AER Benchmark Specification Sheet
1. Test ID:AER-DYN-003
2. Short Description:
This three-dimensional dynamic benchmark in hexagonal core geometry concerns a control rod ejection accident in a VVER-440 core. It includes the modelling of thermal hydraulics in the core and of the resulting reactivity feedback effects. The transient occurs from low power at simulated end-of cycle conditions. There is no reactor scram and after a power excursion the reactor stabilises at a power level determined by the feedback effects. An optional hot channel calculation is also included.
3. Submitted by: Riitta Kyrki-Rajamäki, VTT Energy, Finland
Date: 29.12.1999
4. Reviewed by:P. Dařilek (VUJE), P. Siltanen (IVO)
Date: November 1999
5. Accepted by:M. Makai (AEKI)
Date:March 2000
6. Objective:
This benchmark provides a reasonably realistic test case of a control rod ejection accident, including all feedback effects. It 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 the comparison of results by different codes are also needed for code validation. This benchmark is a further development of the benchmarks AER-DYN-001 and –002. The inclusion of core thermal hydraulic models and of coolant feedback effects into the problem completes the description of core dynamics in this benchmark. The need for a thermal hydraulic circuit model is eliminated by fixing core inlet conditions and the core pressure drop.
The most important quantity to determine the reactor behavior in a rod ejection transient is the reactivity worth of the ejected rod. However, the reactivity worth is given in this benchmark because the consequences of different reactivity worths have been considered already in the earlier benchmarks AER-DYN-001 and -002.
8. Input:
8a. Reactor Core Geometry and Composition
The core configuration of a 180 degree sector of the VVER-440 reactor is shown in Fig. 1. The height of the core is 250 cm and the seven control rods of K6 bank are 200 cm inserted in the initial state as shown in Fig. 2. Reflectors of the core are described by diagonal albedos (ratios of net outgoing current to neutron flux at core-reflector interface) which are held constant during the transient. Alternatively albedos or two-group cross sections can be used to model the control absorbers, but these should be adjusted so that the reactivity worth of the eccentric rod of K6 bank is equal in all calculations.
The following table gives geometric and other data for fuel assemblies and fuel pins. Other materials in the core are not considered in this fast transient.
Pitch of fuel assembly lattice14.7 cm
Number of pins per fuel assembly126
Inner diameter of cladding0.78 cm
Cladding thickness0.07 cm
Outer diameter of fuel pellet0.76 cm
Inner diameter of fuel pellet0.14 cm
Density of fuel10.4 g/cm3
Figure 1.Horizontal map of the VVER-440 reactor in half core symmetry, the same as in AER-DYN-002. Material types 1, 2 and 3 refer to 1.6, 2.4 and 3.6 % enriched fuel assemblies. The fuel followers of K6 control rods are of material type 2 and they are marked here with 6 or the control rod to be ejected with 66. All control rods of K6 bank are 200 cm inserted in the initial state.
Figure 2.Vertical cross section of the core in the initial state with control rods of K6 bank 200 cm inserted.
8b. Neutronic data
The two-group cross sections and other neutronic data for different types (enrichments) of fuel assemblies at temperature T = 260 oC are given in Table 1.
Table 1. Neutronic data for fuel assemblies
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material 1 material 2 material 3 control
1.6 % enr.2.4 % enr.3.6 % enr. absorber
------
D1 (cm)1.34661.33771.33221.1953
D2 (cm)0.371690.369180.365020.19313
a1 (cm-1)0.0083620.0087970.009470.2
a2 (cm-1)0.0642770.0793610.1001 0.8
s (cm-1)0.0168930.0159120.0148880.022264
f1 (cm-1)0.00446810.00555760.00706930.0
f2 (cm-1)0.07407 0.10626 0.15029 0.0
12.55 2.55 2.55
22.43 2.43 2.43
v1 (cm/s)1.25E+71.25E+71.25E+71.25E+7
v2 (cm/s)2.50E+52.50E+52.50E+52.50E+5
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The data is the same as in AER-DYN-002, but the fast absorption cross section a1 rather than the removal cross section r = a1 + s is explicitly shown. All fission power is prompt or there is no delayed energy release (decay heat) and the energy is 200 MeV/fission.
From the total fission power 2.5 % is deposited as radiation heat directly into the coolant of the respective fuel assembly.
The feedback effects from fuel temperature and coolant density changes are modelled as follows. Cross sections depend on the volume averaged absolute temperature Tf (in degrees of Kelvin) of fuel by formula
i = i,0 + ai ( Tf - Tf,0 )
and on the coolant density c (g/cm3) by formula
i = i,0 + bi ( c - c,0 ).
Cross sections i,0 are given in Table 1 and the reference values for temperature and density are
Tf,0 = 533.15 K
c,0 = 0.7937 g/cm3
The feedback coefficients are given in Table 2 and they are equal for all types of fuel. Absorber cross sections (or albedos) are constant in the calculation. The data corresponds to fuel and coolant temperature coefficients, which are typical for end-of-cycle state.
Table 2. Feedback coefficients
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1/D1 1/D2 a1 a2 s
------
coefficient a (1/cmK) - -.00003 --0.00003
coefficient b (cm2/g) 0.4 3.0 - 0.007 0.02
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The feedback correction of coolant density is performed on transport cross sections or actually on inverse values of the diffusion coefficients. Since in this formalism the diffusion coefficients do not depend linearly on coolant density the coefficients b for 1/D cannot be exactly converted to apply to the direct values of the diffusion coefficients D. A first order (for density change) approximation is
b' = - D2 b,
where b' is the feedback coefficient of linear dependence on coolant density for the diffusion coefficient D.
The delayed neutron fractions i of total fission neutrons and the decay constants i for the six groups of delayed neutrons are given in Table 3. Total fraction of delayed neutrons is 0.005 and the constants are same for all types of fuel assemblies.
Table 3. Delayed neutron fractions and decay constants
------
i123456
------
i 0.000190.0010650.000940.0020350.000640.00013
i (s-1) 0.01270.03170.1150.3111.403.87
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The radial and axial reflectors are treated by boundary conditions which are described by diagonal albedos for the fast and thermal groups of neutrons. Instead of cross sections albedos can also be used for control absorbers if these are considered as holes or non-diffusive regions in the calculation. Table 4 shows the albedos that are equal to the data of AER-DYN-002. The albedos are defined as ratios between net outgoing current and flux at the boundary,
Table 4. Albedos g = Jg /g for reflectors and control absorber
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Radial reflectorAxial reflectorAbsorber
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1 0.18732 0.19984 0.40065
2 -0.081293 -0.012173 0.30521
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8c. Heat Transfer in Fuel Rod
All types of fuel assemblies have the same heat transfer characteristics. The fission power (97.5 % of total into fuel) is released uniformly in fuel pellet, 2.5 % is released straight in the coolant. Radial thermal conductivities p and c of fuel pellet and cladding are functions of absolute temperature (K) according to the formulae
1
2
Axial transfer of heat is neglected in fuel pellet and cladding. Thermal capacities of fuel and cladding cp and cc, respectively, depend linearly on temperature similarly to the cladding conductivity.
3
4
The heat transfer data for fuel pellet and cladding are given in Table 5.
Table 5. Heat transfer data in fuel rod
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radial thermal conductivitythermal capacity
, W/Kcm1,2c, J/Kcm 3,4
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fuel pellet0.1610.0030.0012.420.0003
cladding0.1300.0009- 1.470.0008
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The thermal conductance of the gas gap between fuel pellet and cladding is a function of average fuel temperature. It is 0.4 W/Kcm2 below 800 K and grows linearly from 0.4 to 2.0 W/Kcm2 at temperatures from 800 K to 1500 K. Above 1500 K of average fuel temperature the gas gap conductance has the constant value 2.0 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 stationary state. In 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 during the transient is determined so that the pressure difference over the core stays constant. The reactor outlet pressure 121 bar, the pressure difference over the core and the coolant inlet temperature 260 o C are constant during the transient. The total inlet mass flow is 3400 kg/s for the entire core (360) in stationary state.
The flow area of a channel is 87 cm2 and the equivalent hydraulic diameter (both wetted and heated) is 0.85 cm. Inlet orifice of coolant flow is simulated by a spacer with a large friction coefficient at a height of 1 cm above the core bottom. Other spacers or outlet orifice are not included in the problem, but the distributed one-phase friction along the flow channel is chosen to give a stationary state pressure loss that is approximately equal to the pressure loss in a real VVER-440 core at similar conditions.
The pressure loss caused by distributed friction for channel length z is calculated from expression
5
and the local pressure loss by the spacer (inlet orifice) is
6
Kd and Kl are the friction coefficients, G is the coolant mass flux density (kg/m2s), w is the water density, Re is the Reynolds number and 2 is the two-phase friction multiplier (for one-phase flow 2 = 1). Input values for the friction coefficients are
Kd = 22. m-1
Kl = 16. (dimensionless).
The recommended hydraulic submodels in this benchmark problem are as follows:
Non-equilibrium model, subcooled or superheated water and saturated steam.
In the recommended evaporation and condensation model the bulk boiling rate is calculated from the expression
B (kg/m3s) = ( R1 + R2 (1-) ) ( Tw - Ts ) / ( hs,sat - hw,sat )
and the surface evaporation rate after Tclad > Tw,sat is given by
SF (kg/m3s) = QSF / ( hs,sat - hw,sat + Cp (Tw,sat - Tw ) w / s
+ 0.5 Cp (Tclad - Tw,sat ) ( w / s - 1 ) )
where R1 = 50106 W/m3K, R2 = 200106 W/m3K, QSF is heat to coolant (W/m3), is void fraction, h is enthalpy, T is temperature, is density and Cp is specific heat of water. Index w stands for water, s for steam, sat for saturation conditions and clad for cladding surface outside.
The slip ratio is calculated with Zuber-Findlay correlation and the two-phase friction multiplier with Baroczy-Chisholm correlation.
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 stationary state the thermal power is 1.375 kW. The reactor outlet pressure is 121 bar, inlet temperature is 260 oC and coolant flow through the whole core (360) is 3400 kg/s in stationary state. The inlet temperature, the inlet and outlet pressures of the core and so also the pressure difference over the core are kept constant during the transient calculation. All control rods of K6 bank are 200 cm inserted in the initial state.
The most important quantity to determine the reactor behavior in a rod ejection transient is the reactivity worth of the ejected rod. In order to exclude deviations from different reactivity worths the calculations are performed with a fixed value of 0.9834 % or 1.9668 $ for the ejected rod from insertion of 200 cm into fully withdrawn position. The participants of the benchmark should adjust the neutronic data which they use (cross sections or albedos) for the control absorbers so that the correct reactivity worth is obtained. The cross sections for control absorbers are given in Table 1 or alternatively the albedos for control rods are given in Table 4
The reactor outlet pressure is 121 bar, and the coolant inlet temperature is 260 o C. The total inlet mass flow is 3400 kg/s for the entire core (360) in stationary state.
8f. Scenario of the Transient
An eccentric rod of K6 bank is ejected at time t = 0 s. The rod moves with a constant speed of 12.5 m/s which corresponds to 0.16 s for the ejection time. Other rods of the bank remain at 200 cm insertion and no reactor trip is included in the calculation. The calculation should be continued until t = 5 s and preferably to t = 10 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 average in the assembly,
- 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,
- 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 hottest assembly in this transient is obviously the assembly number 167 numbered in the order of the desired results (see next section). Its power factor is 1.39 in nominal full power conditions without inserted control rods. The excess hot channel power factor 1.25 gives a radial hottest rod factor 1.74 (= 1.25*1.39 ) which is a quite typical maximum value in a VVER-440.
The recommended additional thermal hydraulics correlations for DNB and post-DNB phenomena are:
- critical heat flux correlation for DNB margin: Gidropress,
- 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)
Initial State, keywords "k_eff" and "core pressure drop"
Calculation results to be compared include spatial power distributions, axial distributions of coolant density and time functions of various quantities. The multiplication factors keff and the pressure loss over core (bar) at the initial state are also compared. The multiplication factor has keyword "k_eff" and pressure loss over core has keyword "core pressure drop".
Time functions, keyword "time functions"
The time behaviour from 0 to 5 (or 10 ) seconds is compared by the following 14 quantities:
(note that the temperatures are here in C)
- total fission power of the reactor (MW)
- total time integrated fission power (MWs)
- total power transferred to coolant (MW)
- maximum fuel pellet centerline temperature (oC)
- maximum fuel pellet average temperature (oC)
- place of max. fuel cent. temperature, node number from core bottom
- total inlet mass flow (kg/s)
- total outlet mass flow (kg/s)
- inlet mass flux density of the hottest assembly (kg/m2s)
- outlet mass flux density of the hottest assembly (kg/m2s)
- average enthalpy of coolant at core outlet (MJ/kg)
- average void fraction in the core
- maximum outlet void fraction
- maximum outlet thermodynamical steam quality (relative enthalpy)
Values are given at time interval 0.0 - 0.4 s with time step 0.01 s and from 0.4 s to the end time of calculation the step is 0.05 s. These time step are not recommended to use in calculation, but shorter steps are obviously required at least during the first interval. The data array of the results should contain the time and the values of the 14 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 distributions of average coolant density (kg/m3), c = s + (1-)w in channel with maximum boiling are taken at times t = 0.4 s, t = 1.5 s and t = 3.0 s.
Spatial fission power distributions, keyword "power distributions"
Three-dimensional power distributions are given for nodes which consists of one tenth of a core channel (25 cm segment of a fuel assembly). 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 rowwise from left to right and from top to bottom according to Fig. 1.
The power distributions are taken at following times:
- t = 0.0 s, initial stationary state
- t = 0.16 s, ejection time
- time of maximum total power of the reactor
- t = 0.4 s, declining power after the burst by rod ejection
- t = 1.5 s, coolant boiling in some channels
- t = 3.0 s, reactor power close to a new stationary value
Hot channel time functions, keyword "hot channel time functions"
The time behaviour from 0 to 5 (or 10 ) seconds is compared by the following 11 quantities:
- 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 core bottom
- inlet mass flux density of the hot channel (kg/m2s)
- outlet mass flux density of the hot channel (kg/m2s)
- hot channel outlet void fraction
- hot channel outlet thermodynamical steam quality (relative enthalpy)
- maximal oxide layer thickness, % of cladding thickness
- average oxide layer thickness in hot channel, % of cladding thickness
Values are given at time interval 0.0 - 0.4 s with time step 0.01 s and from 0.4 s to the end time of calculation the step is 0.05 s. These time step are not recommended to use in calculation, but shorter steps are obviously required at least during the first interval. The data array 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 average coolant density (kg/m3), c = s + (1-)w in hot channel are taken at times t = 0.4 s, t = 1.5 s and t = 3.0 s.
b. Files, Format
The results should be presented on paper and transferred for comparison by diskette or e-mail. 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.
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: