# Studying the Flow of Gas in the Core of a Reactor Using Discrete Element Method Simulation

## Introduction

Discrete Element Method (DEM) is a technique used to compute the motions and effects associated with a large number of small sized particles. It is also commonly referred to as Distinct Element Method (Rycroft et al. 21306). The process has enabled to numerically simulate a wide array of particles within the same processor. Today, the concept is commonly used to solve a number of problems encountered in the engineering field. Such issues include those related to discontinuous and granular material. It is also used in the simulation of granular flow. In addition, it is also used to simulate rock and powder mechanics (Rycroft et al. 21306). In their article, Rycroft et al. also note that the technique can be used to study the motion of liquid and gas flow (21306). To achieve this, a continuum approach that treats the two materials as fluids is used. For such simulations to take place, computational fluid dynamics is used. In this paper, the author describes how they will use the information provided by Rycroft et al. in studying reactor design and testing (21307).

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## Studying Gas Flow in the Core Using DEM

A DEM simulation can be used to study the flow of gas accurately. The process gives information on local ordering, porosity, and residence-time distribution. For the simulations to be successful and accurate, a number of factors need to be taken into consideration. One of the important factors includes the forces that act on the gas particles. Friction is one of the major forces experienced when gas is in motion (Lane and Metzger 19). It occurs when two air particles come into contact with each other. Contact plasticity also acts on any molecules that come into contact. It is also commonly referred to as recoil (Jebahi et al. 100). It is the effect felt when two particles collide. It is also noted that gravity acts on gas particles. The effect of this force has to be taken into consideration when studying the flow of these substances. The reason is that it tends to increase the mass of particles. In addition, gravitational pull may slow down or increase the velocity of particles depending on the direction of flow. As such, it must be factored in to improve the accuracy of simulations. The attractive potentials of the gas particles in the core are also an important force that should be taken into consideration (Jebahi et al. 114). Such potentials include electrostatic, adhesive, and cohesive forces. The forces make it difficult to determine the nearest neighbour pair. Specialised algorithms need to be used to resolve the effects of these attractive potentials (Rycroft et al. 21310).

Molecular forces associated with the gas in question also need to be taken into consideration when using DEM simulations. The reason behind this is to compensate for the interactions expected to take place between the gas molecules. Of key importance are the coulomb forces (Lane and Metzger 19). They are also commonly referred to as electrostatic forces. According to Azmy and Sartori, these forces act on gaseous molecules that carry electric charges (45). As such, they impact significantly on the accuracy of DEM simulations. Pauli forces of repulsion are also common when dealing with simulation of gas flow. They manifest themselves when two atoms get too close to each other. When this happens, the atoms often repel each other. Van der Waal forces will also have an effect on the motion of gas particles in the core. The force is the totality of both attractive and repulsive forces between molecules (Lane and Metzger 19). However, some of these attractions and repulsions are not regarded as Van der Waal forces. They include the effects resulting from electrostatic attractions and covalent bonds (Jebahi et al. 112). It is noted that the forces affect the movement of gases within the core. An algorithm that puts into consideration the effect of each of these forces is required when simulating the flow of gas in the core. Failure to factor in either of them will have a negative effect on the accuracy of the simulation.

According to Yang, DEM simulations involve taking the sum of all forces acting on each of the gas particles (99). A complex and integrated computation algorithm is used to accurately point out the changes that occur in the velocity of the particles within the core. The algorithm also helps to determine the position of individual particles. According to Azmy and Sartori, DEM simulations also enable one to use the current position of a gas molecule to compute the force that the particle will be subjected to during its next position (48). The loop is continuous and shows the movement of the gas particles throughout the core (Rycroft et al. 21306).

## Simulating Gas Flow in the Core of a Reactor: Methodology

According to Jebahi et al., the simulation process consists of three distinct processes (98). The first is initialisation. It is followed by explicit time-stepping. The last stage is post-processing. The first phase of the simulations commences with the generation of the core model. In the process, particles will spatially orient (Jebahi et al. 99). The particles are then assigned initial velocity. The explicit time-stepping phase calls for nearest neighbour sorting (Jebahi et al. 100). The purpose of the steps is to help decrease the possibility of contact pairs during the simulation. In the process, the number of computation requirements is decreased. For the purposes of the proposed study, the researcher will conduct a monodispersed simulation. To this end, the following factors will be taken into consideration:

• The effect of gravity on the motion of gas particles will be taken to be g = 9.81 ms−2.
• The friction coefficient between the wall and the particles is expected to be µw = 0.7. The assumption made here is that the walls are not toinless.

## Integration Methods used to Describe the Flow of Gas

In their study, Rycroft et al. found that various integration methods can be used in DEM simulations (21310). They include verlet algorithm, symplectic integrators, and the leapfrog method (Azmy and Sartori 48). The first approach entails a numerical technique that integrates Newton’s law of motion. It is mostly used in computer graphics. It helps engineers to compute the flight route taken by gas particles in DEM simulations. The following formulae are used to determine trajectory of the gas particles in the proposed study:

• Newton’s motion equation for a conservative system is

or individually

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Where:

• t represents time.
•  represents the ensemble of position vector of N objects.
• V, on the other hand, is the scalar potential function.
• F is the negative gradient of the potential that gives the ensemble of forces on the particles.
• M in this case represents the mass matrix, typically diagonal with blocks with mass for every particle (Yang 23).

Symplectic integrator is another numerical technique. According to Yang, the computation is based on symplectic geometry (23). It is also based on classical mechanics (Yang 23). It is used in DEM simulations for a number of reasons. The first one is to show the speed and position of particles. It borrows from the Hamilton’s equations, which show the following:

In this case,

• H is the Hamiltonian.
• q is position coordinates,
• P is momentum coordinates (Yang 23).

The Leapfrog method, on the other hand, is similar to verlet algorithm. It shows the updating position of gas particles within the core. It also provides information on the velocity of these particles (Yang 23). The formula used is given below:

In the equation above:

• is position at step.
• is velocity.

Is acceleration, and is size of each time step for a particle (Yang 23).

## Conclusion

It is evident that DEM simulations are important when it comes to the process of designing and testing reactors. The technique enables engineers to use computerised algorithms to obtain data touching on local ordering, porosity, and residence-time distribution. As a result, engineers can accurately anticipate the nature of the flow of particles inside a reactor. It is possible to analyse millions of granular particles using this methodology. The technique is also commonly used to provide accurate data on the flow of gas.

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## Works Cited

Azmy, Yousry, and Enrico Sartori. Nuclear Computational Science: A Century in Review, Dordrecht: Springer, 2010. Print.

Jebahi, Mohamed, Damien Andre, Inigo Terreros, and Ivan Iordanoff. “Discrete Element Modelling of Thermal Behavior of Continuous Materials.” Discrete Element Method to Model 3D Continuous Materials 2.27 (2015): 93-114. Print.

Lane, John, and Philip Metzger. A Review of Discrete Element Method (DEM) Particle Shapes and Size Distributions for Lunar Soil, Cleveland, Ohio: National Aeronautics and Space Administration, Glenn Research Centre, 2010. Print.

Rycroft, Chris, Gary Grest, James Landry, and Martin Bazant. “Analysis of Granular Flow in a Pebble-Bed Nuclear Reactor.” Physical Review 74.1 (2006): 21306 – 21321. Print.

Yang, Qiang. Constitutive Modelling of Geomaterials: Advances and New Applications, Berlin: Springer, 2013. Print.

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