                                500.0                                     FLOWNEX HP Inlet
                                                                                          WKIND LP Inlet
                                                400.0                                     WKIND HP Inlet
                                                300.0
                                                200.0
                                                100.0
                                                  0.0
                                                        0.0       5.0          10.0          15.0            20.0
                                                                              Time [s]
                                                 Figure 8. Temperatures at recuperator inlet after load rejection.

                                                900.0
                                                800.0
              Recuperator temperature [°C]




                                                700.0
                                                                                          FLOWNEX LP Outlet
                                                600.0
                                                                                          FLOWNEX HP Outlet
                                                500.0                                     WKIND LP Outlet
                                                400.0                                     WKIND HP Outlet

                                                300.0
                                                200.0
                                                100.0
                                                  0.0
                                                        0.0        5.0           10.0          15.0            20.0
                                                                               Time [s]


                                                Figure 9. Temperatures at recuperator outlet after load rejection.

The recuperator low pressure inlet temperature increases with approximately 300°C during the event,
while no significant change in temperature is visible at the High Pressure (HP) recuperator outlet. It
can be seen that short circuiting the power turbine results in hotter helium gas entering the Low
pressure (LP) side of the recuperator. Both models here agree very well in trends and in maximal
values.

Figure 10 shows the variation that occur in HP side and in the LP side of the circuit during the event.
The pressure of HP side is taken at the manifold and the pressure of the LP side is taken at Low
Pressure compressor (LPC) inlet.



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COMPARISON OF TWO MODELS FOR A PEBBLE BED MODULAR REACTOR CORE COUPLED TO A BRAYTON CYCLE                                                  #D08



                                             8000.0

                                             7000.0

                                             6000.0


                Pressure [kPa]
                                             5000.0
                                                                                                               FLOWNEX LPC
                                             4000.0                                                            Inlet pressure
                                                                                                               FLOWNEX
                                             3000.0                                                            Manifold presure
                                                                                                               WKIND LPC
                                             2000.0                                                            Inlet pressure
                                                                                                               WKIND Manifold
                                             1000.0
                                                                                                               pressure
                                                              0.0
                                                                    0.0              5.0          10.0         15.0               20.0
                                                                                               Time [s]
             Figure 10. System pressure after load rejection at LPC Inlet and Manifold.

The pressure at the low pressure side of the system increases to a value of approximately 5500 kPa,
whereas the pressure at the high pressure side of the system decreases to a value just above.
The models show a good agreement for this transient.
The figures 11-13 show the effect of load rejection on the reactor core. The change in reactor power,
reactor mass flow and reactor temperature is demonstrated.

                                                             280.0

                                                             260.0
                                 Reactor power [MW]




                                                             240.0

                                                             220.0

                                                             200.0

                                                             180.0

                                                             160.0                                                      FLOWNEX
                                                                                                                        WKIND
                                                             140.0
                                                                     0.0              5.0           10.0         15.0               20.0
                                                                                                  Time [s]
                                                                           Figure 11. Reactor power after load rejection.
                                                             140.0

                                                             120.0
                                  Reactor mass flow [kg/s]




                                                                                                                 FLOWNEX
                                                             100.0
                                                                                                                 WKIND
                                                              80.0

                                                              60.0

                                                              40.0

                                                              20.0

                                                               0.0
                                                                     0.0              5.0          10.0          15.0              20.0
                                                                                                 Time [s]
                                                                       Figure 12. Reactor mass flow after load rejection.




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HTR 2004                                                                                                           Beijing, CHINA, 2004.9




                                           1000.0

                                            900.0

                Reactor temperature [°C]    800.0

                                            700.0                                       FLOWNEX Reactor
                                                                                        inlet temperature
                                            600.0                                       FLOWNEX Reactor
                                                                                        outlet temperature
                                            500.0                                       WKIND Reactor inlet
                                                                                        temperature
                                            400.0                                       WKIND Reactor outlet
                                                                                        temperature
                                            300.0
                                                    0.0         5.0           10.0         15.0             20.0
                                                                            Time [s]


                                                    Figure 13. Reactor temperatures after load rejection.

The reactor power decreases in approximately 30% in both models, or if assumed a control rods
insertion. The large heat capacity of the pebbles prevent a very fast decrease in reactor power. The
reduction in mass flow does not correspond to that and latter decreases considerably, and shows a
decrease of approximately 70% of its initial value.

Figure 13 shows that a sharp change occurs in the reactor inlet temperature. This change occurs due to
the high level of interdependence between the recuperator and the reactor. The reactor inlet
temperature rises in approximately 300°C in both models. However, the reactor outlet temperature
remains almost constant. The reactor outlet temperature does not significantly deviate from its original
value because of the rapid feedback from the fuel temperature to reactivity by which the output power
is adjusted to match the cooling capacity of the reduced helium flow.
The reactor power starts to decrease due to the higher reactor inlet temperature and the lower mass
flow levels.

It can be seen that the models agree reasonably well with each other, and show a similar behavior in
all demonstrations described above.

 6.2 Withdrawal of all control rod after 30 s

In the following transient simulation it is assumed that due to an unknown malfunction of the power
plant all control rod are withdrawn with a hypothetical speed of 100 cm/s. This causes to an
instantaneous increase in reactor power. However, the reactor inlet temperature as well as the reactor
outlet temperature remain nearby constant due to large heat capacity of the core.
As mentioned previously in this paper, the action of withdrawal is simulated with the WKIND core
model only, since the Flownex core model lacks this feature.

Figure 14 shows the change in reactor heat transfer and the change of control rods position that was
initiated after 30 s simulation run time.




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COMPARISON OF TWO MODELS FOR A PEBBLE BED MODULAR REACTOR CORE COUPLED TO A BRAYTON CYCLE                                             #D08




                                     2000.0                                                      300.0
                                     1800.0
                                                                                                 250.0




                                                                                                         Control rods position [cm]
                                     1600.0

               Heat transferr [MW]
                                     1400.0
                                                                                                 200.0
                                     1200.0         WKIND Heat transfer
                                                    to PCU
                                     1000.0         WKIND control rods                           150.0
                                      800.0         position
                                                                                                 100.0
                                      600.0
                                      400.0
                                                                                                 50.0
                                      200.0
                                        0.0                                                      0.0
                                              0.0   5.0   10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0
                                                                     Time [s]


                                        Figure 14. Reactor control rods position and heat transfer.

It can be clearly seen, that simultaneously during the withdrawal a very strong increase in WKIND
reactor heat transfer occurs. This increase is almost seven folds greater than the initial power. The
rapid decrease of power after the strong increase is due to the prompt increase in fuel temperature on
the control rods position, which was calculated by heterogeneous fuel temperature module (see figure
15).




       Figure 15. Reactor fuel temperature after withdrawal of all control rods without scram.



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HTR 2004                                                                                                                                    Beijing, CHINA, 2004.9



For a short time the temperature of the coated particles differs very much compared to the moderator
temperature.
Figure 16 shows this difference during the event.



                                                                      100


                                         Temperature difference [K]
                                                                       90
                                                                       80
                                                                       70
                                                                       60
                                                                        50
                                                                        40
                                                                        30
                                                                        20




                                                                                                                               45.5
                                                                                                                          [s 40.3
                                                                        10




                                                                                                                       m 35.3
                                                                          0



                                                                                                                30.3


                                                                                                                            ]
                                                                              R13
                                                                                    R9




                                                                                                        25.3



                                                                                                                        e
                                                                                         R5
                                                                                               R1




                                                                                                                       Ti
                                                                        Axia
                                                                                              20.2

                                                                            l me
                                                                                    sh

                             Figure 16. Temperature difference between moderator and fuel temperature.

For a short relaxation time this difference reduces the power of the core remarkably. Therefore this
model is much more realistic than a homogeneous model which shows power increase by a factor of
about 80 since the fuel temperature is strongly coupled to the slowly increasing moderator
temperature.
Figure 17 shows a linear plot of fuel temperature, coating temperatures, average moderator
temperature and surface temperature of the spheres in the axial center of the core.

                             1300
                                        Fuel temperature
                             1250
                                        Average moderator
                                        temperature
                             1200       Surface temperature
           Temperature [K]




                                        Inner coating
                             1150       temperature
                                        Outer coating
                                        temperature
                             1100


                             1050


                             1000
                                    0                    10                   20         30            40              50         60   70   80
                                                                                                     Time [s]


   Figure 17. Fuel temperature, coating temperatures, average moderator temperature and surface
                            temperature in the axial center of the core.

Even if the assumed control rod withdrawal is not a realistic accident scenario, the results show that
the reactor temperatures exceed no deign limits even for fast reactivity transients.




                                                                                                      13
COMPARISON OF TWO MODELS FOR A PEBBLE BED MODULAR REACTOR CORE COUPLED TO A BRAYTON CYCLE                                                         #D08


Figure 18 shows the reactor inlet and the reactor outlet temperature.

                                             1200.0

                                             1000.0


                  Reactor temperature [°C]
                                               800.0

                                               600.0

                                               400.0                                       FLOWNEX reactor inlet temperature
                                                                                           FLOWNEX reactor outlet tempeature
                                               200.0                                       WKIND reactor inlet teperature
                                                                                           WKIND reactor outlet temperature
                                                       0.0
                                                             0.0    5.0     10.0    15.0    20.0     25.0      30.0   35.0   40.0   45.0
                                                                                              Time [s]

                                                                          Figure 18. Reactor temperatures.

The current simulation case is shown in order to demonstrate the additional features of the WKIND
core modeled that means the capability of changing the position of the control rods and of calculating
the fuel and the moderator temperature, which exist in the WKIND model but has not yet been applied
in the Flownex model.

6.3 Withdrawal of all control rods and load rejection

The withdrawal of all control rods at the speed of 1 cm/s is initiated and simulated by the WKIND
model at a predefined time (5s). It was specified that a complete shut down by control rods would be
initiated as soon as a power level of 120% has been reached. This causes an immediate decrease in
reactor power at about 22 seconds. Simultaneously a load rejection is initiated in Flownex, in order to
maintain a stable operation of the power turbine.
Figure 19 shows the variations in reactor power and in heat transfer to the PCU.


                                                      300.0

                                                      250.0
                                                                                                                      FLOWNEX Reactor
                                                                                                                      power
                                                      200.0
                                         Power [MW]




                                                      150.0

                                                      100.0

                                                       50.0

                                                        0.0
                                                              0.0            10.0            20.0              30.0          40.0          50.0
                                                                                                    Time [s]


            Figure 19. Reactor power after a control rods withdrawal and load rejection.

Regarding the PCU state variables he results are consistent to the ones obtained in the first transient,
but due to the shut down the reactor power decreases until a level of approximately 10% of its nominal
values at about 50 s.




                                                                                             14
HTR 2004                                                                                                                                         Beijing, CHINA, 2004.9




Figure 20 shows the variation in reactor mass flow.

                                                                140.0

                                                                120.0
                                                                                                                            FLOWNEX Reactor
                                                                100.0                                                       mass flow
                                             Mass flow [Kg/s]
                                                                 80.0

                                                                 60.0

                                                                 40.0

                                                                 20.0

                                                                  0.0
                                                                        0.0         10.0           20.0              30.0         40.0        50.0
                                                                                                          Time [s]


            Figure 20. Reactor mass flow after a control rods withdrawal and load rejection.

A reduction in reactor mass flow is due to the load rejection initiated by the opening of the bypass
valve (BPV).

                                            950.0


                                            850.0
                 Reactor temperature [°C]




                                                                              FLOWNEX Reactor
                                                                              inlet temperature
                                            750.0
                                                                              FLOWNEX Reactor
                                                                              outlet temperature
                                            650.0


                                            550.0


                                            450.0
                                                                 0.0            10.0         20.0              30.0            40.0       50.0
                                                                                                    Time [s]



           Figure 21. Reactor temperatures after a control rods withdrawal and load rejection.

                                                  .
The reactor outlet temperature maintains an almost constant value, whereas the reactor inlet
temperature shows an increase of approximately 200°C.
The models show a satisfactory level of consistency.




                                                                                                    15
COMPARISON OF TWO MODELS FOR A PEBBLE BED MODULAR REACTOR CORE COUPLED TO A BRAYTON CYCLE         #D08


7   Conclusions and Discussion

In this paper two different models for the reactor core were incorporated within a Flownex PCU,
thereby creating a plant wide model. The first model is the Flownex core model and the second one is
the WKIND core model. The integrated core models have been compared for three transient cases.
The control system implemented in the PCU has been kept straightforward throughout the transients,
and focused on keeping the shaft speed within bounds.

In the first transient a load rejection (a generator trip) is simulated. In this case both models have
shown a rather good agreement. Based on this case it can be concluded that coupling Flownex to an
external component via a mutual interface is feasible.

In the second case the withdrawal of all control rods at a speed of 100 cm/s is simulated. The results
obtained by the WKIND model are more important in this case, as the action of changing the rods
position has so far only been featured in this model. From the results attributed in this case inherent
differences between the two core models and their features could be derived. In the Flownex model it
is assumed that the fuel temperature is approximately similar to the moderator temperature in the core.
However, in the WKIND model the calculation of the fuel temperature is done explicitly. Thus, a
major difference between the capabilities and limitations of models exist. The WKIND model by
accounting for the in control rods position demonstrates a more realistic behavior of the core.
Accordingly, it is recommended to modify the Flownex model and feature an option to insert and to
withdraw the control rods for the extension of further control and emergency actions which play a key
role in plant operation simulations.

In the third transient the control rods are withdrawn at the speed of 1 cm/s. In this case there was a
need to simultaneously initiate a load rejection in Flownex to maintain a stable operation. Also here
both models have shown similar results and agree well. The realization of an external transient and is
demonstrated here, yet the coupling methodology should be further improved. Instead of the Flownex
element assimilating a heat source which utilized in the current coupling, a more sophisticated
coupling model should be implemented in order to improve this. Furthermore, since the control system
of the PCU plays an important role in the whole plant behavior and is extremely important for the
simulation of transient and accidental cases, and as it is necessary to model the process behavior in a
larger operating region, and to include the establishment of start-up and shut-down simulations in the
investigations, the control strategies have to be further improved.


For the total PBMR plant it can be concluded that the models agree well. However, some differences
still exist. Thus, it is recommended to extend and improve the models. This is currently done as a part
of an ongoing work which at IKE, which is aiming towards the application of a multidimensional core
neutronics in the reactor models, and thus allows for more possibilities to simulate the thermo-
hydraulics and analyze the natural convection in the core. Additionally, the synchronization of the
time step and the control interaction that characterize the present coupling should be improved.
Nevertheless, the results can be considered acceptable for a conceptual study of the system. The
various transients demonstrated have shown satisfactory results to prove that a successful realization
of the coupling has been accomplished.




                                                  16
HTR 2004                                                                         Beijing, CHINA, 2004.9



References

1. Ion, S, Nicholls, D, Matzie, R, Matzner, D, “Pebble bed modular reactor the first generation 4
    reactors to be constructed”, World Nuclear Association Annual Symposium, London, 3-5
    September, 2003.
2. Greyvenstein, GP, Rousseau, PG, “Basic principles of HTR thermal-hydraulics”, HTR/ECS 2002
    High Temperature Reactor School, Cadarache, France, November 4-8, 2002.
3. Botha, BW, Rousseau, PG, “Simulation investigation of control options for full load rejection in
    the PBMR closed cycle gas turbine power plant”, Proceedings of IGTI Turbo Expo, Amsterdam,
    June 3-6, 2002.
4. Greyvenstein, GP, “An implicit method for analysis of transient flows in pipe networks“, Int. J.
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5. Coetzee, RV, der Merwe, V, Rousseau, PG, FLOWNEX Version 6 USER MANUAL, M-Tech
    Industrial, Potchsfstroom, South Africa, 2003.
6. Rousseau, PG, Greyvenstein, GP, “One-dimensional reactor model for the integrated simulation of
    the PBMR power plant”, Proc of 1st International Conference on Heat Transfer, Fluid Mechanics
    and thermodynamics, Kruger Park, South Africa, 8-10 April, 2002.
7. Du Toit, CG, Greyvenstein, GP, Rousseau, PG, “A comprehensive reactor model for the
    integrated network simulation of the PBMR power plant”, 2003 International Congress on
    Advanced Nuclear Power Plants, Cordoba, Spain, May 4-7, 2003.
8. Kindt, T, Hauque, H, “Recriticality of the HTR-Module Power Reactor after hypothetical
    accidents”, Nuc. Eng. Des. 137, 1992, 107-114.
9. Bernnat, W, Feltes, W, “Models for reactor physics calculations for HTR pebble bed modular
    reactors”, Nuc. Eng. Des. 220, 2003, 331-347.
10. Verkerk, EC, Kikstra, JF, “Comparison of two models for a high temperature reactor coupled to a
    gas turbine”, Nuc. Eng. Des. 220, 2003, 51-65.




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