Transcript Thermal Hydraulics Lectures

THE HEAT TRANSPORT
What is heat transfer ?
 Heat transfer (or heat) is energy in transit (motion) due to a
temperature difference (anology current flow, mass flow)
 Modes :Conduction, Convection and Radiation
How is heat transferred ?
 When a temperature gradient exists in a stationary medium, which
may be a solid or a fluid, we use the term conduction to refer to the
heat transfer that will occur across the medium
 In contrast, the term convection refers to heat transfer that will occur
between a surface and a moving fluid when they are at different
temperatures.
 The third mode of heat transfer is termed thermal radiation. All
surfaces of finite temperature emit energy in the form of
electromagnetic waves. Hence, in the absence of an intervening
medium, there is net heat transfer by radiation between two
surfaces at different temperatures
Why is it important to study it ?
All the three kinds of heat transfer modes prevail in a nuclear
reactor core, however the dominant ones are conduction and
convection.
2
THE HEAT TRANSPORT(continued)
Physical Origins OF Conduction
Conduction may be viewed as the transfer of energy from the more
energetic to the less energetic particles of a substance due to interactions
between the particles. We may speak of the net transfer of energy by
random molecular motion as a Diffusion of energy
Examples :
The exposed end of a metal spoon suddenly immersed in a cup of hot tea
will eventually be warmed due to the conduction of energy through the
spoon.
On a winter day there is significant energy loss from a heated room to the
outside air. This loss is principally due to conduction heat transfer through
the wall that separates the room air from the outside air.
Rate Equation for Conduction
It is possible to quantify heat transfer processes in terms of appropriate
rate equations.These equations may be used to compute the amount of
energy being transferred per unit time. For heat conduction, the rate
equation is known as Fourier’s Law.
For the one dimensional plane wall shown in Figure 2, having a
temperature distribution T(x), the rate equation is expressed as
qx’’ = - k
dT
dx
3
THE HEAT TRANSPORT(contd)
• The heat flux qx’’ (W/m2) is the heat transfer in the x
direction per unit area perpendicular to the direction of
transfer, and it is proportional to the temperature
gradient, dT/dx, in this direction.
• The proportionality constant k is a transport property
known as the thermal conductivity (W/m.K) and is
characteristic of the wall material. The minus sign is a
consequence of the fact that heat is transferred in the
direction of decreasing temperature. Under the steady
state conditions shown in Figure 3, where the
temperature distribution is linear, the temperature
gradient may be expressed as
and the heat flux is then
qx’’ =
k
T2  T1
L
dT

dx
T2  T1
L
4
THE HEAT TRANSPORT(contd)
Convection

The convection heat transfer mode is comprised of two
mechanisms. In Energy transfer due to random molecular
motion (diffusion), there is also energy being transferred by the
bulk, or macroscopic, motion of the fluid. This fluid motion is
associated with the fact that, at any instant, large numbers of
molecules are moving collectively or as aggregates. Such
motion, in the presence of a temperature gradient, will give rise
to heat transfer. Because the molecules in the aggregate retain
their random motion, the total heat transfer is then due to a
superposition of energy transport by the random motion of the
molecules and by the bulk motion of the fluid. It is customary to
use the term convection when referring to this cumulative
transport and the term advection when referring to transport
due to bulk fluid motion
Types of Convection


Forced Convection
Natural Convection
5
THE HEAT TRANSPORT(contd)
Forced Convection
Convection heat transfer may be classified according to the nature of the
flow. We speak of forced convection when the flow is caused by external
means, such as by a fan, a pump, or atmospheric winds.
As an example, consider the use of a fan to provide forced convection air
cooling of hot electrical components on a stack of printed circuits boards.
Natural Convection
In contrast, for free (or natural) convection the flow is induced by
buoyancy forces that arise from density differences caused by
temperature variations in the fluid.
Rate Equation for Convection
For convection heat transfer process, the Newton’s Law of Cooling
expresses the rate equation as:
q’’ = h(Ts – Tf)
where q’’ is the convective heat flux (W/m2) that is proportional to
the difference between the surface and fluid temperatures, Ts and Tf,
respectively.
The proportionality constant h (W/m2 C) is referred to as the
convection heat transfer coefficient. It encompasses all the
parameters that influence convection heat transfer. It particular it
depends on the surface geometry, the nature of fluid motion, and an
assortment of fluid thermodynamic and transport properties.
6
HEAT GENERATION IN REACTORS
In nuclear reactors, the main source of energy is the nuclear
reaction namely, Fission. A second important class, but one
that produces much less energy (relative to fission) is
radioactivity. In nuclear reactors fission, of a heavy nucleus of
Uranium, Plutonium or Thorium splits into two or more lighter
nuclei resulting in a net decrease of mass that ultimately
converts into exothermic energy.
 The average total energy is about 200 MeV per fission in
case of 235U.
 The complete fission of 1 g of 235Unuclei in a fuel element
thus produces a quantity of energy equal to
(Avogadro No. x 200 Mev)/U235 isotope mass
= (6.0225 x 1023 x200)/235.0439 = 0.513 x 1024 Mev
=2.276 x 104 kW-hr
=948 kW-Day
=0.948 MW-Day
7
HEAT GENERATION IN REACTORS(Contd)
Figures to remember
 200 Mev per fission
 1 g of fissionable material per day generates nearly 1 MW of
energy
 approximate energy consumed by normal human during daily
business is 100 Watt
 when we wink eye, the energy consumed is less than 1eV.
Heat Generation Rate in Fuel
‘In a nuclear reactor the role of neutrons is analogous to that of
oxygen in case of a coal fired plant.’
The rate of nuclear heat generation is equal to the rate of reaction
producing energy times the energy per reaction. In general, the rate of
any reaction between mono-energetic neutrons and the nuclei of
material is given by
R = .
(1)
Where  is the macroscopic cross section, cm—1, of the reactor and 
the neutron flux, neutrons/s-cm2. R therefore has the units
‘reactions/s-cm3’
The energy generated in a reaction per unit time and volume is called
volumetric thermal source strength, q’’’, given by
q’’’ = G.R=G..
(2) 8
HEAT GENERATION IN REACTORS(Contd)
Where G is the energy per reaction, MeV. In case of energy by
fission by neutrons of a given distribution [In nuclear reactors
neutrons are available with energies ranges form 17 MeV (Fast)
down to 0.4 eV (Thermal)]
The  is the macroscopic cross section given by  = N
q’’’ = G N
(3)
where N is the density of fissionable fuel in nuclei/cm3. The
value  is the microscopic cross section cm2 for the fissionable
fuel used and the energy distribution of the neutrons in the
reactor. q’’’ has the units of Mev/s cm3
Significance
For heat transfer calculations of a nuclear reactor, it is important
to evaluate the volumetric thermal source strength at different
positions in a reactor core before evaluating the core
temperature distributions, and core heat generation and heat
removal. The neutron flux is obtained from neutronic
analysis/considerations
9
HEAT GENERATION IN REACTORS(Contd)
Example
Calculate the volumetric thermal source strength at a position in a
reactor core in which the neutron flux is 1013. The core is loaded with
a fuel having fissionable fuel density of 8.5 x 1020 nuclei/cm3. The
moderator temperature at the same core position is 60 oC
corresponding to which the effective microscopic cross section is
400 barns.
Solution
N
=
8.5 x 1020
=400 b = 400 x 10-24 cm2
G =
180 Mev/fission
Therefore volumetric source strength, q’’’
q’’’ = G. .N.
= 180 x 8.5 x 1020 x 400 x 10-24 x 1013
= 6.12 x 1014 Mev/s-cm3
= 6.12 x 1014 Mev/s-cm3 x 1.602 x 10-13 w/cm3 per Mev/s-cm3
= 98.04 w/cm3
A fuel rod, having diameter and active fuel length of 3.454 and 306 cm,
respectively, when placed at this location will have an average power
out put of.
=98.04 x  x 1.7272 x 306/1000  281 kW
10
CORE THERMAL DESIGN
• The amount of reactor power generation in a given
reactor is limited by thermal rather than by nuclear
considerations. The reactor core must be operated
at such a power level, that with the best available
heat removal system, the temperatures of the fuel
and cladding anywhere in the core must not exceed
safe limits. Otherwise fuel element damage might
result in release of large quantities of radioactive
material into the coolant, or in core fuel meltdown.
• Reactor cores are usually limited by those
parameters that cause the temperatures to exceed
safe limits. (For KCP Reactors, Fuel Centerline and
Clad Temperatures).
11
Peaking Factors
• Radial peaking factor of a fuel rod is ratio of its power generation to
the average power generated by a rod. (maximum 1.483)
• In axial direction flux also varies like a ‘Cosine Shape’. Power
generated from central region of fuel rod (moderated portion) is
greater than its upper & lower parts.
• Axial peaking factor of a fuel rod at its any location/ portion is ratio of
its power or power density or flux at that location to the average
power or power density or flux of same fuel rod. (maximum 1.525)
Fuel centerline, fuel surface & clad surface Temperatures are
maximum near central portion of fuel rod and least at ends (top/
bottom) of fuel rod.
• Radial peaking factor of a fuel rod depends upon its location in core &
is independent of power level or power density. Radial peaking factor
of each rod in a circle (25 in KCP-3/ 4) is approximately same.
• Axial peaking factor of a fuel rod does not depend upon its location in
core & depends upon power level or power density. Axial peaking
factors of all fuel rods in the core is approximately same.
12
CORE THERMAL DESIGN
From now onwards procedures will be discussed for obtaining
maximum temperatures (fuel, clad and coolant) in a nuclear reactor
with particular emphasis to the PR100.
Coolant Outlet, Maximum Clad and Fuel Centre Line Temperatures
The applicable equations and correlations used for the estimation of
various temperatures of interest are found below. Detailed derivation
of these follow from the basic principles of heat balance.
Axial Variation of Thermal Source Strength
In a reactor core, the axial variation of neutron flux along the fuel
element is given by
(1)
z
  c cos
H
and so is the variation of volumetric source strength for a fuel
element/rod having uniform x-section and enrichment.
z
q  qcos
(2)
H
where q’’’ and qc’’’ are the volumetric thermal source strengths at any
point along the height and centre of the fuel rod, respectively.
c
15
Power Distribution (kW) in Core with All Shutoff Rods Out
Reference Core at 40 MW
A
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25
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21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
B
C
142.8
D
151.3
179.3
164.8
180.2
136.2
142.2
144.4
141.7
136.0
162.1
207.2
187.0
210.2
178.1
184.8
180.8
173.3
161.2
179.6
ASOR
229.7
220.2
204.3
186.2
164.3
141.9
A
231.5
B
C
249.5
260.9
SOR
252.1
231.3
210.5
182.8
150.7
D
E
156.1
188.6
225.2
253.9
EXP
276.5
281.7
280.7
EXP
253.8
ASOR
193.3
155.1
E
F
155.1
190.1
232.5
SOR
284.1
290.4
295.4
295.8
290.1
277.0
262.4
233.6
189.5
153.9
F
G
150.5
184.2
222.8
260.7
290.7
302.6
304.9
306.5
304.4
296.1
285.9
SOR
229.1
183.6
149.6
G
H
173.5
212.0
250.8
287.1
ASOR
313.3
303.6
303.2
305.1
296.4
282.9
255.1
212.2
173.0
H
J
159.6
194.8
237.8
EXP
297.6
308.6
301.3
CT
301.3
308.6
297.6
EXP
237.8
194.8
159.6
J
K
173.0
212.2
255.1
282.9
296.4
305.0
303.2
303.5
313.3
ASOR
287.0
250.8
212.0
173.5
K
L
149.6
183.6
229.0
SOR
285.9
296.0
304.4
306.4
304.9
302.5
290.7
260.6
222.8
184.1
150.4
L
M
153.8
189.4
233.5
262.3
276.9
290.0
295.7
295.3
290.3
284.0
SOR
232.4
190.0
155.0
M
N
154.9
193.2
ASOR
253.7
EXP
280.6
281.6
276.4
EXP
253.8
225.0
188.5
155.9
N
P
150.4
182.6
210.4
231.2
252.0
SOR
260.8
249.4
231.4
207.0
179.1
151.0
P
Q
R
S
141.6
164.1
186.1
204.1
220.0
229.5
ASOR
210.1
186.8
164.5
179.3
161.1
173.2
180.7
184.6
178.0
161.9
135.9
141.6
144.3
142.0
136.1
179.8
142.5
Q
R
S
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
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12
11
10
9
8
7
6
5
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3
2
1
16
29
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27
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16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
A
INDIVIDUAL FUEL CHANNELS FLOW AT KCP-II
B
C
D
E
F
G
22.8
24.6
21.8
22.8
22.4
23.3
20.0
23.4
21.9
22.5
A
22.5
23.4
J
20.5
23.6
23.4
22.3
H
24.9
23.2
L
22.7
20.1
23.5
21.5
22.7
N
P
Q
R
C
D
E
F
G
H
S
22.4
24.3
24.7
M
23.5
21.9
23.9
23.2
22.9
24.9
24.3
22.7
22.6
22.0
24.7
EXP
SOR
ASOR
21.9
22.9
24.5
SOR
26.3
26.6
24.2
23.8
21.7
23.0
24.9
26.1
27.2
25.8
24.3
24.6
23.5
25.4
25.9
ASOR
28.7
25.1
26.1
21.4
24.9
EXP
27.8
30.4
25.5
EXP
23.5
22.4
24.3
28.4
31.5
31.9
26.1
23.8
22.3
ASOR
26.4
30.3
29.6
30.7
24.9
23.0
23.0
25.5
27.4
31.7
29.4
28.0
SOR
21.8
25.4
26.8
31.0
CT
28.8
25.6
23.5
22.1
SOR
28.2
31.2
29.4
27.2
24.6
24.0
26.3
26.4
31.3
31.2
30.7
26.2
ASOR
22.7
25.1
27.7
31.9
31.5
27.6
23.5
19.9
25.7
EXP
26.3
29.5
26.3
EXP
25.1
21.7
24.2
26.0
27.5
ASOR
25.4
21.5
21.7
21.0
23.6
26.3
28.4
26.8
24.3
23.9
22.0
25.2
24.4
27.0
26.0
SOR
25.4
24.7
22.8
ASOR
SOR
EXP
25.1
24.7
22.6
22.0
22.0
23.1
24.0
22.4
21.4
21.4
24.2
24.4
24.8
24.0
21.6
22.3
23.5
21.1
24.2
23.5
22.5
22.3
22.5
20.5
23.7
21.7
19.8
22.4
21.5
20.6
23.0
20.7
21.5
25.7
B
23.6
K
24.5
J
K
L
M
N
P
Q
R
20.4
21.7
22.3
23.3
23.4
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2
1
S
17
COOLANT EXIT TEMPERATURES
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17
16
15
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10
9
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4
3
2
1
A
B
C
D
Coolant inlet Temperature
46
Moderator Height
290
C
cm
M
N
E
F
G
H
66.1
65.2
67.8
66.2
70.6
70.5
71.8
67.0
63.8
77.2
73.8
79.5
71.8
70.3
67.6
EXP
77.3
ASOR
70.5
64.8
77.9
77.3
65.7
78.1
SOR
71.5
69.2
64.4
78.4
70.2
68.6
EXP
75.1
73.0
70.9
75.7
77.9
80.4
78.5
78.8
71.4
68.0
79.2
78.8
ASOR
71.3
66.2
78.0
SOR
70.4
EXP
79.7
74.6
73.4
67.0
75.2
72.8
73.3
66.9
71.0
70.5
68.0
A
B
C
D
E
F
G
71.7
H
J
68.1
68.2
71.5
72.6
71.8
71.8
68.6
69.8
73.8
74.3
63.7
68.7
70.8
77.7
73.5
71.5
77.8
77.7
64.6
73.3
78.9
SOR
77.9
ASOR
EXP
79.1
65.7
69.5
78.4
80.1
79.7
75.8
78.2
81.0
65.8
71.2
78.3
78.1
ASOR
78.0
78.4
65.5
77.9
78.9
75.1
79.5
76.3
66.2
69.7
SOR
79.1
76.3
72.5
78.3
80.4
78.5
75.4
75.1
69.0
EXP
78.2
77.5
71.1
69.1
73.0
80.0
76.2
CT
75.6
72.9
79.7
77.5
68.9
77.8
81.4
77.0
76.1
70.5
79.1
75.2
75.2
78.0
76.6
77.0
76.7
S
63.3
ASOR
79.8
77.5
76.3
78.9
73.6
70.9
79.2
75.3
78.4
ASOR
R
65.7
71.7
SOR
79.4
77.2
72.3
77.7
79.3
80.0
Q
66.1
75.3
EXP
SOR
70.8
72.7
77.0
P
66.9
72.0
77.9
78.2
L
66.1
72.3
73.5
75.3
77.2
K
69.9
76.0
68.2
70.0
68.4
70.9
70.7
65.4
J
69.7
o
65.4
66.7
70.0
66.5
63.8
K
L
M
N
P
Q
R
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9
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1
S
18
29
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10
9
8
7
6
5
4
3
2
1
A
B
C
CLAD SURFACE TEMPERATURES
D
E
F
G
H
81.1
80.0
83.8
81.3
79.9
88.2
84.6
87.6
90.9
82.8
77.4
94.4
90.9
87.9
83.1
99.6
88.4
101.1
94.0
101.5
SOR
90.8
86.3
78.2
103.0
102.0
98.8
88.5
85.1
98.7
EXP
91.9
105.0
101.8
84.3
103.1
ASOR
81.0
101.8
SOR
88.5
EXP
103.0
95.4
92.5
82.5
96.5
92.4
92.2
82.4
89.4
88.1
83.8
A
B
C
D
E
F
G
85.0
H
J
84.5
91.5
90.3
84.9
89.6
90.3
89.7
87.5
94.1
94.8
77.2
85.2
89.5
99.6
93.4
90.6
100.4
100.4
78.7
92.1
101.2
SOR
100.4
ASOR
EXP
103.1
80.3
86.9
101.2
104.4
103.8
97.0
101.6
106.1
80.5
89.3
101.3
101.8
ASOR
101.4
100.6
80.3
101.9
95.9
103.5
99.6
80.9
86.9
SOR
103.2
99.8
103.0
102.0
89.5
98.3
91.7
104.6
102.7
85.5
101.0
102.1
101.2
98.0
102.0
90.5
CT
86.4
EXP
99.5
89.1
93.2
104.3
101.2
98.6
101.5
96.2
80.8
99.4
101.8
100.4
106.4
100.5
85.5
92.5
103.6
98.0
98.0
S
76.8
ASOR
104.0
100.7
100.2
R
88.3
102.4
101.0
99.8
90.3
SOR
103.8
103.6
Q
80.6
96.5
102.0
ASOR
100.6
99.9
88.9
80.4
103.5
91.1
100.3
103.3
P
81.2
96.3
EXP
104.3
EXP
ASOR
79.1
SOR
N
82.4
92.2
99.3
M
90.5
100.1
101.1
99.5
90.5
93.4
97.4
L
81.1
87.8
96.2
98.8
88.8
85.2
88.9
K
86.5
89.0
88.7
J
80.0
82.0
86.8
81.9
77.8
K
L
M
N
P
Q
R
29
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26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
S
19
FUEL SURFACE TEMPERATURES
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
A
B
C
D
E
F
G
H
84.1
83.1
86.9
84.3
82.8
87.9
91.2
103.3
92.6
80.1
104.6
99.0
95.1
91.4
85.9
105.1
92.5
SOR
95.2
89.8
81.0
108.9
107.1
107.6
103.8
92.6
88.3
107.3
EXP
100.8
95.7
92.4
104.8
110.9
106.9
87.5
108.9
107.3
93.1
107.0
105.3
83.3
107.7
SOR
92.3
108.1
96.3
96.6
95.9
85.5
91.5
B
C
D
E
F
G
88.2
H
J
93.2
94.1
93.1
88.5
87.8
95.2
93.9
79.9
88.4
93.6
104.3
97.6
95.6
91.2
98.6
99.2
93.3
86.8
A
105.5
81.5
94.8
105.5
105.6
101.2
ASOR
105.8
SOR
83.2
90.6
106.2
110.0
109.6
92.9
106.5
EXP
108.9
EXP
100.0
85.6
ASOR
83.3
101.6
107.1
112.1
90.4
SOR
107.6
83.6
100.3
109.1
109.1
106.1
95.8
110.2
105.5
108.1
108.8
ASOR
83.8
104.1
107.5
94.7
104.3
88.7
106.0
108.0
107.3
90.1
EXP
108.8
92.7
97.8
110.1
107.3
88.8
105.5
105.6
CT
104.7
S
79.6
96.7
109.1
104.1
104.7
107.7
107.6
112.3
106.5
105.6
R
92.0
ASOR
109.7
106.9
106.3
94.2
SOR
107.0
106.1
Q
83.6
101.1
107.7
ASOR
106.4
100.9
109.7
109.6
106.7
98.6
83.2
109.2
104.6
92.1
109.1
P
84.3
94.9
105.4
EXP
110.2
EXP
ASOR
81.9
SOR
94.2
104.9
106.4
N
85.5
96.5
104.3
M
84.1
91.7
100.7
L
94.0
97.6
102.1
95.0
86.0
92.6
92.4
K
89.7
88.6
92.7
91.8
J
82.8
85.0
89.9
85.0
80.8
K
L
M
N
P
Q
R
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
S
20
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
A
B
C
FUEL CENTER LINE TEMPERATURES
D
E
F
G
H
311.2
316.8
321.3
312.4
299.2
357.3
334.2
358.0
397.4
329.0
287.5
432.3
401.4
355.4
300.9
459.6
365.0
474.3
359.9
519.6
SOR
347.5
519.2
500.8
462.3
391.7
329.5
527.6
EXP
369.7
521.9
466.7
333.2
508.0
ASOR
298.8
521.5
SOR
379.7
EXP
469.3
429.9
374.7
318.9
442.1
405.2
366.4
317.1
379.5
348.4
312.1
A
B
C
D
E
F
G
327.2
H
J
333.7
372.5
365.5
355.4
358.1
373.7
350.4
367.0
423.5
421.1
287.3
330.6
396.0
437.4
405.7
401.0
465.7
474.3
297.1
358.6
437.3
SOR
461.9
ASOR
EXP
514.0
301.7
363.6
460.6
506.6
509.9
431.7
495.1
530.5
298.0
360.1
475.2
512.5
ASOR
503.1
439.8
310.8
535.0
418.3
502.9
528.9
290.1
347.8
SOR
519.7
539.2
520.9
477.8
363.1
523.5
393.9
502.5
532.8
329.8
463.8
519.4
528.3
528.0
496.1
401.5
CT
365.2
EXP
528.2
358.0
431.0
513.9
527.9
526.1
512.1
433.4
358.1
530.7
465.6
522.8
525.5
333.9
402.9
497.2
527.9
526.2
S
361.9
477.9
519.5
539.2
R
294.9
ASOR
508.6
534.1
529.3
501.6
414.8
288.0
511.8
436.5
503.5
ASOR
Q
310.6
378.0
SOR
522.9
528.9
494.9
429.7
298.0
506.1
373.4
467.3
509.7
P
317.5
430.5
EXP
514.8
EXP
ASOR
300.8
SOR
N
317.0
405.1
461.0
M
365.0
444.9
475.0
465.2
350.4
405.7
435.9
L
309.9
378.2
422.0
427.4
368.4
346.8
372.7
K
328.5
364.6
370.4
J
298.8
312.6
323.4
318.2
308.4
K
L
M
N
P
Q
R
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
S
21
Axial Temperature Distribution in the Hottest Channel at 40 MW
Critical Moderator Height :290 cm
Coolant Flow Rate:
Peak Temperatures, (oC)
Active
Fuel Height
Fuel
(cm)
Centreline
0
20.7
34.5
48.3
62.1
75.9
89.7
103.5
117.3
131.1
144.9
158.8
172.6
186.4
200.2
214.0
227.8
241.6
255.4
269.2
290.0
150.50
239.77
320.12
391.15
452.54
504.31
546.43
578.95
602.01
615.67
620.00
615.01
600.52
576.58
542.96
499.56
446.30
383.02
309.85
226.89
132.92
Fuel
Surface
Clad
Surface
87.24
93.43
99.24
104.36
108.72
112.26
114.92
116.64
117.39
117.13
115.84
113.48
110.04
105.56
100.08
93.65
86.40
78.43
69.90
61.01
51.59
86.43
91.48
96.19
100.28
103.70
106.40
108.35
109.49
109.81
109.28
107.90
105.61
102.41
98.32
93.39
87.65
81.21
74.16
66.66
58.85
50.58
30 Igpm
Saturation
Temperature
Local
Coolant
Of Water
Pressure
o
Exit
( C)
(kPa)
82.34
81.62
80.75
79.51
77.92
76.03
73.86
71.47
68.91
66.22
63.47
60.71
58.00
55.40
52.96
50.73
48.77
47.11
45.79
44.83
44.00
137.5
139.1
140.2
141.2
142.2
143.1
144.0
144.9
145.7
146.3
147.1
147.8
148.6
149.3
150.1
150.8
151.5
152.2
152.9
153.6
154.6
335.86
352.13
362.78
373.22
383.48
393.55
403.45
413.20
422.82
432.33
441.77
451.14
460.49
469.82
479.16
488.55
497.99
507.51
517.13
526.86
541.63
22
Axial Temperature Distribution in the Hottest Channel at 48 MW
º
Peak Temperatures, ( C)
Active Fuel Height
(cm)
292
271
257
243
229
216
202
188
174
160
146
132
118
104
90
76
63
47
35
21
0
Fuel Center
127.8
221.1
304.6
378.4
442.2
496.2
540.4
574.8
599.3
614.4
619.8
615.9
602.4
579.5
546.8
504.6
452.5
391.1
319.6
239
148.8
Fuel Surface
53.8
63
71.8
80.3
88.3
94.9
101.4
107
111.6
115.1
117.5
119
119.3
118.6
116.9
114.3
110.8
106.4
101.3
95.5
89.2
Clad Surface
52.9
60.9
68.6
76.1
83.1
89
94.7
99.7
103.9
107.2
109.5
111
111.7
111.4
110.3
108.4
105.7
102.3
98.2
93.5
88.4
Coolant Exit
47
47.8
48.7
50
51.7
53.7
55.9
58.4
61
63.7
66.5
69.3
72
74.6
77.1
79.3
81.2
82.8
84.1
84.9
85.6
Saturation
Temperature of
Water
( ºC)
148.9
147.7
146.9
146.2
145.6
144.8
144.0
143.2
142.3
141.4
140.5
139.6
138.7
137.7
136.8
135.7
134.6
133.4
132.2
131.0
129.0
23
Axial Temperature Distribution
(Hottest and Average Channel of KCP-III)
24
•
Criteria for Safe Operating Power Level
The safe operating power level as a function of moderator
height has been assessed based on the following criteria
which is to be satisfied under all operating conditions i.e.
overpower limiting set point of 110% and low flow set
point of 90%.
The maximum temperatures at fuel centerline, fuel-clad
and clad-coolant interfaces should remain within the
following prescribed limits:
1.
2.
3.
4.
5.
The fuel center line temperature should not exceed 668 oC in
order to avoid the phase change;
The fuel surface temperature should not exceed 200 oC to
prevent formation of uranium-aluminium alloy;
The clad surface temperature should not exceed 130 oC to
preclude corrosion of aluminium by coolant water.
Nucleate boiling should not commence at any point in the
core
The core should have sufficient safety margins against onset
of nucleate boiling and departure from nucleate boiling.
25
Boiling,Sub cooled,Bulk boiling,Saturation Temp.
Boiling:
Process in which the vapours formed with in the liquid when
vapour pressure is equal to the atmospheric pressure.When
temperature of fluid approached saturation temp. boiling starts.
Saturation Temp:
The temp. at which boiling starts.
Sub cooled Nucleate Boiling:
When heating surface temp. is greater that Tsat. But bulk liquid
temperature is below Tsat.(small bubbles form and collapse
before reaching surface temperature.
Bulk Boiling:
When all the liquid is at Tsat(100 oC).During phase change no
increase in Temperature.
Latent Heat of Vaporization:
Heat supplied (at Tsat) to change the phase is called “latent heat
of vaporization.
27
Surface heat flux (w/cm2)
Boiling Regimes
c
f
d
e
b
a
o
Tc – Tf (Clad Surface – Coolant) 0C
28
Boiling Regimes (Contd)
•
•
•
•
•
•
•
(0 to a) Natural / Forced convection heat transfer b/w
clad and coolant.
(a to b) Via Natural/Forced Convection,agitation(bubble
formation),subcooled nucleate boiling at ‘b’(ONB
starts) bubble forms and collapse at clad surface
before reaching bulk liquid.(local/sub cooled boiling)
(b to c) number of bubble formation increases,turbulent
increases and surface heat flux increases.
(bulk/volume boiling)
At point “C” DNB starts.
(c to d) film boiling reduces the heat transfer(partial
film boiling).
(d to e) full film formation which insulate heating
surface.
(e to f) heat transfer is mainly via radiation,super
heated steam.
Back
29
MARGIN to ONB and DNB
Moderator Power
Height
Level
(cm)
(MW)
Peak Temperatures in Hot Channel, ( oC )
(Average Channel)
Fuel Center Fuel Surface Clad Surface Coolant Exit
217
30.05
220
30.41
230
31.84
240
33.20
250
34.55
260
35.90
270
37.27
280
38.63
290
39.97
300
41.31*
619.5
(415.0)
618.8
(409.9)
619.8
(410.6)
619.8
(410.6)
619.6
(410.5)
619.6
(410.5)
619.8
(410.7)
619.7
(410.7)
619.6
(410.7)
619.5
(410.6)
113.5
(91.8)
113.5
(85.8)
114.1
(86.2)
114.6
(86.5)
115.1
(86.8)
115.6
(87.2)
116.2
(87.6)
116.7
(87.9)
117.1
(88.4)
117.6
(88.7)
105.6
(87.2)
105.6
(81.2)
106.3
(81.7)
106.8
(81.9)
107.4
(82.4)
170.8
(82.8)
108.6
(83.2)
109.2
(83.6)
109.8
(83.9)
110.4
(84.3)
72.8
(64.3)
73.2
(60.9)
74.6
(61.8)
75.9
(62.5)
77.1
(63.3)
78.4
(64.0)
79.7
(64.8)
81.1
(65.6)
82.3
(66.3)
83.6
(67.1)
Power, (MW)
(Safety Margin)
ONB
DNB
61.00
(2.03)
61.79
(2.03)
64.63
(2.03)
67.40
(2.03)
70.14
(2.03)
72.63
(2.02)
75.16
(2.02)
77.40
(2.00)
79.90
(2.00)
83.03
(2.01)
94.66
(3.15)
95.80
(3.15)
98.95
(3.11)
104.5
(3.15)
105.2
(3.05)
107.4
(3.00)
111.8
(3.00)
116.0
(3.00)
120.0
(3.00)
123.0
(3.00)
BACK
30
Accident and Transient Analysis
• Accident/ Transient Analysis using Computer
Code “PARET” for different PIEs:
Uncontrolled Moderator Pump up
Withdrawal of a Shutoff rod
Removal of an In Pile Experiment
Accident Drop of an Enriched Fuel Rods
Ramp Reactivity Insertion
Step Reactivity Insertions
31