Mathematical modeling of point kinetic equations with temperature feedback for reactivity transient analysis in MTR

Hala Kamal Girgis Selim

doi:10.1515/kern-2020-0066

Article

Mathematical modeling of point kinetic equations with temperature feedback for reactivity transient analysis in MTR

Hala Kamal Girgis Selim

Published/Copyright: February 14, 2022

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From the journal Kerntechnik Volume 87 Issue 1

Abstract

The behavior of the nuclear reactor in response to any sudden change in reactivity is very important for reactor control. Positive reactivity insertions causes power excursion and could have a destructive impact on the reactor core. The aim of the study is to investigate the safety features of a material test reactor (MTR) during reactivity transient with emphasis on the capability of the mathematical modeling using programming language. Therefore a mathematical model using Python3.6; high-level programming language is developed to solve the point kinetic equations taking into account Doppler and moderator feedback effects. The model is validated with AIREKMOD_RR; point kinetic computer code for reactivity transient analysis in nuclear research reactors. The results of the Python model demonstrate the inherent safety features of the MTR reactor. Also, there is good agreement between the results of the Python model and AIREKMOD_RR code, illustrating the efficiency of the Python model in simulating the behavior of the reactor core under reactivity transient.

Keywords: AIREKMOD-RR; MTR; point kinetic; Python3.6; reactivity insertion; reactor safety

Corresponding author: Hala Kamal Girgis Selim, Nuclear and Radiological Regulatory Authority, 3 Ahmed El-Zomar, Nasr City, Cairo, Egypt, E-mail: halakselim@yahoo.com

Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: None declared.
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

Appendix A

The differential equations in our model are implemented as system differential equations that are solved simultaneously in Python with the “Scipy. Integrate” package using function odeint

y = odeint(model, y0, t)

The function odeint requires the following three inputs:

model: Function name that returns derivative values at requested y and t values as dydt = model(y, t)
y0: Initial conditions of the differential states
t: Time points at which the solution should be reported.

The system equations are represented as follow:

d Y d t = A ∗ Y + B

Y [ 1 ] = P Y [ 2 ] = C 1 Y [ 3 ] = C 2 Y [ 4 ] = C 3 Y [ 5 ] = C 4 Y [ 6 ] = C 5 Y [ 7 ] = C 6 Y [ 8 ] = T f Y [ 9 ] = T c Y [ 10 ] = T m

A [ 1 , 1 ] = ρ − β Λ A [ 1 , 2 ] = λ 1 A [ 1 , 3 ] = λ 2 A [ 1 , 4 ] = λ 3

A [ 1 , 5 ] = λ 4 A [ 1,6 ] = λ 5 A [ 1 , 7 ] = λ 6

A [ 2 , 1 ] = β 1 Λ A [ 2 , 2 ] = − λ 1

A [ 3 , 1 ] = β 2 Λ A [ 3 , 3 ] = − λ 2

A [ 4 , 1 ] = β 3 Λ , A [ 4 , 4 ] = − λ 3

A [ 5 , 1 ] = β 4 Λ A [ 5 , 5 ] = − λ 4

A [ 6 , 1 ] = β 5 Λ A [ 6 , 6 ] = − λ 5

A [ 7 , 1 ] = β 6 Λ A [ 7 , 7 ] = − λ 6

A [ 8 , 1 ] = 1 M f C f A [ 8 , 8 ] = − 1 M f C f R c A [ 8 , 9 ] = 1 M f C f R c

A [ 9 , 8 ] = 1 M c C c R c A [ 9 , 9 ] = − ( 1 M c C c R c + 1 M c C c R m ) A [ 9 , 10 ] = 1 M c C c R m

A [ 10 , 9 ] = 1 M m C m R m A [ 10 , 10 ] = − ( 1 M m C m R m + 2 W M m )

B [ 1 ] to B [ 9 ] = 0.0

B [ 10 ] = 2 W M m T i n

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Received: 2020-09-14

Published Online: 2022-02-14

Published in Print: 2022-02-23

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Articles in the same Issue

https://doi.org/10.1515/kern-2020-0066

Keywords for this article

AIREKMOD-RR; MTR; point kinetic; Python3.6; reactivity insertion; reactor safety