Update geometry interface

[jbreue16]

• BED_LENGTH instead of COL_LENGTH ?
• UNIT_TYPE defines geometry and dimensionality of the column model, e.g. FRUSTUM_COLUMN_MODEL_2D, AXIAL_COLUMN_MODEL_2D, RADIAL_COLUMN_MODEL_2D ? Or should geometry be separated?
• Do we need inner and outer radius in radial model? should we always specify the same in every model, i.e. bed length, some radius and flow rate, can we get everything we need from that for every geometry?

[schmoelder]

As discussed, I would recommend separating the fields into:

• unit_type: column (or even maybe even chromatography)
• geometry: axial | radial | frustum
• dimensionality: 0D | 1D | 2D

This would make it much easier to parse the field without having to split strings.

Note, for the frustum, we probably need some additional curvature parameter because there can be different scenarios with the same inner and outer diameters (e.g. consider an apple sized frustum vs an earth sized frustum with a given "height")

[lieres]

I would like the interfaces of the axial flow, radial flow, and frustum geometries to be as consistent as possible. However, that is actually not quite simple.

Let's focus on 1D transport models for the time being. 2D versions of the radial flow and frustum geometries have different symmetries than the axial flow geometry.

The radial flow geometry (precisely: cylindrical wedge) is a cutout of two concentric cylinders with a specific height and angle, from which the bed height as well as the outer and inner surface areas can be determined.

The frustum geometry (precisely: spherical conical frustum) is a cutout of two concentric spheres with a specific angle, from which the bed height as well as the outer and inner surface areas can be determined.

If volumetric flow rates are specified, the cross-sectional area determines the linear flow rate. In the axial flow geometry, this area is constant and depends on the column (cylinder) radius.

In the radial flow geometry, the area varies along the bed length (radial position) and depends on the height and angle of the cutout. That is, there are many different combinations yielding the same area for a given radial position, which complicates a 2D version of this model.

In the frustum geometry, the area also varies along the bed length (radial position) and depends on the angle of the cutout. In contrast to the axial and radial flow geometries, the outer surface area of the cutout has an upper limit, i.e. when the cutout angle is 180 degrees. However, this should practically not matter.

Now, we need to decide which parameters we want to specify and which to derive from them.

Option 1: Most consistent with the axial flow geometry would be to always specify the outer (larger) surface area and bed height. In addition, the outer cylinder or sphere radius would be required to determine the scale.

Option 2: Most users would probably prefer to specify the outer and inner radius as well as the linear flow rate at the outer (larger) radius. In this case, we could determine the outer and inner areas from the linear flow rate (though we actually don't need them).

Option 3: Since CADET-Process is based on volumetric flow rates, we can specify the outer and inner radius as well as the cutout angle (and cylinder height in the case of the radial flow geometry). From this, we can determine the bed height and surface areas (which we need in this case).

Option 4: Make Option 3 the default but allow users to alternatively specify the linear flow rate at the outer (larger) radius instead of the cutout angle (and cylinder height in the case of the radial flow geometry), i.e., Option 2.

Even though it might seem most intuitive, we should not understand the frustum as an axial flow device with decreasing cylinder radius along the axial dimension, because 1) as mentioned above, this specification would be least consistent with the other geometries, and 2) flat ends would cause varying lengths of the flow paths, as they are not parallel. However, we should provide users with a preprocessing tool that allows them to determine approximate parameters for Options 1-4 from the bed height and different cylinder radii at both column ends.

[lieres]

frustum.pdf

After considering this, I would vote for specifying $r_1$, $r_2$, and $L$ in the interface (alternatively $R_1$, $R_2$, and $\alpha$).