Six group point kinetic equation

Click For Summary

Discussion Overview

The discussion revolves around the numerical solution of the six group point kinetic equations, particularly focusing on scenarios involving constant reactivity changes. Participants are exploring methods to implement these solutions using Mathematica, with an emphasis on the mathematical modeling and numerical techniques involved.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant seeks assistance with the numerical solution of the six group point kinetic equations, specifically with a step change in reactivity.
  • Another participant inquires about the experience with the numerical solution of the six group point kinetic equations under similar conditions.
  • A participant questions whether the solution involves one-group diffusion along with six delayed groups, suggesting that the reactivity should be between 0 and beta.
  • One participant outlines the equations they are attempting to solve, providing specific parameters related to a subcritical reactor and the step reactivity change.
  • Another participant confirms that the Runge-Kutta method is a standard approach for solving coupled differential equations in this context.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the specifics of the numerical solution methods or the equations being used, indicating that multiple approaches and uncertainties remain in the discussion.

Contextual Notes

Participants have referenced specific parameters and equations but have not resolved the mathematical steps or assumptions underlying their approaches. The discussion remains open to various interpretations and methods.

Who May Find This Useful

This discussion may be useful for individuals interested in nuclear engineering, mathematical modeling of reactor kinetics, or numerical methods for solving differential equations.

caldus2311
Messages
6
Reaction score
0
Hello.

I would be very thankful with some help with the numerical solution of the six group point kinetic equations, with the constant reactivity (step change).

I would like to do this with the Mathematica.

Thanks.

Dusan
 
Engineering news on Phys.org
Does anyone have any experience with numerical solution of the 6 group point kinetic equation, with the step reactivity change?

Anyone?

Thanks.
 
Dose the solution involve one-group diffusion with 6 delayed groups, so that one is solving the one group neutron diffusion equation and 6 equations for each group of precursors? Presumably the reactivity is between 0 and beta?

I've solved the inhour equation and one group w/ one delyed, but that was 25 years ago, so I may be slow on this.

What equations are you using?
 
Hello.

I am trying to solve the following 7 equations:
dn(t)/dt=ρ-β/l n(t)+∑6i=1 λiCi+Q0/l

dCi(t)/dt= βi* n(t)/l- λiCi.

Where Q0 is constant extra source with neutrons per second.

Lets say that I have the subcritical reactor with the reactivity ρ=-0.0526, which corresponds to k=0,95 (multiplication factor).

Now I increase the reactivity to ρ=-0.04167 (step reactivity change), which corresponds to k=0,96.

What is the n(t) in 6 group approximation.

I already made the analytical solution with one group approximation and now I am trying to find the numerical six group solution. Most probably I will do this with Runge-Kutta method. I just wanted to ask if there is someone with any experiences?

Thanks
 
Runge-Kutta is the standard approach to solving these couple diff EQs.
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
Replies
4
Views
2K
Replies
4
Views
2K
Replies
4
Views
2K
Replies
1
Views
3K
Replies
16
Views
3K
Replies
5
Views
4K
  • · Replies 11 ·
Replies
11
Views
2K