Understanding Reactor Campaign in Nuclear Power Operations

Reactor campaign
 
Reactor campaign
 (
nr
)
--  
period of the reactor power operation from
one total refueling to another.
1
 
 Reactor power operation is accompanied by
various effects which cause loss of reactivity
or its change.
Therefore, to compensate these effects, the
core at the beginning of the operation in cold,
not poisoned state should have a certain
initial 
reactivity margin
 
mar
 due to additional
fuel load.
The value
   
mar
 
 
defines reactor campaign
.
2
 
С
hange reactivity margin during the reactor
campaign
 
Working hours
, 
day
 
Reactor campaign 
is also determined by
operating capacity (resistance) of the fuel
elements, which largely depends on the
accumulation of fission products.
The accumulation of fission products is
determined by the permissible burnup
fraction and is a characteristic value for a
particular type of reactor.
For VVER it is about 3
5%.
4
 
Reactor campaign
 (
nr
)
 - 
period of the reactor power
operation from one total refueling to another.
Fuel campaign
 (
f
) 
 
is a fuel residence time in the
nuclear reactor core in terms of W
nom
 during a
complete cycle taking into account the n partial
refuelings up to obtaining maximum burnup
fraction:
                            
f
 = n
 
nr
Each unloaded portion of fuel is in a nuclear
reactor 
 
n
 
  
time intervals 
 
nr
between refuellings.
5
 
Nominal power of a nuclear reactor –
--  
is the highest power at which it can operate
in all modes provided for the campaign.
 
6
 
Reactor campaign is measured in the effective
days (hours) 
eff
.
When reactor power operates at various power
levels W
i
 
 W
nom
 during 
i
 calendar days (hours),
reactor campaign in effective days is recalculated
by energy production in the reactor:
            
Q
k
 = 
 W
i
i
 = W
nom
 
eff
,
7
 
Energy production of a nuclear reactor –
-- 
total amount of thermal energy produced
during the reporting calendar period of
nuclear reactor operation.
Potential opportunities for energy production
are characterized by
   
energy store
and 
energy source
.
8
 
Energy content
 of the nuclear reactor core -
energy production from the beginning of its
operation until the exhaustion of 
mar
 when
operating at W
nom
.
Energy resource
 of the nuclear reactor core -
energy production from the beginning of its
operation at W
nom
 until the appearance of
fatal defects of the core in which its further
use is impossible.
9
 
Some increase of 
    
mar
  
 
 
is usually provided
for guaranteed supplying of calculation energy
resources.
Calendar operation time of nuclear reactor
core up to the production of energy resource
is called 
service life
.
10
 
Fleet average unit capability factor (FAUCF).
Reactor campaign can also be expressed via
calendar residence time of fuel in the reactor

i
 and fleet average unit capability factor
during this time (load factor).
11
 
Fleet average unit capability factor (FAUCF) 
of a
nuclear reactor is the ratio of the average reactor
power in the reporting period of time, to the
nominal:
 
FAUCF
 = W
av
 / W
nom
 = (1/ W
nom
)(
W
i
i
 / 

i
)
.
FAUCF is used for quantitative assessment of
reactor use intensity.
12
 
Energy release in the core.
 
13
 
When the nuclear reactor operates, heating of
the core is caused by
:
the transfer of kinetic energy of the fission
fragments to the surrounding atoms and
molecules of the medium
,
moderation and neutron radiative capture in
all components of the core,
absorption of instant  
-radiation
and 
 
and 
-radiation of the fission fragments
and their decay products.
14
 
Distribution of energy released in nuclear
fission of 
235
U by a thermal neutron
 
15
 
The table doesn't consider the contribution of
neutrinos accompanying   
ß-
decay of fission
fragments, although the energy carried away
by them reaches 10 MeV.
This is because neutrinos do not interact with
any substances and, therefore, do not cause
heating of the reactor elements.
Very low additional energy from     
-decay
and delayed neutrons were neglected.
16
 
Kinetic energy of the fragments and 
ß
-
particles is converted into thermal in the
immediate vicinity of the fission points.
All antineutrino energy and part of neutron
energy and 
-quanta are carried away by them
outside the nuclear reactor core.
This is partly compensated by the energy
released in neutron radiative capture
(
7MeV).
17
 
The relative contribution of different energy
carriers, as well as the total fission energy 
E
f
 ,
generated as a result of one fission event,
depends essentially
on the properties of used fissile nuclide (
235
U,
233
U or 
239
Pu),
energy spectrum of neutrons
and absorbing properties of reactor materials.
18
 
The spread of values depending on these
characteristics, can reach 
7%.
That is why, in practical calculations one
usually takes that, on average, per one fission
event energy is released
             Е
f
 = 20
3 МэВ
 = 0,32
10
-10
 J.
19
 
Using these data, by known
:
- 
average density of thermal neutron flux in
nuclear fuel            
Ф
av
, neutron/(cm
2
s)
- 
volume of fuel 
                
V, (cm
3
)
- 
multiplication factor by fast neutrons 
   
(
),
- 
macroscopic fission cross section 
235
U
                                         
f5
, (cm
-1
)
we can estimate 
thermal power
, (W),
of a nuclear reactor,
20
 
thermal power
  
 (W), of a nuclear reactor,
is proportional to the amount of nuclear
fission in fuel in the reactor core per unit time:
 
W = 0,32
10
-10 
Ф
av
 V 
f5 
21
 
Reactor power
, defined by this expression, is
an integral characteristic of the heat release in
the nuclear reactor core.
To evaluate  heat-stressed cores, one cannot
use reactor power , the introduction of special
specific characteristics is required.
22
 
Important characteristics of the
energy-rating of a nuclear reactor are
:
 
specific fuel power
, i.e. reactor power per
mass unit of uranium in the core,
 
W
Gu
 = W / G
u
 = 0.32
10
-10
Ф
av
 V
f5
 / G
u
,
where G
u
 
 mass of uranium loaded into the
core, (kg);
23
 
 specific power per mass unit of fissile material
in the core, 
     
(for VVER 
 
235
U),
W
G5
 = = W / G
5
 = 0.32
10
-10
Ф
av
 V
f5
 / G
5
,
where G
5
 - mass of 
235
U loaded into the core, kg;
 specific volume power (volumetric heat
release density), 
i.e. power per unit of the core
       
W
v
 = W / V = 0.32
10
-10
Ф
av
 
f5
24
Unevenness of energy release
( 
k
v
, k
r
, k
z
 )
 
A reactor always has unevenness of energy
release due to various reasons.
Since thermophysical reactor calculation is
carried out for a maximum load,
it is necessary to establish the reasons due to
which there is a difference between the
average and maximum value of energy
release.
 
Specific power and energy release in even
distribution of all components over the core
and constant neutron spectrum are
proportional to the  neutron flux density
which is distributed over the core as follows:
 
by the height of the cylindrical core without
the reflector:
                Ф
(z)
 = Ф
0z 
cos(
z / H);
 
by the radius of the cylindrical core:
           Ф
(r)
 = Ф
0r 
J
0
(2.405r /R)
 
 
 
 
Specific volumetric heat release 
q
v
, i.e. heat
release per unit volume of nuclear fuel for a
cylindrical core:
     
q
v(r,z)
 = q
vmax
 
J
0
(2.405r / R)
cos(
z / H)
 
Assuming that spatial distribution of heat
release in the core coincides with distribution
of neutron flux density, to move from average
to maximum characteristics of heat release
rate, one can use uneven distribution
coefficients of neutron flux density
.
 
In the case of nuclear fuel  
profiling
, as in case
with VVER reactors, instead of uneven
distribution coefficients of neutron flux density,
one uses 
uneven heat release 
coefficients
determining the degree of energy release
deviation from the average value in different
points of the core.
Uneven heat release coefficients are defined as
the ratio of maximum values of specific
volumetric heat release, by coordinates, to its
average values, by the corresponding
coordinates.
 
Maximum 
uneven coefficient by volume
determines the allowable power of a nuclear
reactor:
k
v
 = k
r
k
z
 = (
Ф
0r
 / 
Ф
av(r)
) / (
Ф
0z
 / 
Ф
av (z)
) =
     = 
q
vmax
 /q
vav
 = w
max
 / w
av
,
 
Uneven distribution coefficients of heat
release by the radius
 k
r 
at the selected height
of the cylindrical core  (z = h):
k
r
 = q
vmax(0,h)
 / q
vav(h)
 =
    = 
q
vmax(0,h)
 / ((1 / R
2
) 2q
v(r,h)
rdr)
,
where: q
vav(h)
 
 
average heat release by the
radius of the core at height 
  
z=h.
 
Heat release unevenness coefficients by
height 
 
k
z
, at the selected radius of the
cylindrical core  (r=R
1
):
k
z
 = q
vmax(R1,0)
 / q
vav(R0)
 =
     = 
q
vmax(R1,0)
 / ((1 / H) q
v(R1,z)
dz)
;
 
In the core (for example, VVER reactors) there
are always fuel assemblies of various
enrichment and  with different burnup.
 
To account for energy release unevenness of a
certain fuel assembly of the core,
irregularity coefficient of energy release
 
k
q
of this FA is introduced,
 which is the ratio of its thermal power q
i
FA
 to
average power of FA by the core:
                   
k
q
 = q
i
FA
 / q
avFA
.
 
Distribution of thermal neutron flux by cross
section of FA is always uneven.
This unevenness is caused by violation of the
uniformity of the lattice, both inside and
outside of the fuel assembly.
Unevenness of energy release distribution by
the cross section of FA
 
   
is considered by
coefficient 
k
FA
 , which is the ratio of maximum
energy release in FE to the average FA by FE
                    
k
FA
 = q
FE
max
 / q
FE
av
 
Values of true heat flux may differ from
calculated due to manufacturing tolerances
for the production of fuel pellets, fuel
elements, fuel assemblies, redistribution of
coolant rate by FA, inaccuracies of calculated
techniques.
These deviations are taken into account by the
so-called 
mechanical unevenness coefficient
k
meh
.
 
One should consider the possibility of power
deviation from the nominal value within limits
caused by the accuracy of its
determination and maintenance.
Furthermore, there may be deviations from
the nominal pressure values, coolant inlet
temperature and its rate.
These deviations are considered by the so-
called 
unevenness power coefficient
            
k
power
.
 
It is also necessary to consider  energy
release  unevenness that arises from the
presence of regulating units CPS in the reactor
core.
It is taken into account by the unevenness
coefficient  k
abs
 and greatly depends on the type
and position of CPS.
Thus, unevenness coefficient by the  reactor
volume, which is a ratio of the maximum energy
release to the average, equals to:
    
k
v
 = k
r 
k
z
k
q
k
ТВС
k
mech
k
power
k
abs
 
 
Nuclear reactor power, at a given allowable
value of maximum specific power is the
greater the closer 
k
v
 
to unity
i.e. the closer energy release at each point of
the core to maximum allowable.
Decreasing
 k
v
 allows to increase nuclear
reactor power in the same volume, increase
fuel burnup greatly, i.e. to reduce the fuel
component of the energy cost.
 
The following methods for 
energy release
flattening
 are used:
1) use of efficient neutron reflectors located
around the core, allowing to reduce neutron
leakage and thereby to flatten the distribution of
thermal neutron flux density and, thus, heat
release.
In thermal reactors, moderator and reflector are
usually made of the same material.
The reflective properties of the substance are
characterized by 
reflection
 
factor
 (albedo)
, equal
to the ratio of the reflected neutron flux to the
incident.
 
Unevenness coefficients by the radius and
height of the cylindrical core with a neutron
reflector are approximately equal:
k
r
 = 2.32(1 + 2
эф
 / (R + 
ef
))
-1
;
k
z
 = 1.57(1 + 2
эф
 / (H + 2
ef
))
-1
;
 
2) Profiling of the fuel by the core:
concentration change (enrichment) of the
fissile nuclide by the radius of the core is
inversely proportional to the distribution of
neutron flux density;
3) profiling of the solid burnable absorber: its
location by the radius and height of the core
in direct relation to the distribution of neutron
density;
 
4) the choice of regulating units CPS in such
quantity and such efficiency so that when
operating at certain power  their location
causes minimum distortion of energy release;
5) the use of liquid burnable absorber. For
VVER, boric acid solution is used.
Residual heat generation
 
Reduction of heat generation rate in the nuclear
reactor after the insertion of a negative reactivity
(shutdown of the reactor) is determined by the
following processes:
- fission of fuel by prompt neutrons;
- thermal inertia of the core material and the amount
of heat accumulated in it;
- fission of fuel by delayed neutrons and
photoneutrons;
- slowing-down of 
 and 
-radiation of fission products
accumulated during the operation of a nuclear reactor.
 
Change in the power after the nuclear reactor
shutdown
 
Power caused by fission by prompt neutrons is reduced
in a fraction of a second.
Accordingly, 
  
W
osk
,
n, 
 
   
decreases i.e. power caused by
slowing-down of fission fragments (W
frag
), deceleration
and capture of neutrons (Wn), absorption of
instantaneous 
-radiation (W
).
In fact, heat power is reduced more slowly due to the
inertia of heat decline accumulated in the nuclear
reactor materials.
Thermal inertia depends on the materials of the core
and heat takeoff conditions.
It can be neglected within a few seconds after the
power reduction.
 
Thermal power 
caused by fission of delayed
neutrons, can be neglected in 3
5min.
The main component of thermal power in any
nuclear reactor, in a few minutes after
shutdown there will be heat release 
W
,
 for a
long period of time due to slowing-down 
, 
-
radiation of fission fragments and their decay
products, which is, in fact, called  
residual
heat
.
To calculate the residual heat power, one uses
formulas proposed by different authors.
 
The most widespread is Wei and Wigner
formula:
W
,
 / W
0
 = 6,5
10
-2
[
ст
-0.2
 
 (
ст
 + 
Т
)
-0.2
]
;
W
,
 / W
0
 = 6,5
10
-3
[
ст
-0.2
 
 (
ст
 + 
Т
)
-0.2
]
;
 
 
 
In formula (1) 
st
 and
  Т
 
 
are given in seconds,
in (2) 
 in days,
 
Graph for the approximate evaluation W
, 
after NR shutdown at 
    Т
>> 
st
.
 
In this fig., this dependence is represented as a
graph, with the help of which we can solve
operational problems associated with residual
heat without cumbersome calculations.
Graphical dependence enables the operator to
perform the following practical tasks:
- 
define 
W
,
 at any moment 
st
 after reactor
shutdown, if it operated per time 
Т
 at power 
W
0
;
- 
evaluate station time 
st
, at the end of which,
after reactor shutdown, 
W
,
 decreases up to the
necessary level to move  on to the autonomous
system of  reactor shutdown cooling.
Heat transfer crisis. 
Conditions of its origin
 
Boiling heat transfer crisis 
is called the
phenomenon of a sharp deterioration in heat
transfer on the heat transfer surface, leading
usually to a rapid increase in its temperature.
Thermal load 
q
cr 
, at which this phenomenon
occurs, is called 
critical
.
 
Despite the fact that the phenomenon of
boiling heat transfer crisis has long been
known, the mechanism of this process has not
yet been studied in full due to the complexity
and diversity of this phenomenon.
Many authors are in favor of the existence of
two modifications of heat transfer crisis.
 
The first modification of crisis is treated as a
consequence of transition of bubble boiling of
the liquid to surface.
This phenomenon is called 
crisis of the first
kind
.
The researchers said that the crisis of the first
kind comes only at high heat fluxes from heat
transfer surface, when coolant is not heated
to boiling or achieved steam quality is low.
 
The most common hypothesis on the
mechanism of the crisis of the first kind is that
in the increase in the specific heat load before
critical values the rate of generation of steam
bubbles is greater than the rate of their
removal from the heated surface;
as a result the heating surface is covered with
a continuous vapor film.
 
Because of the relatively low thermal
conductivity of steam, heat transfer coefficient
dramatically decreases, which entails
overheating of the heat-transfer surface and,
as a consequence, the break of FE tightness.
Critical heat flux 
q
cr
 depends on rate, pressure
and temperature of the coolant, shape and
dimensions of heat transfer surface.
 
This very difficult thermal phenomenon does
not have a general analytical solution yet, but
for different specific cases, empirical
equations are obtained for calculating the 
q
cr
in a certain temperature range.
 
For example, fo rod cylindrical fuel elements
at a pressure 14
20MPa, subcooling to boiling
t
s
 = (10
100)
С
 
  
and coolant rate
 = 1.5
7m/s:
q
cr
 = 35.400(

)
0,5
t
н
0,33
(

 / (

)),
kcal / (m
2
h)
 
To prevent film boiling, it is necessary to
organize the heat takeoff so that in the most
tense fuel elements there is margin by critical
heat load:
            
n = q
cr
 / q
max
= q
cr
/ q
cr
k
v
>1
,
 
 The second modification of the crisis,
called 
crisis of the second kind
,
is interpreted as a result of evaporation or
disruption of water microfilm from the FE
surface.
It is believed that the crisis of the second kind
occurs only with large void fraction exceeding
a certain limit mass void fraction, which is
determined by pressure and mass flux of
coolant.
 
The working hypothesis concerning the
occurrence of crisis of the second kind
connects the development of the crisis
phenomenon with the occurrence of pool
boiling in the heat generating channel.
With a large void fraction in the liquid flow
heated to the saturation temperature, steam
bubbles connecting with each other, can fill
the whole clear opening of the channel.
 
The consequence of this steaming is a decrease in
the liquid circulation rate through the channel,
thereby creating conditions for evaporation of
the water boundary layer on the heat-transfer
surface.
The resulting steam film, has low heat transfer
properties, the temperature of the heating
surface is increased.
A characteristic feature of crisis of the second
kind is its independence from the heat load.
The latter determines only jump of the wall
temperature.
 
The very nature of the crisis phenomenon of
the second kind seems to suggest the ways to
avoid such modes.
It is increase of subcooling of coolant to
boiling, which can be achieved by reducing the
coolant temperature or due to pressure
increase in the first circuit.
 
But coolant temperature decrease is
undesirable due to the fact that in this case
steam parameters reduce and, consequently,
power plant efficiency decreases.
As for the increase of coolant pressure, in the
range of operating pressures of the 1st circuit,
it leads to deterioration of conditions of steam
bubble disruption from the surface of fuel
elements, which facilitates the occurrence of
crisis of the first kind.
 
Heat transfer modes in the core determine
heat engineering reliability
 of the core
 -
- 
it is its ability to keep normal heat removal
from the fuel elements within the specified
time (fuel campaign) during reactor operation
in a stationary mode without exceeding
random deviations of structural and
operational parameters from their nominal
values stipulated in the project.
 
Slide Note
Embed
Share

Reactor campaign in nuclear power operations is crucial for ensuring safe and efficient reactor power operation. It involves managing reactivity margin, fuel residence time, nominal power, and effective days of operation. Reactor campaigns are influenced by various factors such as fuel elements' resistance, accumulation of fission products, and power levels during operation. This article provides insights into the key aspects of reactor campaigns in nuclear reactors.


Uploaded on Jul 17, 2024 | 1 Views


Download Presentation

Please find below an Image/Link to download the presentation.

The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. Download presentation by click this link. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.

E N D

Presentation Transcript


  1. Reactor campaign Reactor campaign ( nr) -- period of the reactor power operation from one total refueling to another. 1

  2. Reactor power operation is accompanied by various effects which cause loss of reactivity or its change. Therefore, to compensate these effects, the core at the beginning of the operation in cold, not poisoned state should have a certain initial reactivity margin mardue to additional fuel load. The value mardefines reactor campaign. 2

  3. hange reactivity margin during the reactor campaign Working hours, day

  4. Reactor campaign is also determined by operating capacity (resistance) of the fuel elements, which largely depends on the accumulation of fission products. The accumulation of fission products is determined by the permissible burnup fraction and is a characteristic value for a particular type of reactor. For VVER it is about 3 5%. 4

  5. Reactor campaign (nr) - period of the reactor power operation from one total refueling to another. Fuel campaign ( f) is a fuel residence time in the nuclear reactor core in terms of Wnomduring a complete cycle taking into account the n partial refuelings up to obtaining maximum burnup fraction: f= n nr Each unloaded portion of fuel is in a nuclear reactor n time intervals nr between refuellings. 5

  6. Nominal power of a nuclear reactor -- is the highest power at which it can operate in all modes provided for the campaign. 6

  7. Reactor campaign is measured in the effective days (hours) eff. When reactor power operates at various power levels Wi Wnomduring icalendar days (hours), reactor campaign in effective days is recalculated by energy production in the reactor: Qk= Wi i= Wnom eff, 7

  8. Energy production of a nuclear reactor -- total amount of thermal energy produced during the reporting calendar period of nuclear reactor operation. Potential opportunities for energy production are characterized by energy store and energy source. 8

  9. Energy content of the nuclear reactor core - energy production from the beginning of its operation until the exhaustion of marwhen operating at Wnom. Energy resource of the nuclear reactor core - energy production from the beginning of its operation at Wnomuntil the appearance of fatal defects of the core in which its further use is impossible. 9

  10. mar is usually provided Some increase of for guaranteed supplying of calculation energy resources. Calendar operation time of nuclear reactor core up to the production of energy resource is called service life. 10

  11. Fleet average unit capability factor (FAUCF). Reactor campaign can also be expressed via calendar residence time of fuel in the reactor iand fleet average unit capability factor during this time (load factor). 11

  12. Fleet average unit capability factor (FAUCF) of a nuclear reactor is the ratio of the average reactor power in the reporting period of time, to the nominal: FAUCF = Wav/ Wnom= (1/ Wnom)( Wi i/ i). FAUCF is used for quantitative assessment of reactor use intensity. 12

  13. Energy release in the core. 13

  14. When the nuclear reactor operates, heating of the core is caused by: the transfer of kinetic energy of the fission fragments to the surrounding atoms and molecules of the medium, moderation and neutron radiative capture in all components of the core, absorption of instant -radiation and and -radiation of the fission fragments and their decay products. 14

  15. Distribution of energy released in nuclear fission of 235U by a thermal neutron 15

  16. The table doesn't consider the contribution of neutrinos accompanying -decay of fission fragments, although the energy carried away by them reaches 10 MeV. This is because neutrinos do not interact with any substances and, therefore, do not cause heating of the reactor elements. Very low additional energy from -decay and delayed neutrons were neglected. 16

  17. Kinetic energy of the fragments and - particles is converted into thermal in the immediate vicinity of the fission points. All antineutrino energy and part of neutron energy and -quanta are carried away by them outside the nuclear reactor core. This is partly compensated by the energy released in neutron radiative capture ( 7MeV). 17

  18. The relative contribution of different energy carriers, as well as the total fission energy Ef , generated as a result of one fission event, depends essentially on the properties of used fissile nuclide (235U, 233U or 239Pu), energy spectrum of neutrons and absorbing properties of reactor materials. 18

  19. The spread of values depending on these characteristics, can reach 7%. That is why, in practical calculations one usually takes that, on average, per one fission event energy is released f= 203 = 0,32 10-10J. 19

  20. Using these data, by known: - average density of thermal neutron flux in nuclear fuel av, neutron/(cm2 s) - volume of fuel - multiplication factor by fast neutrons ( ), - macroscopic fission cross section 235U f5, (cm-1) we can estimate thermal power, (W), of a nuclear reactor, V, (cm3) 20

  21. thermal power (W), of a nuclear reactor, is proportional to the amount of nuclear fission in fuel in the reactor core per unit time: W = 0,32 10-10 avV f5 21

  22. Reactor power, defined by this expression, is an integral characteristic of the heat release in the nuclear reactor core. To evaluate heat-stressed cores, one cannot use reactor power , the introduction of special specific characteristics is required. 22

  23. Important characteristics of the energy-rating of a nuclear reactor are: specific fuel power, i.e. reactor power per mass unit of uranium in the core, WGu= W / Gu= 0.32 10-10 avV f5 / Gu, where Gu mass of uranium loaded into the core, (kg); 23

  24. specific power per mass unit of fissile material in the core, (for VVER 235U), WG5= = W / G5= 0.32 10-10 avV f5 / G5, where G5- mass of 235U loaded into the core, kg; specific volume power (volumetric heat release density), i.e. power per unit of the core Wv= W / V = 0.32 10-10 av f5 24

  25. Unevenness of energy release ( kv, kr, kz ) A reactor always has unevenness of energy release due to various reasons. Since thermophysical reactor calculation is carried out for a maximum load, it is necessary to establish the reasons due to which there is a difference between the average and maximum value of energy release.

  26. Specific power and energy release in even distribution of all components over the core and constant neutron spectrum are proportional to the neutron flux density which is distributed over the core as follows: by the height of the cylindrical core without the reflector: (z)= 0z cos( z / H);

  27. by the radius of the cylindrical core: (r)= 0r J0(2.405r /R) height and radius of the core; zero-order Bessel function; 0z, 0r maximum values of neutron flux density by the height and radius of the core. where: H,R J0 Specific volumetric heat release qv, i.e. heat release per unit volume of nuclear fuel for a cylindrical core: qv(r,z)= qvmax J0(2.405r / R) cos( z / H)

  28. Assuming that spatial distribution of heat release in the core coincides with distribution of neutron flux density, to move from average to maximum characteristics of heat release rate, one can use uneven distribution coefficients of neutron flux density.

  29. In the case of nuclear fuel profiling, as in case with VVER reactors, instead of uneven distribution coefficients of neutron flux density, one uses uneven heat release coefficients determining the degree of energy release deviation from the average value in different points of the core. Uneven heat release coefficients are defined as the ratio of maximum values of specific volumetric heat release, by coordinates, to its average values, by the corresponding coordinates.

  30. Maximum uneven coefficient by volume determines the allowable power of a nuclear reactor: kv= krkz= ( 0r/ av(r)) / ( 0z/ av (z)) = = qvmax/qvav= wmax/ wav, where: wmax , wav maximum allowable and average specific power in the core; kr, kz maximum heat release unevenness coefficients by the radius and height of the core

  31. Uneven distribution coefficients of heat release by the radius krat the selected height of the cylindrical core (z = h): kr= qvmax(0,h)/ qvav(h)= = qvmax(0,h)/ ((1 / R2) 2qv(r,h)rdr), where: qvav(h) average heat release by the radius of the core at height z=h.

  32. Heat release unevenness coefficients by height kz, at the selected radius of the cylindrical core (r=R1): kz= qvmax(R1,0)/ qvav(R0)= = qvmax(R1,0)/ ((1 / H) qv(R1,z)dz); In the core (for example, VVER reactors) there are always fuel assemblies of various enrichment and with different burnup.

  33. To account for energy release unevenness of a certain fuel assembly of the core, irregularity coefficient of energy release kq of this FA is introduced, which is the ratio of its thermal power qiFAto average power of FA by the core: kq= qiFA/ qavFA.

  34. Distribution of thermal neutron flux by cross section of FA is always uneven. This unevenness is caused by violation of the uniformity of the lattice, both inside and outside of the fuel assembly. Unevenness of energy release distribution by the cross section of FA is considered by coefficient kFA, which is the ratio of maximum energy release in FE to the average FA by FE kFA= qFEmax/ qFEav

  35. Values of true heat flux may differ from calculated due to manufacturing tolerances for the production of fuel pellets, fuel elements, fuel assemblies, redistribution of coolant rate by FA, inaccuracies of calculated techniques. These deviations are taken into account by the so-called mechanical unevenness coefficient kmeh.

  36. One should consider the possibility of power deviation from the nominal value within limits caused by the accuracy of its determination and maintenance. Furthermore, there may be deviations from the nominal pressure values, coolant inlet temperature and its rate. These deviations are considered by the so- called unevenness power coefficient kpower.

  37. It is also necessary to consider energy release unevenness that arises from the presence of regulating units CPS in the reactor core. It is taken into account by the unevenness coefficient kabsand greatly depends on the type and position of CPS. Thus, unevenness coefficient by the reactor volume, which is a ratio of the maximum energy release to the average, equals to: kv= kr kz kq k kmech kpower kabs

  38. Nuclear reactor power, at a given allowable value of maximum specific power is the greater the closer kvto unity i.e. the closer energy release at each point of the core to maximum allowable. Decreasing kvallows to increase nuclear reactor power in the same volume, increase fuel burnup greatly, i.e. to reduce the fuel component of the energy cost.

  39. The following methods for energy release flattening are used: 1) use of efficient neutron reflectors located around the core, allowing to reduce neutron leakage and thereby to flatten the distribution of thermal neutron flux density and, thus, heat release. In thermal reactors, moderator and reflector are usually made of the same material. The reflective properties of the substance are characterized by reflection factor (albedo), equal to the ratio of the reflected neutron flux to the incident.

  40. Unevenness coefficients by the radius and height of the cylindrical core with a neutron reflector are approximately equal: kr= 2.32(1 + 2 / (R + ef))-1; kz= 1.57(1 + 2 / (H + 2 ef))-1; where: ef effective additive depending on the type of the reflector, shape of the nuclear reactor core and, approximately, equal to the length of the reflector migration in the material; R, H radius and height of the core;

  41. 2) Profiling of the fuel by the core: concentration change (enrichment) of the fissile nuclide by the radius of the core is inversely proportional to the distribution of neutron flux density; 3) profiling of the solid burnable absorber: its location by the radius and height of the core in direct relation to the distribution of neutron density;

  42. 4) the choice of regulating units CPS in such quantity and such efficiency so that when operating at certain power their location causes minimum distortion of energy release; 5) the use of liquid burnable absorber. For VVER, boric acid solution is used.

  43. Residual heat generation Reduction of heat generation rate in the nuclear reactor after the insertion of a negative reactivity (shutdown of the reactor) is determined by the following processes: - fission of fuel by prompt neutrons; - thermal inertia of the core material and the amount of heat accumulated in it; - fission of fuel by delayed neutrons and photoneutrons; - slowing-down of and -radiation of fission products accumulated during the operation of a nuclear reactor.

  44. Change in the power after the nuclear reactor shutdown

  45. Power caused by fission by prompt neutrons is reduced in a fraction of a second. Accordingly, Wosk,n, decreases i.e. power caused by slowing-down of fission fragments (Wfrag), deceleration and capture of neutrons (Wn), absorption of instantaneous -radiation (W ). In fact, heat power is reduced more slowly due to the inertia of heat decline accumulated in the nuclear reactor materials. Thermal inertia depends on the materials of the core and heat takeoff conditions. It can be neglected within a few seconds after the power reduction.

  46. Thermal power caused by fission of delayed neutrons, can be neglected in 3 5min. The main component of thermal power in any nuclear reactor, in a few minutes after shutdown there will be heat release W , for a long period of time due to slowing-down , - radiation of fission fragments and their decay products, which is, in fact, called residual heat. To calculate the residual heat power, one uses formulas proposed by different authors.

  47. The most widespread is Wei and Wigner formula: W , / W0= 6,5 10-2[ -0.2 ( + )-0.2]; W , / W0= 6,5 10-3[ -0.2 ( + )-0.2]; power of residual heat of the nuclear reactor in time st (station time) after a shutdown; power of a nuclear reactor before shutdown, in which it operated per time T. where: W , W0 In formula (1) stand are given in seconds, in (2) in days,

  48. Graph for the approximate evaluation W, after NR shutdown at >> st.

  49. In this fig., this dependence is represented as a graph, with the help of which we can solve operational problems associated with residual heat without cumbersome calculations. Graphical dependence enables the operator to perform the following practical tasks: - define W , at any moment stafter reactor shutdown, if it operated per time at power W0; - evaluate station time st, at the end of which, after reactor shutdown, W , decreases up to the necessary level to move on to the autonomous system of reactor shutdown cooling.

  50. Heat transfer crisis. Conditions of its origin Boiling heat transfer crisis is called the phenomenon of a sharp deterioration in heat transfer on the heat transfer surface, leading usually to a rapid increase in its temperature. Thermal load qcr, at which this phenomenon occurs, is called critical.

Related


More Related Content

giItT1WQy@!-/#giItT1WQy@!-/#giItT1WQy@!-/#giItT1WQy@!-/#giItT1WQy@!-/#giItT1WQy@!-/#giItT1WQy@!-/#