Implementation of additional variables for the solid/gas interface
 

Dear,


I would like to study the transport by diffusion and convection in the solid and fluid regions of a species. Assuming to have two boxes representative of the solid (1) and gas (2) domains that are connected by means of an interface as reported in Figure 1.


The system can be described by the mass transport equations reported in Figure 2.
https://www.cfd-online.com/Forums/da...AASUVORK5CYIIA
I have created two additional variables C_solid and C_gas which are volumetric [m^-3] and scalar.
At the interface (dotted red line) there is a mass flow of the species from the solid to the gas domain. The boundary condition in this region should ensure the flux continuity as stated in equation reported in Figure 3, but also the discontinuity in the concentration profile at the boundaries between solid and gas phases as shown in Figure 4.
https://www.cfd-online.com/Forums/da...AASUVORK5CYIIA
Thanks to the Fick law, I can introduce a simplified correlation between Cs0 and Cg0 that are functions of the distance (dsol and dgas) from the cell center to the surface in the gas/solid phase and using some assumptions it is possible to obtain an expression of Cs0 and Cg0 in function of Cs and Cg as reported in Figure 5.
https://www.cfd-online.com/Forums/da...lFTkSuQmCCAA==
My requests are:
Is there a method for implementing a boundary condition at the interface able to maintain the flux continuity ensuring the discontinuities of the concentrations?
Is it possible to implement a boundary condition using the stiff-spring?

Thanks in advance for your help!

Kind regards,
Alex

These are all standard options on interfaces in CFX.

Dear Glenn,


probably you are right but until now I faced some issues. For instance, I defined the AV C_solid and C_gas for the solid and for the gas domain, respectively. Then I defined in the Boundary Detail of each side of the Interface the Cs0 and Cg0 as concentrantion value at the interface. Considering that Cs0 and Cg0 are function of C_solid and C_gas, CFX requires the definition of C_solid for the gas domain and C_gas for the solid domain that in my view make no sense from the phisical point of view.
In any case, although I satisfy the requests of CFX, running the analysis, I do not see any comunication in terms of diffusion at the interface between the solid and gas domains.


For sure I am doing something wrong, maybe you may give me a clue, a tip to solve the problem.


Many thanks in any case for your time and your help!


Best regards,
Alex

Why did you define different additional variables in the solid and fluid domains? Why not use the same AV in both domains, then the standard interface will do the communication between domains as you request.

Dear Glenn,


you are right and I have already tried that solution but with only one AV at the interface I can specify only the contact resistance that I can not calculate! the problem that I am simulatin is the permeation of hydrogen from the solid to the gas and it is important to well calculate the concentration Cs0 and Cg0 at the interface.


If you have other suggestions, these are very welcome!


many thanks in any case for your support!


kind regards,
Alessandro

If you use a single AV across the whole simulation, then at the interface you have many options to control the flux at the interface. You can define contact resistance, thin surfaces and source terms. You can also define a different boundary condition to be specified on each side of the interface.

Can you make your interface condition fit one of the existing models?

If not, can you define the interface model you wish to use? (Your first post shows many equations, but without definitions for the terms in the equations that is not much use)

using the same additional variable throughout is the correct approach.

The next step is what that boundary condition means, and see if you can realize it with the existing options.

If you have the same AV on both sides, and use Conservative Interface Flux, the ANSYS CFX solver will enforce

D_fluid * Density_fluid * grad(AV_fluid).Normal area = D_solid * Density_solid * grad(AV_solid).Normal area

Where the AV is a specific quantity, that is (quantity / unit mass).

Will that fit your model?

Dear Glenn and dear Opaque,


first of all I would like to thank you for your answers and please accept my apologies for the late answer but I was studing better the problem.
As suggested by both of you, I agree to use only one AV for the concentration in both domains and, as suggested by Opaque, to define Conservative Interface Flux at the intarface. Using this option, it seems that flux continuity is ensured but also the discontinuities of the concentrations at the interface.
Indeed, reading the paragraph 5.13.3.2. Two Resistance Model with Negligible Mass Transfer (https://www.sharcnet.ca/Software/Ans.../i1306928.html), the problem that I am studing is already integrated and solved in ANSYS CFX.


About this last point, I would like to ask to you some clarification:
1) Is the resistance calculated in eq. 5–247the Additional Variable Contact Resistance?
2) in my case the equilibrium relation between the two concentration at interface is different from the one reported in eq. 5-244 and it is equal to CAas = K^c * sqrt(CAbs*kT0). do you know a way to force CFX to apply this equation?


Many thanks again for your kind support on this argument.


Best regards,
Alex

Can you please define the terms in your equation "CAas = K^c * sqrt(CAbs*kT0)"

Dear Glenn,


the correlation that I wrote represents the Sievert law for the permeation of atomic hydrogen (H) (present in the solid phase) to the molecular hydrogen H2 in the gas phase through the interface.
Using the same notation reported in https://www.sharcnet.ca/Software/Ans.../i1306928.html and with particular reference to the figure in paragraph 5.13.3.2., the equation terms have the following meaning:
- CAas is the concentrantion of the species A at the interface "as" (in may case the solid interface);
- K^c is the Sievert coefficient (function of the temperature);
- CAbs is the concentration of the species A at the interface "bs" (in may case the gas interface);
- k is the equilibrium constant;
- T0 represents the temperature at the interface.


I noticed that in ansys, thanks to the "Two Resistance Model with Negligible Mass Transfer", it is already taken into account the discontinuity of concentrantion at the interface but it is driven by the concentration equilibrium equation 5-244 that is different of my case study.


I would like to force the solver to use my correlation.



do you have any tip tu suggest?


thanks a lot for your interest in any case!


Kind regards,
Alessandro