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Modeling additionial variable solid-fluid interface flux

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Old   September 15, 2015, 08:48
Default Modeling additionial variable solid-fluid interface flux
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Niels Bessemans
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Dear,

I am considering the transport of respiratory gasses (O2 and CO2) in a storage container of apple fruit. There are two domains, one solid domain called “Apple” and a fluid one called “Air”. For both domains, there is no heat transfer, just isothermal at 1°C (274.15 K).

To model the transport of the respiratory gasses O2 and CO2, I have created two additional variables which are volumetric with units [mol m^-3] and are scalar.

Transport in the domains

Apple

In the Apple domain, transport of the additional variables is governed by a diffusive transport equation with kinematic diffusivities of 1.41e-8 m^2 s^-1 and 3.14e-9 m^2 s^-1 for CO2 and O2 respectively. Also, in the “Apple” domain, there is a subdomain called “Respiration” which overlaps the full fruit domain and which contains source terms for the gasses CO2 and O2 which are equal to 0.00001 [mol m^-3 s^-1] and -0.00001 [mol m^-3 s^-1] for the CO2 and O2 sources respectively. There is no source coefficient since the sources are constant values.


Air

In the Air domain, transport of the additional variables is governed by a transport equation with diffusivities of 2e-5 m^2s^-1 and 5e-5 m^2 s^-1 for CO2 and O2 respectively.


Problem statement

The model runs without any problems. However, I would like to add an additional resistance to the additional variable transport over the interface, which is physically located in the fruit skin, but which is not explicitly modeled in the geometry. One could calculate the skin conductance for the transport of each of the additional variables by dividing the diffusivity of each of the additional variables in the fruit skin by the thickness of the fruit skin, which delivers a value of 2.35e-5 and 5.23e-6 for O2 and CO2 respectively, with units of [m s-1], the same units as a convection coefficient. Therefore I would like to ask which is the correct way to implement this additional resistance using ANSYS 16.2.


Can I put at both sides of the inteface between the "Apple' and 'Fruit' domains (AppleAir side 1 and AppleAir side 2) as option “Transfer coefficient” and put the value of the skin conductance like below?


AppleAir side 1
Transfer coefficient
O2/CO2 (which are the additional variables and so are not constant)


AppleAir side 2
Transfer coefficient
O2/CO2 (which are the additional variables and so are not constant)


As far a I understand from the help file, the flux will then be calculated using the specified transfer coefficient and assuming the specified values of O2/CO2 are in the bulk fluid. However, these are not constant.


The second option of CFX is to set both sides on conservative interface flux and put as an addition interface model ‘Additional variable contact resistance’. However, the contact resistance to be specified has as units [m^2 s kg^-1] and is the inverse of the mass flux. This mass flux is dependent on both the concentrations of the additional variables at the fruit skin and their value in the air and is in this case not a constant. Is there a way to overcome this problem?

Kind regards,
Niels

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Old   September 15, 2015, 19:15
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Glenn Horrocks
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On your specific question: I would have thought the contact resistance model for interfaces would be what you are looking for. Is that suitable for what you are doing?

But on the bigger picture: I suspect this model is better done as a multicomponent mixture rather than additional variables. Then the change in composition of the gas due to the change in O2 and CO2 concentrations can be taken into account.
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Old   September 16, 2015, 04:36
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Dear Ghorrocks,

First, thanks for your reply. In general, yes, it would be better to do this model as a multicomponent mixture. However, in this case, I'm doing relatively short transient simulations in which the gas concentrations in the fluid domain do not change much and so, do not alter the fluid properties. Rather than that, I'm interested in the gas gradients that occur in the fruit and the distribution of the gas in the storage container.

I would indeed suppose that the additional variable contact resistance would be the right way to model the resistance. However, according the the CFX help file, the additional variable contact resistance is the inverse of the massflux of the additional variable over the solid-fluid boundary. In this case, the AV contact resistance should not be a fixed value, since the massflux depends both on the the additional variable value at the fruit skin and at the adjacent node in the air. However, I do not know how to implement this properly in ANSYS 16.2 CFX. Do you have an idea about how to do this?

Kind regards,
Niels
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Old   September 16, 2015, 06:20
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I just wanted to make sure you had considered the multicomponent mixture approach. If you have considered it and decided the AV approach is more suitable for your application that is good.

I suspect you have misunderstood the resistance approach (correct me if I am wrong on this). Using the thermal analogy as I find it easier to comprehend the situation for heat:
Contact resistance = Temp Rise/Heat flow, units = K/W.

So when you define a contact resistance it then establishes a proportionality between temp rise and heat flow which the solver uses to solve for the heat flow over the boundary. So contact resistance is not a function of heat flow.

So in your case the resistance establishes the proportionality between the difference in concentrations on either side of the boundary and the mass flux. The solver will work out the concentration difference and mass flux using your resistance number.
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Old   September 16, 2015, 07:41
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Dear Ghorrocks,

I'm not sure if I misunderstood or not, there's not much information in the CFD help about the additional variable contact resistance. As you explained, I understand the physical meaning and the units for the resistance to heat transfer and indeed, the resistance should be a fixed value, since it does not change or isn't a function of any other (flow)variable.

However, the units of the additional variable contact resistance should be [m^2 s kg^-1] according to CFX, which is actually the inverse of the mass flux. If I translate the example of heat transfer to mass transfer the AV contact resistance would be:
AV Contact resistance = Increase in concentration / mass flow, but that would give units kg m^-3 / kg s^-1 = s m^-3, which are not the expected units. And even if I would, how could one be able to calculate this resistance (or contact resistance for heat transfer)?

Kind regards,
Niels
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Old   September 16, 2015, 08:46
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Quote:
Originally Posted by NielsB View Post
Dear Ghorrocks,

I'm not sure if I misunderstood or not, there's not much information in the CFD help about the additional variable contact resistance. As you explained, I understand the physical meaning and the units for the resistance to heat transfer and indeed, the resistance should be a fixed value, since it does not change or isn't a function of any other (flow)variable.

However, the units of the additional variable contact resistance should be [m^2 s kg^-1] according to CFX, which is actually the inverse of the mass flux. If I translate the example of heat transfer to mass transfer the AV contact resistance would be:
AV Contact resistance = Increase in concentration / mass flow, but that would give units kg m^-3 / kg s^-1 = s kg^-1, which are not the expected units. And even if I would, how could one be able to calculate this resistance (or contact resistance for heat transfer)?

Kind regards,
Niels
Maybe you should adjust units using 1 with some units as multiplier. CFX knows nothing about meaning of your add. vars. Consider you want to solve Poisson equation for add. var representing electric potential. So in your equation there is electric conductivity (Sigma) before grad of your add. var. But in equation that CFX solves there is Rho * Dphi. And Dphi have units m^2/s. So you should assign Dphi = Sigma / Rho * 1 [kg S^-1 s^-1] to use this poisson equation for your needs.
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Old   September 16, 2015, 09:33
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Dear Antanas,

Thanks for your reply. I have tried that, but the only possible way (as far as I know, correct me if I'm wrong) to do this in my case is to multiply the skin conductance [m s^-1] with the concentration gradient kg m^-3 which delivers something in the units of kg m^-2 s^-1 which is the desired unit . However, this concentration gradient is a result of the mass transfer over the skin itself. Since the skin resistance can not be a function of the mass flux or any other variable this is wrong...

Kind regards,
Niels
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Old   September 16, 2015, 11:15
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Quote:
Originally Posted by NielsB View Post
Dear Antanas,

Thanks for your reply. I have tried that, but the only possible way (as far as I know, correct me if I'm wrong) to do this in my case is to multiply the skin conductance [m s^-1] with the concentration gradient kg m^-3 which delivers something in the units of kg m^-2 s^-1 which is the desired unit . However, this concentration gradient is a result of the mass transfer over the skin itself. Since the skin resistance can not be a function of the mass flux or any other variable this is wrong...

Kind regards,
Niels
Well it seems to me that CFX wants to see somthing like thikness/(Rho*Dphi) as add. var contact resistanse. And this is reciprocal of something like transfer coefficient.
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Old   September 16, 2015, 11:57
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Dear Antanas,

Thanks for your help. That would indeed deliver a value with the desired units. Unfortunately, I do not know the density of the fruit skin.

Kind regards,
Niels
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Old   September 16, 2015, 12:43
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Quote:
Originally Posted by NielsB View Post
Dear Antanas,

Thanks for your help. That would indeed deliver a value with the desired units. Unfortunately, I do not know the density of the fruit skin.

Kind regards,
Niels
Hmm... Lets forget for a moment about what CFX wants for resistivity. How you would like to set this? What do you know?
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Old   September 17, 2015, 04:20
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Dear Antanas,

The idea I came up with was to first calculated the skin conductance given by: hskin = diffusivity of AV in skin / Skin thickness which are known, units [m/s] like a convection coefficient.

Subsequently I did two simulations using a flat plate with laminar flow over it with a certain concentration in the bulk fluid.

In the first simulation, I specified the concentration as a constant in the plate and in the bulk fluid and calculated the transfer coefficient as a function of distance in the flow direction from the fluid heading edge of the plate.

In the second simulation, I put a value for the transfer coefficient (hskin) and a concentration in the bulk fluid (transfer coefficient boundary condition), and calculated the transfer coefficient again as a function of distance in the flow direction from the fluid heading edge of the plate. I expected the calculated h values from the second simulation to be the total resistance of the one calculated by ansys itself in the boundary layer and the one added by me (1/htot = 1 / (1/hskin + 1/hboundarylayer)). Which was indeed the case.

This seems to be working if the concentration in the bulk fluid does not change. However, in the simulations that I am running now, concentrations in the bulk fluid do change and so this method can not be used I think.
An alternative would be to write some kind of Fortran subroutine to calculate the massflux based on the AV value in the fruit skin and the AV value in the adjacent node in the air, but I do not have any experience with that.


The skin resistance approach should work I think since the skin resistance is equal to (1/hskin)*(1/densityskin). Unfortunately ANSYS expects users to put a density as well.

Kind regards,
Niels
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Old   September 17, 2015, 08:41
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Quote:
Originally Posted by NielsB View Post
Dear Antanas,

The idea I came up with was to first calculated the skin conductance given by: hskin = diffusivity of AV in skin / Skin thickness which are known, units [m/s] like a convection coefficient.

Subsequently I did two simulations using a flat plate with laminar flow over it with a certain concentration in the bulk fluid.

In the first simulation, I specified the concentration as a constant in the plate and in the bulk fluid and calculated the transfer coefficient as a function of distance in the flow direction from the fluid heading edge of the plate.

In the second simulation, I put a value for the transfer coefficient (hskin) and a concentration in the bulk fluid (transfer coefficient boundary condition), and calculated the transfer coefficient again as a function of distance in the flow direction from the fluid heading edge of the plate. I expected the calculated h values from the second simulation to be the total resistance of the one calculated by ansys itself in the boundary layer and the one added by me (1/htot = 1 / (1/hskin + 1/hboundarylayer)). Which was indeed the case.

This seems to be working if the concentration in the bulk fluid does not change. However, in the simulations that I am running now, concentrations in the bulk fluid do change and so this method can not be used I think.
An alternative would be to write some kind of Fortran subroutine to calculate the massflux based on the AV value in the fruit skin and the AV value in the adjacent node in the air, but I do not have any experience with that.


The skin resistance approach should work I think since the skin resistance is equal to (1/hskin)*(1/densityskin). Unfortunately ANSYS expects users to put a density as well.

Kind regards,
Niels
Use 1/hskin * 1 [m^3 kg^-1].
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Old   September 17, 2015, 09:13
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Dear Antanas,

Theoretically, this should work. However, I'm not sure which equation ANSYS solves or handles this AV contact resistance, maybe a correct value for the density is necessary to obtain a physically valid result... In the ANSYS help one can find which equation is solved for the AV transport, but not the AV contact resistance is plugged into this equation. Anyway I will try!

Kind regards,
Niels
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Old   September 17, 2015, 11:18
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Careful here... You must understand how a generic variable, AV, is defined in ANSYS CFX.

If you look at the transport equation being solved, the density used is the fluid density. Otherwise, it would have asked for density earlier in the setup.

On the flux of the AV, it is defined as
Code:
Flux_AV = - Kinematic Diffusivity * Density of Fluid * grad (AV) = Transfer Coefficient_AV * (AV_side1 - AV_side2)
Therefore, you can interpret the transfer coefficient as
Code:
Transfer Coefficient_AV = Kinematic Diffusivity * Density of the Fluid / Thickness
or
Code:
Contact Resistance_AV = Thickness / (Kinematic Diffusivity * Density of Fluid)
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Old   September 17, 2015, 12:14
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Dear Opaque,

Thanks for your reply. Indeed, additional variables are defined per m^3 of fluid according to the CFX guide. However when solving them in the solid domain, I therefore put the material density of the solid the same as the density of the air. So I think it is correct, and the density of the fluid should be used.

Kind regards,
Niels
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