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RAPHAEL Core Physics: Neutronic and thermal-hydraulic
simulation of the HTR-10 and AVR reactors
B. Boer, M. Ding, J.L. Kloosterman
PNR-131-2008-012
Delft University of Technology,Mekelweg 15, 2629 JB, Delft, The Netherlands
October 31, 2008
Summary
The very high temperature reactor (VHTR) is one of the six reactor types selected in theGeneration-IV research program. The VHTR is a graphite-moderated, helium-cooledreactor with a once-through uranium fuel cycle. It is designed to be highly efficient,to be flexible to adopt to the uranium/plutonium fuel cycle, to have a minimal wasteproduction, while retaining its inherently safe characteristics.
The results presented in this report relate to the validation of a coupled neutronicsand thermal-hydraulics code system for the analysis of pebble-bed reactors. It has beenvalidated with experimental data of the HTR-10 and the AVR reactors. The code systemconsist of a new (3D) diffusion code DALTON, which is coupled to the existing thermal-hydraulics code THERMIX. These codes are linked to a procedure for the generation ofneutron cross sections using SCALE-5.
For validation purposes calculation results of normal operation, a Pressurized LossOf Forced Cooling (PLOFC) transient and a Control Rod Withdrawal transient withoutSCRAM have been compared with experimental data obtained in the HTR-10. Of par-ticular interest is the LOFC transient, since the temperature of the coated particle fuelis significantly elevated during this transient, which constrains the power level and tem-perature during normal operation. Therefore, a proper prediction of the temperaturesduring these transient of particular interest for new reactor designs.
Experimental data of the AVR for normal operation, a Depressurized Loss Of ForcedCooling (DLOFC) transient and a transient with coolant mass flow reduction has beenused to further validate and improve the code system.
Although some differences were encountered between the calculation results and theexperimental data it is found that the code system performed satisfactory and can pro-vide in a key element in the development and optimization of pebble-bed reactors.
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Contents
Summary i
1 Introduction 1
2 Overview of the code system 52.1 Processing of neutron cross sections . . . . . . . . . . . . . . . . . . . . . 52.2 DALTON . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3 THERMIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.4 Additional codes and scripts . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3 Results 113.1 Simulation of the HTR-10 . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.1.1 Initial criticality and normal operation . . . . . . . . . . . . . . . . 113.1.2 Simulation of the PLOFC transient . . . . . . . . . . . . . . . . . . 123.1.3 Control Rod Withdrawal without SCRAM . . . . . . . . . . . . . 16
3.2 Simulation of the AVR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.2.1 Decription of the AVR . . . . . . . . . . . . . . . . . . . . . . . . . 193.2.2 Simulation of mass flow dynamic experiment . . . . . . . . . . . . 223.2.3 Simulation of the Depressurized Loss Of Forced Cooling (DLOFC)
Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
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Chapter 1
Introduction
Compared with the pebble-bed type High Temperature Reactors (HTRs), such as theDragon, AVR and THTR reactors that operated in the past, the Very High TemperatureReactor (VHTR) as proposed by the Generation IV initiative [1] is envisaged to operateat elevated conditions, aiming at a helium outlet temperature of 1000 ℃ together witha high fuel burnup level (> 95 MWd/kg U). This has significant consequences for thefuel temperature, not only during normal operation, but especially during a Loss OfForced Cooling (LOFC) incident, in which the maximum fuel temperature of the coreis generally above its nominal value. A higher fuel temperature results in an increaseof the stresses in the fuel coating layers and a consequent possible coating failure. Thisconstrains the power level and operating temperature during normal operation. Theexistence of a validated code system for the evaluation of the fuel temperature duringnormal and LOFC conditions is therefore a key element in the development of the VHTR.
In this report the methodology and validation of a code system for neutronic andthermal-hydraulic analysis of pebble-bed type HTRs is presented. The code system canbe split up in two parts. The first focuses on the generation of nuclear data for thefull-core analysis. This data is used in the second part, which is concerned with theneutronic and thermal-hydraulic analysis of the reactor. The main purpose of the codeis to calculate the fuel temperature for both normal and accident conditions for variousreactor designs. In addition, other parameters of the core, such as the neutron flux andpower profile, can be calculated for the evaluation of the fuel performance.
The neutronic and thermal-hydraulic part of the code system consists of a newtime-dependent (3D) diffusion code DALTON [2] which has been coupled to the ex-isting (2D) thermal-hydraulics code THERMIX [3]. The followed approach for modelingthe HTR dynamics is similar to other recent code systems such as PANTHERMIX[4], NEM(DORT-TD)-THERMIX [5], PEBBED-THERMIX(KONVEK) [6], PARCS-THERMIX [7], in which a diffusion (or transport code) for the neutronics is coupledto THERMIX (KONVEK/DIREKT). Other HTR dynamics codes that do not make useof THERMIX for the thermal-hydraulics are MARS-GCR/CAPP [8] and the TINTE
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Table 1.1: Main characteristics of the HTR-10 and AVR reactor designs.Reactor HTR-10 AVR
First power operation 2000 1967Country China GermanyPower [MWth] 10 46Pebble-bed diameter [m] 1.9 3.0Pebble-bed height [m] 1.8 3.0Power density [MW/m3] 2.0 2.2Efficiency [%] - 30Fuel loading (enr. 235U) UO2 UO2/(U,Th)O2/C2
Enrichment 235U [%] 17 10/17Maximum fuel burnup (MWd/kg) 100 160Coolant Tin [°C] 250 270Coolant Tout [°C] 750 950Pressure [MPa] 2.5 1.1Thermodynamic cycle Steam Steam
code system [9].By linking the DALTON-THERMIX code system (Sec. 2) with SCALE-5 [10] for the
generation of temperature dependent neutron cross sections (Sec. 2.1), a flexible calcula-tion tool is created for modeling and optimization of various HTR designs. The new codesystem is in this regard similar to the established VSOP (Very Superior Old Programs)code system [11], which also combines neutron cross section processing routines with a2D diffusion and thermal-hydraulics model. However, the new code system is able tocalculate various coupled transients, while the VSOP cannot. The past experience withHTR technology provides valuable information for validating codes. Experimental dataconcerning HTR dynamics has been obtained from the operation of the AVR. Severalexperiments were conducted, including a simulation of a Depressurized Loss Of ForcedCooling (DLOFC) incident in 1988 [12]. The main heat sink for the removal of the decayheat during this transient was the steam generator, which is also used during normaloperation and is located above the top reflector within the RPV. In 2003 experimentswere conducted on the HTR-10 reactor in China (see Table 1.1 and Fig. 1.1(a)). In this10 MW pebble-bed research reactor a Pressurized Loss Of Forced Cooling (PLOFC)and a Control Rod Withdrawal (CRW) experiments were performed. This reactor onlyhas a Reactor Cavity Cooling System with a capacity of 200 kW that is located outsidethe Reactor Pressure Vessel (RPV) for the removal of the decay heat during incidents.The passive removal of the decay heat by a RCCS during accident situation was pro-posed first for the HTR-MODUL reactor [13] and is also adopted for modern large sizedesigns, such as the 400 MWth Pebble Bed Modular Reactor (PBMR). The followingchapter (Chap. 2) gives an overview of the code system. In Chap. 3 the results of theHTR-10 and AVR benchmarks are discussed in Secs. 3.1 and 3.2.
2
Reflector
Coolant borehole
Hot helium plenum
Pebble discharge tube
Helium cavity
Helium cavity
Pressure vessel
Control rod
Boronatedcarbon bricks
Pebble bed
Absorber spheres
(a) HTR-10 core layout (b) AVR core layout
Figure 1.1: Schematic overview of the HTR-10 (a) and AVR (b) reactors.
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Chapter 2
Overview of the code system
Fig. 2.1 gives a schematic overview of the coupled code system. A description of each
Figure 2.1: Schematic overview of the coupled code system
component of the system is given in the following sections.
2.1 Processing of neutron cross sections
Before the thermal-hydraulic and neutronic calculations are started, a neutron crosssection (XS) library is created as a function of the fuel and moderator temperaturesand the xenon concentration. For the simulation of the HTR-10 transients both a pointkinetic model [15] with externally calculated reactivity coefficients has been used, as wellas a 2D model in DALTON with space and temperature dependent neutron cross sectionsusing a similar procedure. The procedure uses several modules of the SCALE-5 codesystem [10] in order to take into account the double heterogeneity of the fuel (TRISOand pebble) and the geometry of the reactor. The calculation steps are as follows:
1. First, the TRISO particles in the graphite matrix are modeled by using the CSASIXmodule of SCALE-5. In this module, the NITAWL-III [16] and BONAMI [17]
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modules are used for the evaluation of the resolved and unresolved resonanceswhich are treated by the Nordheim Integral Method and the Bondarenko method,respectively. A one-dimensional discrete ordinates transport calculation using XS-DRNPM [18] is made of a fuel kernel surrounded by cladding (material from thecarbon buffer, IPyC, SiC and OPyC layers) and moderator (graphite) material (seeFig. 2.2). The moderator volume having radius R0 is equal to the volume of thefuel zone of the pebble divided by the number of TRISO’s. From this last calcula-tion homogenized neutron cross-sections are made for ”TRISO material”. For thispurpose a 172 energy group (XMAS) library is used, based on the JEFF2.2/3.0 andJENDL3.3 libraries and processed with NJOY. To account for the fuel-shadowingeffect of the fuel kernels in the graphite matrix of the pebbles a Dancoff factor isused, which is analytically determined [19] and is a function of the number of fuelparticles and the radii of the kernel, the fuel zone and the pebble.
R1R2
Moderator
Cladding
Fuel
TRISO Pebble-Bed
R0
Figure 2.2: TRISO and Pebble model used in calculation of homogenized cross sectionsfor the pebble bed region.
2. The homogenized neutron cross sections for the TRISO material are used in aone-dimensional transport (XSDRNPM) calculation in which a sphere of TRISOmaterial, with radius R1, is surrounded by a layer of graphite and helium withradius R2 (see Fig. 2.2). In this calculation R1 is equal to the fuel zone in thepebble and R2 can be calculated from the packing fraction ψ (=0.61) and the ratioof moderator to fuel pebbles, f , by the following relation:
R2 = 3
√R3
peb
1 + f
ψ(2.1)
If no moderator pebbles are present f equals zero. In the case of the HTR-10f = 43/57 and since the fuel zone of the pebble is 2.5 cm and the pebble outerradius is 3 cm, a value of 4.26 cm is found for R2.This transport calculation results in homogenized cross sections for ”pebble bed
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material”.3. As a last calculation step several one-dimensional transport calculations, repre-
senting a certain axial or radial cross section of the core, are performed. In generalthe geometry consists of a pebble bed region surrounded by graphite reflector re-gions. These regions are split up into several zones to generate zone weighted fewgroup cross sections. In order to model the transverse neutron leakage in these 1Dcalculations the reactor height (or width) is supplied from which a buckling factoris derived. The zone weighted cross sections of these 1D calculations are allocatedto the positions of the corresponding material in the 2D cross section map.
The above described procedure is repeated for several fuel and moderator temperaturesresulting in a 2D temperature dependent cross section library. Directional dependentdiffusion coefficients are calculated with an analytical solution [20] to treat the voidregions in the core, such as the helium plenum above the pebble-bed. Regions containingthe control rods are treated in a separate CSAS run representing a horizontal crosssection of the rod and surrounding material (graphite and pebble-bed). The resultingcell weighted cross sections are transformed to a ’grey curtain’ region for the 2D (r-z)cross section map by conservation of the neutron absorption reaction rates.
For the HTR-10 benchmark both reactivity coefficients as well as zone weighted crosssection have been calculated with the above procedure for a point kinetic model and a2D model in DALTON, respectively.
For the AVR benchmark, zone weighted cross sections with collapsed energy groupstructure could be generated using this last step (3). However, it is chosen to omit thisstep, because the AVR core contains many different pebble types (9) and burnup classes(49). Instead, the homogenized pebble cross sections of the different fuel and pebbletypes of step (2) are mixed according to their presence in several core regions, while thecollapsed group structure contains a relatively large number (9) of energy groups.
2.2 DALTON
The DALTON code can solve the 3D multigroup diffusion equations on structured grids(xyz or rzθ coordinates). The code’s capabilities include both the fundamental andhigher lambda modes and time-eigenvalues through the Arnoldi method by linking withthe ARPACK package. Transient analysis in forward and adjoint mode is possible withor without precursors. The higher eigenmodes are obtained by the use of the ARPACKpackage. Spatial discretization is performed using a second order accurate finite volumemethod. DALTON uses an adaptive time-stepping algorithm that is based on the useof the second order time-accurate Backward-2 scheme. This scheme is fully implicit andunconditionally stable. Whether a time step is accepted in a time-dependent calculationor not depends on the maximum allowed absolute error, ATOL, and relative error, RTOL,
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as supplied by the user. √√√√ 1N
N∑i=1
(LTEi
ATOL + RTOL× φi
)2
≤ 1 (2.2)
where LTE is the local truncation error of the Backward-2 scheme. For prediction of thetime step to be used in the next step, a similar procedure is adopted.
The DALTON code is used to calculate a 2D zone averaged power profile usingneutron cross sections that have been obtained through interpolation using the localtemperature and xenon concentration. In the case that the point kinetic equations areused, a fixed power distribution is scaled to the calculated total power.
2.3 THERMIX
THERMIX(-DIREKT) [3] is a 2D thermal hydraulics code that consists of the two mod-ules THERMIX (heat conduction and thermal radiation) and DIREKT (convection).The power profile calculated by DALTON is used in THERMIX to calculate the tem-perature profile in the reactor at the new time point. For the core region two-dimensionaltemperature profiles for fuel and moderator temperatures of the pebbles are calculated.To this end a one-dimensional calculation for the temperature profile inside the pebblesis used, taking into account that the pebbles have a fuel free (graphite) zone in the outer(0.5 cm) shell.
2.4 Additional codes and scripts
Beside the above described main components of the code system, the following codesand scripts are used in the calculations:
Xenon The xenon concentration is determined using the well known simplified depletionchains for xenon and iodine [21].
MIXER An in-house perl script (MIXER) updates for each calculation step the neutroncross sections by linear interpolation using several routines of the SCALE codesystem [10].
MASTER Depending on the type of transient the MASTER program decides how of-ten data is exchanged between the different codes and what the calculation modetype of the codes has to be, i.e. steady state (eigenvalue) or transient mode. Fortransient calculations DALTON and THERMIX are used consecutively withoutperforming additional iterations. The time step control within the codes is doneindependently of each other. The (global) time step can be chosen manually orwith a control algorithm that ensures convergence and stability of the coupled cal-culation result. The algorithm that was adopted is similar to the time step control
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in DALTON. Following Eq. (2.2), the criterion for a time step to be accepted ornot depends on the maximum allowable absolute error, ATOL, and relative error,RTOL, as supplied by the user. However, instead of the neutron flux φi that is usedin Eq. (2.2), a vector y containing N state variables is used to check the ’global’time step and predict the new step size. A restart of the coupled code systemfrom the previous time point is required if the criterion is not met. The vector ycontains the following variables: the average helium temperature, the average fueltemperature and the total reactor power.The calculation mode type can be adjusted for certain transient simulations, suchas LOFCs (with or without SCRAM), in which the reactor is in a sub-critical con-dition for a long period and therefore the fission power is negligible. In these cases aTHERMIX stand alone calculation is performed combined with an eigenvalue cal-culation in DALTON up to the point of re-criticality, when the calculation modeis switched back to fully coupled dynamics. At this point the flux and precursorlevel are normalized to a low power level, e.g. 1 W.
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Chapter 3
Results
3.1 Simulation of the HTR-10
Beside the calculation of the initial criticality and normal operation of the HTR-10 twotransient cases are investigated for code validation purposes, namely: a simulation of aPressurized Loss Of Forced Cooling (PLOFC) and a Control Rod Withdrawal (CRW),which also leads to the shut down of the blower and consequent shut down of activecore cooling. Theses cases can be considered as one of the most demanding transientsin a nuclear reactor and were performed in the HTR-10 to demonstrate the inherentsafety characteristics of a pebble-bed reactor using only the RCCS as an active heatsink. Results of calculations made of both THERMIX coupled to a point-kinetics model(PK-THERMIX) and a coupled 2D DALTON-THERMIX model are compared withexperimental data from the HTR-10 reactor.
3.1.1 Initial criticality and normal operation
The initial core was composed of a mixture of pebbles containing 5 g of 17 % enricheduranium and pebbles containing graphite only (dummy pebbles) in a ratio of 57:43 [22].The pebble discharge tube and the bottom cone-shaped part of the core region werefilled with dummy pebbles. A mixture of the fuel and dummy pebbles was added tothe core at room temperature until criticality was reached. Criticality was reached afteradding 16890 mixed pebbles at 15 °C corresponding to a pebble-bed height of 123 cmat 27 °C [22].
After the initial criticality has been reached in December 2000 additional fuel anddummy pebbles are added to the core in order to maintain criticality at hot conditions.In the following 820 Equivalent Full Power Days (EFPDs) a mixture of fuel and dummypebbles is added, while the dummy pebbles that filled the entire bottom region of thecore are discharged [23]. After this period, fresh fuel pebbles are added to the core incombination with recycling of fuel pebbles. It is therefore assumed that the core, whenthe transient test were performed in October 2003, consisted of a combination of fuel
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pebbles having a certain burnup value and dummy pebbles.The point of criticality has been calculated with the cross section procedure of Sec. 2.1
combined with a 2D calculation for a fixed temperature of 27 °C. The cross sectiongeneration procedure predicted a k∞ of 1.7625 for the pebble-bed material (see Fig. 2.2),which is close to the value of 1.76155 calculated with TRIPOLI [24]. For a pebble-bedheight of 108 cm and 126 cm DALTON predicts a keff of respectively 0.9698 and 1.0268,which leads to a critical height of 117 cm (TRIPOLI, Hcrit = 117.4 cm). It is expectedthat the treatment of the void regions for the movement of the control rods and theabsorber balls, which were modeled by reducing the density of the graphite in thoseareas, leads to an underestimation of the neutron streaming effects and therefore in anoverestimation of the keff .
In the coupled DALTON-THERMIX calculations it was assumed that the entiredischarge tube was filled with a mixture of fuel and dummy pebbles and that the fuel inthe core has an homogeneous average burnup value. Furthermore, it is assumed that thecontrol rods remain in the upper position. This leads to an keff of 0.9497 and 1.0132 atburnup values of 8.5 % and 6.8 % FIMA, respectively, for a coupled DALTON-THERMIXcalculation.
The results of the temperatures (FIMA = 8.5 %) at specific locations in the core(Fig. 3.5, [25]) of a coupled calculation are presented in Table 3.1. It is noted that thereis an uncertainty in the specific location of the thermocouples. Furthermore, the 2Dmodel in THERMIX does not capture the 3D effects, which are especially important inthe region of the side reflector which contains the holes for the control rods and absorberballs. This can explain the differences in the calculated and measured temperatures.
Table 3.1: Temperatures at several locations (Fig. 3.5) in the HTR-10 calculated withDALTON-THERMIX and measured during operation.
Location Experiment [°C] DALTON-THERMIX [°C]
Top reflector 230 242Side reflector (low) 460 457Metal support structure 180 194Outlet mixing room 810 810
3.1.2 Simulation of the PLOFC transient
The PLOFC simulation is initiated by shutting down the primary helium blower duringsteady state operation of the reactor. As a result the helium flow in the primary loopis stopped and the reactor is isolated from the water cooling systems on the secondaryside of the steam generator. For calculation purposes, it is assumed that the helium flowreduces linearly within 12 seconds [26].
For both the PLOFC and the CRW simulations the reactor conditions and assump-tions were as follows:
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• The reactor has reached steady state operation at partial load of 30% of full power,i.e. 3 MW a the start of the transient in both the calculation model and in reality.
• It is assumed that the primary helium pressure at steady state partial load oper-ation is 2.5 MPa and remains unchanged during the transient. In reality it wasfound that the pressure reduces slowly to 2.4 bar in 2.8 hours [27].
• The measured helium temperatures at reactor inlet and outlet are 215 °C and650 °C respectively at steady state partial load operation were adopted in theTHERMIX model. Helium flow rate is defined by this temperature difference andthe helium pressure.
• The control rods remain at fixed (upper most) position in the DALTON model.The reactivity insertion by rod movement in the CRW simulation is simulated byrescaling the fission source in DALTON and introducing an external reactivity inthe PK model. The power density distribution is assumed to be fixed.
• The temperature at the radial side boundary, where the decay heat removal systemis located, is set to a fixed temperature of 50 °C in THERMIX, while the top andbottom concrete structures surrounding the air cavity in which the reactor is placedwas set to 35 °C. This corresponds to the average water temperature in the decayheat removal system which operated at 206 kW cooling power.
• The dummy pebbles were not modeled explicitly in THERMIX. Instead, all pebbleswere assumed to be fuel pebbles having a reduced thermal conductivity, which wasweighted with the fuel to dummy pebble ratio.
• Reactivity coefficients resulting from a DALTON-THERMIX calculation were usedin the PK model. The following coefficients were used: ρfuel = -8.16·10−5 K−1,ρmoderator = -9.15·10−5 K−1 and ρreflector = 6.41·10−6 K−1.
The calculation and experimental results for the PLOFC are presented in Figs. 3.1,3.2 and 3.3. It can be seen that the helium mass flow reduction causes the temperaturesof the fuel and moderator to increase, resulting in a negative reactivity feedback causedby increased resonance absorption (Doppler effect) in the fuel and the shift in thermalspectrum caused by the moderator temperature feedback. Feedback from the reflectortemperature is small, since the average change in reflector temperature in the beginningof the transient is small. The feedback results in a fast reduction of the fission reactorpower and within 500 s the reactor power is determined by the decay heat power only(See Figs. 3.1).
During the transient, natural convection flows enable relatively cold helium fromthe helium cavities located at the top and bottom of the reactor (see Fig. 1.1(a)) toenter the bottom region of the core. Furthermore, a natural convection flow transportsheat from the bottom to the top of the core. The above described effects cause thebottom of the core to cool down while the top is heat up, which can be seen from thecalculated temperature profiles of the solid structures at the beginning and end of thetransient (Figs. 3.4(a) and 3.4(b)). The temperature at specific positions (see Fig. 3.5)
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0 100 200 300 400 5000
0.5
1
1.5
Time [s]
Pow
er [−
] Experiment
DALTON−THERMIX
PK−THERMIX
Figure 3.1: Reactor (fission) power dur-ing the first 500 seconds during of thePLOFC transient in the HTR-10 mea-sured during the experiment and calcu-lated with the PK-THERMIX and the(2D) DALTON-THERMIX models. It isnoted that the DALTON-THERMIX andexperimental results are almost identical.
0 1000 2000 3000 4000 5000 6000 70000
0.5
1
1.5
Time [s]
Pow
er [−
]
DALTON−THERMIX
PK−THERMIX
Experiment
Figure 3.2: Reactor (fission) power dur-ing the entire calculation domain of thePLOFC transient in the HTR-10 mea-sured during the experiment and calcu-lated with the PK-THERMIX and the(2D) DALTON-THERMIX models.
0 1000 2000 3000 4000 5000 6000 7000−20
−10
0
10
20
30
∆ T
[°C
]
t [s]
FuelModRefl
Figure 3.3: Difference in the Fuel, Mod-erator and Reflector temperatures com-pared to values at normal operating con-ditions used in the PK - THERMIXmodel to determine the temperature re-activity feedback.
300300
300300
300
300
300300
300300300300
400 400 400
400
400
400
400400
500 500
500
500
500500
600
600
600
600600
700
700
700700
800
800
R [cm]
Z [c
m]
Solid Temperature [ºC]
100 200
−100
0
100
200
300
400
500
100
200
300
400
500
600
700
800
(a) t = 0 s
300300 300
300
300
300
300300
300300
300
400 400400
400
400
400400
400
400 400400400400
500
500
500
500
500
500
500
60060
0
600600
600
700
700
700
700
800
800
800
300
R [cm]
Z [c
m]
Solid Temperature [ºC]
100 200
−100
0
100
200
300
400
500 100
200
300
400
500
600
700
800
(b) t = 7200 s
Figure 3.4: Temperature profile of solidstructures at the beginning (a) and end(b) of the PLOFC transient in the HTR-10.
in the reflector, the core outlet and bottom support structure were recorded duringthe experiment [26]. It was found that the largest temperature difference between thebeginning and end of the transient was found for the top reflector, namely +215 °C.Temperature differences in the side reflector were relatively small, but a large decrease
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Figure 3.5: Schematic overview of theHTR-10 reactor design showing measure-ment points for the top reflector, core out-let and metal support structure.
0 2000 4000 60000
200
400
600
800
Time [s]T
empe
ratu
re [°
C]
core outlet
top reflector
metal support structure
Figure 3.6: Temperature during thePLOFC transient of the top reflector, coreoutlet and metal support structure. Themeasured data is shown by the markers,while the solid lines show the calculatedresults.
of the temperature by 315 °C was recorded for the core outlet (located next to the pebblede-fueling chute). Fig. 3.6 shows that both the trend and total temperature differencesof the calculated results from THERMIX for these points are in agreement with themeasured temperature.
According to the measurements, the bottom part of the core has cooled down suf-ficiently to reach criticality again and after 4200 s the core is generating a significantamount of fission power (see Fig. 3.2) according to the measurement. This results in anincrease of the power and corresponding rise in fuel and moderator temperature. Theincrease of fuel and moderator temperature results again in negative reactivity feedback,which causes the reactor power to come down again. This oscillatory behavior occursseveral times until a quasi-stationary situation is reached at elevated temperatures atlow reactor power, which is equal to the power of the decay heat removal system (206kW) [26].
Both the PK-THERMIX and the DALTON-THERMIX model show similar trendsin power and temperature as the measured data. Some differences between the codesand the experiment can be identified:
• The point of re-criticality predicted by the DALTON-THERMIX and PK-THERMIXmodel occurs ∼700 and 500 seconds, respectively, before the measured point. Thelocation of the point depends on the temperatures in the core and their correspond-
15
ing temperature reactivity feedback. The heat transfer from the core to the reactorcavity cooling system and the thermal capacity determine the temperature in thepebble-bed. It was found that the heat transfer to the cooler is overestimated byseveral percent at the end of the transient (6000 s). This results in a faster cooldown of the core and a higher power level at the end of the transient (Fig. 3.2)than in reality.Furthermore, the build up of the 135Xe concentration in the fuel will result in anegative reactivity feedback effect, which will delay the time point of re-criticality.This latter effect was not taken into account in the calculation models. It istherefore expected that including this effect will bring the point of re-criticality ofthe calculated results closer to the measurement.
• The maximum prompt power after re-criticality, 24.5% if the initial prompt poweraccording to the measurement, is better predicted with the DALTON-THERMIXmodel (25.5%) than with the PK-THERMIX model (43.5%). This can be at-tributed to the detailed neutronics (2d) model in the DALTON-THERMIX com-pared to the simplified point kinetic model in PK-THERMIX.
• The power oscillations after re-criticality in DALTON-THERMIX have a shorterperiod than the measurements indicating that the feedback in the DALTON-THERMIX is stronger than in reality. The oscillations are dependent of the fueland moderator temperatures and their corresponding temperature reactivity effect.These temperatures are mainly dependent on the thermal capacity of the graphitein the pebbles. The reduced time period of the oscillations can therefore be soughtin an underestimation of the thermal capacity or an overestimation of the tem-perature reactivity effect of the fuel and moderator in the DALTON-THERMIXmodel.
3.1.3 Control Rod Withdrawal without SCRAM
In a second experiment the loss of flow is combined with a withdrawal of a control rod.The transient is started (time point zero) by withdrawing one control rod at operationalspeed introducing positive reactivity [26], see Fig. 3.7. After 12 seconds, the reactor pro-tection system was initiated by the signal ”power increasing rate exceeds 3.5 %/s”. Thissystem shuts down the helium blower, but because of its mechanical inertia the speed ofthe blower only reduces gradually [26] to 0 % of the nominal speed in approximately 5minutes. At the same time a flapper valve is closed to isolate the reactor from the restof the primary loop.
The mass flow through the core was not recorded during the transient. Therefore,it is assumed that after the initiation of the reactor protection system, the mass flow isreduced linearly and is completely stopped at t= 80 seconds, which corresponds to thereduction in the helium blower speed.
The temperatures and prompt reactor power during the first 500 seconds of the ex-
16
0 20 40 60 80 100 1200
1
2
3
4
5
t [s]
Inse
rted
rea
ctiv
ity [m
k]
Figure 3.7: Inserted reactivity by controlrod withdrawal.
0 1000 2000 3000 4000 5000 6000 7000−10
0
10
20
30
40
50
∆ T
[°C
]
t [s]
FuelModRefl
Figure 3.8: Difference in the Fuel, Mod-erator and Reflector temperatures com-pared to values at normal operating con-ditions used in the PK - THERMIXmodel to determine the temperature re-activity feedback during the CRW tran-sient.
0 100 200 300 400 5000
0.5
1
1.5
2
2.5
Time [s]
Pow
er [−
]
Experiment
DALTON−THERMIX
PK−THERMIX
(a) t ≤ 500 s
0 1000 2000 3000 4000 5000 6000 70000
0.5
1
1.5
2
2.5
Time [s]
Pow
er [−
]
DALTON−THERMIX
PK−THERMIX
Experiment
(b) t ≤ 7000 s
Figure 3.9: Reactor (prompt) power of the HTR-10 during the Control Rod withdrawaltransient of the HTR-10 during; (a) the first 500 seconds; (b) the entire time domain.
periment are shown in Figs. 3.8 and 3.1, respectively. The insertion of positive reactivityby the control rod withdrawal results in a rapid increase of the reactor power in the first30 seconds of the transient. The increase in fuel and moderator temperature causes anegative temperature feedback, which is stronger than the reactivity added by the con-trol rods, and within 500 seconds the contribution of the fission power the total reactorpower is negligible. Criticality is reached again (see Fig. 3.9(b)), after sufficient coolingdown of the core, similar to the core behavior during the PLOFC transient. The reactorreaches the time point of re-criticality earlier compared to the PLOFC transient, sincepositive reactivity was added by the control rod withdrawal.
17
Although the shape of the power history is similar for the first 500 seconds of thetransient, the maximum value reached is significantly lower for the PK-THERMIX (187% of the initial fission power P0) and the DALTON-THERMIX (1.89 P0) calculationcompared to the measured value (2.13 P0). It was found that the maximum powerreached is sensitive to the time point at which the mass flow reduction is initiated andthe mass flow reduction rate. The uncertainty in their exact values could explain thedifference between the calculated and experimental results.
Similar to the PLOFC transient, the calculated point of re-criticality occurs (250seconds for DALTON-THERMIX) before the measured time point and the maximumpower reached after this time point is 22 % of the initial power for DALTON-THERMIXand 36 % for PK-THERMIX compared to the measured 23 %. Similar to what was foundfor the PLOFC transient the point-kinetic results are similar to the DALTON results atthe beginning of the transient. However, at the point of re-criticality the temperatureand power profiles have changed significantly as compared to their shapes at nominalconditions. Therefore, the (2D) DALTON results are in better accordance with theexperiments than the point-kinetic results.
18
3.2 Simulation of the AVR
The DALTON-THERMIX coupled code system for pebble-bed High Temperature Re-actors was further validated by simulation of two dynamic experiments in the AVR.The validation included a rapid mass flow reduction dynamic experiment and a De-pressurized Loss of Forced Cooling (DLOFC) experiment. For the mass flow reductionexperiment, the rotational speed of the blowers dropped rapidly from 100 % to 50 % in62 seconds. In the DLOFC experiment, the long term power (100 hours) of the reactorwas calculated and compared with experiments. Besides the transient calculation, eachexperiment included a coupled steady state calculation to determine the initial conditionfor the transient.
The AVR is an experimental High Temperature Reactor(HTR), built as an exper-iment on industrial scale in Julich, Germany. The reactor had 21 years of successfulpower operation and was used as a test bed for various fuel and refueling strategies[28, 28]. Many important experiments to prove the safety features of HTRs were car-ried out in the AVR [29, 30], such as a simulation of a Depressurized Loss of ForcedCooling (DLOFC) experiment. These experiments provide valuable data for validationof computer code systems.
In this section the code system has further been validated in more detail by twoexperiments of the AVR. The two experiments included a rapid mass flow transient anda DLOFC. In the simulation of the mass flow dynamic experiment, the rotational speedof the blowers dropped rapidly from 100 % to 50 % and the succeeding power oscillationswere simulated. In the DLOFC simulation, the long term behavior (100 hours) of thereactor without active cooling was calculated by the code system. To calculate the initialconditions of the dynamic simulation, a coupled steady state has been performed for eachexperiment.
3.2.1 Decription of the AVR
The AVR has a compact structural arrangement, as shown in Fig. 3.10 and the maintechnical data are illustrated in Table 3.2. The steam generator, the reactor and theblowers are all in the same reactor pressure vessel. Main features of the AVR are highcoolant outlet temperature(950 ℃), pebble fuel, continuous fuel circulation and heliumcoolant.
One difference between the AVR and current HTRs, for example the HTR-10, is thelocation of the steam generators and the blowers. As shown in Fig. 3.10, the two blowersof the AVR are located at the bottom of the inner Reactor Pressure Vessel (RPV), andthe steam generator is located at the top of the inner reactor pressure vessel, while in theHTR-10 the steam generator and blower are located outside the reactor pressure vessel.In the AVR the helium flows through the reactor core from the bottom to the top, and iscooled down in the steam generator. Then, it passes through the narrow space betweenthe reactor barrel and inner reactor pressure vessel, where it cools the reactor barrel and
19
Table 3.2: Technical data of the AVR reactorPrameters Values UnitsCore:Thermal power 46 MWAverage power density 2.6 MW/m3
Number of fuel pebbles 1,000,000Number of shut down rods 4Average height 2.8 mDiameter 3.0 mArrangement Pebble bedFuel elements:Diameter of a fuel element 6.0 cmFuel U, ThU-235 mass per fuel element 1 gEnrichment 10, 16.7, 93 %Thorium mass per fuel element 0, 5, 10 gCoolant blower:Number 2Speed 400-4000 min−1
inner reactor pressure vessel. Finally, the helium reaches the blowers and is circulatedback into the reactor core again. The steam generator is the main and final heat sinkduring normal operation and for decay heat removal.
The main thermal hydraulic parameters of the AVR are shown in Table 3.3. Thereactor can operate in two full load modes: at high outlet temperature (950 ℃) andat low outlet temperature (810 ℃), as shown in the second column of table 3.3. Themass flow dynamic experiment started from the full load, low outlet temperature(810℃) mode. The DLOFC experiment started from an even lower power to be able todepressurize the system. The parameters are presented in the third column in the sametable.
Table 3.3: Main thermal hydraulic parameters of AVRPrameters Full power DLOFC experiment UnitThermal power 46 4 MWCoolant: Pressure 10.8 1.0 barMass flow(helium) 16.3/12.7 1.5 kg/sInlet temperature 275/250 183 ℃Outlet temperature 810/950 810 ℃Steam generator:Inlet temperature 110 130 ℃Mass flow (water) 56 25 t/h
20
Figure 3.10: Schematic overview of the AVR reactor core, adopted from [12]
Figure 3.11 is the horizontal section of the AVR in the A-A position in Fig. 3.10.The section A-A locates the middle of the reactor core in the axial direction. In thefollowing sections, the term of ’middle of reactor’ means the cross section A-A in theaxial direction. An important feature of the AVR is shown in Fig. 3.11. That is, theAVR has four so-called ’reflector noses’ stretching into the pebble bed, which are made ofgraphite. Each reflector nose has a guiding tube for movement of a control rod, which isused to control the reactor during normal operation, shutdown and startup. Each guidingtube holds a control rod, which enters the reflector nose from the bottom. Moreover,some thermocouples in the side reflectors and the reflector noses are also shown in Fig.3.11. There are six thermocouples in the side reflectors (2 inner, 2 middle and 2 outside),shown in the figure with the letters A, B and C respectively. Furthermore, each reflectornose has one thermocouple at the tip(D).
21
Figure 3.11: Horizontal A-A section of the AVR core, adopted from reference [12] showingthe reflector noses and the positions of the thermocouples
3.2.2 Simulation of mass flow dynamic experiment
In March, 1988, a mass flow dynamic experiment was performed in the AVR. The sim-ulations include a coupled steady state and a coupled transient calculation.
Description of the mass flow dynamic experiment
In the mass flow dynamic experiment, the rotational speed of the blowers was linearly re-duced from 100 % to 50 % in 62 seconds. And the mass flow of the primary loop droppedrapidly along with the rotational speed of the blowers. During the whole experiment theposition of the control rods was fixed.
Before the start of the experiment, the reactor operated at full power, low outlettemperature mode. Table 3.3 gives the steady state thermal hydraulic parameters of theAVR before the transient. These parameters were used as input data for the thermalhydraulics code THERMIX.
Coupled steady state calculation of mass flow dynamic experiment
A steady state coupled neutronic and thermal hydraulic calculation was done to calcu-late the initial conditions for the succeeding transient calculation, since the reactor hadoperated at full load steady state before the mass flow changed in the experiment.
The coupled steady state calculation was performed according to the method de-scribed in section 2. In the calculation, DALTON was used in 3D mode. Xenon poison-ing was not included into the calculation during the entire dynamic process, because the
22
mass flow dynamic experiment last only 500 seconds, which is short compared to thedynamic effect of Xenon.
In the procedure, the neutronic calculation adopted a 9 energy groups structure [32],as shown in table 3.4. The first 5 groups belong to fast neutrons and the remaining 4groups are thermal ones. Figures 3.12 and 3.13 show the fast flux and thermal flux inthe middle of the reactor core, A-A section as shown in Fig. 3.10.
The peaks of the thermal flux appear in the graphite noses, in contrast to the fastflux, which is depreciated in the reflector noses. The peaks of the fast flux appear in thezones surrounded by the reflector noses and side reflectors. At the axial position, A-Asection, shown in Fig. 3.12 and Fig. 3.13, no control rods are present and their influencecan not be observed.
Table 3.4: Group structure for AVR calculationUpper(eV) Lower(eV) 9 groups1.5E107 1.83E105 11.83E105 961 2
961 17.6 317.6 3.93 43.93 2.38 52.38 0.414 60.414 0.10 70.10 0.04 80.04 0.0 9
−250 −200 −150 −100 −50 0 50 100 150 200 250−250
−200
−150
−100
−50
0
50
100
150
200
250
Fast flux [cm−2s−1]
X [cm]
Y [c
m]
1
2
3
4
5
6
7
8
9
x 1013
Figure 3.12: Fast flux(1-5 groups) at thestart of the mass flow dynamic experi-ment
−250 −200 −150 −100 −50 0 50 100 150 200 250−250
−200
−150
−100
−50
0
50
100
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Thermal flux [cm−2s−1]
X [cm]
Y [c
m]
1
2
3
4
5
6
7
8
9
10
11x 10
13
Figure 3.13: Thermal flux(6-9 groups)at the start of the mass flow dynamicexperiment
Table 3.5 gives the measured data [12] for full power, low outlet temperature, and the
23
calculated results from DALTON-THERMIX. Although the measured data do not comefrom the mass flow dynamic experiment directly, the mass flow dynamic experiment hasthe same operation status as the measured data. The measured results can give a goodvalidation to the calculated results.
Table 3.5: Steady state temperatures of AVR in full power conditionLocations Exp. (℃) Cal.(℃)Side reflector: Middle 635 645Side reflector: Outside 631 629Bottom reflector 287 289Reactor barrel: Middle 335 324Inner Reactor pressure vessel 251 253Helium outlet temperature 810 8431
1 Average helium temperature in cavity above the top reflector
Transient simulation of mass flow dynamic experiment
After the steady state calculation, the succeeding mass flow transient was simulated inthe DALTON-THERMIX code system. In the calculation, the mass flow of the primaryloop dropped linearly in 62 seconds according to the experimental rotational speed of theblowers. Then, the mass flow was kept constant until the end of the calculation periodof 500 s. The inlet temperature of the reactor dropped about 10 ℃ during the entireexperiment because the steam generator maintained its full load operating condition.
Figure 3.14 illustrates the change of the normalized thermal neutron flux, includ-ing both experimental and calculated data, and the normalized rotational speed of theblowers that was measured during the experiment. The calculated results agree withthe experimental ones very well. The normalized fission power of the reactor shows thesame trend as the thermal flux, as shown in Fig. 3.15.
The change of the fission power is mainly due to the negative temperature coefficientof the reactor since the control rods were kept at a fixed position during the whole exper-iment. Figure 3.16 gives the volumetric average temperature of the fuel pebbles in thereactor core. Once the reactor looses part of the coolant flow, the average temperatureof the fuel pebble increases immediately. The increasing temperature induces negativereactivity, which leads to a decrease of the power. Compared with the mass flow, thepower decrease is slow in the first few seconds, as shown in Fig. 3.15 because the largeheat capacity of the reactor core prevents a fast change of its temperature. Subsequently,the power decreases rapidly along with a decrease of the mass flow and increasing tem-perature. The temperature of the reactor continues to increase after the mass flow hasstabilized at 50 %. The power also continues to decrease after the mass flow keeps con-stant because of the negative reactivity induced by the temperature increase. However,
24
0 100 200 300 400 50030
40
50
60
70
80
90
100
Time [s]
Per
cent
[%]
Relative thermal flux
Relative thermal flux(Cal)Relative thermal flux(Exp)Relative rotate speed(Exp)
Figure 3.14: Normalized thermal flux during the mass flow dynamic experiment
0 100 200 300 400 50030
40
50
60
70
80
90
100
Time [s]
Per
cent
[%]
Relative power
Relative fission power(Cal)Relative thermal flux(Exp)Relative rotate speed(Exp)
Figure 3.15: Normalized fission power flux during the mass flow dynamic experiment
25
0 100 200 300 400 500431
432
433
434
435
436
437
438
Time [s]
Tem
pera
ture
[°C
]
Average temperature of pebble
Average temperature of pebble(Cal)
Figure 3.16: Volumic average temperature of the fuel pebble during mass flow dynamicexperiment
the temperature of the reactor core stops increasing after 80 seconds, as shown in Fig.3.16, because of the continuous decrease of the reactor power. Because the heat capacityof the reactor is very large, the reactor takes about 60 seconds to return to its initialtemperature. After this point, the reactor starts to cool down further, which inducespositive reactivity. This causes the recovery of the reactor power from 150 seconds. Thepower oscillates because of the heat capacity of the reactor and the negative tempera-ture coefficient. However, the power and thermal flux reach a new steady state quicklyafter 300-400 seconds by negative feedback of the negative temperature coefficient. Theaverage temperature of the fuel pebble can not return to its initial value because theinlet temperature decreased about 10 ℃ during the experiment.
The experimental data validates the calculation of the code system well. Both theexperiment and calculations demonstrate the safety of the AVR, or the pebble bedreactor. The AVR has enough large negative temperature coefficient to stablize thereactor power without any interface of operators.
3.2.3 Simulation of the Depressurized Loss Of Forced Cooling (DLOFC)Experiment
Depressurized Loss Of Forced Cooling (DLOFC) is considered as one of the most severeaccident for nuclear power plants. The primary loop of the reactor system loses forcedcooling and pressure, which can damage the fuel in most types of nuclear power reactors,e.g. PWR. However, the high temperature reactor is designed to bear this kind of
26
accident without the active intervention of safety systems.The Depressurized Loss Of Forced Cooling (DLOFC) was simulated in the AVR in
1988[28] in order to demonstrate the inherent safety of the high temperature, pebblebed reactor. The DLOFC experiment has been calculated by the DALTON-THERMIXcode system and the results are compared with the experimental data and analyzed inthis section.
Description of DLOFC experiment
The DLOFC experiment was designed to simulate the AVR losing forced cooling andsystem pressure at full load condition. But, a fast depressurization could not be es-tablished for practical reasons. Alternatively, the helium was pumped into the storagevessel by the gas purification system, but that process would have needed about threedays. However, after three days, the decay heat level of the reactor was substantiallylower than that in a real loss of coolant event, e.g. break of a line of the primary loop.Therefore, the decay heat was simulated by controlling the fission power by moving thecontrol rods.
The entire experiment was divided into three stages: preparation stage, steady stateoperating stage and transient stage. The preparation stage inluced:
1) The excess reactivity was lowered before the experiment by stopping the feed ofnew fuel pebbles. This allowed the control rods to be inserted into the reactorcore only partly during the test, which guaranteed that the power distribution wassimilar to that in a real full power condition.
2) The reactor was shut down and the system pressure was decreased to 1 bar bypumping out the helium from the primary loop system into the storage system.
In the steady state operating stage, the reactor was operated for some days at lowpower level (steam generator power: 4 MW) until the temperature distribution of thefull power was obtained. The operating conditions of the AVR are given in Table 3.3and the temperatures of the main components such as the side refectors and the reflectornose are shown in the second column of Table 3.6.
After the temperature distribution of the full power was achieved, the experimententered the final transient stage. That is, the main part of the experiment was started.In this stage, the blowers were shut down and the reactor lost forced cooling. The decayheat curve for full load conditions ( 46 MW thermal power) was simulated with thefission power by moving the control rods in the reflector noses. The steam generatoroperated normally at about 50 percent of full mass flow in the entire DLOFC experimentaccording to the experimental data in Table 3.3. The inlet temperature of the water ofthe steam generator decreased from 130 ℃ to 60 ℃. The steam generator kept enoughcooling capacity in the entire experiment and was the main heat sink in the DLOFCexperiment.
27
Table 3.6: Steady state temperatures before the DLOFC transientLocations DLOFC Experiment (℃) Calculation (℃)Side reflector: Inner 553 560Middle 545 547Outside 535 531Bottom reflector 207 225Reactor barrel 276 273Inner RPV: Middle of reactor 189 193Top of reactor 196 215Discharge tube 198 189
Coupled steady state calculation of DLOFC experiment
The entire DLOFC experiment has been simulated by the DALTON-THERMIX codesystem, including the steady state before the transient. The calculation steps were asfollows.
1) The initial steady state of the reactor was calculated by performing the coupledneutronics/thermal hydraulic calculation with DALTON-THERMIX.
2) The succeeding transient process was simulated using thermal hydraulic code sys-tem, THERMIX from the initial state calculated in the first step. The simulateddecay heat power obtained in the experiment was provided to THERMIX duringthe DLOFC transient calculation.
The calculation results of the steady state are presented in this section, wihle thetransient part is presented in the next section.
In the steady state calculation, the neutronic calculation also adopted the same 9energy-groups structure as the mass flow dynamic experiment. Moreover, the flux ofthe DLOFC experiment has similar distributions with that of the mass flow dynamicexperiment. The flux of the DLOFC experiment is lower by one order of magnitudethan that of the mass flow dynamic experiment because the power of the reactor is only4 MW during steady state of the DLOFC experiment.
DALTON has been used in 3D mode and obtained the 3D flux and power profile.The 3D power profile was averaged in the azimuthal direction to generate a 2D profilefor THERMIX. The same transfer was adopted in the mass flow dynamic experiment.Figure 3.17 illustrats the final 2D power density distribution of the DLOFC experimentused in THERMIX. The power peak appears in the top outer region of the reactor,rather than in the center of the reactor. The main reason for this is that the zone ofthe power peak is surrounded by the graphite noses and side reflectors. They providesufficient thermal neutrons. Furthermore, the AVR used different fuel pebbles for theinner and outer zones.
28
Figure 3.18 shows the temperature distribution of the reactor before the DLOFCtransient, which was calcuated by the DALTON-THERMIX code system. The reactor iscooled by the blowers before the transient, and the position of the maximum temperatureappears on the top, outside of the core. It is determined by the corresponding powerdensity and the mass flow distribution in the reactor.
The third column in Table 3.6 gives the calculated temperatures of the reactor beforethe DLOFC transient. The results calculated by the code system are in good agreementwith the experimental results, the second column in the table.
0.02
0.02
0.02
0.04
0.04
0.04
0.06
0.06
0.06
0.06
0.08
0.08
0.080.08
0.1
0.1
0.1
0.12
0.12
0.12
0.12
0.12
0.14
0.14
0.08
Power Density [MW/m3]
R [cm]
Z [c
m]
20 40 60 80 100 120 140
50
100
150
200
250
300
350
400
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Figure 3.17: 2D power density profileof the reactor core before DLOFC tran-sient
200200 200
200
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400400 400
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Solid temperature, 0 h [ºC]
R [cm]
Z [c
m]
50 100 150 200 250
−300
−200
−100
0
100
200
300
400
500 0
100
200
300
400
500
600
700
800
900
1000
Figure 3.18: Temperature profile ofsolid structures before DLOFC tran-sient
Transient simulation of DLOFC experiment
The transient of the DLOFC experiment was started after the reactor reached a fullpower temperature distribution. The blowers were shut down and the mass flow of theprimary loop reduced to zero.
Before the transient, the reactor was cooled by forced circulation. The forced con-vection dominated the heat transfer between the reactor and the steam generator. Theconduction and radiation were of less importance than the convection. After the forcedconvection stopped, conduction, radiation and local natural convection all contributedto the heat transfer between the reactor core and the steam generator. Although it iscommonly considered as unimportant in a low pressure system, natural convection did
29
contribute to the heat transfer in the AVR during the DLOFC experiment[12, 33]. How-ever, because the THERMIX is a 2 dimensional code, it can not take into account the3-dimensional geometry of the reactor, especially the ducts in the top reflectors. More-over, THERMIX also underestimates natural convection in the cavity. The deficiencyleads to underestimation of the cooling during the transient calculation in the reactor.In order to simulate the transient and validate the code system, an artificial mass flowwas specified in the transient simulation to model the local natural circulation, thoughthe blowers are stopped and the valves are closed in the primary loop.
Maximum temperature of reactor core
The temperature of the fuel pebbles is the most important parameter for the fuel in-tegrity, but a temperature history of the pebbles during the experiment is not available.However, the maxmimum surface temperature of the fuel pebbles occuring in the tran-sient was recorded by some monitoring pebbles with a ’temperature wire’. They wereput into the reactor core before the transient. The measured maximum temperature ofthe fuel surface was between 1070 ℃ and 1090 ℃ in the DLOFC experiment. The cal-culated maximum fuel temperature is 1041 ℃. The maximum temperature is far belowthe limit temperature of (1600 ℃).
Figure 3.19 illustrates the calculated temperature at the center of the reactor core(A-A section). The measured maximum surface temperature of the fuel pebbles in the entiretransient is also shown as the solid lines in the figure. At the reactor center, the surfacetemperature of the fuel pebbles increases rapidly and reaches the maximum after 25hours. Because of the large heat capacity of the reactor core, the temperature of thereactor core remains well below the limit of 1600 ℃after the reactor looses forced cooling.Then, the temperature decreases slowly until the end of the experiment. Because of thepoor conductivity of the pebble bed, the temperature of the reactor center increases 500℃, and decreases only slightly later on in the experiment, which is the basic behavior ofthe pebble bed, except part of the pebble bed on the top, as shown in Fig. 3.20. Thetop part of the pebble bed can be cooled well by local natural convection, radiation andconduction.
Temperature response of side reflectors
The temperatures of the reflectors were measured during the whole DLOFC experimentin the AVR, see Fig. 3.11 for the location of the thermocouples. The side reflector isone of the most important components among all structures. The reflectors hold thefuel pebbles and are the basic structure of the reactor. Moreover, the graphite reflectorshave a positive reactivity coefficient. Both are important aspects with regard to reactorsafety. Figures 3.21, 3.22 and 3.23 show the measured and calculated temperature valuesof the side reflectors in the middle of the reactor core, A-A section in the axial directionof the reactor. In the radial direction, their postions are shown in Fig. 3.11 as points A,
30
0 20 40 60 80 100550
600
650
700
750
800
850
900
950
1000
1050
1100
Time [h]
Tem
pera
ture
[°C
]
Cal
1070 °C
1090 °C
Figure 3.19: Surface temperature of thefuel pebbles at the center of A-A sectionduring DLOFC
0 20 40 60 80 100550
600
650
700
750
800
850
900
950
Time [h]
Tem
pera
ture
[ºC
]
Cal
Figure 3.20: Calculated temperature ofthe fuel pebbles at the top of pebble bedduring DLOFC
0 20 40 60 80 100450
500
550
600
650
700
Time [h]
Tem
pera
ture
[ºC
]
Side reflector, Inside
CalExp
Figure 3.21: Temperature of the innerside reflector(position A, Fig. 3.11 )during DLOFC
0 20 40 60 80 100450
500
550
600
650
700
Time [h]
Tem
pera
ture
[ºC
]Side reflector, Middle
CalExp
Figure 3.22: Temperature of the middleside reflector (position B, Fig. 3.11 )during DLOFC
B and C respectively. The temperature of the side reflectors increases at the beginningof the transient, because the reactor is short of cooling and the decay heat accumulatesin the reactor. The side reflectors reach the maximum temperature after about 16-22hours according to the experiment. Then, the reactor gradually cools down, dischargingthe heat to the steam generator and the outer reactor pressure vessel by conduction,radiation and natural convection. Compared with the temperature of the center insection 3.2.3, the side reflectors are cooled largely by conducting the heat to the steamgenerator and outer reactor pressure vessel because of its good conductivity.
Temperature response of bottom reflectors
Figure 3.24 shows the temperature of the bottom reflectors. The temperature of thebottom reflectors increases 300 ℃after the forced cooling stops. It only decreases slightlyafter 70 hours. Although the bottom reflectors have a high heat conduction coefficient,
31
0 20 40 60 80 100450
500
550
600
650
700
Time [h]
Tem
pera
ture
[ºC
]
Side reflector, Outside
CalExp
Figure 3.23: Temperature of the outsideside reflector (position C, Fig. 3.11 )during DLOFC
0 20 40 60 80 100200
250
300
350
400
450
500
550
600
Time [h]
Tem
pera
ture
[ºC
]
Bottom reflector
CalExp
Figure 3.24: Temperature change of thebottom reflector during DLOFC
the bottom reflectors are far from the final heat sink in the AVR and the heat has tobe removed by other path ways, such as the side reflectors. Furthermover, local naturalcirculation in this part is small compared to the top of the reactor core.
Temperature response of pebble bed near to reflector nose
In the AVR, the reflector noses stretch into the reactor core, which provide good posi-tions to reflect the behavior of the temperature of the pebbles in the AVR core. Somethermocouples are positioned in the tip of each reflector nose as shown in Fig. 3.11,position D. The behavior of the pebble temperature can be estimated by comparingwith the temperatures of the reflector noses. Figure 3.25 shows the surface temperatureof the pebbles and the tip of reflector nose in the section A-A. The pebble has the sameradial position as the tip of the reflector nose. They follow the same trend. Because theconductivity of the reflector nose is almost 10 times larger than that of the pebble bed,there exists a large difference between the temperature of the reflector nose and that ofthe pebble bed, when the pebble bed is cooled by the conduction in the condition ofthe DLOFC. Despite of the differences between calculated and experimental data, thetemperatures have a similar trend.
Temperature change pattern of reactor core
Figures 3.26, 3.27, and 3.28 illustrate the temperature distributions in the reactor at 5h, 20 h and 50 h. The end temperature after 100 hours of the transient is shown inFig. 3.29. From these figures and Fig. 3.18, the temperature at the lower part of thereactor core increases quickly at the beginning of the transient, because a large amountof heat is transfered from the top to the bottom. Temperature rearrangement dominatesthe behavior of the reactor at this stage and is more important than the cooling. Theprocess lasts about 30 hours according to the calculation. Then, the reactor core enters
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Figure 3.25: Temperature of pebble bed near to the reflector nose
a cooling stage, in which the cooling process dominates the temperature profile of thereactor. The reactor is gradually cooled down by transfering heat to the steam generatorand the outer reactor pressure vessel. The effect of the two stages is reflected in thelocation and value of the maximum temperature. The position moves from outside-topto the center-middle of the core in the first stage and the value decreases gradually inthe second stage.
3.2.4 Conclusions
Both experiments and calculations demonstrate the inherent safety characteristics of theAVR, and most probably of the pebble bed High Temperature Reactor (HTR) in general.The mass flow dynamic experiment demonstrates that the large negative temperaturecoefficients of the reactor can easily compensate for the external added positive reactivity,and that the large heat capacity of the reactor can prevent the fuel temperature fromchanging too quickly and too much.
An HTR can bear the Depressurized Loss Of Cooling (DLOFC) accident by trans-fering heat out of the reactor by conduction, radiation and local natural circulation.During a DLOFC, the core undergoes two different stages. First, the temperature re-arrangement rather than cooling dominates the process, and a large amount of heat isbeing transfered from the top to the bottom in the reactor core. The large heat capacityof reactor core can effectively slow down and stop the temperature increase caused bythe decay heat. This stage lasts about 25-30 hours. In second stage, the reactor transfersthe accumulated decay heat to the heat sink, the steam generator and environment by
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Figure 3.26: Temperature profile ofsolid structures after 5h
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Figure 3.27: Temperature profile ofsolid structures after 20h
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Figure 3.28: Temperature profile ofsolid structures after 50h
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Figure 3.29: Temperature profile ofsolid structures after 100h
conduction, radiation and local natural circulation.The DALTON-THERMIX code system has been validated by the mass flow dynamic
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experiment and the DLOFC experiment in the AVR. The results calculated with the newcode system agrees very well with the experiment values, from which it is concluded thatthe code system can effectively be used for the design and optimization of new (V)HTRconcepts. For a more accurate evaluation of the two experiments, a 3D code would beneeded to calculate the temperatures in the reflector noses.
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3.3 Conclusion
In this report results of the DALTON-THERMIX code system with experimental dataof the HTR-10 and the AVR reactors are compared.
Regarding the modeling of pebble-bed HTRs the following is concluded:
• During normal operation of a pebble-bed reactor the convective heat transfer fromthe pebbles to the helium coolant effectively removes the heat from the core. Only asmall portion (less than 1 % of the total power) of the generated heat is transferredto the surroundings by conduction and thermal radiation. In the absence of forcedcooling during D\PLOFC transients, the value of this small heat loss determinesthe behavior of the reactor. The maximum temperature reached, the rate at whichthe core cools down thereafter and the consequent time point of re-criticality (ifno SCRAM is performed) are largely dependent of this heat loss. Furthermore,the steady state power level reached after re-criticality (no SCRAM) is equal tothe total heat loss of reactor.
• It was found that the heat transfer by natural convection in HTR can also be ofimportance during loss of flow transients, even in a depressurized case. From theAVR benchmark it was learned that natural convection in the top region of thecore has a significant impact on the heat transfer between the core and the steamgenerator. Heat transfer through conduction and radiation alone could not explainthe measured amount of heat transported to the steam generator.
• Small core flows, such as bypass flows for cooling of reflectors and control rods canbe of major importance to the nominal and transient core behavior. This is causedby the resulting effect on the fuel and moderator temperatures, which have a largetemperature reactivity feedback. It is therefore recommended that these flows arerecorded during experiments and are incorporated in benchmark exercises.
• Contamination of boron in the moderator and graphite reflectors as well as theconcentration of boron in the carbon bricks surrounding the reflector has a majorimpact on the criticality of the reactor, caused by its large absorption cross section.
• The large helium cavities containing relatively cold helium at the top and bottomof the reactor have a large influence on the transient behavior. Their presenceinfluences the way that the natural circulation flows are established.
• A point-kinetic model can be an effective tool for modeling the neutronics of smallpebble-bed HTRs for some transients. However, the large change in the temper-ature and power profile during a D\PLOFC transient in an HTR, even in smallcores such as the HTR-10, result in significant differences between the point-kineticand (2D) neutronic calculation results.
Conclusions regarding the DALTON-THERMIX code system:
• The DALTON-THERMIX code system can effectively predict the temperatures inthe core during normal and P\DLOFC transients for small and large pebble-bed
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reactor designs. It captures the dynamic behavior of the reactor and is thereforea useful tool in determining the inherent safety capabilities of pebble-bed HTRdesigns.
• THERMIX underpredicts the natural circulation flows in depressurized transientcases and is therefore conservative with regard to the fuel temperature. Especiallythe description of the flow field in gas cavities is limited in THERMIX and couldbe improved.
• Some 3D geometry effects are not captured by the code system since THERMIXis limited to 2D (r-z). This limitation resulted in a significant difference betweencalculation and experimental result for the temperature of the AVR reflector nose.
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38
Bibliography
[1] U.S. DOE Nuclear Energy Research Advisory Committee and the Generation IVInternational Forum. A Technology Roadmap for Generation IV Nuclear EnergySystems. December 2002.
[2] B. Boer, D. Lathouwers, M. Ding, and J.L. Kloosterman. Coupled neutronics /thermal hydraulics calculations for High Temperature Reactors with the DALTON- THERMIX code system. In International Conference on the Physics of Reactors(PHYSOR), 2008. Interlaken, Switzerland.
[3] S. Struth. Thermix-Direkt: Ein Rechenprogramm zur instationaren zweidimension-alen Simulation thermohydraulischer Transienten. FZ Julich, Germany, 1995.
[4] J. Oppe, J.B.M. de Haas, and J.C. Kuijper. PANTHERMIX (PANTHER-THERMIX) User Manual. Report ECN-I98-019, ECN Petten, June 1998.
[5] Bismark Tyobeka, Kostadin Ivanov, and Andreas Pautz. Utilization of two-dimensional deterministic transport methods for analysis of pebble-bed reactors.Annals of Nuclear Energy, 34:396405, 2007.
[6] W.K. Terry, H.D. Gougar, and A.M. Ougouag. Direct deterministic method forneutronics analysis and computation of asymptotic burnup distribution in a recir-culating pebble-bed reactor. Annals of Nuclear Energy, 29:1345–1364, 2002.
[7] T.J. Downar et al. PARCS: purdue advanced reactor core simulator. PHYSOR-2002, October 2002. Seoul, Korea.
[8] WON-JAE LEE, JAE-JUN JEONG, SEUNG-WOOK LEE, and JONGHWACHANG. Development of MARS-GCR/V1 for Thermal- Hydraulic Safety Anal-ysis of Gas-Cooled Reactor System. Nuclear Engineering and Technology, 37(587),2005.
[9] H. Gerwin and E. Teuchert W. Scherer. The TINTE Modular Code System for Com-putational Simulation of Transient Processes in the Primary Circuit of a Pebble-BedHigh-Temperature Gas-Cooled Reactor. Nuclear Science and Engineering, 103:302–312, 1989.
39
[10] SCALE-5. Modular Code System for Performing Standardized Computer Analysisfor Licensing Evaluations. Oak Ridge National Laboratory, Tennessee, USA, 2005.
[11] H.J. Rutten and K.A. Haas. V.S.O.P. (99/3)-Input Description. Institut fur Sicher-heitsforschung und Reaktortechnik (ISR),Forschungszentrum Julich, 2003.
[12] K. Kruger. Experimentelle Simulation eines Kuhlmittelverlust-Storfalls mit demAVR-Reaktor. PhD thesis, FZ Julich, Germany, 1989.
[13] H. Reutler and G.H. Lohnert. The Modular High-Temperature Reactor. NuclearTechnology, 62(22), July 1983.
[14] OECD. PBMR coupled neutronics/thermal hydraulics transient benchmark - thePBMR-400 core design - benchmark description. Technical Report Draft-V03, Nu-clear Energy Agency, September 2005.
[15] Karl O. Ott and Robert J. Neuhold. Introductory Nuclear Reactor Dynamics. Amer-ican Nuclear Society, 1985. ISBN 0-89448-029-4.
[16] N.M. Greene, L.M. Petrie, and R.M. Westfall. NITAWL-3: Scale system module forperforming resonance shielding and working library production. Technical report,Oak Ridge National Laboratory, 2005. Oak Ridge, Tennessee, USA.
[17] N.M. Greene. BONAMI: Resonance self-shielding by the bondarenko method. Tech-nical report, Oak Ridge National Laboratory, 2005. Oak Ridge, Tennessee, USA.
[18] N.M. Greene, L.M. Petrie, and R.M. Westfall. XSDRNPM: a one-dimensionaldiscrete-ordinates code for the transport analysis. Technical report, Oak RidgeNational Laboratory, 2005. Oak Ridge, Tennessee, USA.
[19] E.E. Bende, A.H. Hogenbirk, J.L. Kloosterman, and H. van Dam. Analytical calcu-lation of the average dancoff factor for a fuel kernel in a pebble bed high-temperaturereactor. Nuclear Science and Engineering, 133(2):147–162, October 1999.
[20] H. Gerwin and W. Scherer. Treatment of the Upper Cavity in a Pebble-Bed HighTemperature Gas-Cooled Reactor by Diffusion Theory. Nuclear Science and Engi-neering, 97:9–19, 1987.
[21] W.M. Stacey. Nuclear Reactor Physics. John Wiley & Sons, Inc., 2001. ISBN0-471-39127-1.
[22] X. Jing, X. Xu, Y. Yang, and R. Qu. Prediction calculations and experiments for thefirst criticality of the 10 MW High Temperature Gas-cooled Reactor-Test Module.Nuclear Engineering and Design, 218:43–49, 2002.
40
[23] Y. Yang, Z. Luo, X. Jing, and Z. Wu. Fuel management of the htr-10 includingthe equilibrium state and the running -in phase. Nuclear Engineering and Design,218:33–41, 2002.
[24] IAEA. Evaluation of high temperature gas cooled reactor performance: Benchmarkanalysis related to initial testing of the HTTR and HTR-10. Technical ReportIAEA-TECDOC-1382, International Atomic Energy Agency, November 2003.
[25] M. Zha, S. Zhong, R. Chen, and S. Li. Temperature Measuring System of theIn-core Components for Chinese 10 MW High Temperature Gas-cooled Reactor.Journal of Nuclear Science and Technology, 39(10):1086–1093, October 2002.
[26] S. Hu, R. Wang, and Z. Gao. Transient tests on blower trip and rod removal at theHTR-10. Nuclear Engineering and Design, 236:677–680, 2006.
[27] S. Hu, R. Wang, and Z. Gao. Safety demonstration tests on HTR-10. In 2ndInternational Topical Meeting on High Temperature Reactor Technology, Beijng,China, September 2004.
[28] R. Baumer et al. AVR: experimental high temperature reactor; 21 years of success-ful operation for a future energy technology. Assoc. of German Engineers (VDI),The Soc. for Energy Technologies,VDI-Verlag GmbH, Dusseldorf, 1990. ISBN 3-18401015-5.
[29] K. Kruger and G.P. Ivens. Safety related experiences with the avr reactor. Spe-cialists’ meeting on safety and accident analysis for gas-cooled reactors, Oak Ridge,Tennessee, May 1985. 61-70.
[30] H. Gottaut and K. Kruger. Results of experiments at the avr reactor. NuclearEngineering and Design, 121:143–153, 1990.
[31] D. Hittner et al. RAPHAEL, a European project for the development ofHTR/VHTR technology for industrial process heat supply and cogeneration. InHTR2006: 3rd International Topical Meeting on High Temperature Reactor Tech-nology, Johannesburg, South Africa, October 2006.
[32] L. Massimo. Physics of high temperature reactors. Pergamon Press, 1st edition,1976. ISBN 0-08-019616-0.
[33] T. Iyoku, W. Jahn, and W. Rehm. Analytical Investigations of the AVR Loss-of-Coolant Accident Simulation Test-LOCA (HTA-5). Technical Report KFA-ISR-IB-3/92, Forschungszentrum Julich, Germany, March 1992.
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