# Heating of molten metal

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December 19, 2016, 06:46
Heating of molten metal
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Join Date: Dec 2016
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Hy all,

for my bachelor-work i need to simulate a molten metal target. This target is rotating in a ring and the heat source is a electron beam. The environmental conditions are vacuum and roomtemperature.
The outer ring is shown in the picture (blue = molten metal, grey = outer ring).

I‘m using OpenFoam 4.1.

My professor suggested the bouyantBoussinesqSimpleFoam, because of the additional centrifugal force.

The start of the simulation is the uniform melting temperature of the metal.
The heat source is a electron beam on the surface.
I was thinking to simplify the case with the assumption that the outer ring rotates very fast. With this I do the assumption that there is a focal track instead of a focal point and over the whole ring are uniform conditions.
I want to define a constant power as energy source. This source should be a 3D-source.

How do i customize the solver for this boundary condition?

But I don‘t know how to customize the Solver for this problem.
Is this the right solver for the problem?
How can I add radiation and which model is the right one?

Do i have to pay attention on other physical conditions, like the marangoni flow?
Have somebody experiences in heating with electron beam and can help me this equations or papers?

Kind regards,
ChrisBa
Attached Images
 Target.jpg (42.6 KB, 45 views)

Last edited by ChrisBa; December 19, 2016 at 09:04.

 December 20, 2016, 06:12 #2 Member   Join Date: Dec 2016 Posts: 65 Rep Power: 2 Please Help me

 December 21, 2016, 06:05 #3 Member   Join Date: Dec 2016 Posts: 65 Rep Power: 2 Hello all, does somebody have knowledge about electron beam melting and maybe implement it in OpenFoam? Kind regards, Christian

 January 3, 2017, 06:04 #4 Member   Join Date: Dec 2016 Posts: 65 Rep Power: 2 Hello, can anyone help me please. Regards Christian

 January 5, 2017, 14:10 #5 Senior Member   Alexey Matveichev Join Date: Aug 2011 Location: Nancy, France Posts: 1,666 Rep Power: 27 Hi, Since it is your bachelor-work you should pose all these questions to your professor. Yet, to start discussion, here is a list of my questions (part of them are the same as in my e-mail): 1. What physical phenomena you would like to simulate? From your post the only thing is clear: you need to describe electron beam energy deposition at the surface. The rest of the list is just more detailed question no. 1: 2. Do you need to simulate steady state or you are interested in transient state? 3. Do you cool your ring somehow? Radiation? Water cooling? Or you have ring of liquid metal, which is heated by electron beam (BTW where is EB gun located?) and at the same time is cooled by big outer ring? 4. Do you need to account for free surface deformation? 5. (partly answering you question about Marangoni flow) Do you have strong temperature gradients in your problem? What are dimensions of your rings? For certain problems buoyancy will just prevail and you can add Marangoni, yet it won't change much overall flow. 6. Do you need to simulate phase change? 7. Do you think you flow is turbulent? 8. Do you need mass transfer? 9. Finally, what do you want to learn from your simulations? Flow field? Temperature distribution?

 January 9, 2017, 05:10 #6 Member   Join Date: Dec 2016 Posts: 65 Rep Power: 2 Hi alexeym, thank you for your help. 1. I want to simulate the heating of molten metal and the flow through heating. I need to descripe the energy desposition at the surface and in the depth, because the electrons penetrate in the metal. Along the way through the metal they lose energy. The outer ring and the molten metal are rotating. Because of this a centrifugal force is acting on the molten metal. The picture "Target" shows the molten metal in blue and the outer ring in grey. 2. At the beginning I should simulate steady state. The boundary conditions are: - The temperature of the 3 faces of the outer ring, that are touching the molten metal, is melting temperature of the molten metal. This temperature need to stay constant. - The enviromental conditions are vacuum and a room temperature - The max. temperature of the molten metall is the evaporating temperatur minus deltaT At the end I should control if there is a steady state or not. 3. The molten metal is cooled through radiation on the free surface and convection through the resulting flow on the 3 faces of the outer ring. At the same there is heating through the electron beam. Did I forget a cooling mechanisms? How the cooling of the outer ring works is not necessary. 4. I can't say that for sure. Is there a deformation in molten state? 5. It is hard to say, if there are strong temperatur gradients. The electron beam is changeable. I don't have a fix power of the beam. 6. No I don't have to simulate this. Maybe at the end of the work, if I have time. 7. I can't say that. 8. The ring of molten metal is closed. So i don't need a mass transfer. 9. I want to learn from the siumlation: - if there is a steady state. - what temperatures are appearing in the steady state - if there is a flow in the profile of the ring (in the picture "Target" the x,y-plane) - the heat flows at the borders I hope you can understand, what i mean. I'm not a native speaker. Regards Christian

 January 9, 2017, 09:57 #7 Senior Member   Alexey Matveichev Join Date: Aug 2011 Location: Nancy, France Posts: 1,666 Rep Power: 27 Hi, More questions: 1. As I understood from what you have described, you do not need to simulation outer ring, it is just constant temperature boundary conditions. Is it correct? 2. What is the angular speed of rotation? I.e. can you assume uniform distribution of beam energy over the inner surface of molten ring? 3. You do not know whether you process is in steady state. You need to check it, or even estimate transience time? 4. Free surface deformation depends on beam energy (obviously). For certain conditions we can neglect it; for certain conditions we can neglect it, though deformations are quite strong; for certain conditions we have to track free surface. 5. You did not mention ring dimensions. Right now from what you have described I see simulation this way: - Simulation is transient, so use bouyantBoussinesqPimpleFoam. - It is 2D with axial symmetry. - You describe your beam as a surface source term using fvOptions. - Solver has radiation source term, so either you configure it, or implement yourself using fvOptions. - You add functionObject, which calculates energy balances of your system. - You run simulation till Ein + Out == 0 (steady state). I hope you can understand, what i mean. I'm not a native speaker also.

 January 9, 2017, 10:36 #8 Member   Join Date: Dec 2016 Posts: 65 Rep Power: 2 1. Correct. I don't need to simulate the outer ring. The ring is represented of the constant temperature condition. The temperature of the 3 faces, that are touching the molten metal, should not rise. 2. For my first simulations i could say, that the angular is very fast. Because of this I have a focal track with uniform conditions. I make the assumption that there are uniform conditions at the whole molten metal ring. At least the min. centrifugal force is fifth times more than the weigth force. 3. I really can't say that. I hope that buoyantBoussinesqPimpleFoam can show me this. 4. The beam energy is variable. When can I neglect it? 5. To make it simple for me. I should make the assumption that the inner diameter is very big. I should simulate the problem in 2D. Because of the great diameter I can neglect the curve. The Solver or the case should make it simple to change this assumption in real dimensions. I don't know the dimensions of the ring or the electron beam. I should learn this through the simulation. At the end I shall make the statement: For this dimensions, this power and this material the condition are fulfilled and the process works. The current status: - I use the boundary conditions empty for 2D - I use buoyantBoussinesqSimpleFoam (Because of the idea that the conditions can be transferred on Pimple) - I want to add the radiation on the surface. But I dont know, what model I should use. I have some questions: 1. How can I describe the source this fvOptions? And can I describe it in the dephts? 2. Can you help me this the radiations? 3. What do you mean with energy balances and functionObject? 4. Which boundary conditions i have to use for the constant temperature of the 3 faces? The temperature should be constant over time at these faces.

 January 9, 2017, 14:55 #9 Senior Member   Alexey Matveichev Join Date: Aug 2011 Location: Nancy, France Posts: 1,666 Rep Power: 27 Hi, 1. You can take a look at implemented sources in \$FOAM_SRC/fvOptions/sources/derived. Again: what is the energy of electrons? what at dimensions of the rings? what is the molten metal? Are you sure, your mesh resolution will be sufficient to resolve energy deposition in depth? 2. What kind of help do you need? Since it is opaque metal, either use corresponding radiation model, or chose emissivity and implement grey body radiation using fvOptions. 3. Energy balances are just energy in - energy out. The easiest way to control it is to integrate temperature over simulation domain (multiply by rho*Cp, add latent heat, and it becomes enthalpy). In steady state total enthalpy of the system is constant. To integrate field over the domain you can use volRegion functionObject (\$FOAM_SRC/functionObjects/field/fieldValues/volRegion). 4. fixedValue? But is it really known and fixed?

 January 10, 2017, 03:45 #10 Member   Join Date: Dec 2016 Posts: 65 Rep Power: 2 Hi, 1. I must find this during the bachelor-work. I don't have concrete dimensions. The source can be from 1eV to 1GeV. The dimensions of the ring can be various. I was thinking of using pure metals. Maybe I must refine my mesh local at the source. 2. I need help with integrating the source and the radiation. I want to begin with the radiation and then with the source. I don't know any of the radiation models of openfoam and how to use them correct. Choosing the right conditions are a great help. 3. This is a example there i need help. 4. I should stay fixed on this temperature. (It's a wish) Thank you very much for your help.

 January 10, 2017, 04:00 #11 Member   Join Date: Dec 2016 Posts: 65 Rep Power: 2 I make a assumption of the ring at the beginning too. I say that the diameter are very big. So I say, that there is no curve for my 2D-case.

 January 10, 2017, 04:31 #12 Senior Member   Alexey Matveichev Join Date: Aug 2011 Location: Nancy, France Posts: 1,666 Rep Power: 27 Hi, So basically we can say that... 1. Problem is not set. Since depending on electron energy you get different deposition mechanism, you get different backscattering, you get different heating and as a result different set of phenomena you need to account for. 2. For some strange reason you would like to simulate electron energy deposition in depth instead of just assuming uniform energy distribution at the surface. 3. For some strange reason you are insisting on simulating flat case instead of axially symmetric. 4. Situation with contact temperature is unclear. Either you can fix it, or you need to get this temperature from simulation and show that it is below melting temperature. So... - get REASONABLE physical description of your system and of what you are trying to simulate. Right now it is "I want to simulate something I know very little about". - construct NUMERICAL MODEL (equations you would like to solve, initial and boundary conditions, etc) of your process. after this you can proceed with TECHNICAL details about implementation of your sources and balances.

 January 10, 2017, 05:04 #13 Member   Join Date: Dec 2016 Posts: 65 Rep Power: 2 Hi, 1. Ok. Are there books or papers, that can help me? 2. Because were is a energy desposition in the depth. The electrons are losing energy by traveling through the material. You are correct that the most heat is at the surface, but there is a heating in the depth too. 3. Do you mean the boundariers cyclic and wedge? Sorry I don't understand, why my assumption is wrong for this. If I use 2D case, I mean the section of the ring in the x,y-plane (picture before), and this piece is really small, then I can neglect the curvature. 4. Ok I understand.

 January 10, 2017, 05:10 #14 Member   Join Date: Dec 2016 Posts: 65 Rep Power: 2 It is possible to make a theoretical model and then adapt this step by step. Or am I wrong?

 January 10, 2017, 05:45 #15 Senior Member   Alexey Matveichev Join Date: Aug 2011 Location: Nancy, France Posts: 1,666 Rep Power: 27 Hi, 1. Google? "electron backscattering", "electron penetration depth". 2. http://digitalcommons.usu.edu/cgi/vi...ontext=mp_post Your penetration depth is of order of mm. Using ESTAR it is possible to estimate penetration depth for GeV electrons. 3. Who said that your assumptions are wrong? They are just strange. Since you can simulate a sector of your ring the same way you simulate "infinite radius" ring, why insist on infinite radius? It is possible to make theoretical model. But the first step is to make it, so step zero is to understand what is happening in your system. And for this you have your advisor.

 January 10, 2017, 07:00 #16 Member   Join Date: Dec 2016 Posts: 65 Rep Power: 2 1. Ok I have to say that I excluded the backscattering. I wanted to solve this problem step by step. The next step is the cooling mechanismen of the molten metal and the correct boundaries for these. You said that I can use opaque or grey body for radiation. I don't understand the models in openfoam for radiation. 2. I look in the pdf. Thanks for this. Thanks for the hint about this program. I have formulas about the penetration depth. 3. Because there aren't real products for this. This bachelor-work starts from the begin of this topic. There are no concrete dimensions I can use. I have to define the measures. Because of this I want to make many assumptions and then adapt that to real. Thanks for this. I talk with my advisor and answer you.

 January 11, 2017, 09:53 #17 Member   Join Date: Dec 2016 Posts: 65 Rep Power: 2 Hi alexeym, I read the pdf of your link. I have to say that the electron desposition, scattering and penetration are very complex. I‘m thinking that only the electron desposition and the penetration are important. Maybe there are experimental equations to describe this.The backscattering is important too. The effects, like Compton scattering, are not important for the simulation. I don‘t want to simulate the way of aelectron through matter. These effects are the cause of the energy desposition. Or am I wrong? Is it possible to integrate the poblem of the energy despostion at the end? The Maragoni-Effect is neglected at the beginning, because you say that it doesn‘t change to much of the flow. At the end maybe I want to integrate it. Now I want to integrate the right model for radiation. I can‘t use the model „ViewFactor“, bacause I don‘t know the design of the ring. (This comes later, because the whole project is research.) The P1-model loses accuracy if the optical thickness is lower than 3. So I‘m thinking, that I can‘t use this, because I don‘t know the dimensions. Or is here the Rosseland-model compiled? I choose the fvDOM model. But I don‘t understand the 3 possible submodels especially the greyMean and wideBandAbsorptionEmission model. What does they mean? I looked in the tutorials for this radiation and I found the name “.*“ for a face in the 0 folder, e.g. in the Idefault in the hotroomRadiaionFvDOM tutorial. What does this mean? Can I make a radiation to the enviroment or is it better to make a default face opposite the molten metal for the radiation between faces? Regards Christian

 January 13, 2017, 02:50 #18 Senior Member   Alexey Matveichev Join Date: Aug 2011 Location: Nancy, France Posts: 1,666 Rep Power: 27 Hi, I do not know why you would like to neglect backscattering and yet insist on spatial distribution of energy deposition. Through backscattering you can lose 50% of beam energy and it has direct influence on heating; while spatial distribution, well, it will have certain effect. Marangoni forces can be neglected in CERTAIN regimes. If you rings has sizes of METERS, then yes, buoyancy and centrifugal forces prevail, otherwise temperature gradients between molten ring and outer ring will produce significant Marangoni flow. And this effect has greater influence on flow conditions than spatial distribution of electron energy deposition. Though all these things concerning PHYSICS of the process should be discussed with your advisor. Here it is OpenFOAM forum, where people can help you to solve your TECHNICAL (and philosophical) problems with OpenFOAM. Once, when I needed radiative heat loss from the surface of liquid metal onto vacuum, I have taken a look at radiation models in OpenFOAM and decided, it is MUCH easier to implement surface source term in energy equation, than go through source code looking for model description and then again go through sources code in search for correct boundary conditions for selected model. You only need to decide if you need to account for absorption by other parts of the ring of emitted energy or not. Any way initially it could be variation of grey body model.

 January 13, 2017, 04:57 #19 Member   Join Date: Dec 2016 Posts: 65 Rep Power: 2 Hy, Thank you very much. I look for all your advices. Sorry that I don't understand your previous advices. Sent from my SM-P900 using CFD Online Forum mobile app

 February 21, 2017, 08:59 #20 Member   Join Date: Dec 2016 Posts: 65 Rep Power: 2 Hy all, can somebody help me wth the energy balance, that alexey mentioned? I don't understand what he means and how to make it. Maybe alexey you can help me one more time. Regards

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