## Fluids

#### Convergence problem with granular temperature partial differential equation

• maliuzair
Subscriber

Hi

I am simulating three phase flow using eulerian-multiphase approach. When I use algebraic temperature formulation for granular phase, simulations work fine, but whenever i switch granular temperature model to partial differential equation, the simulations dont converge. i change the wall boundary conditions accordingly to specularity coefficient of 0.5.

What can be the issue

Best

• Rob
Ansys Employee

We'll need a lot more information on the model to be able to answer that. Please can you post images of the mesh along with boundary conditions and what you're actually trying to achieve. As staff we can't download attachments so unfortunately can't review the case directly: we can look at images.

• maliuzair
Subscriber

Dear Sir, I am simulating fluidization of binary mixture. My problem is as follows

Three phase (1 continuous+2 granular)

Drag: Gidaspow's drag law for air-solid
Symamlal O'brein Symmetric for solid-solid

Granular phase options:
Granular viscosity: Syamlal O'brein
Granular bulk viscosity: lun-et-al
Frictional viscosity: Johnson et al
Granular conductivity: Syamlal O'brein
Solids Pressure: Lun et al
Packing limit: 0.6

Inlet: velocity inlet=air

outlet: pressure outlet

wall boundary conditions:

granular phases:
specularity coefficient: 0.1
particle-wall coefficient of restitution:0.9

Air: no slip

first image is Solid velocity, and the first one is solid volume fraction. These are after divergence.
Best Regards

• DrAmine
Ansys Employee

Quite hard to obtain convergence with transport equation for this funny solids fluctuation named "Granular Temperature" that is I want to ask: do you know the Dirichlet or Newmann conditions for it at the boundary?

Same debugging like any other case: start from scratch, lowe URF's for GT, save residuals for post-processing and check at first with single granular phase

• Rob
Ansys Employee

Can you post an image of the mesh: the contour in the first image doesn't look very smooth.

• maliuzair
Subscriber

Here is the mesh. dimensions are: y: 2.3 m, x: 0.25 m. average cell size: 6 mm*6mm
Particle sizes: 5mm, 0.5 mm

bottom: velocity inlet, top: pressure outlet, sides: walls

• Rob
Ansys Employee

Part of the problem may be the larger particle size as it's quite close to the cell size: they must be smaller.  Also, when you initialised the solution, what did you set for the solids phase?  I'd suggest around 0.55 (packing limit 0.6) otherwise the bed will try and separate VERY quickly in the first few time steps.

• maliuzair
Subscriber

The particle size should be smaller than the cell size. Right? I ll make the grid coarse but the problem is the size of other particle, which is much smaller.

I have two granular phases. So, the total initial volume fraction of solid phases v1 (=0.45)+v2 (=0.15)=0.6. and max packing limit of each phase is 0.6.

Best regards

• maliuzair
Subscriber

the problem with volume fraction and velocity magnitude is also observed in other cases even when granular temperature model is algebraic i.e. phase property instead of partial differential equation. and this problem is with one solid phase present in less quantity. there is no problem with other solid phase which is present in major quantity

• DrAmine
Ansys Employee

The velocity contour plot is weird. Please check it again and ensure deep convergence and oproper settings.

• DrAmine
Ansys Employee

And run transient.

• maliuzair
Subscriber

Sir the problem has been solved APPARENTLY...

the problem was in mesh size. it wasnt fine enough.

Now the issue is that there are two solids. sizes are 5 mm and 0.5 mm. previously average cell size was 6 mm ie greater than both solid sizes.

Now, the cell size is smaller than the size of large particle. the cell size is 3mm. and the contours are fine. I don't understand that. what i know is that cell size should be greater than particle size.

• Rob
Ansys Employee

If you look through the model theory we assume the momentum, mass etc transfer between phases gets passed on a cell basis: if the cells are smaller than a particle the maths is theoretically incorrect and source terms can become too large. However, as you've seen this doesn't always mean it doesn't work.

• DrAmine
Ansys Employee

You know for granular flow all drag models will behave well if one has at least a cell size  not larger then 10 times of particle diameters. For very coarse mesh one requires some high end treatment. This is pronounced for Geldart Particle A or A/B. What rwoolhou wrote is true. But what rwoolhou said is true.

So you are in-between and now it is working for you. Eulerian-Eulerian and mesh refinement is always an issue and very academic.

However still encouraging to run transient.

• maliuzair
Subscriber

dear sir

i didn't understand, what do you mean by transient? the simulations are transient

best regards

• DrAmine
Ansys Employee

You never said that the runs were transient. So for the future if you post contour plots of transient run please mention whether the plots are snapshot at certain time or mean values.

• maliuzair
Subscriber

• maliuzair
Subscriber

The final situation is (eulerian multiphase model, transient simulation)
There are two solid granular phases, with different densities, and with different sizes.

solid 1: density: 500 kg/m3

solid 2: density: 2600 kg/m3

The cases I checked are:

SAME size particles, same densities of solids, partial differential equation of granular temperature... works

DIFFERENT size particle, same densities of solids, partial differential equation of granular temperature... works

same size particle, same densities of solids, ALGEBRAIC GRANULAR TEMPERATURE... works

same size particle, DIFFERENT densities of solids, partial differential equation of granular temperature... DOES NOT work

This density difference is causing trouble in convergence for GRANULAR TEMPERATURE, despite using v low under-relaxation factors for density.

• DrAmine
Ansys Employee

Different mass of particles>Different Weights>Different buoyancy effects>Different Geldart Groups== Different behavior.

• maliuzair
Subscriber

Understood sir, but the issue with granular temperature is numerical, instead of physical (in my opinion). Certainly the behavior of different geldart particles is different. but here the simulations don't converge. the residuals of granular temperature (particularly of heavier particle) and hence of the continuity diverge.

• DrAmine
Ansys Employee

Yes off course that is numerical reasoning behind it but do not forget that the "granular temperature" is an approximation of the real world and is not really famous when it comes to particle kinetics.

Please share with us last settings and models of the "non-converging case"

• maliuzair
Subscriber

2D, Eulerian Eulerian multiphase model

number of phases 3

air, solid 1 (granular), solid 2 (granular)

Pressure-based solver, Transient, gravity...y=-9.8 m/s2

Geometry: 0.25 m * 2.3 m

Average cell size: 7 mm* 7 mm

particle sizes and density:

solid 1:  0.8 mm, 2600 kg/m3

solid 2: 2 mm, 500 kg/m3

BOUNDARY CONDITIONS:

Velocity inlet: air: 0.25 m/s

pressure outlet: atmospheric

Walls: no slip for air,

partial slip for solids (specified shear, x and y components = 0),

Granular conditions: Johnson and Jackson; wall-particle coefficient of restitution = 0.9

SOLUTION METHODS:

PC-simple,

Least Squares cell based,

momentum: 2nd order upwind,

volume fraction: quick,

Granular temperature: 2nd order upwind,

transient formulation: 2nd order upwind

SOLUTION CONTROLS: Default

SOLID PHASES PROPERTIES

granular,

Granular temperature model: partial differential equation

Granular viscosity: Syamlal

Granular bulk viscosity: lun et al

Frictional viscosity: none

Granular conductivity: syamlal

solids pressure: lun et al

Elasticity modulus: Derived

packing limit: 0.63

Particle: particle restitution coefficient: 0.9

Air-solid Drag: Gidaspow

Solid-Solid Drag: Syamlal Obrien symmetric

INITIAL CONDITIONS:

initial volume fraction:

solid 1: 0.52, solid 2: 0.1

• DrAmine
Ansys Employee

You need to account for granular friction(you are starting from incompressible regime), use Gidapow as granular viscosity and a blended Guidaspow for Drag and symmetric syamlal for particle-particle interaction.