bulkDensityTest

Template Info

Target Parameters: rho_p
Contact Models: tangential no_history tangential history rolling_friction epsd rolling_friction epsd2 cohesion sjkr cohesion sjkr2 cohesion adaptive
Particle Shapes: sphere multisphere

Overview

The setup consists of a cylindrical bin entirely filled with particles; see Figure 1. The contained mass is calculated and divided by the volume of the cylinder. The simulation bulk density is then compared with a reference bulk density and the particle density is adjusted to match the simulated with the reference value.

_images/bulkDensity_sketch.png — Figure 1: sketch of the simulation setup. An equilateral cylinder is filled with particles and the particle density is calibrated to match a desired bulk density. $d_{max}$ denotes the maximum particle radius (in case of polydisperse system), $CG$ is the coarsegraining factor and G_D_RATIO is the ratio between the diameter of the cylinder and the diameter of the largest coarsegrained particle.

Figure 1: sketch of the simulation setup. An equilateral cylinder is filled with particles and the particle density is calibrated to match a desired bulk density. $d_{max}$ denotes the maximum particle radius (in case of polydisperse system), $CG$ is the coarsegraining factor and G_D_RATIO is the ratio between the diameter of the cylinder and the diameter of the largest coarsegrained particle.

The reference bulk density of the material, $\rho_{bulk}$ , is provided indirectly by the user through two parameters: the measured bed height, $h_{meas}$ , and the minimum fluidization pressure of the Ergun Test, $\Delta p_{min} = \Delta p (U_{mf})$ , where $U_{mf}$ is the minimum fluidization velocity.

This template is designed to work in conjunction with the volumeFracTest and ErgunTest templates. The intended calibration procedure works as follows: in an appropriate experiment, the pressure drop is measured as function of the inlet velocity, $\Delta p\left(U_{in}\right)$ . From this measurement curve, both the slope of the pre-fluidization pressure buildup and the minimum fluidization velocity $U_{mf}$ can be extracted. First, the bulk density of the material needs to be calibrated. At the minimum fluidization velocity, the drag force acting on the whole bed is equal to the gravity force:

$\rho_{bulk} = \frac{\Delta p_{min}}{h_{meas} g} + \rho_{fluid}$

where $\rho_{fluid}$ is the density of the fluid in which the particles are immersed. Note that this expression neither depends on the drag coefficient of the particles, nor does it explicitly depend on the actual minimum fluidization velocity $U_{mf}$ . This calibration step merely ensures that fluidization occurs at the correct pressure drop. Thus, it is crucial that this calibration is performed prior to calibrating the scale drag with the ErgunTest template.

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. The finished packing is then written to a restart file.

Optimization

The optimization run only performs a single time step to recalculate the bulk density of the material in the cylinder.

Quality function

The quality function is the magnitude of the normalized difference of the target density and the current simulation density.

Measurement file

The reference bulk density is calculated using the pressure drop at minimum fluidization velocity, dpUmf, and the height of the particle bed, hbed. Both parameters needs to be specified by the user in the calibration_case command via the parameter_overrides keyword. Nonetheless, due to current restrictions of the framework, Aspherix® Calibration needs a measurement file to be present. The content of this file is irrelevant and will not affect calibration.

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	20

Note

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

Specific settings

Variable	Default	Meaning
dpUmf	undefined	Reference pressure drop at minimum fluidization velocity [Pa]
hbed	undefined	Reference bed height [m]
si_units	1	Units (1 = si, 0 = cgs)
binning_type	monodisperse_binning	Binning type in neighborlist algorithm

Note

In case of small non-coarsegrained particles (of the order of the micron), it is necessary to set si_units to 0 (see documentation). In case of highly polydisperse system, it is necessary to set binning_type to polydisperse_binning (see documentation).