
#1
Jun310, 04:59 AM

P: 3

a fast reactor composed of U235 in form of a cube(point source,strength So) .
calculate the : critical dimensions, critical volumes, critical masses. discuss more in cases of spherical , cylindrical and cubical cores. can i solve this practice by separating in 3 dimensions? and what is the condition at the center of the cubic.? 



#2
Jun310, 06:12 AM

Admin
P: 21,637

The different geometries will give different leakage rates depending on the fast flux at the boundaries and the total surface area. What should the net current be at the center? 



#3
Jun310, 11:23 PM

P: 688

You could get basic results with 1D diffusion theory with "fast" cross sections. There is a simple formula for geometric buckling in a cube.




#4
Jul710, 02:33 PM

P: 24

reactor's geometry
Classic problem.
You just need to set the material buckling to the geometrical buckling for an homogeneous reactor. I would assume it's all 235. By setting these equal, just solve for the length of the cube's side...then you can get volume and mass. Though this doesn't handle the point source. 



#5
Jul710, 04:19 PM

P: 735





#6
Jul810, 07:35 AM

P: 24

I was indicating that my solution doesn't involve the given So...so I'm not sure how correct it would be.
I'm pretty sure my previous solution is correct. That's how it's usually done in practice problems like that. I guess you could solve a 1D diffusion equation to get a flux profile using So, but that wouldn't really answer any of the questions. I'm not completely sure what is meant by "what is the condition at the center...". 



#7
Jul810, 01:13 PM

P: 18





#8
Jul810, 01:25 PM

P: 24

Kind of what I was thinking.
I think the point source only comes into play in solving the condition considering a uniformly distribution source (from the 235) and the point source at the center. 



#9
Jul810, 01:54 PM

P: 735

If I remember my reactor physics correctly (I'll have to break out my D&H tonight), you can only use the geometric/material buckling equivalence if there is no source. Otherwise, you have a timedependent problem for which you must solve the diffusion equation directly.
edit forget that, he's not trying to solve for flux, he just wants the critical dimensions, which only depend on geometry and materials. The source is irrelevant unless you want to solve for the flux itself. 



#10
Jul810, 01:59 PM

P: 24

That's quite likely.




#11
Jul810, 02:09 PM

P: 735





#12
Jul810, 02:14 PM

P: 24

The buckling should change at least a little since you can accept greater leakage for criticality. The shape would still be a cosine, just one with greater curvature, right?
Or perhaps it would be more like a hump...not cosine. 



#13
Jul810, 02:22 PM

P: 735





#14
Jul810, 02:51 PM

Admin
P: 21,637

I was struggling with a fast reactor made of pure U235! As the question is posed, there is no other structural material or coolant. That's not so much a reactor as a recipe for a nuclear explosive. And by critical, is one refering to prompt critical? Normally we don't take reactors there. I was hoping the OP would elaborate.
For a given volume, the cube has the highest leakage, followed by cylinder, then the sphere which has the lowest leakage. 


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