new example eighth-sphere in milonga

[Jeremy Theler]

Hey guys

After the discussion on saturday, I have added an (in my perspective) improved version of the one-group reflected sphere to the examples directory. You can see it in the latest commit:

https://bitbucket.org/seamplex/milonga/commits/06ba147f53d756457fba96a5ec67466f4f484a22

Note also that FLUX_POST was fixed in the sense that if volumes (elements) are used, the fluxes are written as cell(node)-centered data.

Chaco, please let us know if this improved version fits your needs. An interesting alternative would be to make parametric runs over lc to check convergence.

Also, this is a nice problem to write the "Milonga problem case book" including problems with analytical solutions, benchmarks, etc (like those that Pablo already wrote with the transient branch). Do you have any accompanying text that discusses the analytical solution?

Regards

--

jeremy theler

www.seamplex.com

[Hector Lestani]

Hello all,
I have no written explanation on what we did, but I will explain a little bit now.
We were making analytical comparisons of bare and reflected reactors with spheric and cubic geometries.
A bare spheric critical reactor is supposed to use only 80% of the mass with respect to a bare cubic critical reactor, i.e., a sphere is more efficient than a cube to achieve criticality.
When comparing reflected reactors (always critical), due to a mistake on the iterative scheme*, the cube resulted in less volume than the sphere, which sounded wrong for me. After finding the mistake on the iterative scheme (and we still have to make the fine numbers), we wanted to have milonga's numbers also, because students are familiar with it, they have used it to solve reflected cylindrical reactors in a multigroup scheme.

In the attached files you can see milonga's numbers, K as a function of dimension or volume (for a very gross meshing, provided a finer one would have required more time). There you can see that, as expected by the analytical solutions, a sphere is more efficient than a cube, although after adding a reflector, this difference is vanishing.

We should keep in mind that our hand-made analytical solutions impose null flux at the borders, while milonga imposes null incoming current (which is more correct), so there is a difference in the results.

With more time, besides the parametric calculations on lc as you suggest and I agree, it will be interesting to try different fractions of the sphere. I mean, now we are modeling 1/8th, but we could start modeling a decreasing volume of the sphere, which also requires a mesh refinement, and see when the volume decrease is counterbalanced by the mesh refinement in terms of memory usage and run time.

Any way, I have to leave now.

I expect to come back to this topic afterwards.

Thank you all and look forward to read you here :)


* in a multidimensional geometry, as a cube, an iterative procedure is needed to solve it analytically, because you can only solve one direction at a time and the other 2 dimensions have to be replaced by adding leakage to the absorption.

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[Jeremy Theler]

On Mon, 2018-05-07 at 10:58 -0300, Hector Lestani wrote:

Hello all,
I have no written explanation on what we did, but I will explain a little bit now.
We were making analytical comparisons of bare and reflected reactors with spheric and cubic geometries.

Oh! I never learn! First "why before what" [1] and and then "the five why rule" [2]

[1] https://www.ted.com/talks/simon_sinek_how_great_leaders_inspire_action

[2] https://en.wikipedia.org/wiki/5_Whys

So what you want to do is to compare the keff of a reflected sphere vs a reflected cube, keeping what constant? the mass?

This can be done in milonga with a parametric run on a parameter say f in (0,1). For f = 0, you get a cube. For f = 1 you get a cylinder. How? Start from a cube and apply a fillet operation based on f (because of limitations on the OpenCASCADE kernel f cannot be either 0 or 1, but these two degenerate cases can be treated differently).

See the attached figures for f=0.1, f=0.5 and f=0.9

A bare spheric critical reactor is supposed to use only 80% of the mass with respect to a bare cubic critical reactor, i.e., a sphere is more efficient than a cube to achieve criticality.

See the attached .geo.m4 and .mil. This is what one gets:

gtheler@tom:~/run/milonga/chaco$ milonga cubesphere.mil  
# f     keff
0.1     1.13706
0.2     1.13767
0.3     1.13682
0.4     1.13765
0.5     1.1357
0.6     1.13488
0.7     1.13302
0.8     1.12939
0.9     1.12547
gtheler@to:~/run/milonga/chaco

This is just a bare reactor and the radius/cube length is kept constant. For sure you can see how to generalize it to reflected cases and keeping constant the mass or whatever.

See why I told you that you are "under-using" milonga?

Tell me with what other piece of software (let alone open source) you can do this.

When comparing reflected reactors (always critical), due to a mistake on the iterative scheme*, the cube resulted in less volume than the sphere, which sounded wrong for me. After finding the mistake on the iterative scheme (and we still have to make the fine numbers), we wanted to have milonga's numbers also, because students are familiar with it, they have used it to solve reflected cylindrical reactors in a multigroup scheme.

I bet this scheme can be implemented in wasora so you can actually take the difference between milonga's keff and the "iterative scheme" k.

In the attached files you can see milonga's numbers, K as a function of dimension or volume (for a very gross meshing, provided a finer one would have required more time). There you can see that, as expected by the analytical solutions, a sphere is more efficient than a cube, although after adding a reflector, this difference is vanishing.

ok

We should keep in mind that our hand-made analytical solutions impose null flux at the borders, while milonga imposes null incoming current (which is more correct), so there is a difference in the results.

you can ask milonga to do so by setting BC null instead of BC vacuum

With more time, besides the parametric calculations on lc as you suggest and I agree, it will be interesting to try different fractions of the sphere. I mean, now we are modeling 1/8th, but we could start modeling a decreasing volume of the sphere, which also requires a mesh refinement, and see when the volume decrease is counterbalanced by the mesh refinement in terms of memory usage and run time.

Another easy-bitzy for gmsh+milonga

Any way, I have to leave now.

I expect to come back to this topic afterwards.

Thank you all and look forward to read you here :)

me too :-)

* in a multidimensional geometry, as a cube, an iterative procedure is needed to solve it analytically, because you can only solve one direction at a time and the other 2 dimensions have to be replaced by adding leakage to the absorption.

any equation or reference is appreciated, I though reflected cases did not have anylitical solutions

[Ramiro Vignolo]

Really nice!

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[Hector Lestani]

Answer between lines...

On 07/05/18 15:49, Jeremy Theler wrote:

On Mon, 2018-05-07 at 10:58 -0300, Hector Lestani wrote:

Hello all,
I have no written explanation on what we did, but I will explain a little bit now.
We were making analytical comparisons of bare and reflected reactors with spheric and cubic geometries.

Oh! I never learn! First "why before what" [1] and and then "the five why rule" [2]

[1] https://www.ted.com/talks/simon_sinek_how_great_leaders_inspire_action

[2] https://en.wikipedia.org/wiki/5_Whys

So what you want to do is to compare the keff of a reflected sphere vs a reflected cube, keeping what constant? the mass?

The comparison is between critical masses, i.e., between volumes associated to K=1.

This can be done in milonga with a parametric run on a parameter say f in (0,1). For f = 0, you get a cube. For f = 1 you get a cylinder. How? Start from a cube and apply a fillet operation based on f (because of limitations on the OpenCASCADE kernel f cannot be either 0 or 1, but these two degenerate cases can be treated differently).

See the attached figures for f=0.1, f=0.5 and f=0.9

Very nice for a computational course. Not for a first reactor physics course, where emphasis is put on analytical solutions, we might call this the "Fermi" approach :)

A bare spheric critical reactor is supposed to use only 80% of the mass with respect to a bare cubic critical reactor, i.e., a sphere is more efficient than a cube to achieve criticality.

See the attached .geo.m4 and .mil. This is what one gets:

gtheler@tom:~/run/milonga/chaco$ milonga cubesphere.mil  
# f     keff
0.1     1.13706
0.2     1.13767
0.3     1.13682
0.4     1.13765
0.5     1.1357
0.6     1.13488
0.7     1.13302
0.8     1.12939
0.9     1.12547
gtheler@to:~/run/milonga/chaco

According to this, when you go spherical your K goes down. This could be wrongly interpreted. The reason for such behavior is that when you change these geometries, you are not keeping mass (or volume) constant. Should that be the case, you would obtain higher K as you approach to a sphere.

This is just a bare reactor and the radius/cube length is kept constant. For sure you can see how to generalize it to reflected cases and keeping constant the mass or whatever.

See why I told you that you are "under-using" milonga?

Tell me with what other piece of software (let alone open source) you can do this.

I have no doubts about the great milonga's capabilities. But our focus is put on physics learning at this stage, not on code usage.

When comparing reflected reactors (always critical), due to a mistake on the iterative scheme*, the cube resulted in less volume than the sphere, which sounded wrong for me. After finding the mistake on the iterative scheme (and we still have to make the fine numbers), we wanted to have milonga's numbers also, because students are familiar with it, they have used it to solve reflected cylindrical reactors in a multigroup scheme.

I bet this scheme can be implemented in wasora so you can actually take the difference between milonga's keff and the "iterative scheme" k.

The focus is put on analytical solutions, computer assistance is not allowed during exams.

In the attached files you can see milonga's numbers, K as a function of dimension or volume (for a very gross meshing, provided a finer one would have required more time). There you can see that, as expected by the analytical solutions, a sphere is more efficient than a cube, although after adding a reflector, this difference is vanishing.

ok

We should keep in mind that our hand-made analytical solutions impose null flux at the borders, while milonga imposes null incoming current (which is more correct), so there is a difference in the results.

you can ask milonga to do so by setting BC null instead of BC vacuum

This is really really really great. I didn't know about this BC.
This is going to be very useful next year. This year's practice has already been done.
Thank you for saying this!

With more time, besides the parametric calculations on lc as you suggest and I agree, it will be interesting to try different fractions of the sphere. I mean, now we are modeling 1/8th, but we could start modeling a decreasing volume of the sphere, which also requires a mesh refinement, and see when the volume decrease is counterbalanced by the mesh refinement in terms of memory usage and run time.

Another easy-bitzy for gmsh+milonga

Any way, I have to leave now.

I expect to come back to this topic afterwards.

Thank you all and look forward to read you here :)

me too :-)

* in a multidimensional geometry, as a cube, an iterative procedure is needed to solve it analytically, because you can only solve one direction at a time and the other 2 dimensions have to be replaced by adding leakage to the absorption.

any equation or reference is appreciated, I though reflected cases did not have anylitical solutions

The iterative scheme is described in equations 10-73, page 333 of "Nuclear Reactor Theory", Lamarsh.

Cheers :)

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[Hector Lestani]

One more thing regarding this: "See why I told you that you are "under-using" milonga?"...
I completely agree, we are using a bazooka to kill a fly, we are using a multigroup finite element implementation to solve HOMOGENEOUS one-group diffusive systems... nothing else to add, this speaks on it's own.

Any way, we discuss this every year. We have only one class for this milonga practice. So why not use a simpler and faster code? (just like before milonga existance)... The answer is "we are preparing our students with strong physics knowledge and versatile tools, we just give them the kick-off, it's up to them go deeper and expand possibilities"... Am I selling well our Nuclear Engineering program? jajajaja

Thanks for the valuable exchange guys :)

To view this discussion on the web visit https://groups.google.com/a/seamplex.com/d/msgid/wasora/c2b65bf9-b697-074a-ca46-50691090615a%40cab.cnea.gov.ar.

[Jeremy Theler]

On Mon, 2018-05-07 at 16:33 -0300, Hector Lestani wrote:

Answer between lines...

On 07/05/18 15:49, Jeremy Theler wrote:

On Mon, 2018-05-07 at 10:58 -0300, Hector Lestani wrote:

Hello all,
I have no written explanation on what we did, but I will explain a little bit now.
We were making analytical comparisons of bare and reflected reactors with spheric and cubic geometries.

Oh! I never learn! First "why before what" [1] and and then "the five why rule" [2]

[1] https://www.ted.com/talks/simon_sinek_how_great_leaders_inspire_action

[2] https://en.wikipedia.org/wiki/5_Whys

So what you want to do is to compare the keff of a reflected sphere vs a reflected cube, keeping what constant? the mass?

The comparison is between critical masses, i.e., between volumes associated to K=1.

this way you will always get keff=1, I don't get it...

This can be done in milonga with a parametric run on a parameter say f in (0,1). For f = 0, you get a cube. For f = 1 you get a cylinder. How? Start from a cube and apply a fillet operation based on f (because of limitations on the OpenCASCADE kernel f cannot be either 0 or 1, but these two degenerate cases can be treated differently).

See the attached figures for f=0.1, f=0.5 and f=0.9

Very nice for a computational course. Not for a first reactor physics course, where emphasis is put on analytical solutions, we might call this the "Fermi" approach :)

Well, I would have loved to have something like this back in my times. You know how to solve a cube and a sphere... but what happens in the middle?

Another thing: milonga can perfectly compute the 1d thermal shoulder effect in 2 groups. Can't you show the students these actual results instead of a hand-made plot (like we were shown)?

A bare spheric critical reactor is supposed to use only 80% of the mass with respect to a bare cubic critical reactor, i.e., a sphere is more efficient than a cube to achieve criticality.

See the attached .geo.m4 and .mil. This is what one gets:

gtheler@tom:~/run/milonga/chaco$ milonga cubesphere.mil  
# f     keff
0.1     1.13706
0.2     1.13767
0.3     1.13682
0.4     1.13765
0.5     1.1357
0.6     1.13488
0.7     1.13302
0.8     1.12939
0.9     1.12547
gtheler@to:~/run/milonga/chaco

According to this, when you go spherical your K goes down. This could be wrongly interpreted. The reason for such behavior is that when you change these geometries, you are not keeping mass (or volume) constant. Should that be the case, you would obtain higher K as you approach to a sphere.

sure, I said this was "constant a" approach and that you can work out the details for "constant volume" (see below)

If you help me with my PhD issues I will write a case study for the students :-)

This is just a bare reactor and the radius/cube length is kept constant. For sure you can see how to generalize it to reflected cases and keeping constant the mass or whatever.

See why I told you that you are "under-using" milonga?

Tell me with what other piece of software (let alone open source) you can do this.

I have no doubts about the great milonga's capabilities. But our focus is put on physics learning at this stage, not on code usage.

for sure, but half of milonga's scope is "academic problems" (see https://www.seamplex.com/papers/2014-milonga-design.pdf )

and this cube-sphere problem is something that can help a student to understand how reactor physics work, along with the thermal shoulder effect, parametric runs on the length of a 1D reflected slab, etc

When comparing reflected reactors (always critical), due to a mistake on the iterative scheme*, the cube resulted in less volume than the sphere, which sounded wrong for me. After finding the mistake on the iterative scheme (and we still have to make the fine numbers), we wanted to have milonga's numbers also, because students are familiar with it, they have used it to solve reflected cylindrical reactors in a multigroup scheme.

I bet this scheme can be implemented in wasora so you can actually take the difference between milonga's keff and the "iterative scheme" k.

The focus is put on analytical solutions, computer assistance is not allowed during exams.

too bad :-( I remember in one exam I was asked to integrate and ODE with runge kutta with pencil and paper

This does not make any sense. Invest that time into solving actual problems instead!

In the attached files you can see milonga's numbers, K as a function of dimension or volume (for a very gross meshing, provided a finer one would have required more time). There you can see that, as expected by the analytical solutions, a sphere is more efficient than a cube, although after adding a reflector, this difference is vanishing.

ok

We should keep in mind that our hand-made analytical solutions impose null flux at the borders, while milonga imposes null incoming current (which is more correct), so there is a difference in the results.

you can ask milonga to do so by setting BC null instead of BC vacuum

This is really really really great. I didn't know about this BC.

I know, documentation is missing. Should be done if I can switch back to my PhD thesis...

This is going to be very useful next year. This year's practice has already been done.
Thank you for saying this!

See https://www.seamplex.com/docs/imef-2013-12-15.pdf for some examples

One more thing regarding this: "See why I told you that you are "under-using" milonga?"...
I completely agree, we are using a bazooka to kill a fly, we are using a multigroup finite element implementation to solve HOMOGENEOUS one-group diffusive systems... nothing else to add, this speaks on it's own.

Actually it is milonga's objective to be used to solve academic problems. This is 50% the reason I coded it.

Any way, we discuss this every year. We have only one class for this milonga practice. So why not use a simpler and faster code? (just like before milonga existance)... The answer is "we are preparing our students with strong physics knowledge and versatile tools, we just give them the kick-off, it's up to them go deeper and expand possibilities"... Am I selling well our Nuclear Engineering program? jajajaja

The statement that "milonga is free and open source" ought to be enough.
https://www.gnu.org/education/edu-schools.en.html

On a more practical case, because with milonga you can actually "see" how the flux is distributed. You can pan and rotate the damn sphere. You can change the input parameters. You can play. I'd rather be able to do this than to stick to a plot from a book written in the 1960s. Those students who do not care, can go on with other subjects. But please give the chance to those who do to play and understand physics in a more enjoyable way. In Spanish: "no niegues el genio para no ofender a mediocre"

Thanks for the valuable exchange guys :)

Thank you!

[Hector Lestani]

On 08/05/18 08:21, Jeremy Theler wrote:

On Mon, 2018-05-07 at 16:33 -0300, Hector Lestani wrote:

Answer between lines...

On 07/05/18 15:49, Jeremy Theler wrote:

On Mon, 2018-05-07 at 10:58 -0300, Hector Lestani wrote:

Hello all,
I have no written explanation on what we did, but I will explain a little bit now.
We were making analytical comparisons of bare and reflected reactors with spheric and cubic geometries.

Oh! I never learn! First "why before what" [1] and and then "the five why rule" [2]

[1] https://www.ted.com/talks/simon_sinek_how_great_leaders_inspire_action

[2] https://en.wikipedia.org/wiki/5_Whys

So what you want to do is to compare the keff of a reflected sphere vs a reflected cube, keeping what constant? the mass?

The comparison is between critical masses, i.e., between volumes associated to K=1.

this way you will always get keff=1, I don't get it...

Yes, you are right, you always get Keff=1 but different volumes, so you can compare the fissile masses needed for each geometry, that are not the same (spheric_mass < cubic_mass).

This can be done in milonga with a parametric run on a parameter say f in (0,1). For f = 0, you get a cube. For f = 1 you get a cylinder. How? Start from a cube and apply a fillet operation based on f (because of limitations on the OpenCASCADE kernel f cannot be either 0 or 1, but these two degenerate cases can be treated differently).

See the attached figures for f=0.1, f=0.5 and f=0.9

Very nice for a computational course. Not for a first reactor physics course, where emphasis is put on analytical solutions, we might call this the "Fermi" approach :)

Well, I would have loved to have something like this back in my times. You know how to solve a cube and a sphere... but what happens in the middle?

Another thing: milonga can perfectly compute the 1d thermal shoulder effect in 2 groups. Can't you show the students these actual results instead of a hand-made plot (like we were shown)?

I am sure you would have loved that, I know your interests. But before playing with numerical simulations, students have to be really in touch with the physics and with the models that milonga has inside. After knowing the models, they can discuss the results.

Students calculate by hand the thermal shoulder in a light reflector. When the time for the milonga practice arrives, they compare the shoulder position and height for different reflector cross sections, using milonga, and analyzing the results.

Despite we discuss every year how much time is devoted to analytical and to numerical solutions, we have to fit to the engineering program, regulated by law, inspected by CONEAU, because we give a licensed Engineering diploma. So we discuss a lot, but we can't just make a decision of modifying a course.

A bare spheric critical reactor is supposed to use only 80% of the mass with respect to a bare cubic critical reactor, i.e., a sphere is more efficient than a cube to achieve criticality.

See the attached .geo.m4 and .mil. This is what one gets:

gtheler@tom:~/run/milonga/chaco$ milonga cubesphere.mil  
# f     keff
0.1     1.13706
0.2     1.13767
0.3     1.13682
0.4     1.13765
0.5     1.1357
0.6     1.13488
0.7     1.13302
0.8     1.12939
0.9     1.12547
gtheler@to:~/run/milonga/chaco

According to this, when you go spherical your K goes down. This could be wrongly interpreted. The reason for such behavior is that when you change these geometries, you are not keeping mass (or volume) constant. Should that be the case, you would obtain higher K as you approach to a sphere.

sure, I said this was "constant a" approach and that you can work out the details for "constant volume" (see below)

If you help me with my PhD issues I will write a case study for the students :-)

If I can help you in any way with your PhD thesis, it will be a pleasure for me to do so. I ask nothing in return but the pleasure of helping a well established neutronic code developer ;)
Should you write a case study for the students, keep in mind the limited time available. Don't kill the students. And if you blow their minds, don't make them crazy, ok?

This is just a bare reactor and the radius/cube length is kept constant. For sure you can see how to generalize it to reflected cases and keeping constant the mass or whatever.

See why I told you that you are "under-using" milonga?

Tell me with what other piece of software (let alone open source) you can do this.

I have no doubts about the great milonga's capabilities. But our focus is put on physics learning at this stage, not on code usage.

for sure, but half of milonga's scope is "academic problems" (see https://www.seamplex.com/papers/2014-milonga-design.pdf )

and this cube-sphere problem is something that can help a student to understand how reactor physics work, along with the thermal shoulder effect, parametric runs on the length of a 1D reflected slab, etc

Ok, so we have a line to cooperate on.

When comparing reflected reactors (always critical), due to a mistake on the iterative scheme*, the cube resulted in less volume than the sphere, which sounded wrong for me. After finding the mistake on the iterative scheme (and we still have to make the fine numbers), we wanted to have milonga's numbers also, because students are familiar with it, they have used it to solve reflected cylindrical reactors in a multigroup scheme.

I bet this scheme can be implemented in wasora so you can actually take the difference between milonga's keff and the "iterative scheme" k.

The focus is put on analytical solutions, computer assistance is not allowed during exams.

too bad :-( I remember in one exam I was asked to integrate and ODE with runge kutta with pencil and paper

This does not make any sense. Invest that time into solving actual problems instead!

There is so much to say about this. We could discuss many hours, but I will try to summarize as follows: we want our graduate to be code developers, not code users. Once there was a student here, Germán Theler, perhaps you know him. He is developing a code (with other people) because he spent time solving runge kutta by hand, not because he used an already developed code.

In the attached files you can see milonga's numbers, K as a function of dimension or volume (for a very gross meshing, provided a finer one would have required more time). There you can see that, as expected by the analytical solutions, a sphere is more efficient than a cube, although after adding a reflector, this difference is vanishing.

ok

We should keep in mind that our hand-made analytical solutions impose null flux at the borders, while milonga imposes null incoming current (which is more correct), so there is a difference in the results.

you can ask milonga to do so by setting BC null instead of BC vacuum

This is really really really great. I didn't know about this BC.

I know, documentation is missing. Should be done if I can switch back to my PhD thesis...

This is going to be very useful next year. This year's practice has already been done.
Thank you for saying this!

See https://www.seamplex.com/docs/imef-2013-12-15.pdf for some examples

One more thing regarding this: "See why I told you that you are "under-using" milonga?"...
I completely agree, we are using a bazooka to kill a fly, we are using a multigroup finite element implementation to solve HOMOGENEOUS one-group diffusive systems... nothing else to add, this speaks on it's own.

Actually it is milonga's objective to be used to solve academic problems. This is 50% the reason I coded it.

Any way, we discuss this every year. We have only one class for this milonga practice. So why not use a simpler and faster code? (just like before milonga existance)... The answer is "we are preparing our students with strong physics knowledge and versatile tools, we just give them the kick-off, it's up to them go deeper and expand possibilities"... Am I selling well our Nuclear Engineering program? jajajaja

The statement that "milonga is free and open source" ought to be enough.
https://www.gnu.org/education/edu-schools.en.html

On a more practical case, because with milonga you can actually "see" how the flux is distributed. You can pan and rotate the damn sphere. You can change the input parameters. You can play. I'd rather be able to do this than to stick to a plot from a book written in the 1960s. Those students who do not care, can go on with other subjects. But please give the chance to those who do to play and understand physics in a more enjoyable way. In Spanish: "no niegues el genio para no ofender a mediocre"

Ok, I agree with this.

Thanks for the valuable exchange guys :)

Thank you!

You are welcome :)

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