# 8.3.4. Geometry and Discretization¶

## 8.3.4.1. COORDINATES¶

Data Type: CHARACTER

Coordinate system used in the simulation.

Table 8.25 Valid Values

Name

Default?

Description

Cartesian

Cartesian coordinates.

cylindrical

Cylindrical coordinates.

## 8.3.4.2. IMAX¶

Data Type: INTEGER

Number of cells in the x (r) direction.

## 8.3.4.3. DX(CELL)¶

Data Type: DOUBLE PRECISION

• $$0 \le Cell \le 5000$$

Cell sizes in the x (r) direction. Enter values from DX(0) to DX(IMAX-1).

• Use uniform mesh size with higher-order discretization methods.

• DX should be kept uniform in cylindrical coordinates for strict momentum conservation.

## 8.3.4.4. XMIN¶

Data Type: DOUBLE PRECISION

The inner radius in the simulation of an annular cylindrical region.

## 8.3.4.5. XLENGTH¶

Data Type: DOUBLE PRECISION

Simulation domain length in the x (r) direction.

## 8.3.4.6. X_MIN¶

Data Type: DOUBLE PRECISION

Simulation domain lower bound in the x-direction.

## 8.3.4.7. X_MAX¶

Data Type: DOUBLE PRECISION

Simulation domain upper bound in the x-direction.

## 8.3.4.8. JMAX¶

Data Type: INTEGER

Number of cells in the y-direction.

## 8.3.4.9. DY(CELL)¶

Data Type: DOUBLE PRECISION

• $$0 \le Cell \le 5000$$

Cell sizes in the y-direction. Enter values from DY(0) to DY(JMAX-1). Use uniform mesh size with second-order discretization methods.

## 8.3.4.10. YLENGTH¶

Data Type: DOUBLE PRECISION

Simulation domain length in the y-direction.

## 8.3.4.11. Y_MIN¶

Data Type: DOUBLE PRECISION

Simulation domain lower bound in the y-direction.

## 8.3.4.12. Y_MAX¶

Data Type: DOUBLE PRECISION

Simulation domain upper bound in the y-direction.

## 8.3.4.13. NO_K¶

Data Type: LOGICAL

Flag to disable the third dimension (i.e., 2D simulation).

• Z axis in Cartesian coordinate system

• Theta in Cylindrical coordinate system

Table 8.26 Valid Values

Name

Default?

Description

.FALSE.

3D simulation.

.TRUE.

2D simulation.

## 8.3.4.14. KMAX¶

Data Type: INTEGER

Number of cells in the z-direction.

## 8.3.4.15. DZ(CELL)¶

Data Type: DOUBLE PRECISION

• $$0 \le Cell \le 5000$$

Cell sizes in the z (theta) direction. Enter values from DZ(0) to DZ(KMAX-1). Use uniform mesh size with second-order discretization methods.

## 8.3.4.16. Z_MIN¶

Data Type: DOUBLE PRECISION

Simulation domain lower bound in the z-direction.

## 8.3.4.17. Z_MAX¶

Data Type: DOUBLE PRECISION

Simulation domain upper bound in the z-direction.

## 8.3.4.18. ZLENGTH¶

Data Type: DOUBLE PRECISION

Simulation domain length in the z (theta) direction.

## 8.3.4.19. CYCLIC_X¶

Data Type: LOGICAL

Flag for making the x-direction cyclic without pressure drop. No other boundary conditions for the x-direction should be specified.

Table 8.27 Valid Values

Name

Default?

Description

.FALSE.

No cyclic condition at x-boundary.

.TRUE.

Cyclic condition at x-boundary.

## 8.3.4.20. CYCLIC_X_PD¶

Data Type: LOGICAL

Flag for making the x-direction cyclic with pressure drop. If the keyword FLUX_G is given a value, this becomes a cyclic boundary condition with specified mass flux. No other boundary conditions for the x-direction should be specified.

Table 8.28 Valid Values

Name

Default?

Description

.FALSE.

No cyclic condition at x-boundary.

.TRUE.

Cyclic condition with pressure drop at x-boundary.

## 8.3.4.21. DELP_X¶

Data Type: DOUBLE PRECISION

Fluid pressure drop across XLENGTH when a cyclic boundary condition with pressure drop is imposed in the x-direction.

## 8.3.4.22. CYCLIC_Y¶

Data Type: LOGICAL

Flag for making the y-direction cyclic without pressure drop. No other boundary conditions for the y-direction should be specified.

Table 8.29 Valid Values

Name

Default?

Description

.FALSE.

No cyclic condition at y-boundary.

.TRUE.

Cyclic condition at x-boundary.

## 8.3.4.23. CYCLIC_Y_PD¶

Data Type: LOGICAL

Flag for making the y-direction cyclic with pressure drop. If the keyword FLUX_G is given a value this becomes a cyclic boundary condition with specified mass flux. No other boundary conditions for the y-direction should be specified.

Table 8.30 Valid Values

Name

Default?

Description

.FALSE.

No cyclic condition at y-boundary.

.TRUE.

Cyclic condition with pressure drop at y-boundary.

## 8.3.4.24. DELP_Y¶

Data Type: DOUBLE PRECISION

Fluid pressure drop across YLENGTH when a cyclic boundary condition with pressure drop is imposed in the y-direction.

## 8.3.4.25. CYCLIC_Z¶

Data Type: LOGICAL

Flag for making the z-direction cyclic without pressure drop. No other boundary conditions for the z-direction should be specified.

Table 8.31 Valid Values

Name

Default?

Description

.FALSE.

No cyclic condition at z-boundary.

.TRUE.

Cyclic condition at z-boundary.

## 8.3.4.26. CYCLIC_Z_PD¶

Data Type: LOGICAL

Flag for making the z-direction cyclic with pressure drop. If the keyword FLUX_G is given a value this becomes a cyclic boundary condition with specified mass flux. No other boundary conditions for the z-direction should be specified.

Table 8.32 Valid Values

Name

Default?

Description

.FALSE.

No cyclic condition at z-boundary.

.TRUE.

Cyclic condition with pressure drop at z-boundary.

## 8.3.4.27. DELP_Z¶

Data Type: DOUBLE PRECISION

Fluid pressure drop across ZLENGTH when a cyclic boundary condition with pressure drop is imposed in the z-direction.

## 8.3.4.28. SHEAR¶

Data Type: LOGICAL

Imposes a mean shear on the flow field as a linear function of the x coordinate. This feature should only be used when CYCLIC_X is .TRUE. and the keyword V_SH is set.

## 8.3.4.29. V_SH¶

Data Type: DOUBLE PRECISION

Specifies the mean y velocity component at the eastern boundary of the domain (V_SH), and the mean Y velocity (-V_SH) at the western boundary of the domain.

## 8.3.4.30. FLUX_G¶

Data Type: DOUBLE PRECISION

If a value is specified, then the domain-averaged gas flux is held constant at that value in simulations over a periodic domain. A pair of boundaries specified as periodic with fixed pressure drop is then treated as periodic with fixed mass flux. Even for this case a pressure drop must also be specified, which is used as the initial guess in the simulations.

## 8.3.4.31. CYLINDRICAL_2D¶

Data Type: LOGICAL

Applies the 2.5D model for cylindrical column by combining 2D assumption and axi-symmetric assumption. Li et al. (2015). A 2.5D computational method to simulate cylindrical fluidized beds, Chemical Engineering Science, 123:236-246.

## 8.3.4.32. I_CYL_NUM¶

Data Type: INTEGER

Parameter to control the plate half width and the wedge radius in the 2.5D cylindrical model. This value should be less than half the grid cells in the radial direction (IMAX/2). 

## 8.3.4.33. I_CYL_TRANSITION¶

Data Type: INTEGER

Parameter to smooth the transition from cylindrical to 2D in the 2.5D cylindrical model. 

Table 8.33 Valid Values

Name

Default?

Description

2

Two cell smoothing transition.

1

One cell smoothing transition.

0

No smoothing.

## 8.3.4.34. CPX(CTRL)¶

Data Type: DOUBLE PRECISION

• $$0 \le CTRL \le MAX{\_}CP$$

Location of control points in x-direction.

## 8.3.4.35. NCX(CTRL)¶

Data Type: INTEGER

• $$1 \le CTRL \le MAX{\_}CP$$

Number of cells within a segment (x-direction).

## 8.3.4.36. ERX(CTRL)¶

Data Type: DOUBLE PRECISION

• $$1 \le CTRL \le MAX{\_}CP$$

Expansion ratio (last DX/first DX) in a segment (x-direction).

## 8.3.4.37. FIRST_DX(CTRL)¶

Data Type: DOUBLE PRECISION

• $$1 \le CTRL \le MAX{\_}CP$$

Value of first DX in a segment (x-direction). A negative

value will copy DX from previous segment (if available).

## 8.3.4.38. LAST_DX(CTRL)¶

Data Type: DOUBLE PRECISION

• $$1 \le CTRL \le MAX{\_}CP$$

Value of last DX in a segment (x-direction). A

negative value will copy DX from next segment (if available).

## 8.3.4.39. CPY(CTRL)¶

Data Type: DOUBLE PRECISION

• $$0 \le CTRL \le MAX{\_}CP$$

Location of control points in y-direction.

## 8.3.4.40. NCY(CTRL)¶

Data Type: INTEGER

• $$1 \le CTRL \le MAX{\_}CP$$

Number of cells within a segment (y-direction).

## 8.3.4.41. ERY(CTRL)¶

Data Type: DOUBLE PRECISION

• $$1 \le CTRL \le MAX{\_}CP$$

Expansion ratio (last DY/first DY) in a segment (y-direction).

## 8.3.4.42. FIRST_DY(CTRL)¶

Data Type: DOUBLE PRECISION

• $$1 \le CTRL \le MAX{\_}CP$$

Value of first DY in a segment (y-direction). A negative value will copy DY from previous segment (if available).

## 8.3.4.43. LAST_DY(CTRL)¶

Data Type: DOUBLE PRECISION

• $$1 \le CTRL \le MAX{\_}CP$$

Value of last DY in a segment (y-direction). A negative value will copy DY from next segment (if available).

## 8.3.4.44. CPZ(CTRL)¶

Data Type: DOUBLE PRECISION

• $$0 \le CTRL \le MAX{\_}CP$$

Location of control points in z-direction.

## 8.3.4.45. NCZ(CTRL)¶

Data Type: INTEGER

• $$1 \le CTRL \le MAX{\_}CP$$

Number of cells within a segment (z-direction).

## 8.3.4.46. ERZ(CTRL)¶

Data Type: DOUBLE PRECISION

• $$1 \le CTRL \le MAX{\_}CP$$

Expansion ratio (last DZ/first DZ) in a segment (z-direction).

## 8.3.4.47. FIRST_DZ(CTRL)¶

Data Type: DOUBLE PRECISION

• $$1 \le CTRL \le MAX{\_}CP$$

Value of first DZ in a segment (z-direction). A negative value will copy DZ from previous segment (if available).

## 8.3.4.48. LAST_DZ(CTRL)¶

Data Type: DOUBLE PRECISION

• $$1 \le CTRL \le MAX{\_}CP$$

Value of last DZ in a segment (z-direction). A negative value will copy DZ from next segment (if available).