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Modelling Air-Water Stirred Tank Reactor Using Explicit VOF – Convergence Issues

• SR786
Subscriber

Hello,

I am a new to research and modelling CFD and I am currently looking into modelling a two-phase unbaffled stirred tank reactor (air-water system), where I am interested in tracking the deformation of the air-water interface using transient solver and explicit VOF scheme (with geo-reconstruct scheme).

A few computational details include:

• Turbulence model: Standard k-epsilon
• Discretisation: Body force weighted (pressure), First order (convective + turbulent parameters), Geo-reconstruct (volume fraction)
• Solver: Transient With PISO algorithm
• Mesh: Unstructured (600,000 elements)

I set up a simulation run for a speed of 195 RPM. I should expect to see a transition from a flat liquid surface to a fully developed/pseudo-steady vortex profile over the simulation run. After 1.5 s simulation run time (> 5 impeller revolutions) what I am noticing is that the vortex profile does not remain stable and fluctuates over time (i.e., it goes from flat, then increases in depth and then decrease in depth before returning to a flat surface again). I am unsure as to why this keeps happening?

Some things that I have done to consider enhancing convergence:

• Initialise flow field using steady state solver without VOF (i.e., just water) before switching on VOF (explicit) with transient solver
• Switch on implicit body force (with density set to that of light phase, i.e., 1.225 kg/m^3, in operating condition)
• Use very small time step to satisfy the CFL condition (CFL < 0.5)

However, despite doing all of these options the solution still doesn't converge. I would appreciate any help or guidance as I am stuck at this point. I have attached my residuals for the simulation run below

• Rob
Ansys Employee

How is the free surface shape changing with time? How large is the tank relative to the impellor size: ie if you look at the flow speed is it reasonable to expect the free surface to react within 1.5s? How well resolved is the free surface?

The set up looks mostly OK. For high swirl you may need to consider the Reynolds Stress Model (read the theory to see why). Similarly, geo-recon may be overkill here, so review Compressive.

• SR786
Subscriber

Hi,

The impeller diameter/tank diameter ratio is 1/2. I am using a single reference frame approach to model impeller rotation (suitable for my geometry as there are no baffles).

I am using standard k-epsilon for an initial solution as it’s the most stable/reliable turbulence model (though not accurate for stirred tank reactors)

My issue is that the free surface shouldn’t be starting off from a flat liquid surface, then vortex develops and then later on in solution it returns to flat liquid surface. Rather the vortex will develop slowly over time from flat liquid surface to fully developed profile. I am using geo-reconstruct as many academic papers have used this to model free surface deformation with explicit VOF due to being most accurate,

• Rob
Ansys Employee

And the height? As I haven't seen any results I can't comment. It's possible for a vortex to be unstable, but that'll also show in the free surface shape plots.

• SR786
Subscriber

Hi,

Yes, but the free surface profile shouldn’t be oscillating from flat surface to deformed surface to back to flat surface if the impeller is continuously rotating during simulation (i.e., the impeller isn’t stopping midway through and then restarting again). The pictures below show what is happening to vortex (from post processing) at certain time step where solution is returning to flat surface

• Rob
Ansys Employee

Assuming the solution is converged, well resolved and the vortex stable I agree. If you plot the z coordinate on the free surface (local range) how does it behave? If the vortex isn't stable the height change will cause the surface to level when it hits a certain level of distortion, then the vortex reforms etc.