**4. Hydrodynamic calculations**

As mentioned in prior sections, the design of a chemical reactor involves several steps and disciplines, and simulation hydrodynamic calculations are the first to be carried on. Fluid kinematics deals with describing the motion of fluids without necessarily considering the forces and moments that cause the motion. In this section, we introduce fundamental kinematic concepts related to flowing fluids. We discuss briefly the material derivative and its role in transforming the conservation equations from the Lagrangian description of fluid flow (following a fluid particle) to the Eulerian description of fluid flow (pertaining to a flow field).

The kinematics of experiments under the Lagrangian description involves keeping track of the position vector of each object, xA, xB,. …, and the velocity vector of each object, *VA*, *VB*, …, as functions of time. When this method is applied to a flowing fluid, we call it the Lagrangian description of fluid motion. From a microscopic point of view, a fluid is composed of billions of molecules that are subject to continuous collisions into one another, somewhat like billiard balls, but the task of following even a subset of these molecules is quite difficult, even for our biggest computers.

A more common method of describing fluid flow is the Eulerian description of fluid motion. In the Eulerian description of fluid flow, a finite volume called a control volume is defined, through single piece of volume fluid flows in and out. We do not need to keep track of the position and velocity of a mass of fluid particles of fixed identity. Instead, we define field variable functions of space and time, within the control volume [3–5]. For example, the pressure field is a scalar field variable for general unsteady tridimensional fluid flow in Cartesian coordinates:

Pressure field:

$$
\vec{P} = P(\vec{\varkappa}, \vec{\jmath}, \vec{\varkappa}, \mathfrak{r}) \tag{1}
$$

We define the velocity field as a vector field variable in a similar fashion: Velocity field:

$$
\vec{\nabla} = \mathbf{V}(\vec{x}, \vec{y}, \vec{z}, t) \tag{2}
$$

Likewise, the acceleration field is also a vector field variable:

Acceleration field:

$$
\vec{d} = a\left(\vec{x}, \vec{y}, \vec{z}, t\right) \tag{3}
$$

Collectively, these (and other) field variables define the flow field. The velocity field of Eq. 2 is expanded in Cartesian coordinates (x, y, z) and (i, j, k) as:

$$V = \left(\vec{u}', \vec{v}', \vec{w}\right) = u\left(\mathbf{x}, y, z, t\right)\hat{i} + v\left(\mathbf{x}, y, z, t\right)\hat{j} + w\left(\mathbf{x}, y, z, t\right)\hat{k} \tag{4}$$

We will leave for other texts the mathematical development of the Lagrangian and Eulerian descriptions since we are interested in a qualitative interpretation more than the mathematical concepts. In the Eulerian description, we do not really care what happens to individual fluid particles, but we are concerned with the pressure, velocity, acceleration, etc., of whichever fluid particle happens to be at the location of interest at the time of interest. The Eulerian description is often more convenient for fluid mechanic applications. Furthermore, experimental measurements are generally more suited to the Eulerian description [3–5].

#### **4.1 First hydrodynamics**

In this work, the intention is to resolve and analyze one of the most important steps during the chemical reactor design process, in particular, for a case related to a photocatalytic reactor. This section establishes the importance of hydrodynamics in chemical reactor design for water remediation focusing in photocatalytic reactors. The fluid dynamics is a part of the reactor design process that among the simulation activities should be resolved in the first place. Fluid dynamic results can be complemented by chemical reaction simulation, chemical species, radiation from light source effects, etc.

#### **4.2 Proposed model to incorporate CFD calculations in chemical reactor design**

In this type of reactors, the phenomena occurring in the device may be explained by four different processes: (i) fluid mechanics, (ii) heat transfer (radiation), (iii) mass transport, and (iv) chemical reaction. These different processes may be considered the steps to follow or a design methodology. It works better if used as a recirculated cyclic process because at some point some experimental parameters will be needed. For example, a kinetic intrinsic model for the chemical degradation of the selected pollutant(s) is needed as input. The kinetic parameters are obtained from experimentation and will be used as input data in the CFD modeling. Another advantage obtained from CFD is the possibility to build new scenarios using these input data, for example, the use of a bigger size or more complex reactor under different flow dynamics or optical conditions.

A photocatalytic reactor used a light source or sunlight as energy source to trigger the chemical reaction. Modeling facilitates the designer to run the chemical reactor under different scenarios that may be later compared with results obtained with experimentation when a physical device is available. There are different chemical reactor methodologies or guidelines; in **Figure 1** the reader may find a general methodology proposed for the specific case of photocatalytic reactor design.

In the design of a chemical reactor, knowledge of the chemical kinetics process involved is needed. Kinetic parameters should follow a mechanistic model, so they may be used during the simulation beyond the operational limits used to obtain them. The reaction modeling is an area under development due to the difficulty of accurate methodologies to obtain appropriate kinetic parameters that may be used during the

**91**

*Hydrodynamic Analysis on a Photocatalytic Reactor Using ANSYS Fluent®*

simulation. For each specific reactor type, the recommendation is to consult the latest literature to define the guidelines in order to define the kinetic parameters [3–5].

As mentioned in prior sections, this chapter will deal with hydrodynamic calculations related to a photocatalytic reactor. While any intelligent, computer-literate person can run a CFD code, the results obtained may not be physically correct. The case proposed within this chapter has been included as an academic example only. Therefore, the goal of this chapter is to present guidelines or the basic steps for a

The examples presented here have been obtained with the commercial computational fluid dynamic code ANSYS Fluent® [6, 7]. Other CFD codes would yield similar but not identical results. Sample CFD solutions are shown for incompress-

In this case, an academic example of a photocatalytic reactor design process is included. More specifically, the intention is to develop the hydrodynamic simulation of the photocatalytic reactor. The data that can be obtained from hydrodynamic simulation permits a detailed definition of the flow motion features, for example, fluid speed in the reaction zone, fluid pressure distribution, and the use of these data as input for further calculations such as distribution of energy from light source, photocatalytic reaction, etc. To achieve these calculations, literature and operational basic requirements were studied in order to define fundamental criteria

With the definition of basic dimensions, it is possible to start using CAD tools to build 3D models that will provide the reactor geometric features that will be needed during CFD simulations. Creo 4.0 and SolidWorks 2016 were used to develop the 3D models of the proposed reactor. For hydrodynamic calculations ANSYS Fluent®

To be able to grow an understanding of the basic reactor design criteria, it was needed to consult the bibliography in different functional areas. The design intent is to build a photochemical reactor of an appropriate size to support laboratory capabilities for testing of nanoparticles after those are synthetized by our research group. It is important for this design to simplify as much as possible the reactor operation.

ible laminar flow, without heat transfer and chemical reaction.

to assign basic dimensions to the reactor geometry.

versions 18.2 and 19 were used [6, 7].

**5.1 Initial calculations**

*DOI: http://dx.doi.org/10.5772/intechopen.89782*

*Proposed methodology for photocatalytic reactor design.*

**4.3 CFD calculations**

**Figure 1.**

hydrodynamic simulation.

**5. Case of study**

*Hydrodynamic Analysis on a Photocatalytic Reactor Using ANSYS Fluent® DOI: http://dx.doi.org/10.5772/intechopen.89782*

**Figure 1.**

*Computational Fluid Dynamics Simulations*

→ *u*, → *v*, → → *a* = *a*( → *x*, → *y*, →

field of Eq. 2 is expanded in Cartesian coordinates (x, y, z) and (i, j, k) as:

*w*) = *u*(*x*, *y*, *z*,*t*)*i*

ments are generally more suited to the Eulerian description [3–5].

Collectively, these (and other) field variables define the flow field. The velocity

+ *v*(*x*, *y*, *z*,*t*)*j*

^

^

We will leave for other texts the mathematical development of the Lagrangian and Eulerian descriptions since we are interested in a qualitative interpretation more than the mathematical concepts. In the Eulerian description, we do not really care what happens to individual fluid particles, but we are concerned with the pressure, velocity, acceleration, etc., of whichever fluid particle happens to be at the location of interest at the time of interest. The Eulerian description is often more convenient for fluid mechanic applications. Furthermore, experimental measure-

In this work, the intention is to resolve and analyze one of the most important steps during the chemical reactor design process, in particular, for a case related to a photocatalytic reactor. This section establishes the importance of hydrodynamics in chemical reactor design for water remediation focusing in photocatalytic reactors. The fluid dynamics is a part of the reactor design process that among the simulation activities should be resolved in the first place. Fluid dynamic results can be complemented by chemical reaction simulation, chemical species, radiation from

**4.2 Proposed model to incorporate CFD calculations in chemical reactor design**

by four different processes: (i) fluid mechanics, (ii) heat transfer (radiation), (iii) mass transport, and (iv) chemical reaction. These different processes may be considered the steps to follow or a design methodology. It works better if used as a recirculated cyclic process because at some point some experimental parameters will be needed. For example, a kinetic intrinsic model for the chemical degradation of the selected pollutant(s) is needed as input. The kinetic parameters are obtained from experimentation and will be used as input data in the CFD modeling. Another advantage obtained from CFD is the possibility to build new scenarios using these input data, for example, the use of a bigger size or more complex reactor under

A photocatalytic reactor used a light source or sunlight as energy source to trigger the chemical reaction. Modeling facilitates the designer to run the chemical reactor under different scenarios that may be later compared with results obtained with experimentation when a physical device is available. There are different chemical reactor methodologies or guidelines; in **Figure 1** the reader may find a general methodology proposed for the specific case of photocatalytic reactor design.

In the design of a chemical reactor, knowledge of the chemical kinetics process involved is needed. Kinetic parameters should follow a mechanistic model, so they may be used during the simulation beyond the operational limits used to obtain them. The reaction modeling is an area under development due to the difficulty of accurate methodologies to obtain appropriate kinetic parameters that may be used during the

In this type of reactors, the phenomena occurring in the device may be explained

*z*,*t*) (3)

+ *w*(*x*, *y*, *z*,*t*)*k*

^

(4)

Acceleration field:

*V* = (

**4.1 First hydrodynamics**

light source effects, etc.

different flow dynamics or optical conditions.

**90**

*Proposed methodology for photocatalytic reactor design.*

simulation. For each specific reactor type, the recommendation is to consult the latest literature to define the guidelines in order to define the kinetic parameters [3–5].

#### **4.3 CFD calculations**

As mentioned in prior sections, this chapter will deal with hydrodynamic calculations related to a photocatalytic reactor. While any intelligent, computer-literate person can run a CFD code, the results obtained may not be physically correct. The case proposed within this chapter has been included as an academic example only. Therefore, the goal of this chapter is to present guidelines or the basic steps for a hydrodynamic simulation.

The examples presented here have been obtained with the commercial computational fluid dynamic code ANSYS Fluent® [6, 7]. Other CFD codes would yield similar but not identical results. Sample CFD solutions are shown for incompressible laminar flow, without heat transfer and chemical reaction.
