Fluidized bed test

Description

This text describes how to calibrate the fluid-particle drag model using a bulk density, a volume fraction and a fluidized bed test; see Figure 1.

Figure 1: Sketch showing a) bulk density test, b) volume fraction test and c) fluidized bed test.

Introduction

Particle fluidization depends on the bulk density of the packed bed, volume fraction of the system (i.e., ratio between particle volume and container volume) and drag coefficients between particle and fluid. The calibration workflow presented here consists of three steps: 1) calibration of the particle density, 2) calibration of the scaling coefficient for the particle volume and 3) calibration of the scaling coefficient for the drag force. These steps correpond to the calibration templates bulk density test, volume fraction test and Ergun test respectively.

The calibration is performed using a sequential approach, as specified by the run sequential at the bottom of the input script. This means that the particle density, the scaling factor for the particle volume (see volScal in the CFDEM®coupling documentation) and the scaling for the drag force (see scaleDrag in the CFDEM®coupling documentation) are calibrated one after the other.

Note

In the sequential approach, coefficients that have been already calibrated are used as fixed material properties in the following calibration steps.

The coefficient triplet returning the best agreement between reference and simulated data represents the solution of the calibration.

Detailed descriptions

Contact model and coarsegraining factor

The contact model and the coarsegraining factor are defined in the file settings/contact_model.txt. The models used in this tutorial are: Hertz normal, tangential history, rolling friction epsd2. The cohesion model is switched off and the surface model is set to default. More information about the contact models allowed by the templates can be found in the respective documentations. The calibration simulations are performed with a coarsegraining factor 2.

Material properties and particle size distribution

The values of the fixed material parameters and the initial, minimum and maximum values of the target material parameters are defined in the file settings/materials.txt.

Warning

Not all the parameters specified in materials.txt are used by the simulations, as it depends on the contact models selected in contact_model.txt

The particle size distribution is defined in the file settings/particle_sizes.txt.

Calibration case settings

The tutorial consists of three calibration_cases of the template bulk density test, volume fraction test and Ergun test.

Some template-specific settings of the calibration case are defined in the file settings/tests.txt. Other more general settings, like the number of iterations of the calibration procedure, can be found in the file settings/general.txt.

Running the tutorial and analyzing the results

The user can run the tutorial via command line as follows:

aspherix-calibration run -in ergun_test.casx

The results of the three sequential calibration steps are collected in the folders calibration_rho_p, calibration_CFD_volFracScale and calibration_CFD_scaleDrag.

Bulk density test result

The convergence of the calibration is reported in the file calibration_rho_p/results/conv.dat, which reads as follows:

# nIter      rho_p         qf_total
  1          1100          0.288655
  3          833.333       0.0237463
  8          862.963       0.0109649
 15          853.086       0.000605465

The iteration returning the lowest value of the quality function is the number 15, where the quality function measures the discrepancy, in absolute value, between the reference and the simulated bulk density.

Volume fraction test result

The convergence of the calibration is reported in the file calibration_CFD_volFracScale/results/conv.dat, which reads as follows:

# nIter   CFD_volFracScale    qf_total
  1       0.55                0.412096
  2       0.85                0.091448
  4       0.95                0.015188
 15       0.938889            0.003354
 21       0.935185            0.00059

The iteration returning the lowest value of the quality function is the number 21, where the quality function measures the discrepancy, in absolute value, between the reference and the simulated volume fraction. The fact that CFD_volFracScale < 1 implies that particles are slighly porous, which means that the DEM volume needs to be scaled down by a factor smaller than one before being translated into a voidfraction field for the CFD domain.

Ergun test result

The convergence of the calibration is reported in the file calibration_CFD_scaleDrag/results/conv.dat, which reads as follows:

# nIter    CFD_scaleDrag    qf_total
  1         2.05            0.354244
  3         0.75            0.0832562
  9         0.605556        0.0269864
 16         0.621605        0.0235446

The iteration returning the lowest value of the quality function is the number 16. The comparison between the reference and the simulated scaled pressure drops can be seen in Figure 2.

Figure 2: scaled pressure drop across the particle bed (reference and simulation 16).

In summary, the result of the calibration consists of the following parameter triplet:

rho_p = 853.086
CFD_volFracScale = 0.935185
CFD_scaleDrag = 0.621605

Calibration with multispheres

The used can substitute spherical particles with multispheres (see Figure 3) by changing the ergun_test.casx input file as follows:

particle_template p1 shape multisphere file ms.txt
#particle_template p1 shape sphere radius ${rp1}
particle_distribution p templates p1 mass_fractions ${mf1}

The shape of the multisphere is defined in the file ms.txt. Each line corresponds to a particle forming the multisphere, while the columns contain, in order, the x, y, z coordinates of the particle center and its radius.

By rerunning the calibration, the following parameter triplet is obtained:

rho_p = 843.21
CFD_volFracScale = 0.935185
CFD_scaleDrag = 0.252469

Figure 3: Ergun test using multispheres.