# A Multiphase Eulerian Granular Model with Population Balance and Drift Model for Settling Bed Simulation

## Eulerian Multiphase Granular.zip: A Tutorial on Granular Flow Simulation Using the Eulerian Multiphase Model

Granular materials, such as sand, gravel, powder, or pellets, are ubiquitous in nature and industry. They exhibit complex behaviors that depend on the interactions between the grains and the surrounding fluid, such as air or water. Understanding and predicting these behaviors is essential for many applications, such as geotechnical engineering, mining, pharmaceutical production, food processing, energy conversion, and environmental protection.

## Eulerian Multiphase Granular.zip

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However, modeling and simulating granular flows is not a trivial task. It requires sophisticated methods that can capture the discrete nature of the grains, the continuous nature of the fluid, and the coupling between them. One of these methods is the Eulerian multiphase model, which treats each phase as a separate fluid with its own momentum and continuity equations. The Eulerian multiphase model can handle high concentrations of solid particles, complex geometries, and various interphase interactions.

In this article, we will introduce the Eulerian multiphase model and its applications to granular flow simulation. We will also present a tutorial on how to use a file called Eulerian Multiphase Granular.zip, which contains a sample case of granular flow in a mixing tank. This tutorial will demonstrate how to set up, run, and analyze a granular flow simulation using ANSYS FLUENT, a commercial computational fluid dynamics (CFD) software. By following this tutorial, you will learn how to use the Eulerian multiphase model for your own granular flow problems.

## Eulerian Multiphase Model

The Eulerian multiphase model is one of the multiphase models available in ANSYS FLUENT. A multiphase model is a mathematical framework that describes the behavior of two or more phases (or materials) that coexist in a domain. In ANSYS FLUENT, there are four types of multiphase models: volume of fluid (VOF), mixture, Eulerian, and discrete phase.

The Eulerian multiphase model is suitable for simulating flows with high concentrations of dispersed phases (such as solid particles or droplets) that have significant momentum exchange with each other and with the continuous phase (such as air or water). The Eulerian multiphase model solves a set of momentum and continuity equations for each phase in an Eulerian reference frame (i.e., fixed in space). The coupling between the phases is achieved through the pressure field and interphase exchange coefficients that account for drag, lift, virtual mass, turbulent dispersion, heat transfer, mass transfer, etc.

The advantages of the Eulerian multiphase model are that it can handle complex geometries (such as porous media or rotating devices), large numbers of particles (up to several millions), wide range of particle sizes (from microns to centimeters), different particle shapes (such as spheres or cylinders), different particle properties (such as density or viscosity), different particle behaviors (such as elastic or plastic), different fluid properties (such as compressible or incompressible), different fluid behaviors (such as laminar or turbulent), different boundary conditions (such as inlet or outlet), and different physical phenomena (such as heat transfer or chemical reactions).

The applications of the Eulerian multiphase model are numerous and diverse. Some examples are: fluidized beds, pneumatic conveying, cyclone separators, spray dryers, coal combustion, gas-liquid reactors, solid-liquid extraction, sedimentation, erosion, landslides, avalanches, etc.

The challenges and limitations of the Eulerian multiphase model are mainly related to the accuracy and computational cost of the simulation. The accuracy depends on the choice and calibration of the interphase exchange coefficients, which are often empirical or semi-empirical and may not capture all the physics involved in the multiphase flow. The computational cost depends on the number of phases, the number of equations, the grid resolution, the time step, and the convergence criteria. The Eulerian multiphase model can be computationally intensive and require high-performance computing resources.

## Granular Flow Simulation

Granular flow is a type of multiphase flow that involves solid particles moving under the influence of gravity, fluid forces, and interparticle forces. Granular flow can be classified into two regimes: dense and dilute. In dense granular flow, the particles are closely packed and interact frequently with each other through collisions and friction. In dilute granular flow, the particles are widely dispersed and interact mainly with the fluid through drag and lift.

Simulating granular flow is important for understanding and optimizing the performance of various processes and devices that involve granular materials. For example, simulating granular flow can help design more efficient fluidized beds for chemical reactions, more effective cyclone separators for particle separation, more reliable spray dryers for powder production, more clean coal combustion for energy generation, more safe landslides for geohazard assessment, etc.

There are different methods and techniques for simulating granular flow, depending on the regime, the scale, and the complexity of the problem. Some of these methods are: discrete element method (DEM), lattice Boltzmann method (LBM), smoothed particle hydrodynamics (SPH), molecular dynamics (MD), finite element method (FEM), finite volume method (FVM), etc. Each method has its own advantages and disadvantages in terms of accuracy, efficiency, robustness, and applicability.

The benefits of simulating granular flow are that it can provide detailed information on the behavior of the granular material, such as velocity, pressure, temperature, concentration, stress, strain, porosity, etc. It can also reveal the underlying mechanisms and phenomena that govern the granular flow, such as particle-fluid interaction, particle-particle interaction, particle-wall interaction, heat transfer, mass transfer, chemical reaction, phase change, etc. It can also enable parametric studies and sensitivity analyses to explore the effects of different factors on the granular flow.

The challenges of simulating granular flow are mainly related to the complexity and uncertainty of the problem. The complexity arises from the nonlinear and non-equilibrium nature of the granular flow, which can exhibit various patterns and transitions depending on the initial and boundary conditions. The uncertainty arises from the lack of accurate and reliable data on the properties and parameters of the granular material, such as size distribution, shape distribution, density distribution, friction coefficient, rest coefficient, restitution coefficient, etc. These challenges require careful validation and verification of the simulation results against experimental data or analytical solutions.

## Eulerian Multiphase Granular.zip Tutorial

Eulerian Multiphase Granular.zip is a file that contains a sample case of granular flow in a mixing tank. The mixing tank has a cylindrical shape with a diameter of 0.5 m and a height of 0.5 m. The tank is partially filled with water and solid particles. The water level is 0.3 m and the solid volume fraction is 0.4. The water has a density of 1000 kg/m3 and a viscosity of 0.001 Pa.s. The solid particles have a density of 2500 kg/m3 and a diameter of 0.001 m. The tank has a rotating impeller at the bottom that creates a radial flow of water and particles. The impeller has a diameter of 0.1 m and a rotational speed of 100 rpm.

The purpose of this tutorial is to demonstrate how to use the Eulerian multiphase model to simulate the granular flow in the mixing tank. The tutorial will show how to download, unzip, and run the tutorial files using ANSYS FLUENT, how to set up the model parameters and boundary conditions, how to initialize and iterate the solution, how to monitor and visualize the results, and how to analyze and interpret the simulation output.

The following table summarizes the steps and commands for the tutorial:

Step

Command

1. Download and unzip the Eulerian Multiphase Granular.zip file from this link:

Right-click on the link and select "Save link as..." to save the file to your desired location. Then, right-click on the file and select "Extract all..." to unzip the file.

2. Launch ANSYS FLUENT and open the Eulerian Multiphase Granular.cas file from the unzipped folder.

Double-click on the ANSYS FLUENT icon on your desktop or start menu to launch the software. Then, click on "File" > "Open" > "Case..." and browse to the location of the Eulerian Multiphase Granular.cas file. Click on "Open" to load the case file.

3. Check the geometry and mesh of the mixing tank.

Click on "Display" > "Grid" > "Display Grid" to view the geometry and mesh of the mixing tank. You should see a cylindrical tank with an impeller at the bottom and a mesh with about 200,000 cells.

4. Check the model settings and boundary conditions.

Click on "Define" > "Models" > "Multiphase..." to open the Multiphase Model panel. You should see that the Eulerian multiphase model is selected with two phases: water (phase-1) and solid (phase-2). Click on "Edit..." for each phase to check their properties and interactions. You should see that water is incompressible, laminar, and has constant properties, while solid is granular, kinetic-theory-based, and has constant properties except for viscosity, which is Gidaspow-based. You should also see that there are drag, lift, virtual mass, turbulent dispersion, wall lubrication, and frictional stress interactions between the phases.

Click on "Define" > "Boundary Conditions" to open the Boundary Conditions panel. You should see that there are four boundaries: inlet, outlet, wall, and impeller. Click on "Edit..." for each boundary to check their settings. You should see that inlet is a velocity-inlet type with a radial velocity of 0.1 m/s for both phases, outlet is a pressure-outlet type with a gauge pressure of 0 Pa for both phases, wall is a wall type with no slip condition for both phases, and impeller is a moving-wall type with a rotational speed of 100 rpm for both phases.

5. Initialize and iterate the solution.

Click on "Solution" > "Initialization" > "Initialize" to initialize the solution from the inlet boundary. You should see that the solution is initialized with the inlet values for velocity, pressure, and volume fraction for both phases. Click on "Solution" > "Run Calculation" to open the Run Calculation panel. You should see that the number of iterations is set to 1000, the time step size is set to 0.01 s, and the number of time steps is set to 100. Click on "Calculate" to start the iteration process. You should see that the residuals and monitors are displayed in the console and graphics windows. You should also see that the solution converges after about 500 iterations.

6. Monitor and visualize the results.

Click on "Solution" > "Monitors" > "Residuals..." to open the Residual Monitors panel. You should see that there are residual monitors for continuity, x-velocity, y-velocity, and z-velocity for both phases. You should also see that the convergence criterion is set to 1e-6 for all residuals. Click on "Plot" to plot the residual history. You should see that the residuals drop below the convergence criterion after about 500 iterations.

Click on "Solution" > "Monitors" > "Surface..." to open the Surface Monitors panel. You should see that there are surface monitors for torque-z and moment-z for the impeller boundary. These monitors measure the torque and moment exerted by the fluid and solid phases on the impeller. Click on "Plot" to plot the surface monitor history. You should see that the torque and moment reach steady values after about 500 iterations.

Click on "Display" > "Contours" > "Filled..." to open the Filled Contours panel. You should see that there are contour variables for velocity, pressure, volume fraction, and granular temperature for both phases. You can select any variable and any phase to display its contour plot on the geometry. For example, you can select volume fraction and solid phase to display the contour plot of solid volume fraction in the mixing tank. You should see that the solid particles are distributed in a radial pattern due to the impeller action.

Click on "Display" > "Vectors" > "Display Vectors" to open the Display Vectors panel. You should see that there are vector variables for velocity and relative velocity for both phases. You can select any variable and any phase to display its vector plot on the geometry. For example, you can select velocity and water phase to display the vector plot of water velocity in the mixing tank. You should see that the water velocity is radial near the impeller and tangential near the wall.

7. Analyze and interpret the results.

Click on "Report" > "Fluxes..." to open the Fluxes panel. You should see that there are flux variables for mass flow rate, volume flow rate, momentum flux, energy flux, etc. for both phases. You can select any variable and any boundary to calculate its flux value across that boundary. For example, you can select mass flow rate and outlet boundary to calculate the mass flow rate of water and solid phases exiting the mixing tank. You should see that the mass flow rate of water is about 0.05 kg/s and the mass flow rate of solid is about 0.033 kg/s.

Click on "Report" > "Forces..." to open the Forces panel. You should see that there are force variables for pressure force, viscous force, drag force, lift force, etc. for both phases. You can select any variable and any boundary to calculate its force value acting on that boundary. For example, you can select drag force and impeller boundary to calculate the drag force of water and solid phases acting on the impeller. You should see that the drag force of water is about 0.8 N and the drag force of solid is about 0.5 N.

Click on "Report" > "Summary..." to open the Summary panel. You should see that there are summary variables for domain, boundary, and phase statistics. You can select any variable and any domain, boundary, or phase to display its summary value. For example, you can select minimum and maximum volume fraction and solid phase to display the minimum and maximum solid volume fraction in the domain. You should see that the minimum solid volume fraction is 0 and the maximum solid volume fraction is 0.6.

The results of the simulation can be used to evaluate the performance and efficiency of the mixing tank. For example, you can compare the mass flow rate, torque, and moment of the impeller with different rotational speeds, particle sizes, or particle concentrations. You can also analyze the distribution and dynamics of the solid particles in the tank, such as their radial and tangential velocities, their granular temperature, their porosity, etc. You can also investigate the effects of different interphase interactions, such as drag, lift, virtual mass, etc. on the granular flow.

## Conclusion

In this article, we have introduced the Eulerian multiphase model and its applications to granular flow simulation. We have also presented a tutorial on how to use a file called Eulerian Multiphase Granular.zip, which contains a sample case of granular flow in a mixing tank. We have shown how to download, unzip, and run the tutorial files using ANSYS FLUENT, how to set up the model parameters and boundary conditions, how to initialize and iterate the solution, how to monitor and visualize the results, and how to analyze and interpret the simulation output.

We hope that this article has helped you understand the basics of the Eulerian multiphase model and its capabilities for granular flow simulation. We also hope that this article has inspired you to use the Eulerian multiphase model for your own granular flow problems. If you want to learn more about the Eulerian multiphase model or granular flow simulation, you can refer to the following resources:

### - ANSYS FLUENT User's Guide: __https://www.ansys.com/-/media/ansys/corporate/resourcelibrary/techbrief/ansys-fluent-users-guide.pdf__ - ANSYS FLUENT Theory Guide: __https://www.ansys.com/-/media/ansys/corporate/resourcelibrary/techbrief/ansys-fluent-theory-guide.pdf__ - ANSYS FLUENT Tutorial Guide: __https://www.ansys.com/-/media/ansys/corporate/resourcelibrary/techbrief/ansys-fluent-tutorial-guide.pdf__ - ANSYS FLUENT Multiphase Flow Webinar: __https://www.youtube.com/watch?v=QyjyL4w3F9E__ - ANSYS FLUENT Granular Flow Webinar: __https://www.youtube.com/watch?v=Z6nYfYxZ4Jg__ FAQs

Here are some frequently asked questions about the Eulerian multiphase model and granular flow simulation:

What is the difference between the Eulerian multiphase model and the discrete phase model?

The Eulerian multiphase model treats each phase as a separate fluid with its own momentum and continuity equations, while the discrete phase model treats one phase as a fluid and the other phases as discrete particles that are tracked individually or statistically.

What is the difference between granular flow and fluidized flow?

Granular flow is a type of multiphase flow that involves solid particles moving under the influence of gravity, fluid forces, and interparticle forces. Fluidized flow is a special case of granular flow where the fluid forces are strong enough to suspend or fluidize the solid particles.

What are some examples of granular materials?

Some examples of granular materials are sand, gravel, powder, pellets, seeds, grains, pills, beads, etc.

What are some parameters that affect granular flow?