The reactivity coefficient is a very important parameter for safety and Stability of reactors operation. To provide the safety analysis of the reactor, the calculation of changes in reactivity caused by temperature is necessary because it is related to the reactor operation. The objective is to study the effect of the temperature reactivity coefficients of fuel and moderator of the PWR core, as well as the moderator density and boron concentration on fluid density, reactivity, void fraction. peak fuel clad temperature and time to core uncover were found for two feedback cases. This paper focuses on the effect of the Reactivity feedback, of the 6" (6-inch) Cold Leg SBLOCA sequences in a 4-loop PWR Westinghouse nuclear power plant with a scram for various feedback, moderator density coefficient, MDC, moderator temperature coefficient, MTC, the fuel temperature coefficient, FTC, and boron concentrations. Dragon neutronic code is used for calculating reactivity's coefficient which is used in RELAP5 thermal hydraulic computer code to simulate the effect of Reactivity feedback during Cold Leg SBLOCA. The plant nodalization consists of two loops; the first one represents the broken loop and the second one represents the other three intact loops. In the present analysis two models in RELAP5 code for computation of the reactivity feedback, separable and tabular models are used. The 6-inch break size was chosen because the previous work [1], showed that it was the worst size break in a 4-loop PWR Westinghouse. The results show that the neglecting of the reactivity feed-back effect causes overheating of the clad and that the importance of the reactivity feed-back on calculating the power (reactivity) which the key parameter that controls the clad and fuel temperatures to maintain them below their melting point and therefore prevent core uncover and fuel damage where the fuel temperature, clad temperature and core water level are in the range.

1. ineering & Management (IJMREM)International Journal of Modern Research in Eng
||Volume|| 2||Issue|| 1||Pages|| 37-44 || January 2019|| ISSN: 2581-4540
www.ijmrem.com IJMREM Page 37
Reactivity Feedback Effect on the Reactor Behaviour during
SBLOCA in a 4-loop PWR Westinghouse Design
S. Helmy
Nuclear and Radiological Regulatory Authority (NRRA), Cairo, Egypt
------------------------------------------------------ABSTRACT----------------------------------------------------
The reactivity coefficient is a very important parameter for safety and Stability of reactors operation. To provide
the safety analysis of the reactor, the calculation of changes in reactivity caused by temperature is necessary
because it is related to the reactor operation. The objective is to study the effect of the temperature reactivity
coefficients of fuel and moderator of the PWR core, as well as the moderator density and boron concentration on
fluid density, reactivity, void fraction. peak fuel clad temperature and time to core uncover were found for two
feedback cases. This paper focuses on the effect of the Reactivity feedback, of the 6" (6-inch) Cold Leg
SBLOCA sequences in a 4-loop PWR Westinghouse nuclear power plant with a scram for various feedback,
moderator density coefficient, MDC, moderator temperature coefficient, MTC, the fuel temperature coefficient,
FTC, and boron concentrations. Dragon neutronic code is used for calculating reactivity's coefficient which is
used in RELAP5 thermal hydraulic computer code to simulate the effect of Reactivity feedback during Cold
Leg SBLOCA. The plant nodalization consists of two loops; the first one represents the broken loop and the
second one represents the other three intact loops. In the present analysis two models in RELAP5 code for
computation of the reactivity feedback, separable and tabular models are used. The 6-inch break size was chosen
because the previous work [1], showed that it was the worst size break in a 4-loop PWR Westinghouse. The
results show that the neglecting of the reactivity feed-back effect causes overheating of the clad and that the
importance of the reactivity feed-back on calculating the power (reactivity) which the key parameter that
controls the clad and fuel temperatures to maintain them below their melting point and therefore prevent core
uncover and fuel damage where the fuel temperature, clad temperature and core water level are in the range.
KEYWORDS: Reactivity feedback 6" Small-break loss-of-coolant accident Thermal hydraulic phenomena 4-
loop PWR Core uncovery.
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Date of Submission: Date, 12 January 2019 Date of Accepted: 15. January 2019
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I. INTRODUCTION
RELAP5 T.H system code has been developed for best-estimate transient simulation of light water reactor
coolant systems during postulated accidents. The code models the coupled behavior of the reactor coolant
system and the core for large and small loss-of-coolant accidents. RELAP5 code is the simplest model that can
be used to compute the power in a nuclear reactor. The power is computed using point kinetics approximation.
There are two options for the computation of the reactivity feedback. The first option is the separable point
reactor kinetics model and the other is tabular point reactor kinetics. In Separable Feedback Model The model
assumes feedback effects from moderator density and fuel, moderator temperatures. It is called the separable
model because each effect is assumed to be independent of the other effects. The tabular feedback model
computes reactivity from multi-dimensional table. The tabular model overcomes the objections of the
separable model since all feedback mechanisms can be nonlinear and interactions among the mechanisms are
included (e.g., the dependence of the moderator density feedback as function of the moderator fluid temperature
may be modeled). The four-dimensional table lookup and interpolation option (TABLE4A) computes reactivity
as a function of moderator densities, liquid moderator temperature, fuel temperature, and boron concentration.
In our work, TABLE4A is used [2]. Previous studies showed that, SBLOCA scenarios are depend on many
factors such as reactor design, break location, Safety injection set points, break size, boron concentration. Also,
the 6-inch break size was chosen because the previous works showed that it was the worst size break in a 4-loop
PWR Westinghouse [1&3] SBLOCA is characterized by five periods: blow-down, natural circulation, loop seal
clearance, boiloff, and core recovery, [4]. Kinetics parameters for the standard UO2 fuel and nitride fuel (UN-
U3Si2-UB4) have been developed from PARCS stand-alone full-core calculations to provide complete loss of
primary flow and small break (SB). Feedback coefficients included in the model are fuel temperature (Doppler),
coolant temperature, coolant density, and boron. Kinetics parameter inputs to the TRACE point-kinetics model
[5].

2. Reactivity Feedback Effect on the Reactor Behaviour…
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Water density and boron concentration were generated by the SRAC2006 code. The core calculations for
determination of the reactivity coefficient parameter are done by using NODAL3 code. The calculation results
showed that the fuel temperature, moderator temperature and boron reactivity coefficients. For the water density
reactivity coefficients, the positive reactivity occurs at the water temperature less than 190 o
C [6]. The AP1000
designed has a better inherent safety since it has the negative total feedback reactivity coefficients. The negative
reactivity coefficient ensures the reactor can stabilize the power when the reactor condition changes, such as fuel
and moderator temperature increase when the power goes to the nominal level [7-12]. The fuel temperature
coefficient (FTC) is reactivity change per fuel temperature change where the moderator temperature and density,
as well as boron concentration, are maintained at constant condition.
PLANT NODALIZATION: The plant nodalization is shown in Figure 1. The nodalization consists of two
loops; broken loop and intact loop. The intact loop simulates the three loops other than the loop containing the
pressurizer which represents the broken loop. The nodalization simulates all the main components of the reactor,
such as the reactor vessel internals, main coolant pumps, steam generators, pressurizer, feed water systems…etc.
For each loop, the ECCs is simulated as two-time dependent junctions (represent the charging system and the
safety injection system) and accumulator. The ECCs capacity for the intact loop is three folds that of the broken
loop. The charging system injects water at primary pressures less than the nominal pressure based on a low
pressurizer water level signal. The safety Injection system serves in the pressure range from 10.34 Mpa and up
to the atmospheric pressure. The accumulators cover the pressure range less than 4.136 Mpa. The core is
simulated as one average channel divided to seventeen radial volumes and also six axial volumes and connected
to the lower and upper plenums. Table 2 presents the main components and their equivalent code number in the
nodalization.
Figure (1) NPP Nodalization [1].

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Table 2 Main Plant Components and the Corresponding Nodalization Numbers
Component Equivalent Code
Hot Leg 100, 200
Cold Leg 116,118, 216, 218
Steam Generator Primary Side 108, 208
Steam Generator Secondary Side 170-180, 270-280
Reactor Primary Pumps 113, 213
Pressurizer/ Accumulators 150 / 190, 290
Main Feed Water System (Main/Auxiliary) 182, 282 / 184, 284
Safety Injection System 191-192, 291-292
Charging System 193-194, 293-294
Reactor Core coolant channel (one channel) 335
Fuel Heat Structures 336
Break Valve 505
II. RESULTS
This result presents the key parameters during the 6-inch SBLOCA. Two groups (A&B) for comparison from
the results during the 6" break Cold Leg loss of coolant accident (SBLOCA) sequences with a scram. The fuel
rod is divided into six vertical nodes and also seventeen radial volumes. In order to investigate the temperature
distribution within the fuel rod,
The group (A) : In real case the reactor scram signal appears as the reactor pressure reached to the set- point
and consequently the control rods start to drop into the core. In the analysis, the calculations is performed with
and without reactivity feed-back, where the reactor scram signal is assumed to be activated at105 sec from the
start reactor operation. This group is comparison between the results with and without feedback Reactivity. In
group (A) the Separable model used to calculate the feedback Reactivity. The dragon neutronic code is used to
calculate the reactivity for all moderator densities (733~73.3 kg/m3
) and for (Doppler coefficient) fuel
temperatures (600, 800, 1000, and 1400K). Figures (2) and (3) demonstrate the variation of the coolant density
and reactivity, respectively through the core. With feedback, which simulate by the bold curve and regular
curve simulate without feed back. In case of without feed back the coolant density decreasing (20 kg/m3
) as the
coolant temperature increasing and maxim reactivity reached at -25 dollar at 400 sec. where in case with feed
back the negative reactivity increased till -55 dollar at 250 sec and density increased till reached (380 kg/m3
).
Figures (4) and (5) show core void fraction and core collapsed water level respectively from figure 4 due to
reactivity feedback the maximum void about 0.8 from figure 5 the minimum core water level is 7 m so there is
no core uncover with reactivity feedback in case without feedback core water level decreases rapidly and its
upper parts are uncovered for a period of time sufficient for heating up the core fuel elements respectively for
case without feed back PCT of 864 K occurs at nearly 430 sec. but in case with feed back the increasing
negative reactivity due to decreasing in density. The core power decreases and the coolant temperature
decreasing so the coolant density increasing again and the core water level increasing to cover the fuel elements
and the clad temperature decreasing reached (550 K) as shown in figure (6).

4. Reactivity Feedback Effect on the Reactor Behaviour…
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0
0.2
0.4
0.6
0.8
1
1.2
0 200 400 600 800 1000 1200
Time (sec)
Voidfraction
voidgfeed 335050000
voidgfeed 335060000
voidg 335050000
voidg 335060000
0
4
8
12
16
0 200 400 600 800 1000 1200
Time (sec)
corewaterlevel(m)
core levelfeed m
core level m
Fig. (5) core water level with and without feedback Reactivity with time.
Fig. (4) Void fraction in the core at the two upper zones with and without feedback
Reactivity with time.

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200
400
600
800
1000
0 200 400 600 800 1000 1200
Time(sec)
Cladtemerature(K)
httempfeed 3360004 17 (K)
httempfeed 3360005 17 (K)
httemp 3360004 17 (K)
httemp 3360005 17 (K)
Fig. (6) cald temperature at fourth and fiveth axial nodes with and without
feedback Reactivity with time.
The second group (B) from results
For Tabular model: for a four-dimensional table (TABLE4a), the dragon code is used to calculate the reactivity
for:
1- Moderator densities (733~73.3 kg/m3
)
2- Fuel temperatures (600~1400K)
3- Moderator temperatures (560~620K)
4- Boron concentration (0-1200ppm)
In this group, both Separable and Tabular (table4) models are compared to analyze the reactivity feed-back
effect. During Cold Leg SBLOCA, the moderator temperature increases and density decreases, and this lead
the negative reactivity component, as shown in figures (7&8) for both separable and tabular models.
Fig. (7) Comparison between Separable and tabular feedback Reactivity for the coolant Density with
time

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For separable model the total reactivity is just the summation of the coolant density reactivity and moderator and
fuel temperature reactivity. In tabular model, the total reactivity is a function of the four reactivities, since all
feed-back mechanisms are dependent the above three and boron concentration. Therefore, the absolute
reactivities calculated by the tabular model are smaller than the separable model, although the coolant density is
smaller than that calculated by separable model as shown in figures 8&9. As shown in figure 10 there is no core
uncover for two cases separable and tabular model.
Fig. (8) Reactivity for the reactor with time at Separable and tabular feedback Reactivity
Fig. (9) Void fraction in the core at the two upper zones at Separable and tabular feedback Reactivity

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Fig. (10) Core water level with time at Separable and tabular feedback Reactivity
The power decreases with the decrease in the flow rate, ( SBLOCA) due to negative net reactivity feed-back
which is dominated by the negative density reactivity feed-back as the coolant heat-up (the coolant density
reactivity is much greater than Doppler reactivity). As the power decreases the fuel and clad temperatures also
begin to de crease, as shown in figure 11. The reactivity will increase due to Doppler effect, and this is the
positive reactivity component (Doppler reactivity).
Fig. (11) Clad temperature at fourth axial nodes with time at Separable and tabular feedback
Reactivity .

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III. CONCLUSIONS
In this study, the characteristic of the 4-loop PWR Westinghouse nuclear power plant for reactivity feedback
coefficients, such as fuel temperature, moderator temperature, moderator density, as well as boron concentration
have been evaluated by using Dragon code. All reactivity coefficients of the reactor are negative. Two cases of
comparison during the worst consequences occur at 6-inch break size, case A comparison between T.H behavior
used Relap5 code with and without feedback (Separable model), and case B comparison between Separable and
tabular calculation. The results show that the importance of the reactivity feed-back on calculating the power
which the key parameter that controls the clad and fuel temperatures to maintain them below their melting point
and therefore prevent core uncover and fuel damage where the fuel temperature, clad temperature and core
water level are in the range.
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