[c_023]

Hello everyone,

I am currently trying to simlate the subcritical flashing of butane (liquid -> two-phase supersonic) through a CD nozzle. For that I implemented a Homogeneous Equilibrium Model (HEM) in Ansys Fluent (Question is not really software-related, more Physics-related, therefore this thread is started in the General Forum).

After several iterations (Steady state) the flow Patterns look physically right, then, while the solution seems to converge, shock waves start to form at the nozzle Exit, leading to high pressure Patches in the supersonic two-phase Jet exiting the nozzle, which cause the Density to rapidly increase, and then trigger completely unphysical behaviour with pressure Patches reaching unphysically high values, which then makes the solver either crash (completely diverge) or produce a pattern of seeminlgy random Patches of maximum pressures that are then limited by the solver Limits.

The Butane is flashed from liquid state at approx. 20 bar into two-Phase state at approx. 4 bar. The HEM model works well for benchmark cases (e.g. ERCOFTAC test cases) and is working in the following way: An enthalpy-based formulation of the Energy equation to calculate the specific enthalpy, then >Refprop lookuptables with bilinear Interpolation to get all material properties depending on pressure and enthalpy. The mesh is a very dense (>200k cells for 2d axisymmetric for a Domain of approx. 20x500mm), purely hexahedral mesh with max skewness below 0.5 and refinements near walls and in the nozzle and where shock waves are believed to occur. The behaviour occurs in Steady-state and pseudo-transient and transient simulations, and also occurs no matter what turbulence model is used (also when running laminar). Also, a pressure-gradient mesh Adaptation did not help resolve this.

Did anyone ever work on a similar project and encounter similar problems? Maybe HEM is not at all capable of simulating such a flow (I found many publications on CO2 flashing with HEM, but nothing on Butane or Propane and the likes)? Could it be that the high pressure hotspots that form in the region where shock waves are expected could be avoided when including a relaxation of the thermodynamic equilibrium, so that the high pressure in the shock wave does not increase density immediately?

Maybe someone has dealt with something similar with another software (openfoam, cfx,...) - I would be glad to hear about any experiences with this kind of case.

Thanks in Advance!

[Eifoehn4]

Dear c_023,

i think you are facing the problem of spurious pressure/velocity oscillations arising with real EOS. They are severe, especially near the critical point.
Without a modification of your underlying numerics they won't disappear. Most of the fixes available in literature violate the energy conservation.

Regards

[c_023]

Thank you for your helpful answer - I believe that this is the reason for my divergence issues.. Do you (or maybe anyone else) have experience on overcoming such problems in Fluent? To my knowledge changing the underlying numerics in Fluent is not really possible... And all equations Fluent can solve for are based on conservation principles.. Does anyone have an idea on how to fix this? Maybe artificially smoothing the density change inside the fluid propertie tables or imposing strong gradient limiters?

[Eifoehn4]

Dear c_023,

i am no commercial CFD user. From a numerical point of view, you have to change the way how the energy equation is discretized. I think Fluent uses the total energy as evolution equation. You would have to change this by using a pressure evolution equation.

There are some more advanced fixes, but all of them are non-conservative. Artificial viscosity may help, but would not be a nice solution.

Regards

[c_023]

Thank you for pointing me in the right direction, I will try to overcome the problems this way. If I succeed I will post the solution here, if anyone ever has to tackle the same problem.