Reactivity Power and Temperature Coefficients Determination of
the TRR
Ahmad Lashkari
Nuclear Science and Technology Research Institute (NSTRI),
Atomic Energy Organization of Iran
Tehran 14399-51113, Iran
[email protected]
ABSTRACT
The aim of this paper is to present the experimental results of the power and temperature
coefficient of reactivity of the Tehran Research Reactor (TRR) at the Nuclear Science and
Technology Research Institute (NSTRI) of Iran. In this work in addition to the previous method,
new methods were used to measure the reactivity coefficient of TRR. The experiments were
performed in the TRR reactor with 33 MTR fuel elements in the core. At the first method, we
determined the isothermal coefficient of TRR and then calculated power and temperature
coefficient of reactivity. This method is very similar to the method that is used to determine the
power coefficient of IPR-R1 TRIGA reactor. One of the new methods used in this study is
comparing the situation of control rod positions in two cooling modes (natural and force) at the
same power of TRR. The difference between two control rod configurations is caused by the
temperature difference in coolant in two modes. With measuring the reactivity difference and
coolant temperature, we can calculate reactivity coefficient. The last new method is much more
efficient than the above methods, using the dynamic behaviour of reactor power due to change
of reactor core temperature. The main advantage of this method is that we can measure the
reactivity coefficient of reactor very fast and independent of the control rods worth and
positions. The average values of the temperature and power reactivity coefficient of the fuel
and the coolant in TRR are:
α_T (F)=1.95 pcm/°C, α_T (m)=13.57 pcm/OC
α_p (F)=0.16 pcm/kW, α_p (m)=0.89 pcm/kW
1
INTRODUCTION
The portion of reactivity change arising from the effect of energy production is called
reactivity feedback, which includes temperature and void coefficient of reactivity. Temperature
coefficients of reactivity due to fuel, coolant and moderator component of a reactor core are
defined as the change in reactivity per unit change in average temperature of that component.
If αT,j represents the temperature reactivity coefficient of a component j then they can be written
as:
ρ
(pcm/ 0 C )
T j
(1)
k eff  1
 10 5 (pcm)
k eff
(2)
α T, j 
ρ
416.1
416.2
Where keff is effective multiplication factor corresponding to average temperature “T” of
the core component “j”. This paper reports the results of a set of experiments to determine the
power and temperature coefficient of reactivity of the Tehran Research Reactor (TRR). For
calculation of these parameters the values of isothermal temperature coefficient are needed. The
isothermal temperature coefficient was measured by observing the reactivity change with core
temperature. In this work in addition to the previous method, new methods were used to
measure the reactivity coefficient of TRR. The experiments were performed in the TRR reactor
with 33 MTR fuel elements in the core. At the first method, we determined the isothermal
coefficient of TRR and then calculated power and temperature coefficient of reactivity. This
method is very similar to the method that is used to determine the power coefficient of IPR-R1
TRIGA reactor [1]. One of the new methods used in this study is comparing the situation of
control rod positions in two cooling modes (natural and force) at the same power of TRR. The
difference between two control rod configurations is caused by the temperature difference in
coolant in two modes. With measuring the difference reactivity and coolant temperature, we
can calculate reactivity coefficient. The last new method that is much more efficient than the
above methods is using the dynamic behavior of reactor power due to change of reactor core
temperature. The main advantage of this method is that we can measure the reactivity
coefficient of reactor very fast and independent of the control rods worth and positions.
2
METHODOLOGY
One of the operating conditions that effect on the reactivity of a reactor core is
temperature. Changes in temperature will cause changes in reactivity. The direction of the
changes and its magnitude are great importance in the reactor safety and control. If the
temperature change is uniform throughout the core, as would be in a homogeneous reactor, the
temperature effect on the reactivity can be expressed only by a simple temperature coefficient,
αISO, defined as the change in reactivity per degree change in temperature [2]:
∆ρ
α
∆
(3)
Where Δρ and ΔT are the changes in reactivity and temperature, respectively. The
negative reactivity feedback, , produced by a temperature increase ΔT is then:
ISOT
Assuming that ISO is constant over the range of temperature T. This ISO is sometimes
called the isothermal temperature coefficient or the zero-power temperature coefficient [2].
Heterogeneous reactor changes in temperature during operation are not uniform, that is, they
are not the same in the moderator as in the fuel. In such a reactor we have to distinguish between
the reactivity arising in the cooling, or moderator, and that arising in the fuel, and, accordingly,
define a coolant temperature coefficient, T(M), and a fuel temperature coefficient, T(F).
These coefficients in general are different in magnitude and in response time. Effects on the
fuel, for instance, resonance absorption (Doppler Effect) or thermal distortion of fuel elements
are regarded as prompt, while effects on the moderator or coolant are delayed. The power
coefficient of reactivity is defined as
α
∆ρ
∆
(4)
Where P is the change in power.
Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 14 ̶ 17, 2015
416.3
To obtain the contribution of the fuel to P and thus the fuel power coefficient, P(F),
in a reactor, we have to subtract T(M), the effect arising in the moderator due to the change
in moderator temperature, T(M). An approximate value for T(M) would be:
ΔρT(M)= αISO ΔT(M)
(5)
Then, the fuel and moderator power coefficient of reactivity are given by
ΔρT(F)=Δρ - ΔρT((M)
α F
α M
∆ρ
∆
∆ρ
∆
(6)
(7)
(8)
In this work, the temperature of coolant was measured easily but we haven’t any facility
to measure the temperature of the fuel plate. In this research we used CONVECT code to
determine the fuel plat temperatures. CONVECT is a steady state code used to analyses of
natural convection of MTR type reactors [3]. With measuring the coolant temperature and
calculating the fuel temperature, the temperature coefficients are defined as:
α
T
α T
∆ρ
∆
∆ρ
∆
(9)
(10)
Temperature coefficients are the main safety parameters that are used in two natural and
force cooling system.
2.1
The Tehran Research Reactor
The TRR is a pool type research reactor, in which light water serves as coolant,
radiological shielding as well as neutron moderating medium and reflector. The reactor is
designed and licensed to operate at a maximum thermal power level of 5 MW. The reactor core
assembly is located in a two-section pool and may be operated in either pool. One of the sections
contains experimental facilities, like beam tubes, rabbit system, and thermal column. The other
section is an open area for bulk irradiation studies. The major components of TRR are the pool
(including embedment and accessories), bridge and support structure, core, cooling system,
control and instrumentation, ventilation system, and the experimental facilities. Elements of the
reactor core are arranged in a 9 by 6 grid plate structure. Details of reactor description and core
parameters are given in TRR- Safety Analysis Reports (SAR).
3
RESULT AND DISCUSSION
3.1
Isothermal Temperature Coefficient Measurement
In these experiments, the reactor was shut down for a one week, so the reactor was xenon
poisoning free with low background signal. Reactor was critical at 1kW and the positions of
SRs were written. The inlet and outlet temperature of the coolant was measured by
thermocouple. In 1kW the difference between inlet and outlet was about 1.5 °C. The power of
reactor was increased by positive insertion by RR and set power to 20, 50, 80 and 100 kW. In
Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 14 ̶ 17, 2015
416.4
each power the rod positions and the inlet and outlet coolant temperature were measured. Table
1 shows all data information at all power, only the position of RR changed due to temperature
increment. The average temperature of coolant is the average of inlet and outlet coolant
temperature and easily measured by two thermocouple. Also the CONVECT code was used to
calculate the fuel and coolant temperature in each scenarios. The results show a good agreement
between experimental and simulation results of coolant temperatures. Because we have not any
facility to measure the fuel temperature, we have to rely on calculation results. Calculations
show that the temperature of the fuel and the coolant are the same in low powers and we can
show the both temperature with a one temperature that is named isothermal temperature. After
20 kW the difference between the coolant and fuel temperature increased. So we can calculate
the isothermal temperature coefficient at 20 kW with a good approximate.
Table 1: Results of isothermal temperature coefficient of reactivity
CONVECT
Power
Tin
(kW)
28.5
28.5
28.5
28.5
28.5
30
33
36.5
38
39.5
Tave(m) Tave(F).
29.13
31.19
32.65
33.65
34.201
29.13
31.55
33.59
35.20
36.14
Tave(m) TPool
29.25
30.75
31.95
33.25
34
28.5
28.5
28.5
28.5
28.5
SRs
RR
63.5
63.5
63.5
63.5
63.5
34
38
43
45.2
47.5
∆
∆
Δρ/
Δρ
∆T(m)
∆T(m)
(pcm)
pcm/kW
0
20.8
46.8
58.24
70.2
0
1.5
3.25
4
4.75
13.87
14.4
14.56
14.78
1.04
0.94
0.73
0.70
At the first and before doing any experiments the RR was calibrated and the worth of RR
determined. Fig.1 shows the RR integral worth of reactivity. The ratio of the reactivity changes
to the average coolant temperature at the 20 KW is about 13.87 (pcm/OC) and named isothermal
temperature coefficient. The ratio of the reactivity changes to the coolant temperature at higher
powers increases. The reason of this increment is that at the higher powers the average
temperature of the fuel plate is higher than the average temperature of coolant. For example at
the power 100 kW the fuel average temperature is higher than coolant about 20C. The
incremental trend of this parameter at higher power shows the accuracy of method.
300
250
Reactivity (pcm)
1
20
50
80
100
Tout
Rods
position
200
150
100
50
0
0
20
40
60
80
100
Rod position ( %)
Figure1: RR reactivity worth verse rod position.
Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 14 ̶ 17, 2015
416.5
At the next power with measuring the average coolant temperature and total reactivity
changes, we can calculate the reactivity changes due to fuel temperature increment.
Column 8 of table 2 shows the reactivity changes due to the fuel temperature. In the last
two columns of the table 2 power reactivity coefficients of the fuel and coolant were reported
for 3 powers 50, 80 and 100 kW. The average of these coefficients is about 0.15 and 0.75
(pcm/kW) respectively. In this paper only the power reactivity coefficient report
experimentally. In the next step we used CONVECT code to calculate Tf and Tm at each powers.
The difference between Tf and Tm at three powers 50, 80 and 100 kW were calculated and
shown in the table 2. The ratio of Δρ (F)/ ΔT (F) gives the temperature reactivity of the fuel.
The average value for three powers 50, 80 and 100 KW is 1.95 (pcm/0C). Also α m is easily
calculated for three powers and the average value of this parameter is 12.57 (pcm/0C). The last
four columns of table 2 shows the power and temperature reactivity coefficients.
Table 2: Temperature and power coefficient of reactivity for the power intervals measured
Power
(KW)
CONVECT
Δρ
∆T(m)
Δρ/
∆T(m)
Δρ(m)
Δρ
(F)
∆T(F)=
TF-Tm
Tave(m)
Tave(F).
Unit
0C
0C
pcm
0C
pcm/0C
pcm
pcm
1
20
50
80
100
29.13
31.19
32.65
33.65
34.201
29.13
31.55
33.59
35.20
36.14
0
20.8
46.8
58.24
70.2
0
1.5
3.25
4
4.75
13.87
14.4
14.56
14.78
0
20.81
45.08
55.48
65.88
0.00
1.72
2.76
4.32
3.2
α F
α m
α F
α m
0C
pcm/0C
pcm/0C
Pcm/
kW
Pcm/
kW
0
0.36
0.94
1.55
1.94
1.83
1.78
2.23
12.57
12.78
12.55
0.17
0.14
0.13
0.90
0.69
0.66
Comparing the Control Rods Position in Two Natural and Force Cooling System
Modes
In this method the control rods position was compared in two natural and force cooling
modes at 80 kW. The reactivity difference between two modes is distributed to the fuel and
moderator temperature. Table 3 shows all temperature measurements and control rods position.
According to CONVECT calculation in the natural circulation mod, the temperature of the fuel
and the coolant are the same with a good approximation. With using α F obtained from the
previous method, we calculated the value of α m with this new method. As can be seen, the
new value is (14.2 pcm/0C) a little higher than the previous value.
Table 3: Coolant temperature coefficient of reactivity for the power 80 kW.
CONVECT
Power
(KW)
Tin
0
C
Tout
0
C
80 F
80 N
27
27
27.5
37.5
3.3
Tave(m)
0
C
Tave(F)
0
C
27.25
32.2
27.3
33.7
Tave(m)
0
C
TPool
0
C
27.25
32.25
27
27
Rods
position
SRs
63
63
RR
26
43.5
Δρ
(pcm)
0
83.3
ΔT(m)
C
ΔT(F)
0
C
Δρ(F)
pcm
Δρ(m)
pcm
α m
pcm/0C
0
5
0
6.5
0
12.35
0
68
14.2
0
Measurement of Reactivity Coefficient According to Inhour Equation
In this method a new technique was used to measure the temperature reactivity
coefficient. Increasing the temperature of the reactor core causes applying negative reactivity
feedback and vice versa decreasing the temperature makes positive reactivity. In this method,
reactor power was set at specific power in natural cooling system. The inlet and outlet
temperature of coolant were measured with thermocouple. With changing the cooling system
mode from natural to force, a positive reactivity inserted to the reactor and the power of the
reactor was beginning to increase. With measuring doubling time and using the inhour equation,
the reactivity worth of temperature changing in the reactor component is calculated directly
Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 14 ̶ 17, 2015
416.6
from equation 11-12. The advantage of this method is the measuring of the reactivity worth
without control rods dependence.
∑
(11)
∑
(12)
Where:
: Reactivity
: delayed neutron fraction for group i
: Prompt neutron lifetime (s)
/
: Reactor period
T1/2: doubling time
: Decay constant of delayed neutron group i
In this work one group delayed neutron approximation was used in inhour equation. In
table 4 the results of this method are shown only for 60 kW power. Doubling time was measured
about 102.47s and the reactivity was calculated about 68 (pcm). Similar to the previous
methods, the average temperature of the fuel was calculated by CONVECT code. With using
the value of α F the value of α m was obtained from the new method (12 pcm/0C).
Table 4: Coolant temperature coefficient of reactivity for the power 60 kW.
Cal.
4
Power
(kW)
Tin
Tout
60
27
36
Tave(m)
Tave(F).
31.60
32.71
Tave(m)
TPool
T1/2
Δρ
(pcm))
ΔT(m)
ΔT(F)
Δρ
(F)
Δρ
(m)
α m
pcm/0C
31.5
27
102.47
68
4.5
5.71
10.8
57.2
12.7
CONCLUSIONS
The experiments were performed in the TRR reactor with 33 fuel elements in the core.
At first, it was determined the isothermal coefficient of 13.87 (pcm/0C). As it was shown, most
of the negative reactivity change with increasing power must be attributed to the change in the
coolant temperature. The coefficient due to the fuel heating was very small. Then, we can
conclude that the power coefficient of reactivity of the coolant is the main contributor to the
power coefficient of reactivity in TRR.
The aim of this paper is to present the experimental results of the power and temperature
coefficient of reactivity. In this work in addition to the previous method, two new methods were
used to measure the reactivity coefficient of TRR. At the first method, we determined the
isothermal coefficient of TRR and then calculated power and temperature coefficient of
reactivity. The first new method used in this study is comparing the situation of control rod
positions in two cooling modes (natural and force) at the same power of TRR. The difference
between two control rod configurations is caused by the temperature difference in coolant in
two modes. With measuring the difference reactivity and coolant temperature, we can calculate
reactivity coefficient. The last new method is much more efficient than the above methods. The
main advantage of this method is that we can measure the reactivity coefficient of reactor very
Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 14 ̶ 17, 2015
416.7
fast and independent of the control rods worth and positions. In each section reactivity
coefficient are calculated and finally the average values of the temperature and power reactivity
coefficient of the fuel and the coolant in TRR are:
αT (F)=1.95 pcm/0C, αT (m)=13.57 pcm/0C
αP (F)=0.16 pcm/kW, αP (m)=0.89 pcm/kW
REFERENCES
[1]
GENERAL ATOMIC, Safeguards summary report for the New York University
TRIGA Mark I Reactor. San Diego, 1970. (GA-9864).
[2]
DUDERSTADT, J.J.; HAMILTON, L.J. Nuclear Reactor Analysis. New York, N.Y.: J.
Wiley & Sons (1976).
[3]
29. Abatte., P., CONVEC V 3.40, A program for Thermal-hydraulic Analysis of a MTR
core in Natural Convection (2002).
Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 14 ̶ 17, 2015