ErgunTest

Template Info

Target Parameters: CFD_scaleDrag CFD_scaleDH
Contact Models:
Particle Shapes: sphere multisphere

This case simulates the fluidization of a packed bed in a cylindrical container; see Figure 1. The inlet velocity increases linearly from the initial velocity CFD_Ustart (normally 0 m/s) to the final velocity CFD_Uend (which should be around 80% of the reference fluidization velocity). This calibration template is used to calibrate one of the two scaling factors for the drag model, namely CFD_scaleDrag or CFD_scaleDH.

_images/ergunTest_setup.png — Figure 1: Simulation result obtained from `ErgunTest` calibration template. A fluid flow enters through the lower base of the cylinder and fluidizes the packed bed.

This template is designed to work in conjunction with the bulkDensityTest and volumeFracTest templates, and relies on properly calibrated bulk density and (if necessary) scaled volume fraction. While the pressure drop at the minimum fluidization velocity $U_{mf}$ only depends on the bulk density of the material, the minimum fluidization velocity itself, and consequently the slope of the pressure drop as function of inlet velocity, $\Delta p \left( U_{in} \right)$ , also depends on the drag coefficient of the particles.

This case is sensitive to the CFD_scaleDrag and CFD_scaleDH parameters. The former scales the hydrodynamic drag force directly, while the latter scales the hydraulic diameter of the particles prior to drag force computation.

Note

Both parameters need to be provided as either param_calibration or param_fixed.

Warning

Only use one of the two parameters as target_parameter. Calibrating both target parameters at the same time does not make sense, and will most likely yield unsatisfactory results.

Simulation phases

Initialization

During the initialization, particles are poured into a cylindrical bin. The simulation automatically stops when the bin is full and the particles have settled. This is achieved by monitoring their kinetic energy. Then particles above $h_{bed,sim}=2 D$ , where $D$ is the diameter of the cylinder, are removed and a short settling period is run.

Optimization

The optimization run is a CFDEMcoupling simulation where the fluid flow is linearly increased from CFD_Ustart to CFD_Uend over the timespan CFD_Uramptime.

Quality Function

The quality function is the sum of the squared distances between the scaled pressure profiles obtained from the referece and the simulation at several sampling points:

$q = \sum_i \left( \Delta p_{sim}(u_i)/h_{bed, sim} - \Delta p_{ref}(u_i)/h_{bed,ref} \right)^2$

Measurement file

This case requires measurement data in either CSV or a space-delimited format. Lines beginning with # are discarded. The first two columns of the data file are interpreted as inlet velocity in m/s and pressure drop in Pa, respectively. Example measurement files could look like

# Ergun measurement data
# u_in dp
0.1     1e2
0.2     2e2
........

or like

# measurement 1.1.2020
# [other header info]
# ....
# u_in,dp,expansion,temperature
0.1,1e2,1.0,300
0.2,2e2,1.01,307
.....

where in the second example all other columns except the first two are discarded.

Note

ErgunTest expects the measurement file to contain data up to at least 80% of the fluidization velocity, but to end prior to fluidization. Including velocity/pressure data above the minimum fluidization velocity will inevitably yield wrong calibration results.

Template parameters

General settings

Parameter	Default
scaleweight	1
pairGranModel	hertz
pairTangential	history
pairCohesion	off
pairRollingFriction	epsd
pairSurface	default
NPROC	4
dumpT	0.01 s
dump	0
G_D_RATIO	10

Note

G_D_RATIO is the ratio of cylinder diameter and largest coarsegrained particle diameter

Specific settings

Variable	Default	Meaning
CFD_timestep	5e-4	Timestep for the CFD part of the simulation [s]
CFD_writeInterval	0.01	CFD write interval [s]
CFD_Ustart	undefined	Inlet velocity at start of simulation [m/s]
CFD_Uramptime	undefined	Velocity ramp time [s]
CFD_Uend	undefined	Inlet velocity at end of simulation (~80% Umf) [m/s]
hbed_ref	undefined	Height of the particle bed in the reference experiment [m]
cfdemSolverBinary	cfdemSolverPimple	CFD-DEM solver