The scenario considered in this verification case is such that eight spherical particles are fixed into an air planar Couette flow (as shown in Figure 3.13: Lift Force verification case (particles centralized, in red; CFD cell nodes colored by Fluid Velocity; air inlet and outlet indicated with red arrows.), and it is modeled using the 2-Way Fluent (unresolved) CFD coupling method, using both the Mei and Saffman lift force laws. Numerical results are compared to analytical lift force data, showing good agreement.

Figure 3.13: Lift Force verification case (particles centralized, in red; CFD cell nodes colored by Fluid Velocity; air inlet and outlet indicated with red arrows.

The analytical lift force data used as reference to verify this case was calculated with both Mei (Equation 3–4) and Saffman (Equation 3–5) lift coefficient correlations implemented as equations, in order to calculate the lift force (Equation 3–6) for each law. The same properties values used to calculate the analytical data were used to set up the project into Rocky, and these input parameters are presented in Table 3.7: Verification case input parameters.

(3–4)

(3–5)

(3–6)

The case is initialized in Fluent with the proposed velocity field for the air flow. Thus, we can process only the first output to compare the results with the analytical data, because of that we will not consider any perturbations in the fluid velocity field caused from the collision with the particles (what makes the calculation of analytical data simpler).

Table 3.7: Verification case input parameters.

Parameter	Value	Unit
Physical Model:
Gravity (X)	0
Gravity (Y)	0
Gravity (Z)	0
Solid Properties (Particles):
Shape	Sphere	-
Diameter	0.1	-
Rotations	Enabled	-
Inlet Type	Particle Custom Inlet	-
Number of Particles	8	-
Material Bulk Density	1600
Material Young's Modulus	108
Material Poisson's Ratio	0.3	-
Fluid Properties (Fuent):
Domain Length (X)	5	m
Domain Length (Y)	5	m
Domain Length (Z)	20	m
Inlet Velocity	3y+1
Outlet Gauge Pressure	0	Pa
Walls Shear Condition	Specific Shear	-
Walls Shear Stress (X)	0	Pa
Walls Shear Stress (Y)	0	Pa
Walls Shear Stress (Z)	0	Pa
Density	1.225
Viscosity
2-Way Fluent Properties
Drag Law	Morsi & Alexander	-
Morsi & Alexander Parameters (K1)	0	-
Morsi & Alexander Parameters (K2)	0	-
Morsi & Alexander Parameters (K3)	0	-
Lift Law (first run)	Saffman	-
Lift Law (second run)	Mei	-
Solver Parameters:
Simulation Duration	0.1	s
Output Frequency (CFD)	0.1	s
Output Frequency (DEM)	0.1	s

The Rocky project was run twice (once for each lift force law) and the results can be compared to the reference (Figure 3.14: Comparison between simulation and analytical results of lift force for the 8 fixed particles.). For each particle, the lift force versus position was plotted, totalizing eight dots for each law (one per particle). In the same plot, the analytical solution is also plotted as dashed and dotted lines, allowing the visualization of the good agreement between the analytical and simulation results.

Figure 3.14: Comparison between simulation and analytical results of lift force for the 8 fixed particles.

In the second plot (Figure 3.15: Absolute lift force error for each particle.), it is possible to visualize the absolute error between the Rocky simulation results and the analytical data for each run. For every particle, the relative error is approximately 0.04%, ensuring strong correlation between the solutions. The solutions results are also presented in Table 3.8: Results correlation for both lift force laws., as well as the ratio between the analytical and the Rocky simulation results.

Figure 3.15: Absolute lift force error for each particle.

Table 3.8: Results correlation for both lift force laws.

Law	Particle Y-position [m]	Target Force [N]	Rocky Force [N]	Ratio[-]
Saffman	0.625	0.37625	0.37667	0.99
	1.125	0.57297	0.57319	0.99
	1.625	0.76941	0.76972	0.99
	2.125	0.96586	0.96624	0.99
	2.625	1.1623	1.1627	0.99
	3.125	1.3587	1.3592	0.99
	3.625	1.5552	1.5558	0.99
	4.125	1.7516	1.7523	0.99
Mei	0.625	0.63224	0.63249	0.99
	1.125	0.96210	0.96248	0.99
	1.625	1.2919	1.2924	0.99
	2.125	1.6218	1.6224	0.99
	2.625	1.9517	1.9524	0.99
	3.125	2.2815	2.2824	0.99
	3.625	2.6114	2.6124	0.99
	4.125	2.9413	2.9424	0.99