The Discrete Element Method (DEM) (Cundall & Strack, 1979) is a Lagrangian method originally developed for the simulation of bulk solids and then extended to the entire field of particle technology. This method solves the Newton's equations of motion for translation and rotation of the particles. In these equations, impact forces of particle-particle and particle-wall interactions are considered. Other forces such as electrostatic or Brownian forces can also be implemented if necessary. In order to describe the collisions of particles, the soft-sphere approach was chosen. When two particles collide, they actually deform. This deformation is described by an overlap displacement of the particles. A schematic representation of the forces on the particles in the soft-sphere model is depicted in Figure 17. This approach uses a spring-dashpot-slider system to calculate the behaviour of the particles during the contact time. The soft-sphere model allows contacts of a particle with more neighbouring particles during a time step. The net contact force acting on a particle is added in the case of multiple overlapping. This model for contact forces was first developed by Cundall (Cundall & Strack, 1979), who proposed a parallel linear spring-dashpot model for the normal direction and a parallel linear spring-dashpot in a series with a slider for the tangential direction. A comparison of the performance of several soft-sphere models can be found in (Di Renzo & Di Maio, 2005; Stevens & Hrenya, 2005). There, also the Hertz-Mindlin (Mindlin, 1949) non-linear soft-sphere model used in the present work is analysed. This model proposes a normal force as a function of the normal overlap δn, the Young's modulus of the particle material and the particle radii. The damping force in normal direction depends on the restitution coefficient, the normal stiffness, and the normal component of the relative velocity between the particles. The tangential force depends on the tangential overlap δt, on the shear modulus of the particle material, and on the particle radii; while in the damping force in tangential direction the tangential stiffness and the tangential component of the relative velocity between the particles are considered.

Fig. 17. Contact forces between two particles following the soft-sphere model

While the DEM model was originally used in environments without fluid, increasing efforts have been made to extend this model to the mixture of fluid and particles. For that, a coupling of the DEM calculations with the fluid flow simulation is necessary to be able to include the hydrodynamic forces in the particle simulation. An important aspect in the calculation of particles in a fluid is the energy dissipation into the surrounding fluid. In viscous fluids, there are, in contrast to air, two additional effects that lead to energy losses. The drag force leads to lower particle velocities and when a particle is about to hit a surface or another particle, a deceleration occurs. This is due to the drainage of the fluid, which is located in the gap between the two particles or the particle and the surface. In his work

The Discrete Element Method (DEM) (Cundall & Strack, 1979) is a Lagrangian method originally developed for the simulation of bulk solids and then extended to the entire field of particle technology. This method solves the Newton's equations of motion for translation and rotation of the particles. In these equations, impact forces of particle-particle and particle-wall interactions are considered. Other forces such as electrostatic or Brownian forces can also be implemented if necessary. In order to describe the collisions of particles, the soft-sphere approach was chosen. When two particles collide, they actually deform. This deformation is described by an overlap displacement of the particles. A schematic representation of the forces on the particles in the soft-sphere model is depicted in Figure 17. This approach uses a spring-dashpot-slider system to calculate the behaviour of the particles during the contact time. The soft-sphere model allows contacts of a particle with more neighbouring particles during a time step. The net contact force acting on a particle is added in the case of multiple overlapping. This model for contact forces was first developed by Cundall (Cundall & Strack, 1979), who proposed a parallel linear spring-dashpot model for the normal direction and a parallel linear spring-dashpot in a series with a slider for the tangential direction. A comparison of the performance of several soft-sphere models can be found in (Di Renzo & Di Maio, 2005; Stevens & Hrenya, 2005). There, also the Hertz-Mindlin (Mindlin, 1949) non-linear soft-sphere model used in the present work is analysed. This model proposes a normal force as a function of the normal overlap δn, the Young's modulus of the particle material and the particle radii. The damping force in normal direction depends on the restitution coefficient, the normal stiffness, and the normal component of the relative velocity between the particles. The tangential force depends on the tangential overlap δt, on the shear modulus of the particle material, and on the particle radii; while in the damping force in tangential direction the tangential stiffness and the tangential

component of the relative velocity between the particles are considered.

Fig. 17. Contact forces between two particles following the soft-sphere model

While the DEM model was originally used in environments without fluid, increasing efforts have been made to extend this model to the mixture of fluid and particles. For that, a coupling of the DEM calculations with the fluid flow simulation is necessary to be able to include the hydrodynamic forces in the particle simulation. An important aspect in the calculation of particles in a fluid is the energy dissipation into the surrounding fluid. In viscous fluids, there are, in contrast to air, two additional effects that lead to energy losses. The drag force leads to lower particle velocities and when a particle is about to hit a surface or another particle, a deceleration occurs. This is due to the drainage of the fluid, which is located in the gap between the two particles or the particle and the surface. In his work (Gondret et al., 2002), Gondret presents the coefficient of restitution as a function of the Stokes number St (Equation 16), which describes the ratio of the dynamic response time of a particle to flow changes and the characteristic flow time. He determined empirically a critical Stokes number of about 10. Below this value, a particle does not bounce when it hits a wall and instead remains in contact with it.

$$\text{St} = \frac{1}{9} \frac{\rho\_s \mathbf{v} \times \mathbf{x}}{\mu} \tag{16}$$

In a centrifugal field, the hydrodynamic forces (drag, lift, torque) play a crucial role and must be included in the calculation of the particle trajectories. Therefore the fluid flow and particles movement have to be computed alternatively. A scheme of the coupling between the CFD software FLUENT and the DEM software EDEM can be seen in Figure 18. At first, the flow will be determined with CFD, then for each position in the computational domain, the velocity, pressure, density and viscosity of the flow are transferred to DEM in order to calculate the hydrodynamic forces and include them in the balance. Afterwards, the fluid flow will be computed again considering the influence of the particles as an additional sink term in the momentum equations. This sink term include the force transmitted to the particles by the fluid.

Fig. 18. Coupling between CFD and DEM

Some authors have already simulated such complex multiphase flows in other separation equipment such as filters and hydrocyclones (Chu et al., 2009; Chu & Yu, 2008; Dong et al., 2003; Ni et al., 2006). Nevertheless due to the high velocity gradients and complex interactions between the phases, the simulation of multiphase flow and in particular the sediment behaviour in centrifugal field is still an unsolved challenge. The advantage of this approach is that an accurate description of the flow, the particle paths and the sediment behaviour can be obtained. However, the amount of simulated particles and its size is limited due to the computational demand.

### **5.1 Particles simulation parameters**

The calculation in CFD must be run as an unsteady case when coupled with DEM. The DEM time steps are typically smaller than the CFD time steps in order to correctly capture the contact behaviour. The choice of time steps in DEM simulation is of great importance in order to achieve stability in the calculation but does not perform very long calculations, although still representing the real particle behaviour. Therefore it is necessary to analyse

Computational Fluid Dynamics (CFD) and

results of this simulation are depicted in Figure 19.

Discrete Element Method (DEM) Applied to Centrifuges 123

sediment build-up it is not possible to use periodic boundaries as was done for the simulation of the fluid. Moreover, we chose this geometry with the VOF model for air and liquid in order to investigate the interaction between the multiphase model and the use of DEM to calculate the particles. The calculations were made with the software ANSYS

The coupled simulation was performed with a rotational speed of 2550 rpm. For this rotational speed, the Stokes settling velocity of the particles is by two orders of magnitude higher than the Stokes settling velocity of the quartz particles used in the experiments. The

Fig. 19. Particles and path lines simulated with EDEM coupled with a two-phase simulation

The particles are injected at the inlet pipe with the same axial velocity as the fluid. They hit the top of the feed accelerator and gain in radial velocity. Afterwards, they move through the air core until they hit the liquid pool. There, under the effect of the centrifugal force, the particles perform spiral path lines, as shown in Figure 19 on the right, until reaching the wall or already settled particles. The lower plot in Figure 19 shows a vertical plane of the centrifuge with the particles in the region near the feed accelerator where the sediment is built. Due to the drag force of the axial flow in the rotating pool, the particles move first to higher axial positions. Then, near the wall, they move backwards because of the recirculation layer. The evolution of the sediment can be observed in Figure 20 as a function

of a centrifuge in FLUENT and coloured by velocity magnitude

FLUENT 12.0.16 and EDEM 2.3, which include a coupling feature for both programs.

the forces acting on the particles to determine the different time scales. In the case presented, the Hertzian contact time - the total time of contact in Hertz theory of elastic collision -, the particle sedimentation time - the time required for a particle to settle one diameter -, and the particle relaxation time - the time for a particle to adapt to the surrounding fluid flow - are considered. On the basis of these, the smallest time step must be chosen so that all physical phenomena are represented. In the simulations presented, the Hertzian contact time is the smallest time scale and, thus a time step tDEM = 10-6 s was chosen in the DEM software, while in the CFD a time step tCFD = 10-4 s was sufficient.

The size of the particles was defined as a logarithmic normal distribution with a mean diameter of 200 µm and a standard deviation of σ = 10 µm. Simulations with smaller particles lead to divergence of the calculation despite of the small time steps set. Thus simulations with lower densities of the particles and rotational speeds were performed to obtain similar settling velocities as with small quartz particles (mean diameter of 2.07 µm, s=2.15 µm) which were used in the experiments. In order to reproduce the experimental concentration of approximately 0.5 vol. %, 100,000 particles per second were injected at the inlet of the centrifuge for the simulation. In future work, the comparison of predicted and experimentally determined sediment build-up will show whether the simulation methodology leads to correct predictions.

For the contact models, a parameter setting is needed to represent the real particle behaviour. The information needed is mainly about the physical properties of the particle system because the spring and damper constants are calculated as a function of the shear modulus and the Poisson's ratio of the particle and wall materials. The coefficient of restitution depends on the Stokes particle number. The friction coefficient is an empirically determinable property, which can be found in the literature for various material combinations. Some authors have already determined this friction coefficient for sand and glass particles for DEM (Asaf et al., 2007; Li et al., 2005). Here, shear experiments of a sediment made of quartz particles were performed in a Jenike shear cell under normal pressure in order to calculate the friction coefficient as was done by (Hartl & Ooi, 2008).

Table 3. Parameters used in the DEM simulation

### **6. Prediction of the sediment build-up by means of DEM**

The geometry of the centrifuge in which the particle trajectories and the sediment build-up were simulated is shown in Figure 15. For the simulation purpose of predicting the

the forces acting on the particles to determine the different time scales. In the case presented, the Hertzian contact time - the total time of contact in Hertz theory of elastic collision -, the particle sedimentation time - the time required for a particle to settle one diameter -, and the particle relaxation time - the time for a particle to adapt to the surrounding fluid flow - are considered. On the basis of these, the smallest time step must be chosen so that all physical phenomena are represented. In the simulations presented, the Hertzian contact time is the smallest time scale and, thus a time step tDEM = 10-6 s was chosen in the DEM software,

The size of the particles was defined as a logarithmic normal distribution with a mean diameter of 200 µm and a standard deviation of σ = 10 µm. Simulations with smaller particles lead to divergence of the calculation despite of the small time steps set. Thus simulations with lower densities of the particles and rotational speeds were performed to obtain similar settling velocities as with small quartz particles (mean diameter of 2.07 µm, s=2.15 µm) which were used in the experiments. In order to reproduce the experimental concentration of approximately 0.5 vol. %, 100,000 particles per second were injected at the inlet of the centrifuge for the simulation. In future work, the comparison of predicted and experimentally determined sediment build-up will show whether the simulation

For the contact models, a parameter setting is needed to represent the real particle behaviour. The information needed is mainly about the physical properties of the particle system because the spring and damper constants are calculated as a function of the shear modulus and the Poisson's ratio of the particle and wall materials. The coefficient of restitution depends on the Stokes particle number. The friction coefficient is an empirically determinable property, which can be found in the literature for various material combinations. Some authors have already determined this friction coefficient for sand and glass particles for DEM (Asaf et al., 2007; Li et al., 2005). Here, shear experiments of a sediment made of quartz particles were performed in a Jenike shear cell under normal pressure in order to calculate the friction coefficient as was done by (Hartl & Ooi, 2008).

> **Parameter Value**  Particle radius (µm) 200 Particle density (kg/m3) 1016 Shear modulus particle (Pa) 2.2·108 Shear modulus wall (Pa) 7.0·1010 Poisson's ratio particle (-) 0.25 Poisson's ratio wall (-) 0.30 Restitution coefficient (-) 0.010 Static friction coefficient (-) 0.787 Rolling friction coefficient (-) 0.100

The geometry of the centrifuge in which the particle trajectories and the sediment build-up were simulated is shown in Figure 15. For the simulation purpose of predicting the

while in the CFD a time step tCFD = 10-4 s was sufficient.

methodology leads to correct predictions.

Table 3. Parameters used in the DEM simulation

**6. Prediction of the sediment build-up by means of DEM**

sediment build-up it is not possible to use periodic boundaries as was done for the simulation of the fluid. Moreover, we chose this geometry with the VOF model for air and liquid in order to investigate the interaction between the multiphase model and the use of DEM to calculate the particles. The calculations were made with the software ANSYS FLUENT 12.0.16 and EDEM 2.3, which include a coupling feature for both programs.

The coupled simulation was performed with a rotational speed of 2550 rpm. For this rotational speed, the Stokes settling velocity of the particles is by two orders of magnitude higher than the Stokes settling velocity of the quartz particles used in the experiments. The results of this simulation are depicted in Figure 19.

Fig. 19. Particles and path lines simulated with EDEM coupled with a two-phase simulation of a centrifuge in FLUENT and coloured by velocity magnitude

The particles are injected at the inlet pipe with the same axial velocity as the fluid. They hit the top of the feed accelerator and gain in radial velocity. Afterwards, they move through the air core until they hit the liquid pool. There, under the effect of the centrifugal force, the particles perform spiral path lines, as shown in Figure 19 on the right, until reaching the wall or already settled particles. The lower plot in Figure 19 shows a vertical plane of the centrifuge with the particles in the region near the feed accelerator where the sediment is built. Due to the drag force of the axial flow in the rotating pool, the particles move first to higher axial positions. Then, near the wall, they move backwards because of the recirculation layer. The evolution of the sediment can be observed in Figure 20 as a function

Computational Fluid Dynamics (CFD) and

taken from the simulation domain.

Discrete Element Method (DEM) Applied to Centrifuges 125

position calculation of the particles. Thus in Figure 21 on the left, the particles calculated in FLUENT acquire higher axial positions when compared to the particles calculated with EDEM. The reason for this disagreement is the difference in the axial flow pattern, where the velocities oscillate until a quasi-steady state is achieved. However, qualitatively both particle trajectories are in good agreement. The tangential velocity of the particles is represented in Figure 21 on the right. The tangential velocity of the particles is almost zero in the regions where there is no liquid. Then, they are accelerated in tangential direction until reaching the bowl wall. There, a deviation between FLUENT and EDEM appears. The particles in EDEM hit the sediment and the tangential velocity diminishes because the wall rotation is not taken into account here, but in FLUENT, no particle accumulation is considered and, thus all particles are calculated until they reach the wall. Once they have reached the wall, they are

The location and quantity of the particles are stored as a variable in FLUENT representing the volume fraction of the particles, as can be seen in Figure 22 on the left. However, for the flow calculations they are considered as points where a momentum exchange occurs. The drag force of the flow acting on the particles is subtracted from the momentum equation diminishing the flow in regions where the particles accumulate. Figure 22 on the right represents the volume fraction of air in the centrifuge. The effect of the particles on the flow can be seen as the water jet coming from the inlet accelerator falls down in the axial position until it reaches the liquid pool due to the particles weight and the momentum sink term.

Fig. 21. Comparison of the particle trajectories obtained in FLUENT and EDEM: left: axial position versus radius; right: tangential velocity of the particles and the fluid versus radius

of the calculated particles for two different rotational speeds of the liquid pool. For the case with lower rotational speed, 686 rpm, the first settled particles deposit at the wall and are pushed to lower axial positions because of the recirculation layer near the wall and due to the lower normal pressure, 3 kPa, acting on the sediment, which allows the influence of the gravity. Then, particles deposit on the sediment and it growths from the wall to the inner part of the centrifuge in radial direction. The sliding of the sediment in this case is due to the relationship of low normal pressure and high shear stress acting on it. In the case of higher rotational speed in the liquid pool, 1937 rpm, the particles travel radially direct to the bowl wall and the sediment formed is flat. The particles settling in the next time steps slide to the side of the sediment which grows along the wall rather than in the radial direction.

In this study the value of the friction coefficient between particles and between particles and wall was constant. Changes of this parameter would also lead to changes in the sediment behaviour under certain conditions of normal pressure and shear stress. A further investigation in this field, including the experimental determination of the friction coefficient for different materials and particle size distributions, is needed. Here only the basis of the coupling methodology was studied.

Fig. 20. Sediment built at the bowl wall as a function of the particles simulated with EDEM coupled with a two-phase simulation of a centrifuge in FLUENT and coloured by velocity magnitude for two different rotational speeds

In order to ensure that the coupling between both programs works and that the hydrodynamic forces are correctly passed from FLUENT to EDEM, the particle trajectories calculated with the coupling and with FLUENT were evaluated. Although the time steps and the mathematical method used in FLUENT to calculate the particles is different from the time steps and algorithm used in EDEM, the results are comparable as shown in Figure 21. Another different is that in FLUENT, the particles were calculated using a static flow field at a certain time step whereas in EDEM, the flow field was calculated alternating to the

of the calculated particles for two different rotational speeds of the liquid pool. For the case with lower rotational speed, 686 rpm, the first settled particles deposit at the wall and are pushed to lower axial positions because of the recirculation layer near the wall and due to the lower normal pressure, 3 kPa, acting on the sediment, which allows the influence of the gravity. Then, particles deposit on the sediment and it growths from the wall to the inner part of the centrifuge in radial direction. The sliding of the sediment in this case is due to the relationship of low normal pressure and high shear stress acting on it. In the case of higher rotational speed in the liquid pool, 1937 rpm, the particles travel radially direct to the bowl wall and the sediment formed is flat. The particles settling in the next time steps slide to the

side of the sediment which grows along the wall rather than in the radial direction.

basis of the coupling methodology was studied.

magnitude for two different rotational speeds

In this study the value of the friction coefficient between particles and between particles and wall was constant. Changes of this parameter would also lead to changes in the sediment behaviour under certain conditions of normal pressure and shear stress. A further investigation in this field, including the experimental determination of the friction coefficient for different materials and particle size distributions, is needed. Here only the

Fig. 20. Sediment built at the bowl wall as a function of the particles simulated with EDEM coupled with a two-phase simulation of a centrifuge in FLUENT and coloured by velocity

In order to ensure that the coupling between both programs works and that the hydrodynamic forces are correctly passed from FLUENT to EDEM, the particle trajectories calculated with the coupling and with FLUENT were evaluated. Although the time steps and the mathematical method used in FLUENT to calculate the particles is different from the time steps and algorithm used in EDEM, the results are comparable as shown in Figure 21. Another different is that in FLUENT, the particles were calculated using a static flow field at a certain time step whereas in EDEM, the flow field was calculated alternating to the position calculation of the particles. Thus in Figure 21 on the left, the particles calculated in FLUENT acquire higher axial positions when compared to the particles calculated with EDEM. The reason for this disagreement is the difference in the axial flow pattern, where the velocities oscillate until a quasi-steady state is achieved. However, qualitatively both particle trajectories are in good agreement. The tangential velocity of the particles is represented in Figure 21 on the right. The tangential velocity of the particles is almost zero in the regions where there is no liquid. Then, they are accelerated in tangential direction until reaching the bowl wall. There, a deviation between FLUENT and EDEM appears. The particles in EDEM hit the sediment and the tangential velocity diminishes because the wall rotation is not taken into account here, but in FLUENT, no particle accumulation is considered and, thus all particles are calculated until they reach the wall. Once they have reached the wall, they are taken from the simulation domain.

The location and quantity of the particles are stored as a variable in FLUENT representing the volume fraction of the particles, as can be seen in Figure 22 on the left. However, for the flow calculations they are considered as points where a momentum exchange occurs. The drag force of the flow acting on the particles is subtracted from the momentum equation diminishing the flow in regions where the particles accumulate. Figure 22 on the right represents the volume fraction of air in the centrifuge. The effect of the particles on the flow can be seen as the water jet coming from the inlet accelerator falls down in the axial position until it reaches the liquid pool due to the particles weight and the momentum sink term.

Fig. 21. Comparison of the particle trajectories obtained in FLUENT and EDEM: left: axial position versus radius; right: tangential velocity of the particles and the fluid versus radius

Computational Fluid Dynamics (CFD) and

Discrete Element Method (DEM) Applied to Centrifuges 127

**7. Evaluation of the computational demand for predicting flow in centrifuges**  The prediction of flow pattern in centrifuges requires a high computational demand that increases with the maximum velocity in the system. Accordingly to Equation 17, the highest

velocity is reached at the bowl wall and increases linearly with the rotational speed.

2 60 *n v r*

Figure 24 shows the computational demand in hsim/(hflow time 3.6 10-3) (dimensionless) against circumferential velocity in m/s for different simulations which include two and three dimensional problems, one and two-phase simulations, and different models to predict turbulent flow. The simulations were performed with Win xp 32 bit desktop computers using an Intel Core 2 Duo E4500 2.2 GHz processor, 2 GB DDR 2 memory running at 266 MHz (2 x 1GB Kingston) and a ASrock motherboard (dual channel memory). All data are averaged values. For reasons of readability, the standard deviation is not stated, because it is too small to be included in the plot. Evaluating the diagram on the left side of Figure 24, it is remarkable how costly the VOF method for simulating two-phase flow for the two and three dimensional cases is. Moving from one to two phases causes the same increase in computational demand as moving from a two to a three dimensional grid and simultaneously increasing the cell number by one order of magnitude. However, the size of the grid does not necessarily increase the computational time. The convergence in a fine grid is faster and the influence of the rotating geometry overcomes the one of the grid when

Fig. 24. Correlation of computational demand in hsim/(hflow time 3.6 10-3) and circumferential velocity: for one and two-phase modelling, two and three-dimensional geometries, and different sizes of the geometry (left); dependence on turbulent model used (right), 715000

cells, three-dimensional and single-phase model

(17)

Fig. 22. Contours of the volume fraction in the FLUENT simulation domain; left: particles; right: air

The effect of the sediment on the flow pattern is shown in Figure 23, where the tangential and axial velocity values are represented. The tangential velocity values are lower than in the simulation without particles because of the momentum exchange between the fluid and the particles. Furthermore the tangential velocity is lower in the lower part of the centrifuge, where most of the particles can be found. The interface radius is not constant over the height of the centrifuge, as can be observed in Figure 22 on the right. Therefore the values of the tangential and axial velocity of the water in Figure 23 begin for lower radii in the lower part of the centrifuge. The form of the axial flow pattern does not change qualitatively except for the height where the particles accumulate, around 0.02 m. There, the axial velocity takes approximately the value zero due to the exchange of momentum between fluid and particles. At the wall, where the sediment is located, there is no axial flow in contrast to the simulation without particles. This fact shows how important is to consider the sediment build-up in the multiphase flow simulation of a centrifuge. However this also carries an increase of the computational effort.

Fig. 23. Averaged values over the circumferential position for different axial positions of the centrifuge obtained in FLUENT coupled with EDEM, left: tangential velocity values versus radius; right: axial velocity versus radius

Fig. 22. Contours of the volume fraction in the FLUENT simulation domain; left: particles;

The effect of the sediment on the flow pattern is shown in Figure 23, where the tangential and axial velocity values are represented. The tangential velocity values are lower than in the simulation without particles because of the momentum exchange between the fluid and the particles. Furthermore the tangential velocity is lower in the lower part of the centrifuge, where most of the particles can be found. The interface radius is not constant over the height of the centrifuge, as can be observed in Figure 22 on the right. Therefore the values of the tangential and axial velocity of the water in Figure 23 begin for lower radii in the lower part of the centrifuge. The form of the axial flow pattern does not change qualitatively except for the height where the particles accumulate, around 0.02 m. There, the axial velocity takes approximately the value zero due to the exchange of momentum between fluid and particles. At the wall, where the sediment is located, there is no axial flow in contrast to the simulation without particles. This fact shows how important is to consider the sediment build-up in the multiphase flow simulation of a centrifuge. However this also carries an

Fig. 23. Averaged values over the circumferential position for different axial positions of the centrifuge obtained in FLUENT coupled with EDEM, left: tangential velocity values versus

right: air

increase of the computational effort.

radius; right: axial velocity versus radius

#### **7. Evaluation of the computational demand for predicting flow in centrifuges**

The prediction of flow pattern in centrifuges requires a high computational demand that increases with the maximum velocity in the system. Accordingly to Equation 17, the highest velocity is reached at the bowl wall and increases linearly with the rotational speed.

$$v = \frac{2 \cdot \pi \cdot n}{60} \cdot r \tag{17}$$

Figure 24 shows the computational demand in hsim/(hflow time 3.6 10-3) (dimensionless) against circumferential velocity in m/s for different simulations which include two and three dimensional problems, one and two-phase simulations, and different models to predict turbulent flow. The simulations were performed with Win xp 32 bit desktop computers using an Intel Core 2 Duo E4500 2.2 GHz processor, 2 GB DDR 2 memory running at 266 MHz (2 x 1GB Kingston) and a ASrock motherboard (dual channel memory). All data are averaged values. For reasons of readability, the standard deviation is not stated, because it is too small to be included in the plot. Evaluating the diagram on the left side of Figure 24, it is remarkable how costly the VOF method for simulating two-phase flow for the two and three dimensional cases is. Moving from one to two phases causes the same increase in computational demand as moving from a two to a three dimensional grid and simultaneously increasing the cell number by one order of magnitude. However, the size of the grid does not necessarily increase the computational time. The convergence in a fine grid is faster and the influence of the rotating geometry overcomes the one of the grid when

Fig. 24. Correlation of computational demand in hsim/(hflow time 3.6 10-3) and circumferential velocity: for one and two-phase modelling, two and three-dimensional geometries, and different sizes of the geometry (left); dependence on turbulent model used (right), 715000 cells, three-dimensional and single-phase model

Computational Fluid Dynamics (CFD) and

steps according to the controlling forces and phenomena.

data, especially in terms of the axial velocity profile.

C2 resistance coefficient, m-1

volumetric force, N m-3

tangential force, N

 p pressure, Pa (N m-2) pc permeability, m2 rbowl bowl radius, m rweir weir radius, m

drag force, N

normal force, N

dV difference in mass balance, %

k turbulent kinetic energy, m2 s-2

n revolutions per minute, rpm

rboundary layer radius of boundary layer, m

L length of the rotor of the centrifuge, m

Cμ constant of the k-ε turbulence model, dimensionless

cycle, can be used.

**9. Notation**

F

Fd

Ft

Fn

Discrete Element Method (DEM) Applied to Centrifuges 129

it proves that the coupling method can be applied for rotating geometries such as centrifuges. The particle trajectories and the sediment build-up agree qualitatively with the expected results. Particles travel through the air core and enter the liquid pool, where they describe spiral paths until they reach the wall or already settled particles to form a sediment. The volume occupied by the particles has not been considered in the calculation of the fluid but the effect of the particles is taken into account by a sink term in the momentum equation. Thus in the flow pattern obtained in FLUENT, the fluid velocity is approximately zero where the sediment is located. The consideration of the particle volume in the calculation of the fluid is a gap in the methodology. A simulation with three Euler phases air, liquid and particles - calculated in EDEM could be a possible but computationally very expensive solution. The method is complex and there is still some effort needed to reduce the particle size without significantly increasing computing time. A possibility to reduce the computational time is to divide the computational domain into regions with different time

There is a substantial increase in computational demand with the increase in rotational speed. This limits the predictions to low rotational speeds when standard workstation computers are used for the calculations. If supercomputers are accessible as it will be the case in research at universities, predictions for high rotational speed are possible. But before advancing to higher rotational speeds it is important to improve the accuracy of the simulations of flow in centrifugal force fields and validate the models with experimental

In order to run a sanity check for the simulations in FLUENT or EDEM, it is not sufficient to evaluate the residuals and mass balance. For new methodologies or boundary conditions, for example when simulating centrifuges, it is necessary to compare different turbulent models, transient and stationary calculation methods and most important to validate the simulation methodology proposed with experimental data. Once validated, geometry and parameters can be changed and the advantage of CFD, which is a fast change to evaluation

simulating centrifuges. This is concluded by comparing the three dimensional, single-phase calculations with a grid size of 215000 cells with the simulations with a grid of 715000 cells. The same effect is observed when comparing the three dimensional, two-phase simulations with different cell sizes and different size of geometry. All data is well fitted with a single function for each of the two compared sets of calculations. Looking at the differences between the turbulent models, all simulations exhibit a comparable computational demand. The RSM is the model with the highest computational demand whereas the large-eddy simulation needs less computational resources than all other models evaluated. This is unexpected since the LES is usually rated as more demanding than the RSM. This is explainable due to the single equation modelling of turbulence in the subgrid, the low degree of turbulence in the case presented and the fine mesh that was constant in all cases presented in the diagram on the right side of Figure 24. The k-e RNG and the k-w simulations require comparable computational resources. This is in agreement with the theory, because both models are similar to each other except of the modelling of the near wall region.

### **8. Conclusions**

The results presented show that the prediction of the flow pattern in centrifuges by means of computational fluid dynamics give good results for evaluation of the tangential acceleration efficiency. The predictions are in good agreement with the measurements conducted with Laser Doppler Anemometry. Nevertheless the axial fluid profiles do not depict the true case accurately. The calculated axial velocity profiles give reasonable results close behind the inlet, but the widening of the inlet jet is not distinguishable in the simulations. The axial velocity profile is essential for the calculation of the cut size and the sediment distribution in the centrifuge, thus any significant deviation from the true case is not acceptable. It was demonstrated that the Reynolds Stress Model (RSM) and the large-eddy simulation (LES) do not increase the accuracy of the predictions when compared to the results obtained using the k-e RNG and k-w model, but increase the computational demand in case of the RSM. All models predict a short-circuit flow between inlet and outlet. The flow pattern does not change with increasing rotational speed or throughputs, only the maximum fluid velocity increases with higher throughputs as expected. This behaviour was observed in single and two-phase simulations.

The geometry of the feed accelerator is decisive for the axial flow pattern developed in the centrifuge. A radial feed impacting on the surface of the liquid pool leads to an axial boundary layer flow similar to the one predicted and experimentally verified by other authors such as Glinka (Glinka, 1983). The design of the feed accelerator and its efficiency is essential for a good centrifugal performance. If the liquid is not accelerated to the angular velocity of the bowl, the rotating pool exhibits a significant lag in tangential velocity when compared to the rigid body rotation. The proposed feeding system via rotating inlet bores leads to an efficient tangential acceleration of the fed suspension.

Particles with a diameter of 200 µm were calculated for the first time in a centrifuge using a coupling between the simulation of the flow in FLUENT and the simulation of the particles in EDEM. The results show a good agreement between particles simulated in FLUENT only considering the hydrodynamic forces and the results from EDEM, which implies that the hydrodynamic forces are correctly transferred from one program to the other. Furthermore it proves that the coupling method can be applied for rotating geometries such as centrifuges. The particle trajectories and the sediment build-up agree qualitatively with the expected results. Particles travel through the air core and enter the liquid pool, where they describe spiral paths until they reach the wall or already settled particles to form a sediment. The volume occupied by the particles has not been considered in the calculation of the fluid but the effect of the particles is taken into account by a sink term in the momentum equation. Thus in the flow pattern obtained in FLUENT, the fluid velocity is approximately zero where the sediment is located. The consideration of the particle volume in the calculation of the fluid is a gap in the methodology. A simulation with three Euler phases air, liquid and particles - calculated in EDEM could be a possible but computationally very expensive solution. The method is complex and there is still some effort needed to reduce the particle size without significantly increasing computing time. A possibility to reduce the computational time is to divide the computational domain into regions with different time steps according to the controlling forces and phenomena.

There is a substantial increase in computational demand with the increase in rotational speed. This limits the predictions to low rotational speeds when standard workstation computers are used for the calculations. If supercomputers are accessible as it will be the case in research at universities, predictions for high rotational speed are possible. But before advancing to higher rotational speeds it is important to improve the accuracy of the simulations of flow in centrifugal force fields and validate the models with experimental data, especially in terms of the axial velocity profile.

In order to run a sanity check for the simulations in FLUENT or EDEM, it is not sufficient to evaluate the residuals and mass balance. For new methodologies or boundary conditions, for example when simulating centrifuges, it is necessary to compare different turbulent models, transient and stationary calculation methods and most important to validate the simulation methodology proposed with experimental data. Once validated, geometry and parameters can be changed and the advantage of CFD, which is a fast change to evaluation cycle, can be used.

### **9. Notation**

128 Applied Computational Fluid Dynamics

simulating centrifuges. This is concluded by comparing the three dimensional, single-phase calculations with a grid size of 215000 cells with the simulations with a grid of 715000 cells. The same effect is observed when comparing the three dimensional, two-phase simulations with different cell sizes and different size of geometry. All data is well fitted with a single function for each of the two compared sets of calculations. Looking at the differences between the turbulent models, all simulations exhibit a comparable computational demand. The RSM is the model with the highest computational demand whereas the large-eddy simulation needs less computational resources than all other models evaluated. This is unexpected since the LES is usually rated as more demanding than the RSM. This is explainable due to the single equation modelling of turbulence in the subgrid, the low degree of turbulence in the case presented and the fine mesh that was constant in all cases presented in the diagram on the right side of Figure 24. The k-e RNG and the k-w simulations require comparable computational resources. This is in agreement with the theory, because both models are

The results presented show that the prediction of the flow pattern in centrifuges by means of computational fluid dynamics give good results for evaluation of the tangential acceleration efficiency. The predictions are in good agreement with the measurements conducted with Laser Doppler Anemometry. Nevertheless the axial fluid profiles do not depict the true case accurately. The calculated axial velocity profiles give reasonable results close behind the inlet, but the widening of the inlet jet is not distinguishable in the simulations. The axial velocity profile is essential for the calculation of the cut size and the sediment distribution in the centrifuge, thus any significant deviation from the true case is not acceptable. It was demonstrated that the Reynolds Stress Model (RSM) and the large-eddy simulation (LES) do not increase the accuracy of the predictions when compared to the results obtained using the k-e RNG and k-w model, but increase the computational demand in case of the RSM. All models predict a short-circuit flow between inlet and outlet. The flow pattern does not change with increasing rotational speed or throughputs, only the maximum fluid velocity increases with higher throughputs as expected. This behaviour was observed in single and

The geometry of the feed accelerator is decisive for the axial flow pattern developed in the centrifuge. A radial feed impacting on the surface of the liquid pool leads to an axial boundary layer flow similar to the one predicted and experimentally verified by other authors such as Glinka (Glinka, 1983). The design of the feed accelerator and its efficiency is essential for a good centrifugal performance. If the liquid is not accelerated to the angular velocity of the bowl, the rotating pool exhibits a significant lag in tangential velocity when compared to the rigid body rotation. The proposed feeding system via rotating inlet bores

Particles with a diameter of 200 µm were calculated for the first time in a centrifuge using a coupling between the simulation of the flow in FLUENT and the simulation of the particles in EDEM. The results show a good agreement between particles simulated in FLUENT only considering the hydrodynamic forces and the results from EDEM, which implies that the hydrodynamic forces are correctly transferred from one program to the other. Furthermore

similar to each other except of the modelling of the near wall region.

leads to an efficient tangential acceleration of the fed suspension.

**8. Conclusions**

two-phase simulations.

Computational Fluid Dynamics (CFD) and

*Ansys Fluent 12.*,

321-340

2-3, 101-116

*Mechanics*, 24, 2, 183-202

*Technology*, 179, 3, 104-114

*Geotechnique*, 29, 1, 47-65

*Mashinostroenie*, 6, 13-14

*Physics of Fluids*, 14, 2, 643-652

1312

657-659

Discrete Element Method (DEM) Applied to Centrifuges 131

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### **10. Acknowledgments**

We acknowledge support by Deutsche Forschungsgemeinschaft and Open Access Publishing Fund of Karlsruhe Institute of Technology.

### **11. References**

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 LES large-eddy simulation RBR rigid body rotation RSM Reynolds Stress Model VOF Volume of Fluid St Stokes number

δ thickness of the axial boundary layer, mm

ε turbulent kinetic energy dissipation rate, m2 s-3

density difference between liquid and solid, kg m-3

specific turbulent kinetic energy dissipation rate, s-1

We acknowledge support by Deutsche Forschungsgemeinschaft and Open Access

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y+ characteristic width of viscous sublayer, dimensionless

t time, s

v

Greek letters

Indices

q phase

**10. Acknowledgments**

**11. References**

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**CFD and Thermography Techniques**

**Applied in Cooling Systems Designs**

The focus of this work consists in optimizing the water flow inside a water cooled electric motor frame, aiming at the maximization of the power/frame size ratio, the minimization of pressure drop and the avoidance of hot spots. For the development of this work

For many years water cooled electric motors have been used by industry, especially in specific applications that require features that can not be provided by conventional fan cooled motors. Among theses features are a better power/frame size relation, low noise

Cooling by means of water circulation is frequently used in large motors, typically frame sizes above IEC 315. A justification for this practice not to be widely used in smaller motors is its higher cost compared to air cooling systems. However, provided that it presents some technical and/or economical viability, water cooling can also be used in smaller frame sizes. The technological progress have resulted in the development of new tools that facilitate the study of this motor type, such as the computational fluid dynamics and the thermography techniques, which consist, respectively, in the use of numeric models applied to fluid

The following advantages and disadvantages of this kind of motor can be mentioned, in

computational fluid dynamics (CFD) and thermography techniques were used.

mechanics and the obtaining of the motor surface temperature distribution.

The outside waste deposit on the frame does not damage the motor cooling;

 The heat removed from the motor is not directly dissipated into the environment; Possibility of using the same cooling fluid of the load and/or machine where it is

No problems with waste deposit on the external fan blade;

It can be used in totally enclosure environment;

**1. Introduction**

levels, enclose applications, among others.

**2. Benefits and drawbacks**

**2.1 Advantages**

installed;

 Lower noise level; Higher efficiency;

comparison with air cooled motors.

Greater power/frame size ratio;

Samuel Santos Borges and Cassiano Antunes Cezario *Research and Technological Innovation Department, WEG*

*Brazil*

Zubkov, V. A. & Golovko, Y. D. (1969). Flow of Liquid in Rotor Outlet of a Tubular Centrifuge. *International Chemical Engineering*, 9, 3, 403-406 **7**


**Acknowledgements**

The author thanks Dr. Nurmalasari Darsono and Dr. Yudhi Rinanto for providing the experimental results, and also Suvia Widyaningrum and Intan Ria Neliana for their assistances. The authors also thank the PUSNAS 2017 - Research Grant and University of Jember for the support of funding.


**Correlation between TDR and FDR Soil Moisture Measurements at Different Scales to Establish Water Availability at the South of the Yucatan Peninsula Correlation between TDR and FDR Soil Moisture Measurements at Different Scales to Establish Water Availability at the South of the Yucatan Peninsula**

DOI: 10.5772/intechopen.81477

Judith Guadalupe Ramos Hernández, Jesus Gracia-Sánchez, Tania Patricia Rodríguez-Martínez and José Adalberto Zuñiga-Morales Judith Guadalupe Ramos Hernández, Jesus Gracia-Sánchez, Tania Patricia Rodríguez-Martínez and

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.81477

José Adalberto Zuñiga-Morales


**3. Limits of CALM for drinking water by U.S-EPA, WHO, BOBS**

To provide guidance in resolving the contamination of drinking water by microorganisms and heavy metals, WHO has developed guidelines and water safety plans

#### **Table 1.**

*Permissible limits of CALM in drinking water as prescribed by USEPA, WHO, and BOBS [2, 3, 62].*

for drinking water quality [2]. The guidelines highlight that the proposed permissible threshold values are designated as provisional, given the practical difficulties of treating drinking water up to these required standards [2]. However, water authorities are encouraged to make an effort to maintain pollutants' concentrations below the guideline values.

**Table 1** summarizes the maximum contamination level (MCL) for Cd, As, Pb, and Hg as proposed by BOBS, WHO, and the US EPA [2, 3, 63]. Control measures, such as pre-treatment, coagulation, flocculation, sedimentation, filtration, and disinfection, are highlighted as crucial steps during drinking water treatment processes [2, 64]. The piping system of the treatment plant and of the distribution network must be taken into consideration to avoid the unintended input of residual heavy metals through corrosion and leaching of plumbing networks. Proper maintenance and regulation or survey procedures of the treatment plant to prevent contamination help in determining the presence of unwanted HMs and the eventual removal of internal accumulation of deposits.


**1. Introduction**

42 Current Issues of Water Management

Komatina, D. (2011a). The Framework Agreement on the Sava River Basin – a basis for sustainable development of the region, submitted for publication in *Danube News* Komatina, D. (2011b). Development of navigation on the Sava River – an integrated

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*The Dublin Statement on Water and Sustainable Development*, 1992, Available from:

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in the field of water management. *Hrvatske vode*, Water Management Journal, Vol.

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ISRBC. (2010b). *The 2006 Hydrological Yearbook of the Sava River Basin*, Available from:

ISRBC. (2011a). *Strategy on Implementation of the FASRB*, Available from:

ISRBC. (2011c). *Nautical and Tourist Guide of the Sava River*, Available from:

approach, submitted for publication in *Danube News*

http://transfer.message.at/\_ZJyVSK80VdDitR *Protocol on Navigation Regime to the FASRB*, 2004, Available from: http://www.savacommission.org/basic\_docs

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http://www.savacommission.org/publication

http://www.savacommission.org/basic\_docs

http://www.savacommission.org/basic\_docs

http://www.savacommission.org/publication

In recent years a major effort has been done to make water quality modelling tools available for water resources management at a river basin scale. The European water framework directive clear states that these tools must be used in making the diagnostic of surface water bodies water quality status and to anticipate the impact of measures to be implemented in order to achieve a good ecological status by 2015 in European waters (European Commission 2000; Rekolainen 2003; Horn et al. 2004; Ravesteijn & Kroesen 2007; Volk et al. 2008).

In order to make modelling tools usable by all the actors enrolled in water resources management process at river basins, these tools must be simple, user-friendly and robust. Water managers have shown strong interest in the integration of model tools throughout the use of graphical interfaces in their activities (Borowski & Hare 2007). These tools must be able to establish water management scenarios but it is well known that water managers have lack of time for training in the use of complex systems. Also software and hardware costs appear to be an important constrain in implementing these tools.

Several solutions are being implemented throughout European countries, resulting from the development and integration of different software packages using different integration technologies (Dudley et al. 2005, Berlekamp et al. 2007, De Kok et al. 2009).

This chapter presents a hydroinformatic environment (Price, 2000) specifically designed for a Portuguese north-western river basin (river Cávado) in order to define, simulate and analyse hydrodynamics and water quality management scenarios – the ODeCav System. The software solution was designed to be operated in a web environment, taking advantage of the integration capabilities of this software environment and the user friendliness of web interfaces. It is composed of the following main components: water monitoring data-bases, hydrodynamics and water quality river models, and reports facilities for the presentation of output results. The applicability of this hydroinformatic environment is exposed in the study of waste water treatment plants (WWTP) discharges impacts on the river water quality for different river flow regimes.

Web-Based Decision Support Framework for

such as degradation of organic matter.

masses mixing conditions.

this purpose.

(Figure 1).

Water Resources Management at River Basin Scale 45

framework, as much inclusive as possible that cover simple water quality processes, such as the modeling of accidental releases of conservative pollutants, or more complex processes,

For problems involving conservative substances it is only considered the transport of the substance in the water through advection and diffusion. The evaluation of the extensions and durations of accidental discharge can be carried out recurring to a model in which the accidental discharge is modeled by a conservative substance. In addition to the cases of accidental discharge, these simple models also have practical interest to quantify the residence times and to analyze the effect of different hydrodynamic conditions in the water

The majority of elements and substances in aquatic environments have reactions with other elements and/or substances, resulting in their transformation (decrease or increase in concentration). Bacterial contamination arising from discharges of domestic wastewater or diffuse sources, for example, can be modeled by taking up a 1st-order decay law. The behavior of many other substances (or species) can be approximated by considering the decay or growth of a second order, such as biochemical oxygen demand (BOD) or algae. The reaction coefficients should be established mainly through the available field data or laboratory tests. Dissolved oxygen (DO) is a common environmental element used to characterize the water quality in water systems. The analysis of the impact caused by discharges with a high concentration of organic matter may be made to quantify the effects in terms of variations in concentrations of dissolved oxygen in the water column, due to the decomposition of organic matter contained in wastewater discharges. The water quality processes library used in this work is one of the most complete for surface water quality modeling and includes all the relevant processes allowing the establishment of either

complex water quality processes or simple ones depending on data availability.

The developed technological platform is mainly based on a database system and a set of hydrological, hydrodynamic and water quality models, operated using web interfaces. It comprises functionalities for query and analysis of the river network (information system), hydrodynamic and water quality models operation (modelling system), and results analysis (analysis system). Besides this, the platform provides the following additional services: user's management, document management and monitoring data store and display. The user's management service allows restricting or not the access to various content, as well as the permissions to run/execute or to view/consult/query the simulations results. The document management service allows the users to perform simple tasks, such as publication of papers and upload/download of work documents. The monitoring data functionalities provides a framework for gauge and water quality stations installed in the river basin, allowing its analysis, validation, and integration using a specifically designed database for

The website responsible for the system interaction with the end users is divided into four main sections that allow access to the features mentioned above: Project, Information, Modelling and Analysis. These sub-menus are the main options from the navigation menu

**2.2 Web-based hydroinformatic environment**


**Author details**

*Cytogenetics - Classical and Molecular Strategies for Analysing Heredity Material*

**2. Contribution of environmental constituents in mutation**

the inherent form.

**3. Conclusion**

innovative research.

results in genetic deficiencies cause.

Throughout the world, skin melanoma is the 19th most widespread cancer. Usually, almost all types of skin cancers are related to environmental factors including contact with immense ultraviolet radiation or due to sun exposure. Environmental mutagens may be synthetic or natural agents in nature

[74, 113–116]. these mutagens produce genetic mutations or expand mutational activities during the life span [117, 118]. Most of the environmental mutagens possess genotoxic effects on the next generation via germ cells and continue in

Besides ultraviolet radiation, other radioactive, heavy metals, organic solvents

or chemicals, viruses, bacteria, etc. also perform a role to cause cell damage [119–122]. Even, consumption of cigarette smoke, dietary contaminants including mycotoxin, aflatoxin B1, fat consumption, and unorganized stress are themselves integral environmental factors that contribute to cytokeratin disruptions [123]. All these agents are come in contact with the human through directly via skin & lungs or by ingestion. From this channel, these circulate in the body (blood, lymph glands, muscles, bones, tissues, and organs) and initiate mutations. In mutagenesis, these all mutagens penetrate directly to cellular and nuclear membranes and damage DNA by cross-linking (chemically gluing) two bases together. Sometimes, Mutagenesis is also caused by aberrant DNA methylation (epigenetic change) at the genomic level and post-translational modifications at the protein level. Finally, this

Cytokeratins are essential protectors of epithelial structure found in the intracytoplasmic cytoskeleton of epithelial tissue. The occurrence of mutation in cytokeratin genes generates several genetic dermal disorders. In this genetic alteration, several environmental factors (ultraviolet, reactive oxygen species (ROS), deaminating agents, polycyclic aromatic hydrocarbon (PAH), ethylnitrosourea, azide, dyes, and heavy metals) take place as mutagen factors. The present chapter conclusively stated different cytokeratins disorders caused by environmental mutagens, i.e., synthetic or natural mutagens. In the end, based on environmental mutagens contributions, it can be stated that the genetic and epigenetic effects, arise/enhance through environmental mutagens/carcinogens, are the subject of

**144**

Vishnu Sharma1 \*, Tarun Kr. Kumawat1 , Garima Sharma1 , Rashi Garg1 and Manish Biyani1,2

1 Department of Biotechnology, Biyani Girls College, Jaipur, Rajasthan, India

2 Department of Bioscience and Biotechnology, Japan Advanced Institute of Science and Technology, Japan

\*Address all correspondence to<EMAIL_ADDRESS>
© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


**About the Editors**

#### **Lavinia Chiara Tagliabue**

Dr. Lavinia Chiara Tagliabue, Associate Professor, of Computer Science Department, University of Turin, Turin, Italy.

Her research interests are related to sustainability and sustainable buildings; environmental and energy protocols; energy saving; renewable energies; energy retrofit and NZEB; BIM to BEM (building information modeling to building energy modeling) interoperability; cognitive buildings; behavioral design; probabilistic models; building management systems (BMS), Digital Twins.

#### **Ibrahim Yitmen**

Dr. Ibrahim Yitmen, Associate Professor, Department of Construction Engineering and Lighting Science, School of Engineering, Jonk ¨ oping University, J ¨ onk ¨ oping, Sweden. ¨

His research interests are related to digital transformation in the AEC industry; digital twin-based smart built environment; augmented reality/mixed reality for cognitive buildings; integration of digital twins and deep learning for smart planning and construction; blockchain technology in construction supply chains; cyber-physical systems for construction 4.0; integration of unmanned aerial vehicles and BIM for construction safety planning and monitoring.


**Author details**

Eliege Jullia Eudoxia dos Santos1 , Amanda Teixeira Sampaio Lopes1 and Bianca Mendes Maciel1,2\*

1 Graduation Program in Animal Science, Santa Cruz State University, Ilhéus, Bahia, Brazil

2 Department of Biological Sciences, Santa Cruz State University, Ilhéus, Bahia, Brazil

\*Address all correspondence to<EMAIL_ADDRESS>
© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.