In this verification case, the pressure drop along a fixed bed of spherical particles is evaluated using the Ergun[5] dense flow drag law, which is modeled using the 2-Way Fluent (unresolved) CFD coupling method. For more information about how CFD models and methods are implemented in Rocky, refer to the Rocky DEM-CFD Coupling Technical Manual. The case illustration is shown in Figure 3.9: Fixed bed with 0.5 m height of spherical particles within a container..

Figure 3.9: Fixed bed with 0.5 m height of spherical particles within a container.

The Ergun [5] correlation for the pressure losses accompanying the flow of fluids through a fixed bed of granular material can be expressed as follows:

(3–3)

where:

The equations shown in the last section can be resolved and equivalent results can be calculated by Rocky considering the same input data and boundary conditions. The input parameters for this verification case setup are presented in Table 3.5: Verification case input parameters..

Table 3.5: Verification case input parameters.

Parameter	Value	Unit
Physical Model:
Gravity Y	-9.81
Geometry (Container):
Length (X)	0.1	m
Length (Y)	0.8	m
Length (Z)	0.1	m
Solid Properties (Geometry):
Material Density	7850
Material Young's Modulus	1011
Material Poisson's Ratio	0.3	-
Solid Properties (Particle):
Bed Height	0.5	m
Shape	Sphere	-
Diameter	3.95	mm
Rotations	Enabled	-
Input Type	Volume Fill	-
Input Mass	10	kg
Material Bulk Density	500
Material Young's Modulus	108
Material Possions's Ratio	0.3	-
Fluid Properties (Fluent):
Domain Length (X)	0.1	m
Domain Length (Y)	0.8	m
Domain Length (Z)	0.1	m
Fluent Mesh Size	10	mm
Inlet Velocity	0.275	m/s
Outlet Gauge Pressure	0	Pa
Walls Shear Condition	Free Slip	-
Density	1000
Dynamic Viscosity	0.001
2-Way Fluent Properties:
Drag Law	Ergun[5]	-
Solver Parameters:
Simulation Duration	1.0	s

After running the Rocky case as specified, the results can then be compared to the analytical values. Here, the static pressure loss along the bed height is shown in Figure 3.10: Rocky simulation results using 2-Way Fluent coupling showing the static pressure along the fixed bed at the last timestep. and Figure 3.11: Comparison of static pressure [kPa] for the Rocky simulation and reference results.. The numerical solution given by Rocky presents strongly correlated values to those obtained by the analytical expression.

Figure 3.10: Rocky simulation results using 2-Way Fluent coupling showing the static pressure along the fixed bed at the last timestep.

Figure 3.11: Comparison of static pressure [kPa] for the Rocky simulation and reference results.

The absolute and relative errors for the pressure drop are compared in Figure 3.12: Absolute and relative errors.. The maximum absolute error for the pressure drop error is around 1.0 kPa. The maximum relative error is around 2.3%.

Figure 3.12: Absolute and relative errors.

Table 3.6: Pressure target lists the value for the total pressure drop on the fixed bed. This includes the target value calculated by the analytical expression as compared to the value calculated by Rocky. A Ratio of 1.00 shows a strong correlation between the results.