Temperature on Interface Side
 

Dear all,


I have two Domains: Domain 1 and Domain 2. They contain Steel (Domain 1) and Gas (Domain 2). (the steel is modeled as a fluid). Unfortunately both materials need to be defined in both domains.


In Between these i have a Fluid Fluid interface called "Cathode"


I would like to use the temperature at Cathode Side 1 in an CEL expression.


I tried calling it as "Cathode Side 1.Steel.T" but it was not recognized in the Pre-Processor.



Leaving it simply as "T" will give me the error:
+--------------------------------------------------------------------+
| ERROR #001100279 has occurred in subroutine ErrAction. |
| Message: |
| NAME_MOD: Error finding variable "TEMP" |
| |
| |
| |
| |
| |
+--------------------------------------------------------------------+




leaving it as "Steel.T" will give me the error:
+--------------------------------------------------------------------+
| ERROR #001100279 has occurred in subroutine ErrAction. |
| Message: |
| Stopped in routine Could not find phase directory. |
| |
| |
| |
| |
| |
+--------------------------------------------------------------------+




In the end i would like to make for example the heat flux to the Domain 1 from the interface Cathode Side 1 dependent from Cathode Side 1.Steel.T as well as Cathode Side 2.Gas.T


Could anyone guide me to the right direction?

It is not simple to refer to variables on the other side of an interface.

The normal way of adding or removing heat at an interface is by using a source term. Will that work in your case?

Dear Glenn,


Thank you for your quick reply.


The problem that i am trying to model is a coupling of an electrical arc to a cathode. In our model the coupling is dependent on the temperature of the arc-plasma on one side and of the cathode surface on the other side.


Therefore even the heat source as a source term would need to gather the information from both sides.


What would the general way be to refer to a field variable (like temperature T) in either one domain?

Can you share the equation you are trying to use for your interface model?

ANSYS CFX provides an interface model where the flux can be approximated as Coefficient * Grad(Variable).Normal. Would that be of any use to you?

Dear Opaque,


Thank you for your interest in my problem!


So the model is a bit more complicated than i described at first.


So the heat flux to the surface of the steel domain is sqrt(current_density^2)*15[V]. It comes from an ionisation energy, that the ions from the plasma deposit on the surface. Thermal conduction is negligible to this contribution.


So in order to get the current density right, i need to solve for the electric field and for this i think i will have to set a Wall Transfer Coefficient on the interface boundary.


To be honest i am not quite sure how to define the wall transfer coefficient yet, but in general the model that im using will decrease the attachment (current density) when the temperature on the plasma side is low, but also when the temperature of the steel side approaches boiling temperature.


Additionally the temperature on the plasma side is lowered locally in the very close proximity of the interface by the evaporated steel atoms.



I am thinking it should be possible to model this by a sort of electrical conductivity, which will depend on the temperature on both sides of the interface.


When i chose the side dependent option for the electric field, it seems like i can define a Wall Transfercoefficient on either side of the interface, is this correct?




I would also think that using the gradient is probably not helpful, because between the plasma and the steel there will be a temperature jump within the dimension of one element.

This sounds easy to implement as a source term on the interface. No need for your complicated approach.

Why does the electric field depend on the wall thermal conditions?

This looks like quite a complex model you are considering to implement. The first step in complex models like this is to work out the mathematics of what you want to implement - it does not sound like you know this yet, so you should not consider implementation yet.

Dear Glenn,


Thank you very much for your interest in my model.


The mathematical/physical approach was described in detail in this paper: https://iopscience.iop.org/article/1...61-6463/ab2bd9


However, until now we considered a fixed value for the temperature of the plasma. Now we would like to adopt a coupled arc-weld pool simulation, where the temperature of the plasma is determined by the Joule Heating in the arc.


To your question, why the current density is dependent on the wall temperature:
This is a pecularity of the arc-cathode interaction. The current density is (in our approach) mainly determined by the density of available ions near the cathode (the velocity of the ions is assumed as fixed by the bohm criterion). This ion density is dependent on two things: the density of available atoms as well as the local plasma temperature (which determines the ionization degree). In our approach the density of available atoms is increased by atoms that evaporate from the heated surface (so the wall temperature is neccessary). Also, in our aproach, the local plasma temperature is decreased by the mixing of the plasma fluid with the cold cathode vapor (which carries the temperature of the wall). Therefore the conditions on both sides need to be considered. Of course this is only an approximate approach as the true dimensions of this so called "cathode sheath" are of the order of nanometers, where kinetic theory would need to be applied.


Is there a way to adress the sides of the interface via a User Routine? Or could you direct me to a good resource on the Fortran API of Ansys CFX?

There is no easy way to access it. You would have to dive into the Fortran routines to do it. There is a simple description of the fortran interface in the CFX documentation (Solver Modeling Guide) but it does not go into details of the MMS (memory management system) and you would definitely need to access the MMS for this. For details of the MMS you would need to talk to ANSYS support. Even better, ANSYS runs fortran training courses every now and again.

A fundamentals question.... Doesn't an interface have the same temperature on both sides of the interface? In a solid-fluid interface, the outside surface of the solid is the same temperature as the wall temperature of the fluid?

Dear Glenn,


Thanks for the advice! I will consider contacting a local Ansys Support Service!



Regarding your question: Of course on a microscopic scale, the temperature would be continuous. However, at these scales (~micrometers to nanometers) the concept of temperature starts to loose its meaning, because they are at the order of the mean free paths.
In general the temperature of the plasma will be in the order of 10000K while the cathode surface will be below 3000K. However, a continuous temperature distribution between these two entities over a relatively big spacial distance would mean that the plasma would lose its ionisation, it would become inconductive and the coupling would not occur. The exact interplay of the relevant length scales is still not 100% clear to me, but there have been considerations based on assumptions the for Debey length (associated with the space charge sheath, usually the shortest ~20-500nm), and the ionization length (~10µm) or thermal relaxation length (~100-300µm). However out of these, the thermal relaxation length is usually the largest.


Most current theories are based on this paper:

https://iopscience.iop.org/article/1...-3727/28/9/015


However, this theory does not take into account the influence of the metal vapour and therefore surface temperatures of over 4000K are achieved. For steel this would be way beyond boiling, so the mechanism must be different. This is why we suggest the cooling of the local plasma temperature (in the ionization layer) by the metal vapor. But the question of the relevant length scales, i.e. how deep the influence of the metal vapor penetrates the plasma and in what ratio this penetration stands to the ionization length, is still not entirely clear to me, as i havent found yet the data on the collision cross-sections at the specific conditions.

Three somewhat independent comments:

Interfaces in CFX are implemented on the assumption that the external face of the solid is the same temperature as the wall face of the fluid. If you are trying to make these temperatures different, I think you will find you cannot make them different temperatures as CFX is hard-coded to make them the same.

There are the Interface models of thermal contact resistance and thin material which do allow these faces to have different temperatures, but the model used to link the temperatures is a simple thermal resistance model. If you do some mathematical gymnastics you might be able to these these models to do what you want. This is be by far the easiest way of doing it if you can.

CFX has no plasma model. You have pointed out that the normal assumption about thermal boundary layers for the Navier Stokes equations do not apply due to the plasma physics - which is saying CFX does not have a thermal boundary model suitable for modelling plasma. If you still think CFX is an appropriate code to model your application and you just want to adapt the boundary layer stuff to work for your plasma case then an alternative approach would be to modify the thermal boundary layer model in CFX to be more suitable for plasma.

Dear Glenn


Thank you for your explanation.


It is interesting to hear that the temperature at the interface has to be the same for both sides. My idea was actually to make the temperature boundary condition adiabatic on both sides, however with a specifically set heat source term. Maybe this is another obstacle.


however i also need to add: the steel is not considered as a solid, as it melts into a liquid melt. Therefore the interface is considered as a fluid-fluid interface, but i am quite certain, that the obstacles about the impossibility of a temperature jump will still remain the same, also in this case.


But, as i said, i would like to themally decouple both sides anyways, i just need a way to couple them for the electric field. But here, again, i need to consider the conditions on both sides of the interface.


Best Regards

If the interface is adiabatic then it is not an interface, it is a pair of adiabatic domain boundaries. And if you couple these boundaries yourself (ie do your own special type of interface) then maintaining boundedness, accuracy, numerical convergence and conservation are not easy. There would be a PhD project just in getting this interface to work.

Sorry, yes, you mentioned steel is a liquid here. But as you say it makes no difference - the interface has the same temperature on both sides.

While you have mentioned that the length scale for the plasma is very small, I think you might find that in your case applying the heat to the boundary as a normal source term, but then handling the special physics of the plasma near the wall as some sort of special thermal conductivity or wall function like approach will be much more tractable. This will use the inherent assumptions of CFX and things will be applied in standard methods (eg source terms).

Hanging over this is the fact that CFX has no models for plasma, and in general I recommend against people using CFX for plasma modelling. Anybody who uses CFX for plasma modelling is always going to be making a square peg fit in a round hole. Maybe a different CFD package (one with a plasma model - if that exists?) would be more suitable.

Most likely too late, but...

T * inside()@Interface Side Name