**3. Methodology**

#### **3.1 Study area**

The research was conducted at Olabisi Onabanjo University, College of Engineering and Environmental Studies, Ibogun Campus, Ifo, Ogun State, Nigeria located 240°SW on the Longitude 3.0990 and latitude 6.8080. The location has an annual average temperature of about 28.5°C and wind speed of about 4 m/s. The average relative humidity is about 63%. The study was performed in the selected

lecture room where ventilation is normally achieved through opening of doors, windows and Mechanical ventilation system (ceiling fans). This lecture hall is representative of lecture halls in many Nigerian higher institutions especially in the southwestern region of Nigeria.

## **3.2 CFD model**

The pseudo steady-state incompressible Reynolds-averaged Navier–Stokes (RANS) method is applied due to the computational cost and modelling accuracy. The standard k � ε two-equation turbulence model has been modelled for this study. All room simulation scenarios modelled only considered wind-driven ventilation in isothermal conditions. The model equations are as follows.

#### *3.2.1 Flow and energy equations*

The general classical equations describing the flow in a room are represented as follows.

i. Continuity equation:

$$\frac{\partial P}{\partial t} + \frac{\partial}{\partial \mathbf{x}\_1}(pU\_1) = \mathbf{0} \tag{1}$$

*3.2.2 Turbulence model*

In Vector forms,

Turbulent kinetic energy (TKE, k)

*DOI: http://dx.doi.org/10.5772/intechopen.92725*

Energy dissipation rate (ε)

*3.2.3 Setting up a CFD model*

**Figure 5.** *CFD model chart.*

**85**

*∂εui ∂xi*

¼ *∂ ∂xi*

[33–34] and is also used for the present study.

*∂kui ∂xi*

*Computational Analysis of a Lecture Room Ventilation System*

¼ *∂ ∂xi*

*vt σk ∂k <sup>∂</sup>xi* <sup>þ</sup> *<sup>c</sup>*1*<sup>ε</sup>*

*vt σk ∂k <sup>∂</sup>xi* <sup>þ</sup> *<sup>v</sup>*

> *ε k v ∂ui ∂x <sup>j</sup>* þ *∂u <sup>j</sup> ∂xi ∂u <sup>j</sup>*

The solutions to Eqs. (5) and (6) require that the fluctuating velocity term in Eq. (5) and the fluctuating temperature term in Eq. (6) be represented by "equivalent" time-mean terms. All available turbulence models are semi-empirical and do not produce the same results. The two equation kinetic energy, k, and its dissipation rate, ε model is one of the most popularly used turbulence models applied by most researchers who studied the numerical solution of air flow in rooms and cavities

Computational fluid dynamics can be set up using the chart below in **Figure 5**.

*∂ui ∂x <sup>j</sup>* þ *∂u <sup>j</sup> ∂xi*

(7)

*<sup>k</sup>* (8)

*∂xi* � *c*2*<sup>ε</sup> ε*2

ii. Momentum (Navier-Stokes) equation:

$$\begin{aligned} \frac{\partial}{\partial t} (\rho U\_i) + \frac{\partial}{\partial \mathbf{X}\_i} \left( \rho U\_i U\_j \right) &= -\frac{\partial p}{\partial \mathbf{X}\_i} + \frac{\partial}{\partial \mathbf{X}\_j} \left( -\rho \overline{u\_i u\_j} \right) + \frac{\partial}{\partial \mathbf{X}\_j} \left[ \mu \left( \frac{\partial U\_i}{\partial \mathbf{X}\_j} + \frac{\partial U\_j}{\partial \mathbf{X} i} \right) \right] \\ &+ \mathbf{g}\_i (\rho - \rho\_r) \end{aligned} \tag{2}$$

iii. Thermal energy equation:

$$\frac{\partial}{\partial t}(\rho T) + \frac{\partial}{\partial X\_j} \left(\rho U\_j T\right) = \frac{\partial}{\partial X\_i} \left(-\rho \overline{u\_i T'}\right) \tag{3}$$

It is noted that for the computational model used in this study that Eq. (3) has no effect on the airflow in the room as isothermal conditions were considered. However, Eq. (3) is considered for the solar chimney model. Ui represents the time-mean velocity component in the Xi direction while u is the fluctuating velocity components in the xi direction. For turbulent flows, the viscous stress term on the right hand side of Eq. (2) is neglected as it is usually much smaller than the Reynolds stress term in the equation. For a case of steady incompressible flow and fluctuating velocities described by a suitable turbulence model, the effect of a fluctuating flow is represented by means of time-independent flow equations as shown below

$$\frac{\partial}{\partial X\_j}(\rho U\_i) = \mathbf{0} \tag{4}$$

$$\frac{\partial}{\partial \mathbf{X}\_j} \left( \rho \mathbf{U}\_i \mathbf{U}\_j \right) = -\frac{\partial p}{\partial \mathbf{X}\_i} + \frac{\partial}{\partial \mathbf{X}\_j} \left( \rho \overline{u\_i u\_j} \right) + \mathbf{g}\_i (\rho - \rho\_i) \tag{5}$$

$$\frac{\partial}{\partial \mathbf{X}\_j} \left( \rho \mathbf{U}\_j \mathbf{T} \right) = \frac{\partial}{\partial \mathbf{X}\_i} \left( -\rho \overline{u\_i \mathbf{T}} \right) \tag{6}$$

*Computational Analysis of a Lecture Room Ventilation System DOI: http://dx.doi.org/10.5772/intechopen.92725*

### *3.2.2 Turbulence model*

lecture room where ventilation is normally achieved through opening of doors, windows and Mechanical ventilation system (ceiling fans). This lecture hall is representative of lecture halls in many Nigerian higher institutions especially in the

The pseudo steady-state incompressible Reynolds-averaged Navier–Stokes (RANS) method is applied due to the computational cost and modelling accuracy. The standard k � ε two-equation turbulence model has been modelled for this study. All room simulation scenarios modelled only considered wind-driven venti-

The general classical equations describing the flow in a room are represented as

�*ρuiuj* <sup>þ</sup>

*∂Xi*

*ρuiuj*

ð Þ¼ *pU*<sup>1</sup> 0 (1)

(3)

*∂ ∂Xj μ ∂Ui ∂Xj* þ *∂Uj ∂Xi*

þ *gi ρ* � *ρ<sup>r</sup>* ð Þ (2)

�*ρuiT*<sup>0</sup> 

ð Þ¼ *ρUi* 0 (4)

<sup>þ</sup> *gi <sup>ρ</sup>* � *<sup>ρ</sup><sup>i</sup>* ð Þ (5)

�*ρuiT* (6)

lation in isothermal conditions. The model equations are as follows.

*∂P ∂t* þ *∂ ∂x*<sup>1</sup>

> *∂Xi* þ *∂ ∂Xj*

ii. Momentum (Navier-Stokes) equation:

*ρUiUj* ¼ � *<sup>∂</sup><sup>p</sup>*

> *∂ ∂t*

ð Þþ *<sup>ρ</sup><sup>T</sup> <sup>∂</sup>*

*∂Xj*

*<sup>ρ</sup>UjT* <sup>¼</sup> *<sup>∂</sup>*

It is noted that for the computational model used in this study that Eq. (3) has no effect on the airflow in the room as isothermal conditions were considered. However, Eq. (3) is considered for the solar chimney model. Ui represents the time-mean velocity component in the Xi direction while u is the fluctuating velocity components in the xi direction. For turbulent flows, the viscous stress term on the right hand side of Eq. (2) is neglected as it is usually much smaller than the Reynolds stress term in the equation. For a case of steady incompressible flow and fluctuating velocities described by a suitable turbulence model, the effect of a fluctuating flow is represented by means of time-independent flow equations as shown below *∂ ∂Xj*

southwestern region of Nigeria.

*Zero-Energy Buildings - New Approaches and Technologies*

*3.2.1 Flow and energy equations*

i. Continuity equation:

*∂ ∂Xi*

iii. Thermal energy equation:

*∂ ∂Xj*

**84**

*ρUiUj* ¼ � *<sup>∂</sup><sup>p</sup>*

> *∂ ∂Xj*

*∂Xi* þ *∂ ∂Xj*

*<sup>ρ</sup>UjT* <sup>¼</sup> *<sup>∂</sup>*

*∂Xi*

**3.2 CFD model**

follows.

*∂ ∂t*

ð Þþ *ρUi*

In Vector forms, Turbulent kinetic energy (TKE, k)

$$\frac{\partial k \overline{u\_i}}{\partial \mathbf{x}\_i} = \frac{\partial}{\partial \mathbf{x}\_i} \left( \frac{v\_t}{\sigma\_k} \frac{\partial k}{\partial \mathbf{x}i} \right) + \nu \left( \frac{\partial \overline{u\_i}}{\partial \mathbf{x}\_j} + \frac{\partial \overline{u}\_j}{\partial \mathbf{x}\_i} \right) \tag{7}$$

Energy dissipation rate (ε)

$$\frac{\partial \overline{\boldsymbol{\alpha}} \overline{\boldsymbol{u}}\_{i}}{\partial \mathbf{x}\_{i}} = \frac{\partial}{\partial \mathbf{x}\_{i}} \left( \frac{\boldsymbol{\nu}\_{t}}{\sigma\_{k}} \frac{\partial \boldsymbol{k}}{\partial \boldsymbol{x} i} \right) + c\_{1x} \frac{\varepsilon}{k} \boldsymbol{\nu} \left( \frac{\partial \overline{\boldsymbol{u}}\_{i}}{\partial \mathbf{x}\_{j}} + \frac{\partial \overline{\boldsymbol{u}}\_{j}}{\partial \mathbf{x}\_{i}} \right) \frac{\partial \boldsymbol{u}\_{j}}{\partial \mathbf{x}\_{i}} - c\_{2x} \frac{\varepsilon^{2}}{k} \tag{8}$$

The solutions to Eqs. (5) and (6) require that the fluctuating velocity term in Eq. (5) and the fluctuating temperature term in Eq. (6) be represented by "equivalent" time-mean terms. All available turbulence models are semi-empirical and do not produce the same results. The two equation kinetic energy, k, and its dissipation rate, ε model is one of the most popularly used turbulence models applied by most researchers who studied the numerical solution of air flow in rooms and cavities [33–34] and is also used for the present study.

#### *3.2.3 Setting up a CFD model*

Computational fluid dynamics can be set up using the chart below in **Figure 5**.

**Figure 5.** *CFD model chart.*

**Figure 6.** *Computational domain for analysis.*

## *3.2.4 The physical model*

This is the geometry of the area for the simulation. It constitutes the site plan and the room. The cross-ventilated building model used in this model is showed in **Figure 6**. The computational model was sized 17.4 m 9 m 3 m (length width height). The building height served as the reference length scale H. Two openings with dimension 2.4 m 1.5 m (width height) were installed at the rear end of both the windward walls.

*3.2.7 Initial and boundary conditions*

*Grid (mesh) generation for computational domain.*

*Computational Analysis of a Lecture Room Ventilation System*

*DOI: http://dx.doi.org/10.5772/intechopen.92725*

couple the pressure and velocity equations.

**Wind velocity (m/s) Solar radiation (W/m<sup>2</sup>**

**Figures 8**–**10**.

**Table 4.**

**Figure 8.**

**87**

*Solar radiation input.*

*Boundary conditions.*

**Figure 7.**

*3.2.8 Solution method*

The boundary conditions (**Table 4**) and the initial conditions are then set. The reasonable set up of physical quantities at the boundaries of the flow domain affect the overall accuracy of the CFD model. Initial conditions are essential for all CFD model. **Figure 8** indicates the point where solar radiation effect is introduced into the model, **Figure 9** shows the points initially set as flow outlets into the lecture hall, while **Figure 10** shows the wind inlet into the model. It is noted that an open corridor exists under the hanging roof and aid inflow to the lecture hall as shown in

The solution method used is the SIMPLE Algorithm method. SIMPLE is an acronym for Semi-Implicit Method for Pressure Linked Equations. It is used to

0.05–2.0 200–1000 1 K - ε (Realisable)

**) Pressure outlet (atm) Turbulence model**

The temperature range of the location is between 22 and 35°C, the outdoor relative humidity is between 35 and 90% and the wind speed is between 2.0–6.0 m/s. The lower value of the wind speed was used as the maximum for the computational analysis being the worst case scenario.

#### *3.2.5 Grid generation of physical model (meshing)*

In the CFD set up, the field is subdivided into several grids and the partial differential equations governing a flow field (e.g. velocities, temperature pressure, etc.) are solved at all points of the field [33, 35] as shown in **Table 3**.

In order to analyse fluid flow, flow domains are split into smaller sub domains. The process of obtaining an appropriate mesh is called grid generation (**Figure 7**).

#### *3.2.6 Discretise the governing equations*

After meshing, the governing equations are then discretised and solved in each of these sub domains. ANSYS Fluent uses the finite volume method for equation discretisation, which was used to perform the simulations in this study.


**Table 3.** *Grid analysis.* *Computational Analysis of a Lecture Room Ventilation System DOI: http://dx.doi.org/10.5772/intechopen.92725*

#### **Figure 7.** *Grid (mesh) generation for computational domain.*
