Multiphase Porous Media Flow - Convergence Issues
 

System Description:

Two phase solid-gas flow. The sold being sand particles and the gas is air. Air is injected through a nozzle that entrains the sand particles up a ramp and the mixture hits a filter. The filter ideally filters out the sand particles which drop into a collection area while the air exits the system. A picture of this system can be seen below:

http://img.photobucket.com/albums/v2...7/Surfaces.png

The nozzle is the square portion in the blue region on the left hand side. The end of the rectangle is the velocity inlet. The green line at the top right is where my porous media zone is (No the exact geometry used, but had a picture on hand). The pink is the sand initially and the blue is the air initially.


FLUENT Model Details:

• Pressure-Based Solver
• Transient
• Eulerian-Eulerian Model
• k-epsilon model

Porous Media Zone

Relative Velocity Resistance Formulation

Porosity: 0.8

• Air
  • Viscous Resistance (Direction 1): 4.76E10
  • Viscous Resistance (Direction 2): 4.76E10
  • Inertial Resistance (Direction 1): 4.79E-6
  • Inertial Resistance (Direction 2): 4.79E-6
• Sand
  • Viscous Resistance (Direction 1): 4.76E13
  • Viscous Resistance (Direction 2): 4.76E13
  • Inertial Resistance (Direction 1): 0.00479
  • Inertial Resistance (Direction 2): 0.00479

Boundary Conditions

• Velocity Inlet ("Nozzle") - 345 m/s
• Outlet (Top of Porous Media Zone) - 0 ga Pressure

Solution Methods

• Scheme - Phase Coupled SIMPLE
• Gradient - Least Squares Cell Based
• Momentum - First Order Upwind
• VF - First Order Upwind
• Turbulent KE - First Order Upwind
• Turbulent Dissipation Rate - First Order Upwind
• Transient Formulation - First Order Implicit

Solution Controls


Under Relaxation Factors

• Pressure - 0.3
• Density - 1
• Body Forces - 1
• Momentum - 0.5
• Granular Temperature - 0.2
• Turbulent KE - 0.8
• Turbulent Dissipation Rate - 0.8
• Turbulent Viscosity - 1

Problem

I have solved this case without the porous media zone and just using a pressure outlet. My issue was that particulate was flowing out of the outlet and not being collected as desired. The case runs fine until the Volume Fraction becomes anything but 1 (all air) at the porous media zone. An example of the residuals up until this point is shown below:

http://img.photobucket.com/albums/v2...ortoFilter.png

The volume fraction of air at this point is shown below. The rectangle section at the top right is my porous media zone:

http://img.photobucket.com/albums/v2...ortoFilter.png

Then I get to this point:

http://img.photobucket.com/albums/v2...Divergence.png

And the residuals begin to flat line or really struggle to converge.


What has been tried to remedy the problem:

• variable time steps
• messing with the Courant number
• second order discretizations
• adjusting the porous media parameters
• under-relaxation factors

All to no avail.

I did get it converging for a little while but then this happened:

http://img.photobucket.com/albums/v2...ingResults.png

And it diverged very soon after.


Any ideas on what I can try? Do all of my settings look correct?

Thanks!
Mike

I have still been working at this to no avail. I doubt my values for the viscous and inertial resistance though. I used a orifice style flow bench to find the pressure drop versus velocity curve. I then fit the curve with a quadratic function and used the coefficients to solve for alpha and C2. However, I'm unfamiliar with "typical" values and am not sure that it is right. Here is my data and the plot. The filter is just a coffee filter so I wouldn't expect it to be too restrictive.

http://img.photobucket.com/albums/v2...ata_Filter.png

hai
wats the boundary condition imposed on the filter material. u need to create a bc such that only air passes through and sand is retained

As far as I know there is no option for such a boundary condition; hence the use of the porous media. If I'm incorrect please let me know.

to selectively transport one component u will have to write UDF

That is one method, but a porous media zone should work as well as you can apply different resistances to each phase. Therefore I apply a large viscous and intertial resistance to the solid phase to prevent it from passing through the porous zone.

I did manage to get the problem to converge and prevent the solid phase from flowing through the porous zone. I removed the visous resistance for air as this should not really be a factor.

It is working great, but I have it currently set as a variable time step and to converge it is stepping at 1e-8 seconds. As you can imagine with about 200 iterations per time step this solution is taking a LONG time.

Does anyone have any hints/tips to speed up convergence in this case?

Thanks,
Mike

Please, how did you arrived at the value of the viscous and inertia resistance?

I really need to find values for the inertia and viscous resistance of fired pottery clay and sand as well.

anyone who can help, please?

Thanks in advance

James

Hi
if you want to use the pressure-velocity curve for estimation of alpha(m-2),C2(m-0 (two coefficients for porous media) you have to divide pressure by depth of packing the use slope to evaluate alpha and c2.
dP/H=alpha*mu*U+(0.5rho*C2*U*U)