modelling of the vver-440 reactor for determination of the spatial weight function of ex-core...
TRANSCRIPT
MODELLING OF THE VVER-440 REACTOR FOR DETERMINATION OF THE SPATIAL WEIGHT
FUNCTION OF EX-CORE DETECTORS USING MCNP-4C2 CODE
Gabriel Farkas, Vladimír Slugeň
SUT Bratislava
Objective
Determination of the spatial weight function of ex-core detectors for the VVER-440 reactor type, taking into account different operational parameters such as power, burn-up, boric acid concentration and position of the control assembly group No 6.
Concept of the spatial weight function
The spatial weight function of the ex-core detector provides relationship between the spatial neutron flux density (or fission density) distribution in the reactor core and the ex-core detector response.
Definition of the weight function of ex-core detector
The weight function can be defined in various ways.
In this case, the weight function is a multivariable function which gives the average number of reactions in the ex-core detector for one neutron born with Watt fission spectra in the twentieth of a fuel pin in different core positions.
Application
The weight function of the ex-core detector will be useful for:
▪ interpretation of reloads startup rod drop measurements
▪ evaluation of the ex-core detector response at deep subcritical reactor conditions
▪ safety analysis of the reactor
▪ other applications.
DETERMINATION OF THE WEIGHT FUNCTION
CALCULATION OF THE FISSION DENSITY DISTRIBUTION
CALCULATION OF THE SINGLEWEIGHT VALUES BY MCNP-4C2
FITTING AN ANALYTICAL FUNCTION ONTO THE SINGLE WEIGHT
VALUES
SPATIAL WEIGHT FUNCTION OF THE EX-CORE DETECTOR
SPATIAL FUNCTION OF THE FISSION DENSITY DISTRIBUTION
EX-CORE DETECTOR RESPONSE
Determination of the Reaction Rate – Weight Value
The weight function is detector dependent function.
The reaction rate – average number of reactions occurred in the ex-core detector for one source neutron will be calculated by MCNP tally multiplier card according to the expression:
0
)()( dEEENR R
R - reaction rate (weight value)
N - atomic density of the 3He
Φ(E) - neutron fluency in a 3He filled neutron sensitive volume of the detector
σR(E) - microscopic cross section of the (n, p) reaction for 3He isotope
The calculation model
n Considering the fact that the ex-core detectors are located symmetrically, it is sufficient to model only one of the detectors and the core region in its vicinity.
n The model of the core is divided into two region – source region created by fuel assemblies from which neutrons are started and scattering region from which neutrons are not started, but it is present due to its neutron scattering effects.
• The geometric model extends to the core region from which the contribution to the ex-core detector response is not negligible.
• In respect to the symmetry conditions it is not necessary to calculate contributions from both sides of the symmetry plane.
Ex-core detector
source region
scattering and absorption
region
plane of symmetry
spatialweight
function
A A
A A
Reactor pressure vessel
Barrel
Core basket
Part of the reactor
core
Surveillance specimen channel
RPV cladding
CoolantSheet metal
Sixth of the reactor
coreChannel
Ex-Core Detector
HORIZONTAL SECTION OF THE MODELConsidering the objective to determine the weight function with high accuracy, the reactor core, space between the core and the ex-core detector and the detector itself are modelled in the finest possible detail.
Reactor pressure vessel
Barrel
Core basket
Fuel assembly
Coolant
Sheet metal
Ionization chamber
Biological shielding
Channel of ionization chamber
Twentieth of a fuel pin
Calculation of the single weight values
WEIGHT FUNCTION
Plane of symmetry
12.2
cm
VERTICAL SECTION OF THE MODEL
The weight function gives the average number of reactions
occurred in the ex-core detector for one source neutron born in
the twentieth of a fuel pin in different core positions.
The signal of the detector is given by the weight function and fission density function product and its integration over the whole core
region in interest.
MCNP model of the fuel assembly
Fuel pin with enrichment 3.3%
Fuel pin with enrichment 3.6%
Fuel pin with enrichment 4.0%
Spacer capture rod
Spacer grid
Casing
Investigations will be started to determine the influence of two burn-up levels and two boric acid concentration levels – zero and the maximal on the weight values.
If there will be shown weight function independence on the operational parameters such as burn-up, boric acid concentration and others during the whole reactor operation cycle, it is possible consider the weight function as invariable, i. e. generalize the function, and determine the detector response to the neutron flux density distribution during the whole cycle of operation.
MCNP model of the FA – horizontal cross sections
protective grid carrier grid
fuel pins/spacer grid
MCNP model of the FA – vertical cross sections
upper part of the FA bottom part of the FA
Head
Compensation volume/
fixation string
Foot
Carrier grid
Carrier grid of the core
basket
Protective grid
twentieths of fuel pins
MCNP model of the CA fuel part
upper part bottom part
Joining rod
Head
Foot
MCNP model of the reactor components
barrel
core basket
surveillance specimen channel
distance strip
RPV
horizontal cross section vertical cross section
Ex-core detector
Transfer function between the channel
and the detector-detection efficiency
Channel of the ex-core detector
Reactor core
Spatial weight function of the ex-core detector
Spatial weight function of the ex-core detector
channel
Spatial weight function of the ex-core detector as a composite function
Considering prospective replacement of the existing ex-core detectors for another detector types in the future, it is possible to reach the spatial weight function for the channel of the ex-core detector and after that to determine an additional transfer function between the ex-core detector channel and new known detector type.
Consequently, the final spatial weight function of the ex-core detector is given as a composite function of these two function.
Fitting an analytical function
• An analytical function will be fitted onto the single weight values in two steps.
• The first step will be to find an optimal analytical function which follows reliably vertical distribution of the calculated single weight values – vertical (one-dimensional) fitting.
• The second step will be a horizontal (two-dimensional) fitting which means that an analytical function will be fitted onto calculated and by vertical fitting “smoothed” weight values.
Summary
• The exact knowledge of the spatial weight function of the ex-core detector can be very useful for solution and interpretation of various reactor physical, operational and safety problems, in particular for interpretation of reloads startup rod drop measurements and for evaluation of the detector signal at deep subcritical reactor conditions.
• Calculation of weight values and fitting of the weight function will be completed soon.