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Smoothly Varying Cross Section Column 1D

Group /input/model/unit_XXX - UNIT_TYPE - COLUMN_MODEL_1D

This geometry describes an axial flow column whose cross section area varies smoothly along the flow path and is prescribed by the user, see Smoothly varying cross section GRM. It is selected by GEOMETRY \(= \texttt{SMOOTHLY_VARYING}\) and is only available for the DG spatial discretization, since the area is given at the DG nodes.

Only the geometry fields differ from the axial flow cylinder; all remaining fields of the unit (NCOMP, COL_POROSITY, TOTAL_POROSITY, NPARTYPE, PAR_TYPE_VOLFRAC, COL_DISPERSION, INIT_C, INIT_STATE, the reaction and particle subgroups, and the discretization group) are identical to Axial Flow Column 1D.

UNIT_TYPE

Specifies the type of unit operation model

Type: string

Range: \(\texttt{COLUMN_MODEL_1D}\)

Length: 1

GEOMETRY

Column geometry

Type: string

Range: \(\texttt{SMOOTHLY_VARYING}\)

Length: 1

CROSS_SECTIONAL_AREA_AT_NODES

Cross section area at every DG node, in the ordering of the bulk solution, i.e. element by element from the column inlet at \(x = 0\) to \(x = \texttt{BED_LENGTH}\), with the nodes of each element in ascending order. Since neighbouring elements share their interface node, that node appears twice, once as the last entry of the left and once as the first entry of the right element, and the two entries must be equal. The area has to be strictly positive.

Unit: \(\mathrm{m}^2\)

Type: double

Range: \(> 0\)

Length: \((\texttt{POLYDEG} + 1) \cdot \texttt{NELEM}\)

The nodes are the Legendre-Gauss-Lobatto nodes of each element, which are also written out by WRITE_COORDINATES, so a convenient way to obtain them is to run the same discretization once with any other geometry and evaluate the intended area profile at the reported coordinates.

BED_LENGTH

Column length. NOT optional for this geometry.

Unit: \(\mathrm{m}\)

Type: double

Range: \(> 0\)

Length: 1

FORWARD_FLOW

Flow direction of the column. If set to 1, the flow runs from \(x = 0\) towards \(x = \texttt{BED_LENGTH}\), i.e. the inlet is the end whose area is the first entry of CROSS_SECTIONAL_AREA_AT_NODES.

Type: bool

Range: \(\{0,1\}\)

Length: NSEC

Group /input/model/unit_XXX/discretization - UNIT_TYPE - COLUMN_MODEL_1D

The discretization group is the one of Axial Flow Column 1D, with two restrictions:

• SPATIAL_METHOD must be \(\texttt{DG}\). There is no Finite Volume variant of this geometry, because the area is prescribed at the DG nodes.

• USE_COLLOCATION_DG must be \(0\), which is the default for every geometry other than the axial flow cylinder.

Note that CROSS_SECTIONAL_AREA_AT_NODES depends on POLYDEG and NELEM, so it has to be recomputed whenever the discretization is refined.