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 Lionheart February 25, 2020 01:44

Scaled Euler-Lagrange Simulation

Hey simulation comissioners,

I am trying to simulate a particle flow out of a pressure vessel using the Euler-Lagrange method. To optimise the calculation time I am trying to scale the Navier Stokes equations, which should result in a system of dimensionless equations.

To consider the momentum loss of the continuous phase (air) due to the high particle mass load of circa 1 kg particles / 1 kg air, I am using the fully coupled model. This adds an additional source term in the momentum equation of air. In the CFX solver theory guide (see chapter 6.2) is written, that the new source can be expressed by: dS=-F_D dt

Where F_D is the drag force defnined by: F_D=-0.5 c_D rho_f A_f |u_s| u_s
When you multiply this source with the particle number rate (necessary after the theory guide) it has the entity [kg m/s²]. But in fact it should be [kg /m² s] to fit with the other terms in the NS-equation. So it has to be volume specific. But I got no clue how to solve this problem.

Did anybody before tryed to simulate a particle flow dimensionless?

I am pleased if you could help me.

Best regards Terry Jeffords

 ghorrocks February 25, 2020 16:45

Why are you adding this source term? The fully coupled particle model already has it included. Why do you want to include it twice?

With particle loads as high as you describe the Lagrangian particle model does not sound suitable. Wouldn't a Eularian particle model be more appropriate?

Finally, CFX is a dimensional solver, so most people run it normal unit systems like m/s/kg. You can non-dimensionalise it, for simple single phase flows that is simple enough but it starts getting complex when you have complex models like a multiphase model to non-dimensionalise. Why non-dimensionalise your simulation? Were you getting problems when you ran it as a dimensional solver?

 Lionheart February 26, 2020 01:55

Hello Glenn,

this source term is added to the Navier Stokes equations if you want to capture the momentum loss of the continuous phase due to the high particle mass load. Otherwise it would not be physically correct. And I do not want to add this source term twice I just want to add a coefficient to it to make the whole equation dimensionless.

Well the problem is, that even though the mass fraction is high, the volume fraction is low with circa 1E-4 m³ particle / m³ air. So mass fraction is important for the momentum coupling and the volume fraction is important for the decision of Euler-Euler oder Euler-Lagrange. And I am not sure if Euler Euler works with such low volume fractions. What do you think?

Well I am getting no problems when running it dimensional, but some guys in literature down in their rabbid holes said the accuracy raises and computational effort decreases if you numerically solve something dimensionless. But so far the only thing I see is that the human effort raises ^^

Thank you very much so far

 Gert-Jan February 26, 2020 03:48

With this small amount of volume fraction, I would opt for Lagrangian. However, the choice for Lagrange or Euler also depends on the question that you want to answer when doing CFD. What do you want to get out of it? E.g., if you have a size distribution, and want to know where goes what, then Lagrangian is easier to customize and to get the relevant data out of the simulation.

 ghorrocks February 26, 2020 05:15

So you are trying to non-dimensionalise the built-in particle to fluid coupling force? Is that correct? Yes, this is going to be challenging. I would do a literature search to see how other researchers have non-dimensionalised multiphase flows. It is not trivial to do this, and there are likely to be several ways you can do it. I am not familiar with them, but I have studied works which non-dimensionalised thermal convection and that was complex enough (let alone trying to convince a dimensional solver to act in a non-dimensional way).

The mass fraction of particle is high but the volume fraction is low - OK. There are other factors in deciding Langrangian or Eularian. Lagrangian gives the precise track of a sample of particles, Eularian has many more models available to it (particle collison, wall lubrication, fluidised bed and many more - Lagrangian models don't have these options). Lagrangian models are only applicable to low particle volume fractions, but Eularian models can handle volume fractions from 0 to much higher.

Quote:
 But so far the only thing I see is that the human effort raises
Yes, I was thinking exactly the same thing. Non-dimensionalisation can reduce round off errors and that can improve convergence and give more accurate and faster simulations. But if you are not getting significant round off errors in the first place then the gain will be negligible. A naive implementation of a dimensional solver can easily result in big round off errors, but CFX is a highly developed, well verified and optimised solver. It has many methods used to keep round off errors under control.

In other words, unless you know you are getting round off errors the non-dimensionalisation you propose is unlikely to help in CFX. If you are writing your own code then non-dimensionalisation is one of the easiest ways to keep round off errors down - I suspect that is what the papers you are reading have in mind.

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