"Velocity" in the external function setup

thomas.fuchs · June 9, 2021, 1:05pm

Dear Cadet-Team,

I was wondering, what the “velocity” of the external profile in /input/model/external/source_XXX expresses. According to cadet.github.io its unit is 1/s, not m/s. How can I set this velocity so that, e.g. a 0.1 m column is crossed by the profile in 10 s?
The velocity of the external profile is not coupled to the Flow Rate in that unit, right?

Best regards,
Thomas

j.schmoelder · June 10, 2021, 6:45am

Edit: Now that I had a coffee, I can think a bit clearer…

Hi Thomas,

after consulting with @s.leweke, he informed me that in fact the column length is normalized. So the velocity is 1/s with respect to a column with unit length.

The code actually has a nice visual explanation:

github.com

modsim/CADET/blob/62222c7036638ee179084b21e50aa575ff247b21/src/libcadet/model/extfun/LinearInterpolationExternalFunction.cpp#L83

    
      
          		// 
          		// The coordinate system of the external profile begins at the column outlet
          		// and points backward to the column inlet.
          		//
          		//       1 / velocity                                                 0
          		//    t <---|---------------------------------------------------------|
          		//           _________________________________________________________
          		//          |                                                         |
          		//   Inlet  |  =>               Column                            =>  | Outlet
          		//          |_________________________________________________________|
          		//
          		//
          		//          The column moves along the profile to the left with _velocity.
          		//          Thus, after some time, the coordinate system has shifted:
          		//
          		//       1 / _velocity + t        (1 - z) / _velocity + t             t
          		//    t <---|------------------------------|--------------------------|-------------|
          		//           _________________________________________________________
          		//          |                                                         |
          		//   Inlet  |  =>               Column                            =>  | Outlet
          		//          |_________________________________________________________|

Since this is not really clear from the documentation, I will add some more explanation.

You are also correct in assuming that this velocity is completely independent of the flow rate. This way you have a lot of freedom to design these external functions.

I’ve actually already started preparing a tutorial on some of the advanced features of CADET (i.e. parameter sensitivities, external functions etc.). Maybe you want to have a look? Feedback is always appreciated.

01_advanced_features_demonstration_solution.ipynb (175.5 KB)
or if you prefer, a pdf:
01_advanced_features_demonstration_solution.pdf (201.0 KB)

Best regards

Johannes

For anyone reading this, looking for answers how to interpret the velocity of the unit operations, I recommend reading on this section of the documentation.

In summary, we recommend using the column diameter and volumetric flow rate, since this is what’s used in multi-unit-operation systems. Then the velocity is automatically determined from the continuity equation, taking into account the porosity. We mostly use the velocity field just to reverse the flow direction of the column (e.g. for flip flow chromatography).

thomas.fuchs · June 10, 2021, 2:32pm

Hi Johannes,

thank you very much for this explanation!

Best regards,
Thomas

soumi · August 7, 2021, 9:14pm

Thanks - this was helpful!

soumi · September 7, 2021, 12:07am

Hi,

I had a follow-up question - is there any way to vary (sectionwise) the velocity of the external function profile?

Thanks,

lieres · September 7, 2021, 2:44pm

Hi Suomi,

You can specify and function of time and space as external function. So changes in the speed of a signal travelling along the column can be specified within that function.

Eric