Mass sink: Complete removal of a species at defined region

Torsten · January 11, 2018, 09:04

Hi,

I investigate a filter and consider for my simulations only one fiber. A sketch of the issue is attached.

For that model the particles within my fluid are considered as dispered fluid (thus a Euler-Euler view). The particle is going to be absorbed if it is within the circle $d_{fiber} + d_{particle}$ , dashed circle in the sketch.

Therefore I introduced a (continuity) mass sink through a subdomain in my CFX model (version 14.5). (Subdomain -> Fluid sources -> Continuity)

My issue lies in the sink intensity. I created an expression, if the the particle is not within that circle, my source term is zero kg/m3/s annd if it is within it becomes a high negative value multiplied by the volume fraction of the particle to prevent problems if the volume fraction is already zero.

- If I choose a too high value, the continuty equation wants to remove to much particles, which are not there. --> computational error
- If I choose a too small value, the volume fraction is not becoming zero --> physical error

Does anyone know a way to implement that mass sink properly: all particles which are within that circle are going to be removed from the calculation? Just like what the minimal absorption radius does for dispered solids.

Thanks in advance
Torsten

evcelica · January 11, 2018, 09:14

You have to set up this source sink to work with your time step. The Dirichlet boundary condition must not take out more than all of the fluid in that time step or it becomes negative or unstable.
This means with a larger removal constant you need a smaller time step.

There are ways to do source term linearization instead, but I have just used the time step method in the past.

Source = -Constant * AdditionalVariableValue
where:
Constant <= (1 / timeStep)

Torsten · January 11, 2018, 09:55

Thank you for your quick reply

with timeStep you are talking about the (physical) TimeScale, right?
For that I created an expression, too.

TimeScale = $\frac{d_{fiber}}{u_0}$

Applying your suggestion to my description above the expression should look like:

$source = if(\sqrt{x^2+z^2} \leq \frac{d_{fiber} + d_{particle}}{2}$ , $\frac{-1 [kg/m^3]}{TimeScale} * Particle.Volume Fraction, 0 [kg/m^3/s])$

Did I get it right?

evcelica · January 11, 2018, 12:33

Yes that looks right.
I would probably make a separate meshed zone for the area in the absorption region, and just apply the subdomain to that volume instead of using the whole sqrt(x^2+z^2) thing, which will be subject to discretation errors and possibly impossible to get grid independence.

You could look into source term linearization as well, but I don't know how to do it.

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January 11, 2018, 09:14		#2
evcelica Senior Member Erik Join Date: Feb 2011 Location: Earth (Land portion) Posts: 1,167 Rep Power: 23	You have to set up this source sink to work with your time step. The Dirichlet boundary condition must not take out more than all of the fluid in that time step or it becomes negative or unstable. This means with a larger removal constant you need a smaller time step. There are ways to do source term linearization instead, but I have just used the time step method in the past. Source = -Constant * AdditionalVariableValue where: Constant <= (1 / timeStep)

January 11, 2018, 09:55		#3
Torsten New Member Join Date: Sep 2017 Location: Dortmund, Germany Posts: 11 Rep Power: 8	Thank you for your quick reply with timeStep you are talking about the (physical) TimeScale, right? For that I created an expression, too. TimeScale = $\frac{d_{fiber}}{u_0}$ Applying your suggestion to my description above the expression should look like: $source = if(\sqrt{x^2+z^2} \leq \frac{d_{fiber} + d_{particle}}{2}$ , $\frac{-1 [kg/m^3]}{TimeScale} * Particle.Volume Fraction, 0 [kg/m^3/s])$ Did I get it right?

January 11, 2018, 12:33		#4
evcelica Senior Member Erik Join Date: Feb 2011 Location: Earth (Land portion) Posts: 1,167 Rep Power: 23	Yes that looks right. I would probably make a separate meshed zone for the area in the absorption region, and just apply the subdomain to that volume instead of using the whole sqrt(x^2+z^2) thing, which will be subject to discretation errors and possibly impossible to get grid independence. You could look into source term linearization as well, but I don't know how to do it.