Tuesday, January 8, 2008

CFD limitations for stirred vessel applications

The widening application of computational fluid dynamics by academics working on pharma problems, as evidenced in presentations at the AIChE Annual Meeting in Salt Lake City in November, prompted this note on the limitations of that approach for design space and QbD work.

CFD results can have a high impact in a presentation or paper, but unfortunately this can mask the invalidity of the underlying calculations. Our company was a leading exponent of CFD before facing the fact that its limitations prevented us addressing many customer problems, especially those involving stirred tanks.

Validating CFD:
No CFD results for stirred vessels / reactors should ever be presented or relied upon without quantifying their validity by comparison with established data:
  1. A quick overall validation check is the torque on the agitator, obtained by integrating momentum flow on a surface around the impeller(s), which can be verified using known power numbers (Po).
  2. Another important check is integrating the epsilon (W/Kg, rate of turbulent energy dissipation per unt mass) over the fluid volume; this should nearly equate in a turbulent system to the power input calculated using a known Po.
  3. The effects of grid size on any CFD results should always be checked; it can be very difficult to obtain a 'grid-independent' solution.
  4. More detailed validation tests include flow visualization (requires a lab set-up and tracer test techniques or similar) or careful velocity measurements.

CFD and Design Space / QbD:
For QbD purposes, CFD can shed light on elements of a problem or behaviours of a vessel under certain limited conditions, e.g. in single-phase flow (no particles, drops, bubbles), at steady state (is there really a steady state?) and without chemistry occurring, if you have the expertise, time and resources to set up a significant project to produce these results. However much the same level of insight can be obtained using a five minute calculation and an engineering correlation :)

For Design Space exploration, multiple parametric calculations would need to be performed, increasing the project duration by orders of magnitude, producing results that potentially cannot be relied upon.

Too negative? No, just realistic. CFD excels in automotive / airflow / aerospace and generally in single-phase non-reacting systems with well-defined turbulence and a steady state. Those situations are rarely of interest for Pharma API development and scale-up.

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