Taken into account the unbalance axial of the powe- 123docz.net

The 12 The 12 self-powered detectors fingers contain each 6 self-powered detectors

C. Aeroball system for monitoring power distribution in the reactor core. The fundamental function of that movable nuclear fixed

4. Taken into account the unbalance axial of the power in the protectrion chains;

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XIX.1.Steady state

XIX.1.Steady state ΔΔI = 0 I = 0

The establishing of the set-point constitutes of the linearization descrbed The establishing of the set-point constitutes of the linearization descrbed preveously. It is effectuated with a power distribution in the form preveously. It is effectuated with a power distribution in the form

ô truncked cosinus ằ (with:

Fz = 1.55 & F

Fz = 1.55 & FΔΔH = 1.55 [ 1 + 0.2 ( 1 – p )]H = 1.55 [ 1 + 0.2 ( 1 – p )]

p: is the percent of the power.

XIX..2.Transient conditions XIX..2.Transient conditions

To compensate the transit time between the measured points & the To compensate the transit time between the measured points & the reactor core, the delays due to the captors & to the scram chains, it is reactor core, the delays due to the captors & to the scram chains, it is

necessary to introduce ô forward & delay ằ boxes.

The taken into account the uncontrolled withdrawal of a RCCA reactor on The taken into account the uncontrolled withdrawal of a RCCA reactor on power leads to the modification of the ô k ằ coefficient , to avoid the power leads to the modification of the ô k ằ coefficient , to avoid the

boiling crisis.

More however, to enhance the response time of the

More however, to enhance the response time of the Δop, we introduce a Δop, we introduce a derivate term.

derivate term.

XIX.3. Instrumentation & setting errors XIX.3. Instrumentation & setting errors

The taken into account of these errors leads to the modification of the The taken into account of these errors leads to the modification of the

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XIX.4. Taken into account of the unbalance of the axial power XIX.4. Taken into account of the unbalance of the axial power

The taken into account of the unbalance of the axial power leads to the The taken into account of the unbalance of the axial power leads to the introduction of a penalty . The following figure give the form of the introduction of a penalty . The following figure give the form of the penalty fte & fsp for the two chains. These penalties are given as penalty fte & fsp for the two chains. These penalties are given as

indicative values, in effect, they vary versus of the cycle indicative values, in effect, they vary versus of the cycle

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Figure XIX.5.1: Penalty functions applied to ΔTop & ΔTe (cycle 1 & others Figure XIX.5.1: Penalty functions applied to ΔTop & ΔTe (cycle 1 & others

THERMAL-HYDRAULIC IN NUCLEAR REACTOR

XIX.5. Mass flow reductions XIX.5. Mass flow reductions

The possible domaine power-frequency in class 1 leads to the primary The possible domaine power-frequency in class 1 leads to the primary

mass flow between 93.8% to 102.2% of the nominal mass flow.

If we do not modify the thresholds

If we do not modify the thresholds ΔΔTte & Tte & ΔΔop, the protections risk to be op, the protections risk to be not safisfied in case of uncontrolled withdrawal of a RCCA at Pn, not safisfied in case of uncontrolled withdrawal of a RCCA at Pn, whereas the mass flow is reduced. This leads to the introduction of the whereas the mass flow is reduced. This leads to the introduction of the

terms dependent on the mass flow:

- For

- For ΔTop: a positive term when the mass flow decreases in order to ΔTop: a positive term when the mass flow decreases in order to obtaint a linear power at hot point independent of the mass flow;

obtaint a linear power at hot point independent of the mass flow;

- For

- For ΔΔTte : a negative term when the mass flow decreases in order to Tte : a negative term when the mass flow decreases in order to assure the respect of the DNBR > 1.3

assure the respect of the DNBR > 1.3

Fundamental recalls of thermal-hydraulic & neuton aspects.

A.Thermal aspect A.Thermal aspect

The energy produced in a NSSS results from the release of heat due to The energy produced in a NSSS results from the release of heat due to fission reaction in the assembly of fuel rods. The reactor coolant that fission reaction in the assembly of fuel rods. The reactor coolant that flows around these rods evacuate this heat energy & transfers it to the flows around these rods evacuate this heat energy & transfers it to the

steam generator steam generator

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The heat evacuated from the core by the reactor coolant is charactertized The heat evacuated from the core by the reactor coolant is charactertized by a certain number of magnitudes. For a 1600 MWe class NSSS these by a certain number of magnitudes. For a 1600 MWe class NSSS these

values are:

Reactor Power

Reactor Power Q = 4590 MWth Q = 4590 MWth Mass flow rate

Mass flow rate M = 83.380 t/hM = 83.380 t/h Increase in enthalpy

Increase in enthalpy

Average power of:

Fuel assembly

Fuel assembly 19 MW 19 MW One fuel rod

One fuel rod 72 KW72 KW

Average power density fuel rod:

Linear power q’

Linear power q’ 166 W/cm166 W/cm Surface q’’

Surface q’’ 57 W/cm257 W/cm2

Volume q’’’

Volume q’’’ 241 W/cm3241 W/cm3

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B. Neutron aspects B. Neutron aspects

The distribution of the power in the core is not uniform & large disparities The distribution of the power in the core is not uniform & large disparities exist betwwen the different zones, resulting from the non_uniform of exist betwwen the different zones, resulting from the non_uniform of

the neutron flux in the core due to nuclear physics.

To recall, neutron flux is expressed in n/cm2 and is related at each point To recall, neutron flux is expressed in n/cm2 and is related at each point

in the fuel to the thermal power release by the equation:

q’’’ = ∑

q’’’ = ∑ff ỉ ỉthth x 3.2 x 10 x 3.2 x 10 -11-11 Where :∑

Where :∑ff is the effective fission cross-section in cm-1 & the ỉ is the effective fission cross-section in cm-1 & the ỉthth is the is the thermal flux in n/cm2.s.

thermal flux in n/cm2.s.

Or :

Or : P(W) = (VΣ P(W) = (VΣff ФtФthh) / 3.1x10) / 3.1x101010 1. Shape of the neutron flux

1. Shape of the neutron flux

In considering the form of the neutron flux, one distinguishes between 1) In considering the form of the neutron flux, one distinguishes between 1)

the radial distribution & 2) the axial distribution.

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a) Radial flux distribution a) Radial flux distribution::

For a homogeneous reactor (a theoretical case), the radial flux For a homogeneous reactor (a theoretical case), the radial flux distribution is a Bessel function J0 (shape 1). Because of the presence distribution is a Bessel function J0 (shape 1). Because of the presence of a neutron reflector (the water surrounding the core or a metallic of a neutron reflector (the water surrounding the core or a metallic structure installed & because of different fuel enrichment zones loaded structure installed & because of different fuel enrichment zones loaded according to a certain fuel loading pattern the flux distribution as according to a certain fuel loading pattern the flux distribution as function of the radius is in reality more complex than the Bessel function of the radius is in reality more complex than the Bessel function as shown in the following figure. According to the fuel function as shown in the following figure. According to the fuel management strategies used in 80s & the fuel loading patterns which management strategies used in 80s & the fuel loading patterns which followed from these, the most enriched fuel assembly are loaded at the followed from these, the most enriched fuel assembly are loaded at the periphery of the core & the lowest at the centre in order to get a flatned periphery of the core & the lowest at the centre in order to get a flatned

power distribution (shape 2).

Modern fuel management strategies currently used require that the Modern fuel management strategies currently used require that the highest fuel-enrichment zone be loaded at the centre and the lowest at highest fuel-enrichment zone be loaded at the centre and the lowest at the periphery in order to decrease the amplitude of the neutron the periphery in order to decrease the amplitude of the neutron leakage & then increase the initial core reactivity & consequently the leakage & then increase the initial core reactivity & consequently the

THERMAL-HYDRAULIC IN NUCLEAR REACTOR

Obviously, the immediate consequence is an increase in the core peaking Obviously, the immediate consequence is an increase in the core peaking factors. The safety analysis must be reviewed to demonstrate that the factors. The safety analysis must be reviewed to demonstrate that the

safety margins are still acceptable.

Figure XX.1: Radial distribution of neutron flux Figure XX.1: Radial distribution of neutron flux

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b) Axial neutron flux distribution.

When the core is homogenous & at the beginning of the life (BOL) & zero When the core is homogenous & at the beginning of the life (BOL) & zero power (shape 1), the curve of the flux distribution has the shape of a power (shape 1), the curve of the flux distribution has the shape of a

cosinus function.

The reactor power level increasing to full power, the coolant temperature The reactor power level increasing to full power, the coolant temperature being higher towards the top of the core while being roughly constant being higher towards the top of the core while being roughly constant towards the bottom (according to the core average temperature towards the bottom (according to the core average temperature variation versus the power level), neutron moderation is more effective variation versus the power level), neutron moderation is more effective towards the bottom of the core where the water density is the highest towards the bottom of the core where the water density is the highest

(less effective towards the top where the density is the lowest).

This leads to an axial gradient of reactivity that induces a slight bulge in This leads to an axial gradient of reactivity that induces a slight bulge in

the axial flux distribution towards the base of the core (shape 2).

After few months of operation at full power, the fuel is burned up faster After few months of operation at full power, the fuel is burned up faster in the region where the neutron flux is higher i.e. a little bit lower than in the region where the neutron flux is higher i.e. a little bit lower than the mid-axis. On the other hand, the fuel is burned up more slowly at the mid-axis. On the other hand, the fuel is burned up more slowly at the axial core extremities. The consequence is a so-called ô double the axial core extremities. The consequence is a so-called ô double

THERMAL-HYDRAULIC IN NUCLEAR REACTOR

Taken into account the unbalance axial of the power in the protectrion chains;

Constraints of the thermal-hydraulic core design

Heat conduction in fuel assembly