(53a) Dynamical Analysis of Velocity Time Series in a Binary Fluidized BED: MODEL Validation with Radioactive Particle Tracking (RPT) Experiments

1. Introduction

Fluidized Bed owing to numerous advantages are extensively utilized in industrial processes. However, due to its complex hydrodynamics and lack of complete understanding, accurate scale up such units is challenging. Therefore, gaining more insights into the complex hydrodynamics of such system is the need of the hour. Euler-Lagrange Model/Discrete Particle Model (DPM), arguably gives more physically realistic results when compared to Euler-Euler model. The present study seeks to capture the complicated flow pattern of such beds using Discrete Element Model (DEM). For validation of the efficacy of the simulations, a direct comparison is made with a experimental technique that is Lagrangian in nature, viz. Radioactive Particle Tracking (RPT) (Roy et al., 2021).

Real fluidized beds are polydisperse in nature, and hence it is important that the polydispersity is captured by the DEM simulation technique. While a full treatment of polydispersity is beyond the scope of this work, this work focuses on the study of a binary fluidized bed – examining its hydrodynamics both via CFD-DEM and RPT.

For complete understanding of hydrodynamics of fluidized beds, along with time-averaged data, dynamic analysis of the data is equally important. It is an important tool used in various fields of engineering to study the behavior of systems that evolve over time. Dynamical analysis helps to design, optimize and control complex systems, as well as to understand the underlying physical mechanisms and interactions that govern their behavior. Therefore, study of both time-averaged and time-resolved data is of utmost importance. For time-resolved analysis, Fast Fourier Transform (FFT) is employed which comes under the category of Frequency Domain Analysis. At the later part of the project, state space analysis i.e., Chaos Analysis is also employed to capture the spacio-temporal patterns encountered in a Fluidized Bed.

2. Methodology

2.1 CFD-DEM simulation of a laboratory-scale Binary Fluidized Bed

CFD-DEM simulation of a laboratory-scale 3D binary fluidized bed has been carried out consisting of glass beads of 0.5- and 2-mm diameter particle sizes. To carry out these simulations opensource software package OpenFOAM-CFDEM-LIGGGHTS is used. With the aim of determining the contact forces between the particles, Hertzian model was used. Effect of bed composition was checked on overall hydrodynamics of the system by varying the coarser particle fraction from 10 – 40% at different superficial gas velocities.

Particle governing equations

The governing equation for the translational and rotational motion of a particle can be written as:

(2)

Fi,p , Fi,w are the contact force due to particle-particle and particle-wall interactions respectively. Fi,c refers to the cohesive forces between particles. The contact forces (normal and tangential) are determined using the following equations. The accuracy of DEM simulation depends upon the parameters: spring stiffness (k_n), damping coefficient (), coefficient of friction (µ). Therefore, selection of these parameters has been done after extensive literature survey.

(4)

(5)

If the following relation is satisfied, then sliding occurs and the tangential contact force is obtained using equation (7),

(6)

(7)

Gas phase governing equations:

Continuity equation

(8)

Momentum equation:

(9)

Where S_p is the source term for the drag force due to the interaction between the gas-phase and particulate phase.

(10)

The δ-function ensures that the reaction force acts as a point force at the position of the particle in the system. V represents the volume of the cell, V_a is the volume of the particle.

• Fast Fourier Transform

Post processing of the simulation data (i.e., instantaneous velocity of the particle) is carried out using Fast Fourier Transform (FFT). It uses a recursive approach that breaks down the signal into smaller sub-signals, computes the Fourier transform of each sub-signal, and then combines the results to obtain the overall Fourier transform of the signal.

Time series of instantaneous velocity measurements from the fluidised bed is collected. It is ensured that the data is properly aligned and normalized to remove any bias or drift that might affect the FFT analysis. The data is also be windowed to reduce spectral leakage. The FFT algorithm is applied to obtain the frequency spectrum of the instantaneous velocity, thus providing information about the frequency content of the signal.

• Chaos Analysis

Chaos analysis is used in the later part of the project to study the behavior of fluidized bed that exhibits unpredictable and sensitive dependence on initial conditions. Parameters like the Kolmogorov entropy and Correlation Dimension are calculated both from the DEM simulations as well as the RPT data.

To estimate the Kolmogorov entropy, two points on the attractor that are closer than a certain length scale is followed in time, until their distance has grown larger than the length scale. By choosing number of such pairs, the entropy is determined with high precision. The Kolmogorov entropy increases continuously with superficial velocity for a fixed aspect ratio of the system. The other parameter calculated is the correlation dimension, which expresses the amount of space occupied by the attractor.

3. Results

Figure 1., shows the time-averaged axial mean velocity and time-averaged axial RMS velocity of binary mixture containing 10% 2 mm and 90% 0.5 mm glass bead particles. This simulation was carried out at 1.1 times minimum fluidization velocity employing different drag models Gidaspow (Gidaspow, 1994), Di Felice (Di Felice, 1994) and Koch-Hill (Koch et al., 2001).

The final presentation will discuss these results as well as many other to elucidate the validation of CFD-DEM results with RPT.

4. Conclusions

The observations from simulation were that due to increase in jetsam fraction (2 mm), the mean velocity of flotsam fraction (0.5 mm) was reduced. A reduction in solids fluctuations was also seen both in time-averaged and time-resolved profile. As the bed consists of a distribution of particle sizes, the mixing pattern of the polydisperse bed is studied.

References

Di Felice R. (1994). The voidage function for fluid-particle interaction systems. Int J Multiph Flow, 20(1), 153-159.

Gidaspow, D., (1994). Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions. Academic Press.

Koch, D.L. and Hill, R.J. (2001). Inertial effects in suspension and porous-media flows. Annual Review of Fluid Mechanics, 33, 619-647.

Roy, S., Pant, H.J., & Roy, S. (2021). Velocity characterization of solids in binary fluidized beds. Chemical Engineering Science, 246, 116883.