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1. Test ID: AER-DYN-004
Short Description:
This three-dimensional dynamic benchmark in hexagonal core geometry concerns a boron dilution event in a VVER-440 reactor core. The core is initially in a hot subcritical state with all control rods inserted. A slug of boron diluted and cooler water is injected into the core by forced flow corresponding to the operation of one reactor coolant pump. The core experiences a prompt supercritical power excursion and becomes subcritical again as the slug leaves the core. The geometrical definition is similar, but more realistic than in earlier dynamic benchmarks. For a realistic exercise in safety analysis, the nuclear cross section data are not given. Rather, participants are requested to use their own best estimate data. However, specified key reactivity parameters are normalised to given values, implying adjustments to the best estimate cross section data. A hot channel calculation is included as an additional option.
Submitted by: Riitta Kyrki-Rajamki, VTT Energy, Finland
Date: 3.4.2000
4. Reviewed by: (name)
Date:
5. Accepted by: (name)
Date:
6. Objective:
This benchmark problem concentrates on the interaction of neutron kinetics and thermal hydraulics modelling in the core. It is also a test for the tracking of boron and temperature fronts in the core. Furthermore, this problem is an exercise in the use of own nuclear data libraries, subject to the requirement of normalising important reactivity parameters (indicators) to given values. This is a typical requirement in conservative safety analyses. This test is suitable for the comparison of results calculated by different three-dimensional core dynamics codes.
7. Rationale for Test Setup:
Due to the complicated and interacting physical phenomena that need to be modelled in real safety analyses, it is not possible to base the validation of three-dimensional core dynamics codes only on mathematical benchmarks or measurements. Realistic test problems for comparison of results by different codes are also needed for code validation.
Local boron dilution events have in recent years been discovered to have the potential to cause reactivity accidents. The generic scenario chosen for this test is the injection of a diluted coolant slug into the core by restart of the first reactor coolant pump. In this test, the core inlet conditions are specified, which eliminates the need to model the primary circuit. The coolant flow rate is set to correspond to one operating reactor coolant pump. The transient occurs in beginning-of-cycle conditions with a high boron concentration in the coolant. Thereby, the effect of thermal hydraulics on the transient is maximised while still avoiding the numerical difficulties in modelling of natural circulation flow. 60-degree symmetry is assumed for the coolant inlet conditions. This makes it possible to model a separate flow channel for each fuel assembly in most codes.
It should be recognised that accurate calculation of the propagation of diluted slugs with conventional numerical methods is not straightforward, especially in low flow conditions. Standard thermal hydraulic methods that are used in accident analysis codes are not always suitable for tracking of a boron front and can produce non-conservative results due to numerical diffusion and dispersion.
8. Input:
8a. Reactor Core Geometry and Composition
The core configuration of a 60 degree sector of the first loading of a VVER-440 reactor is shown in Fig. 1. There are 3 different enrichments of the fuel and the burnup is zero. The height of the whole core is 356 cm. The height of the heated part of the core is 244 cm and the six control rod groups (37 control rods) are fully inserted in the initial state. The height of the active fuel follower parts of the control rods is 234 cm, the uppermost 10 cm part of these fuel rods contains steel inserts. Unheated parts below and above the heated core are included in the model. Their heights are: "lower part" 64 cm and "upper part" 48 cm, respectively.
The following table gives geometric and other data for fuel assemblies and fuel pins. Other materials in the core are not considered in this rather fast transient.
Pitch of fuel assembly lattice 14.7 cm
Number of pins per fuel assembly 126
Inner diameter of cladding 0.78 cm
Cladding thickness 0.07 cm
Outer diameter of fuel pellet 0.76 cm
Inner diameter of fuel pellet 0.14 cm
Density of fuel 10.4 g/cm3
Figure 1. Horizontal map of the VVER-440 reactor in 1/6 core symmetry for fourth dynamic AER benchmark including standard location numbers of assemblies. The core is equal to the core of the third dynamic benchmark AER-DYN-003 (Ref.1). Material types 1, 2 and 3 refer to 1.6, 2.4 and 3.6 % enriched fuel assemblies. All control rods are fully inserted in the initial state, marked here with doubling of the fuel type number (11 or 22).
8b. Neutronic data
The best estimate data of each participant will be used for the two-group cross sections and other neutronic data for different types (enrichments) of fuel assemblies. Reflectors of the core can be described with albedos or reflector nodes with own cross sections. Alternatively albedos or two-group cross sections can be used also to model the control absorbers.
In reality, only part of the fission power is prompt. However, the description of the decay heat is not included in the benchmark and all fission energy is released promptly. The energy/fission is determined with the data of each participant. No xenon is modelled in the benchmark. From the total fission power 2.5 % is deposited as radiation heat directly into the coolant of the respective fuel assembly.
The reactivity feedback effects from fuel temperature, coolant density and boron density changes are modelled with each participant as accurately as wished. The reactivity coefficients of the whole core in the reference state are given. The reference state is the hot zero power state with no control rods inserted and with critical boron concentration. The participants should tune their dependence of cross sections on local conditions in order to achieve the given reactivity coefficients. Thus unnecessarily large differences in the results are avoided. The amount needed in the tuning should be reported in the results.
The reactivity coefficients of the whole core in the reference state are:
- isothermal fuel temperature (Doppler) coefficient r/Tf = -3.0 pcm/K
(uniform temperature change in core)
- coolant density coefficient including coolant temperature effects
r/rm = 1.3 pcm/kg m-3
- boron concentration coefficient r/CB = -10.8 pcm/ppm.
The fractions bi of delayed neutrons in each fuel type, and the decay constants li for the six groups of delayed neutrons are not given. The total fraction of delayed neutrons in the whole core is 0.00726 in the reference state. This value should be achieved by tuning.
The boron concentration in the initial state is the critical boron concentration of the reference state. The reactivity of the subcritical initial state (subcriticality) with all control rods inserted is - 10 283 pcm; the definition of reactivity is (keff - 1.) / (keff). The subcriticality of the initial state affects the timing of the power peak. Therefore the participants of the benchmark should adjust the neutronic data which they use for the control absorbers (cross sections or albedos) so that the correct subcriticality is obtained.
The most important quantity to determine the reactor behavior in a boron dilution transient is the reactivity worth of the diluted slug. In order to exclude large deviations in the results due to different reactivity worths the calculations are performed with a fixed value of the static overcriticality of the slug, which is 2270 pcm. The static overcriticality means the reactivity value of a stationary core state, where the boron concentration is 1014 ppm less and the coolant and fuel temperatures 30 C less than in the initial state; i.e. the maximum disturbance defined for the transient in chapter 8f is assumed to prevail in the whole core. The fixed overcriticality should be achieved when the initial subcriticality and reactivity coefficients are tuned to the given values.
8c. Heat Transfer in Fuel Rod
All types of fuel assemblies have the same heat transfer characteristics. Most of the total fission power, 97.5 %, is released in the fuel pellets, radially uniformly inside the pellet; 2.5 % is released straight in the coolant. Radial thermal conductivities and thermal capacities of fuel pellet and cladding are described with best data of each participant. Axial transfer of heat is neglected in fuel pellet and cladding.
The thermal conductance of the gas gap between fuel pellet and cladding is not known very accurately. Therefore a function of average fuel temperature is given here, to avoid unnecessary deviations. It is simplified from best estimate BOC data. The conductance is 0.3 W/Kcm2 below 800 K and grows linearly from 0.3 to 1.4 W/Kcm2 from 800 K to 1900 K. Above 1900K of average fuel temperature the gas gap conductance has the constant value 1.4 W/Kcm2.
8d. Hydraulic Data
Each fuel or control assembly in the core consists of a flow channel. Since all of them are assumed hydraulically equal the mass flow distribution is almost uniform between the channels in the stationary state. In the stationary state and during the transient the mass flow distribution between the assemblies is determined on the basis of the pressure balance over the core. The total inlet mass flow in the initial state is given and during the transient it is determined so that the pressure difference over the core stays constant.
The geometry of the VVER core with control rod followers is very complicated. Therefore the following average hydraulic geometry is given for a flow channel representing each assembly (including control rod locations).
For simplicity, the flow areas of the axial parts of a channel are all the same: 89 cm2 in the lower part, heated core, and upper part. The equivalent wetted hydraulic diameter is 0.86 cm for all axial parts, and the equivalent heated diameter is 0.89 cm for the heated core part.
The pressure loss caused by distributed friction for channel length _z is calculated from expression
SEQ Equation \* ALPHABETICA
and the local pressure loss by the spacer or inlet orifice is
SEQ Equation \* ALPHABETICB
Kd and Kl are the friction coefficients, G is the coolant mass flux (kg/m2s), rw is the water density, Re is the Reynolds number and f2 is the two-phase friction multiplier (for one-phase flow f2 = 1). Input values for the friction coefficients are:
lower core upper
Kd m-1 0 12.2 5.43
Kl (dimensionless) 17.17 10*0.2225 0
The recommended hydraulic submodels in this benchmark problem are as follows:
- Non-equilibrium model, subcooled or superheated water and saturated steam.
- The slip ratio is calculated with Zuber-Findlay correlation.
- The two-phase friction multiplier with Baroczy-Chisholm correlation and with homogeneous model at local pressure losses.
- Heat transfer from cladding to coolant is determined with Dittus-Boelter correlation in convection area and with Thom correlation during boiling.
8e. Initial Conditions
In the initial stationary state the reactor outlet pressure is 121 bar, inlet temperature is 260 C, and coolant flow through the whole core (360) is 1200 kg/s. The inlet and outlet pressures of the core (including unheated parts), and thus also the pressure difference over the core are kept constant during the transient calculation.
The initial fission power level is 4.775 mW [10-9 MW]. This corresponds to the level maintained in the subcritical core by uniform spontaneous fission source of 400 neutrons/cm3.
The boron concentration in the initial state is the critical concentration of the hot zero power state with no control rods inserted, i.e. in the reference state, typically about 1400 ppm.
8f. Scenario of the Transient
The decreasing of the boron concentration and coolant temperature at the core inlet begins at time t = 1 s with a ramp of 1 s. The amount of dilution is - 5.8 g/kg in boric acid concentration (or - 1014 ppm boron concentration), and the cooling of water is - 30 C (or - 0.142 MJ/kg in enthalpy). The cold diluted slug has a volume of 8.5 m3 after the ramp, which is 7105 kg of water with temperature 230 C. The amount of the total inlet mass flow after the ramp should be integrated by each code, because the time of the ending of the slug depends on the mass flow level during the power transient. After the 8.5 m3 slug has entered the core, there is again a ramp of 1 s back to the original values. The calculation should be continued until t = 20 s.
8g. Hot channel option
Optionally also a hot channel is calculated in the benchmark, because its calculation is very important in the safety analyses. Some new thermal hydraulics phenomena are included into the benchmark with hot channel: heat transfer crisis (DNB) calculation, post DNB heat transfer calculation and oxidation of the cladding.
The hot channel definition:
- excess power factor 1.25 to the power of the hottest assembly,
- time-dependent axial power distribution the same as in the hottest assembly,
- fuel, gas gap and cladding property correlations the same as in the whole core,
- the coolant flow area per fuel rod is the same as in the average channel, also the hot channel includes the unheated lower and upper parts of the flow channel,
- the recommended hydraulics correlations are the same as in the whole core
- hot channel inlet mass flow is determined on the basis of pressure balance over the core including the unheated lower and upper parts of the flow channels
- the heat transfer mode is changed to post-DNB in a calculation node, after the DNB margin is less than 1.33 at this node.
The recommended additional thermal hydraulics correlations for DNB and post-DNB phenomena are:
- critical heat flux correlation for DNB margin: Gidropress without form factor,
- film boiling heat transfer after DNB occurrence: Groeneveld correlation,
- cladding oxidation by Baker-Just model.
9. Hardware and Software Requirements: memory, files, appr. comp. time
10. Output:
a. Expected Results (primary, secondary)
Calculation results to be compared include some key parameters, spatial power distributions, axial distributions of coolant and boric acid density and time functions of various quantities. Some of the key parameters in different states are compared before and after the tunings.
Results of tuning, maximum etc., keyword "key parameters"
- Critical boron concentration in the reference state before and after tuning (ppm)
- Total fraction of delayed neutrons, b, before and after tuning (pcm)
- Reactivity coefficients (3) before and after tuning in the reference state
r/Tf (pcm/K), r/rm (pcm/kg m-3), r/CB (pcm/ppm)
- Subcriticality of initial state before and after tuning (pcm)
- Static overcriticality with disturbances in the core, before and after tuning (pcm)
- Pressure difference over the whole core (356 cm) in the initial state (bar)
- Maximum fission power (MW)
- Time of maximum fission power (s)
These values should be in the result file in the order listed above after the keyword.
Time functions, keyword "time functions"
The time behaviour from 0 to 20 seconds is compared for the following 15 quantities given after each time value (note that the temperatures are here in C) :
- time (s)
- total fission power of the reactor (MW)
- reactivity (pcm)
- total power transferred to coolant (MW)
- maximum fuel pellet centerline temperature (oC)
- maximum fuel pellet average temperature (oC)
- axial place of maximum fuel center temperat., node number from active core bottom (1-10)
- radial place of maximum fuel center temperature, location number of assembly from Fig. 1
- total inlet mass flow density into the lower axial part of the core (kg/s)
- total outlet mass flow density out from the upper axial part of the core (kg/s)
- inlet mass flux of the hottest assembly (into the lower part) (kg/m2s)
- outlet mass flux of the hottest assembly (from the upper part) (kg/m2s)
- average enthalpy of coolant at core outlet from the upper part (MJ/kg)
- average boron concentration in the active (heated) core (ppm)
- maximum outlet void fraction from the upper part
- maximum outlet thermodynamical steam quality (relative enthalpy) from the upper part
Values are given with time steps 0.01 s during the fission power peak, and with time steps 0.1 s before and after the peak. (These time steps are not a recommendation to be used in the calculation which should be optimized by each participant.) The data file of the results should contain the time and the values of the 15 quantities (in the given order) for successive time points. The first point t = 0.0 s corresponds to the initial stationary state of the reactor.
Axial distributions, keyword "axial distributions"
The axial distribution of the average coolant density (kg/m3), rc = ars + (1-a)rw, and of the average boric acid density (g/m3), rB, in the heated active core part of the flow channel with maximum boiling are given at time intervals of 0.5 s from 0 to 20 s. The distributions are given in two arrays after the keyword. First array contains in the first column the time points and the next columns contain the coolant density values from first node to last node. The second array is similar to first one containing the boric acid density values.
Spatial fission power distributions, keyword "power distributions"
Three-dimensional power distributions are given for nodes which consist of one tenth of a core channel (24.4 cm segment of a fuel assembly); however, the calculations can be made with more nodes in the axial direction. Each distribution is normalized to unity over the total core volume including the absorber parts of inserted control assemblies. The values of the distributions are given for the ten axial layers of nodes in the same order as in previous three-dimensional benchmarks. The nodes are numbered axially from bottom to top of the core and radially from left to right and from top to bottom, see Fig. 1.
Altogether 12 power distributions are given: one from the reference state without inserted control rods, and 11 from the ordinary transient calculation at following times:
- t = 0.0 s, initial stationary state, and at t = 1.0 s initial subcritical state
- time of maximum total power of the reactor
at time intervals of 2.5 s (8 distributions from 2.5 to 20 s)
The reference state should be given fist after the keyword and then the other states in the order according to the time.
Hot channel time functions, keyword "hot channel time functions"
The time behaviour from 0 to 20 seconds is compared by the following 11 quantities given after each time value:
- time (s)
- minimum DNB margin with Gidropress correlation
- maximum fuel pellet centerline temperature (oC)
- maximum fuel pellet average temperature (oC)
- maximum cladding outside temperature (oC)
- place of max. fuel cent. temperature, node number from active core bottom (1-10)
- inlet mass flux density of the hot channel to the lower part (kg/m2s)
- outlet mass flux density of the hot channel from the upper part (kg/m2s)
- hot channel outlet void fraction from the upper part
- hot channel outlet thermodynamical steam quality (relative enthalpy) from the upper part
- maximal oxide layer thickness, % of cladding thickness
- average oxide layer thickness in hot channel, % of cladding thickness
Values are given with time step 0.1 s. This time step is not recommended to be used in the calculation, because shorter steps are obviously required at least during the power peak. The data file of the results should contain the time and the values of the 11 quantities (in the given order) for successive time points. The first point t = 0.0 s corresponds to the initial stationary state of the reactor.
Hot channel axial distributions, keyword " hot channel axial distributions"
The axial distributions of the average coolant density (kg/m3), rc = ars + (1-a)rw in the heated core part of the hot channel are given at time intervals 0.5 s. The values are given in an array in which the first column contains the time points and the next columns contain the corresponding coolant density values from first node to the last node.
b. Files, Format
The results should be presented on paper and transferred for comparison by diskette or e-mail.
The results should be in one file in which the data is in the order listed above. Keywords delimited by apostrophes should be written before each type of output data and each distribution (three-dimensional and axial) should be preceded by the time for the distribution. If all data is not given, zeros should be put instead.
The results should be in one ASCII (.txt) file. The order of the results should be the same as listed above. The format of the file should be:
ORGANISATION
"key parameters"
data
"time functions"
data
"keyword"
data
11. References
1. R. Kyrki-Rajamki, Definition of the Fourth Three-Dimensional Hexagonal Dynamic AER Benchmark Problem, Proc. Sixth Symposium of AER, p. 237, KFKI Atomic Energy Research Institute, Budapest (1996). (Slightly revised version documented after the meeting of AER working group D on VVER Safety Analyses in Budapest 5-7 May 1997.)
2. R. Kyrki-Rajamki, HEXTRAN Results of the 4th Hexagonal Dynamic AER Benchmark, Boron Dilution in Core, Proc. Seventh Symposium of AER, p. 361, KFKI Atomic Energy Research Institute, Budapest (1997).
3. A. Kereszturi, Gy. Gyenes and M. Telbisz, Calculation of the Fourth AER Kinetic Benchmark Problem with KIKO3D, Proc. Seventh Symposium of AER, p. 375, KFKI Atomic Energy Research Institute, Budapest (1997).
4. S. A. Danilin, M. P. Lizorkin and V. P. Pehterev, Solution of the Fourth AER Benchmark Problem with Code Package ATHLET/BIPR8KN, Proc. Seventh Symposium of AER, p. 399, KFKI Atomic Energy Research Institute, Budapest (1997).
5. U. Rohde and D. Lucas, Solution of the 4th AER Dynamic Benchmark by Use of the Code DYN3D with Particle-in-cell Method for the Description of Boron Transport, Proc. Seventh Symposium of AER, p. 387, KFKI Atomic Energy Research Institute, Budapest (1997).
6. J. Hadek, Results of the Fourth Three-dimensional Dynamic AER Benchmark Problem Calculations, Proc. Seventh Symposium of AER, p. 351, KFKI Atomic Energy Research Institute, Budapest (1997).
7. R. Kyrki-Rajamki, Comparison of the First Results of the 4th Hexagonal Dynamic AER Benchmark, Boron Dilution in Core, Proc. Seventh Symposium of AER, p. 321, KFKI Atomic Energy Research Institute, Budapest (1997).
8. R. Kyrki-Rajamki, Results of a 3D reactor dynamics benchmark problem on boron dilution in the core. Proceedings of the International Conference on the Physics of Nuclear Science and Technology, October 5-8 1998, Long Island, NY, USA (1998).
Recommended Solution:
No reference solution is available, it is recommended to make comparisons with all results available.
a, Method
The recommended methods for the solution are:
The neutron kinetics is modelled by the two-group diffusion equations in homogenized fuel assembly geometry and solved with different advanced nodal methods. Time discretization is carried out with implicit methods which allow flexible choices of time steps. The thermal hydraulics of the core is calculated in separate axial hydraulic channels. One or several fuel assemblies can be connected with a channel but this is not recommended. Heat transfer calculation with several radial meshes is done for an average representative fuel rod in each node. The two-phase flow model is based on at least four conservation equations for mass, momentum and energy of water and steam and it is able to consider thermal non-equilibrium effects.
New solution methods have to be applied in hydraulics to reduce the effects of numerical diffusion on the boron dilution front. It is important to recognize that the normal thermal hydraulic methods used in accident analyses codes are not always suitable for boron front tracking and in many cases the results can be very nonconservative.
b, Data, Estimated Error
13. Summary of Available Solutions
Solutions have been received from VTT Energy from Finland with the HEXTRAN code, Ref. 2, KFKI Atomic Energy Research Institute from Hungary with KIKO3D, Ref. 3, Kurchatov Institute from Russian Federation with ATHLET/BIPR8, Ref. 4, Research Centre Rossendorf from Germany with DYN3D, Ref. 5, and Nuclear Research Institute Rez from Czech Republic with DYN3D, Ref. 6. The first results were presented at the Seventh Symposium of AER in 1997, Ref. 7.
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