**4.3 Laminar flow regime**

Two different set of calculations are presented in the next paragraphs, the first one is based in results obtained from laminar flow regime models. Results for pressure calculations are presented in **Figure 4**. These calculations required an input velocity with different values relatively low to obtain laminar flow through a double layer porous zone built with zeolite and soil. Velocity values used in this section are *v1* = 0.005 m/s, *v2* = 0.01 m/s, *v3* = 0.02 m/s, *v4* = 0.03 m/s, and *v5* = 0.04 m/s.

Pressure effects are displayed in **Figure 4**, to understand pressure-drop in a layer-by-layer contour plot that illustrates water flow moving through zeolite and soil layers modeled as porous media within ANSYS-Fluent.

The higher the input velocity, the higher pressure is required to make the flow pass through the porous media, for specific pressure values a scale in pascals is shown by the side of each simulation to help interpret the contours color in the image.

In **Figure 5** are presented contour plots of velocity to illustrate how water is applied gradually into the model. Water is applied using an input velocity with low values to keep the flow under laminar regime in y-axis negative direction (downwards). Velocity decreases as the flow advances through the pipe and porous zone represented by the two layers simulating zeolite and soil. Each velocity contour plot includes a scale with velocity values in meters per second to facilitate the interpretation of each color included in the contour plot. For a better understanding of pressure drop, a graph showing pressure drop profile was generated based in results for laminar flow regime computations as displayed in **Figure 6**. This profile is built as a scatter plot using y-axis or height in the model as the *x-coordinate* or abscissa and, pressure drop was represented in the *y-ordinate*. The scatter plot displays an overall view of the pressure drop as y-axis values change through the pipe and porous zone. To analyze further the effects on pressure drop for laminar flow regime simulations, pressure values at different locations were calculated, specifically, at the inlet and outlet for each layer of porous media zone (boundaries). Also, pressure drop for each layer was calculated by finding the difference between pressure values at layers inlet and outlet (this difference will be referred to as delta pressure values). **Table 1** contains pressure and delta pressure calculations numerical results.

### *Applications of Computational Fluid Dynamics Simulation and Modeling*

#### **Figure 4.**

*Contour plots corresponding to results for pressure from laminar flow regime calculations using a double layer model porous zone. (a)* v*<sup>1</sup> = 0.005 m/s, (b)* v2 *= 0.01 m/s. (c)* v3 *= 0.02 m/s, (d)* v4 *= 0.03 m/s, (e)* v5 *= 0.04 m/s.*

#### **4.4 Turbulent flow regime**

Results for pressure calculations obtained from turbulent flow model simulations are presented in **Figure 7**. These calculations required an input velocity with different values to obtain turbulent flow through our model with a double layer porous zone built with zeolite and soil.

*A CFD Porous Materials Model to Test Soil Enriched with Nanostructured Zeolite Using… DOI: http://dx.doi.org/10.5772/intechopen.100487*

#### **Figure 5.**

*Contour plots corresponding to results for velocity in y-direction from laminar flow regime calculations using a double layer model porous zone. (a)* v*<sup>1</sup> = 0.005 m/s, (b)* v2 *= 0.01 m/s. (c)* v3 *= 0.02 m/s, (d)* v4 *= 0.03 m/s, (e)* v5 *= 0.04 m/s.*

Velocity values used in this section are *v1* = 0.04 m/s, *v2* = 0.05 m/s, *v3* = 0.1 m/s, *v4* = 0.2 m/s, *v5* = 0.3 m/s, *v6* = 0.4 m/s, *v7* = 0.5 m/s. Pressure effects as displayed in **Figure 7** represent pressure drop for our models under turbulent flow regime in a

**Figure 6.** *Graph showing pressure drop results for laminar flow regime calculations using a double layer model porous zone. (a)* v*<sup>1</sup> = 0.005 m/s, (b)* v2 *= 0.01 m/s. (c)* v3 *= 0.02 m/s, (d)* v4 *= 0.03 m/s, (e)* v5 *= 0.04 m/s.*

layer-by-layer contour plot to illustrate water flow through zeolite and soil layers modeled as porous media within ANSYS-Fluent.

The higher the input velocity, the higher pressure is required to make the flow through the porous media, for specific pressure values a scale in pascals is shown by *A CFD Porous Materials Model to Test Soil Enriched with Nanostructured Zeolite Using… DOI: http://dx.doi.org/10.5772/intechopen.100487*


**Table 1.**

*Laminar flow regime pressure-drop numerical results at the boundaries between different layers (zeolite over soil) to analyze flow through porous zone.*

the side of each simulation to help interpret the contours color in the image. In comparison with laminar flow, water flow velocity and pressure present higher values.

In **Figure 8** are presented contour plots of velocity to illustrate how water flows through the porous zone. Water is applied using an input velocity with low values just enough to keep the flow as turbulent with a direction in y-axis with or without negative sign (downwards).

Velocity decreases as the flow advances through the porous zone represented by the two layers simulating zeolite and soil. Each velocity contour plot includes a scale with velocity values in meters per second to facilitate the interpretation of each color included in the contour plot.

For a better understanding of pressure drop, a graph showing pressure drop profile was generated for turbulent flow calculations as displayed in **Figure 9**. Similarly, as it was done with laminar flow, the profile is built with a scatter plot using y-axis or height in our model as the *x-coordinate* and pressure drop is represented in the *y-ordinate*. Also, to analyze further the effects on pressure drop for laminar flow regime simulations, pressure values at the boundaries for each layer of the porous media zone. Pressure drop for each layer in the turbulent model was calculated by finding the difference between pressure values at layers considering an inlet and an outlet. **Table 2** contains pressure and delta pressure numerical results.

#### **4.5 Effects on zeolite and soil layers**

Porous zone flow is simulated as a region that presents resistance to the fluid flow. When water is introduced in the system each layer representing a porous material presents a difficulty to allow flow through which can be measured with the pressure drop calculated on those areas. Due to its properties, zeolite layer presents the higher pressure drop values. Zeolite and soil material parameters to represent materials properties used within this work are based in textbook values [1, 8, 35] and can be modified as required depending on the specific properties of the materials that need to be simulated. The input velocity is also important regarding how pressure drop displays its profile and relative values, in general, the higher the input velocity value, the higher the pressure drop in the porous zone areas. Such effect occurs in laminar flow and turbulent flow. However, pressure drop may be higher in turbulent flow due to velocity input values are higher too. This model may be useful for future developments where the porous materials properties are modified or when one needs further studies related to water distribution in the system.

## *Applications of Computational Fluid Dynamics Simulation and Modeling*

#### **Figure 7.**

*Contour plots for pressure obtained from turbulent flow regime numerical results corresponding to calculation with different velocity inputs using a double layer porous zone, the velocity values used were: (a)* v1 *= 0.04 m/s, (b)* v2 *= 0.05 m/s. (c)* v3 *= 0.1 m/s, (d)* v4 *= 0.2 m/s, (e)* v5 *= 0.3 m/s, (f)* v6 *= 0.4 m/s, (g)* v7 *= 0.5 m/s.*

*A CFD Porous Materials Model to Test Soil Enriched with Nanostructured Zeolite Using… DOI: http://dx.doi.org/10.5772/intechopen.100487*

#### **Figure 8.**

*Contour plots for velocity in y-axis obtained from turbulent flow regime numerical results corresponding to calculations with different velocity inputs using a double layer porous zone, the velocity values used were: (a)* v1 *= 0.04 m/s, (b)* v2 *= 0.05 m/s. (c)* v3 *= 0.1 m/s, (d)* v4 *= 0.2 m/s, (e)* v5 *= 0.3 m/s, (f)* v6 *= 0.4 m/s, (g)* v7 *= 0.5 m/s.*

**Figure 9.**

*Graph showing pressure drop results for turbulent flow regime calculations using a double layer model porous zone. (a)* v1 *= 0.04 m/s, (b)* v2 *= 0.05 m/s. (c)* v3 *= 0.1 m/s, (d)* v4 *= 0.2 m/s, (e)* v5 *= 0.3 m/s, (f)* v6 *= 0.4 m/s, (g)* v7 *= 0.5 m/s.*

### **5. Conclusions**

Computational fluid dynamics (CFD) is used as a powerful tool to analyze multiphysics problems in a wide variety of applications. To analyze porous materials ANSYS-Fluent offers an interesting scheme that enables the study of a fluid through a porous material. A bi-layer model was built to represent a layer of zeolite placed

*A CFD Porous Materials Model to Test Soil Enriched with Nanostructured Zeolite Using… DOI: http://dx.doi.org/10.5772/intechopen.100487*


#### **Table 2.**

*Turbulent flow regime pressure-drop calculations at the boundaries between different layers (zeolite over soil) to analyze flow through porous zone.*

over a layer of soil and both interacting with a water flow. Laminar and turbulent flow regimes were analyzed successfully with the approach proposed which represents an attempt to systematically analyze different nanostructured zeolites interacting with different soil types.
