*2.3.2 Model setup and boundary conditions*

The steady-state conditions were used in the CFD analysis of the single-phase airflow inside the room. The full buoyancy model was considered, where the fluid density was a function of temperature or pressure, and was applied. The air was modelled as ideal gas with the reference buoyancy density of 1.185 kg/m3 (an approximate value of the domain air density). The solution scheme is a pressurevelocity coupled with a pressure-based solver. The standard k-ε turbulence model was chosen for good results' accuracy with the robustness of the solution [4]. The wall function considered was scalable wall function. The mesh should be

**Figure 8.** *3D model view and HVAC split unit of the computational modelled room.*

sufficiently fine to accurately model convective heat transfer and fluid flow near the walls; for this reason the parameter y + must have a value of approximately to 11.25. The turbulence parameters were defined by testing three values of turbulence intensity 1% (low), 5% (medium) and 10% (high) as a variable in ANSYS CFX setup. The temperatures of S10, S12, S5 and S2 sensors were monitored until reaching the steady state. The results obtained for the S10 sensor were 6.69°C, 6.70° C and 6.75°C for the low, medium and high intensity, respectively. For the S12 sensor, the results were 18.21°C, 18.18°C and 18.22°C; for the S5 sensor, 19.13°C, 19.12°C and 19.13°C; and for the S2 sensor, 19.22°C, 19.21°C and 19.22°C. Therefore, the maximum deviations are 0.2°C; this value is lower than the error of the Data Logger Testo 174 used (0.5°C).

**Table 2** summarises the energy (surface temperature) and momentum (air velocity) boundary conditions used in the CFD models, each wall and experiment. Experimental measurements show a linear relation between each surface temperature and the width (floor and ceiling) or height (vertical walls). As described before, the surface temperature measurements were carried out using K-type Thermocouple. These readings were done manually at the end of each experiment, when the room reached a steady-state condition. As a matter of example of the surface temperature gradient, **Figure 9** shows the surface temperatures plotted against the sensor location height for Wall 3. The graph shows also a linear regression function linking both variables.

#### *2.3.3 Mesh verification*

An important aspect when developing CFD models is the selection of an appropriate mesh. The number of cells and their shape and size should guarantee a meshindependent solution while achieving a good trade-off between the result accuracy and computational cost. The used mesh type was a nonstructured mesh formed with tetrahedral cells. The tetrahedral cell offered less degrees of freedom per cell and fixed better the desired geometry. The mesh was denser at the proximities of the wall surfaces and at the split unit discharge outlet, being zones where the temperature and velocity gradients are more pronounced. A first approximation of the minimum numbers of cells of the domain was calculated using the formula recommended by the German Guideline [6] shown in Eq. (1).

$$N = 44.4 \cdot 10^3 \cdot V^{0.38} \tag{1}$$

of approximately to 11.25. To obtain a mesh configuration that offers a good tradeoff between accuracy and computing costs, it is necessary to establish a mesh refinement process. The method chosen was the one developed by Celik et al. [15]. This process consists in selecting three different grids with different coarseness definition: a coarse grid, a basic grid and a fine grid. The CFD results of the variables of interests are compared with one another to justify the best compromise between

**Experiment Limits Energy Momentum** Experiment 1 HVAC Tin = 8 [°C] Vin = 2.2 [m/s]

*Calibration Methodology for CFD Models of Rooms and Buildings with Mechanical Ventilation…*

*DOI: http://dx.doi.org/10.5772/intechopen.89848*

Experiment 2 HVAC unit Tin = 8 [°C] Vin = 2.7 [m/s]

Experiment 3 HVAC Tin = 8 [°C] Vin = 2.7 [m/s]

Experiment 4 HVAC Tin = 8 [°C] Vin = 2.2 [m/s]

Wall 1 T1(Y) = 20 [°C] No slip wall Floor T2(X) = 1.315X + 19.97 [°C] No slip wall Wall 3 T3(Y) = 0.9857Y + 23.12 [°C] No slip wall Ceiling T4(X) = 0.9788X + 26.54 [°C] No slip wall Wall 5 T5(Y) = 0.9857Y + 22.52 [°C] No slip wall Wall 6 T6(Y) = 0.9857Y + 22.52 [°C] No slip wall

Wall 1 T1(Y) = 20 [°C] No slip wall Floor T2(X) = 1.315X + 19.97 [°C] No slip wall Wall 3 T3(Y) = 0.9857Y + 23.12 [°C] No slip wall Ceiling T4(X) = 0.9788X + 26.54 [°C] No slip wall Wall 5 T5(Y) = 0.9857Y + 22.52 [°C] No slip wall Wall 6 T6(Y) = 0.9857Y + 22.52 [°C] No slip wall

Wall 1 T1(Y) = 20 [°C] No slip wall Floor T2(X) = 1.315X + 19.97 [°C] No slip wall Wall 3 T3(Y) = 1.467Y + 34.18 [°C] No slip wall Ceiling T4(X) = 0.9788X + 26.54 [°C] No slip wall Wall 5 T5(Y) = 0.9857Y + 22.52 [°C] No slip wall Wall 6 T6(Y) = 0.9857Y + 22.52 [°C] No slip wall

Wall 1 T1(Y) = 20 [°C] No slip wall Floor T2(X) = 1.315X + 19.97 [°C] No slip wall Wall 3 T3(Y) = 1.467Y + 34.18 [°C] No slip wall Ceiling T4(X) = 0.9788X + 26.54 [°C] No slip wall Wall 5 T5(Y) = 0.9857Y + 22.52 [°C] No slip wall Wall 6 T6(Y) = 0.9857Y + 22.52 [°C] No slip wall

The first step is to estimate the coarse grid features. This is calculated according to the before mentioned criteria. The number of cells was 170,924 and the average cell size (h) was of 10 cm. This last parameter can also be estimated using Eq. (2) [15], where *h* is the cell size, ΔV is the volume of each i element, and N is the number of

accuracy and computational cost.

*Boundary conditions for CFD model.*

grid cells:

**15**

**Table 2.**

where:

N = number of finite elements of the volume.

V = volume of the studied space.

In the case of the experiment of this chapter, the volume accounts for 34.47 m3 (12.4 m<sup>2</sup> x 2.8 m), and the number of elements according to the above formula is of 170,924 cells. On the other hand, a common recommendation [6] for CFD cell size when applied to internal environment in buildings is around the 10 cm size for rooms of less than 5 m length. This size should be smaller on zones where significant temperature or velocity gradients were to be expected [14].

In order to capture the temperature and velocity gradients inside of the velocity boundary layer and thermal boundary layer, it is necessary to analyse at least 10 nodes that fall inside these boundary layers. Therefore, this effect can be considered relevant when the sensors are located in a near-wall position or when calculating local convective heat transfer coefficients. To correctly capture gradients inside the boundary layer, the parameter that controls the correct solution of the viscous sublayer is y+. This dimensionless parameter depends on the turbulence model. Thus, for standard k-ε and the scalable wall function, the parameter y + must have a value


*Calibration Methodology for CFD Models of Rooms and Buildings with Mechanical Ventilation… DOI: http://dx.doi.org/10.5772/intechopen.89848*

#### **Table 2.**

sufficiently fine to accurately model convective heat transfer and fluid flow near the walls; for this reason the parameter y + must have a value of approximately to 11.25. The turbulence parameters were defined by testing three values of turbulence intensity 1% (low), 5% (medium) and 10% (high) as a variable in ANSYS CFX setup. The temperatures of S10, S12, S5 and S2 sensors were monitored until reaching the steady state. The results obtained for the S10 sensor were 6.69°C, 6.70° C and 6.75°C for the low, medium and high intensity, respectively. For the S12 sensor, the results were 18.21°C, 18.18°C and 18.22°C; for the S5 sensor, 19.13°C, 19.12°C and 19.13°C; and for the S2 sensor, 19.22°C, 19.21°C and 19.22°C. Therefore, the maximum deviations are 0.2°C; this value is lower than the error of the Data

**Table 2** summarises the energy (surface temperature) and momentum (air velocity) boundary conditions used in the CFD models, each wall and experiment. Experimental measurements show a linear relation between each surface temperature and the width (floor and ceiling) or height (vertical walls). As described before, the surface temperature measurements were carried out using K-type Thermocouple. These readings were done manually at the end of each experiment, when the room reached a steady-state condition. As a matter of example of the surface temperature gradient, **Figure 9** shows the surface temperatures plotted against the sensor location height for Wall 3. The graph shows also a linear regression function linking both variables.

An important aspect when developing CFD models is the selection of an appropriate mesh. The number of cells and their shape and size should guarantee a meshindependent solution while achieving a good trade-off between the result accuracy and computational cost. The used mesh type was a nonstructured mesh formed with tetrahedral cells. The tetrahedral cell offered less degrees of freedom per cell and fixed better the desired geometry. The mesh was denser at the proximities of the wall surfaces and at the split unit discharge outlet, being zones where the temperature and velocity gradients are more pronounced. A first approximation of the minimum numbers of cells of the domain was calculated using the formula

In the case of the experiment of this chapter, the volume accounts for 34.47 m3 (12.4 m<sup>2</sup> x 2.8 m), and the number of elements according to the above formula is of 170,924 cells. On the other hand, a common recommendation [6] for CFD cell size when applied to internal environment in buildings is around the 10 cm size for rooms of less than 5 m length. This size should be smaller on zones where significant

In order to capture the temperature and velocity gradients inside of the velocity boundary layer and thermal boundary layer, it is necessary to analyse at least 10 nodes that fall inside these boundary layers. Therefore, this effect can be considered relevant when the sensors are located in a near-wall position or when calculating local convective heat transfer coefficients. To correctly capture gradients inside the boundary layer, the parameter that controls the correct solution of the viscous sublayer is y+. This dimensionless parameter depends on the turbulence model. Thus, for standard k-ε and the scalable wall function, the parameter y + must have a value

*<sup>N</sup>* <sup>¼</sup> <sup>44</sup>*:*<sup>4</sup> � <sup>10</sup><sup>3</sup> � *<sup>V</sup>*<sup>0</sup>*:*<sup>38</sup> (1)

recommended by the German Guideline [6] shown in Eq. (1).

N = number of finite elements of the volume.

temperature or velocity gradients were to be expected [14].

V = volume of the studied space.

Logger Testo 174 used (0.5°C).

*Computational Fluid Dynamics Simulations*

*2.3.3 Mesh verification*

where:

**14**

*Boundary conditions for CFD model.*

of approximately to 11.25. To obtain a mesh configuration that offers a good tradeoff between accuracy and computing costs, it is necessary to establish a mesh refinement process. The method chosen was the one developed by Celik et al. [15]. This process consists in selecting three different grids with different coarseness definition: a coarse grid, a basic grid and a fine grid. The CFD results of the variables of interests are compared with one another to justify the best compromise between accuracy and computational cost.

The first step is to estimate the coarse grid features. This is calculated according to the before mentioned criteria. The number of cells was 170,924 and the average cell size (h) was of 10 cm. This last parameter can also be estimated using Eq. (2) [15], where *h* is the cell size, ΔV is the volume of each i element, and N is the number of grid cells:

$$h = \left[\frac{1}{N} \sum\_{i=1}^{N} (\Delta V\_i) \right]^{1/3} \tag{2}$$

*<sup>p</sup>* <sup>¼</sup> <sup>1</sup> ln ð Þ *r*<sup>21</sup>

*DOI: http://dx.doi.org/10.5772/intechopen.89848*

**Table 4.**

**Figure 10.**

**17**

*experiment n. 2).*

*q p*ð Þ¼ *ln <sup>r</sup>*

i and j mesh, *eij* is the error between i and j mesh (%), and *p*, *q p*ð Þ and *s* are the

**Sensor ∅<sup>1</sup> (°C) ∅2(°C) ∅3(°C)** *ε***<sup>21</sup> (%)** *ε***<sup>32</sup> (%) GCI12 (%) GCI23 (%) Measurement**

1 18.21 18.19 17.93 0.08% 1.46% 0.01% 0.21% 2.27% 2 17.02 17.03 16.76 0.02% 1.61% 0.00% 0.03% 2.57% 3 16.44 16.47 16.20 0.16% 1.65% 0.02% 0.23% 2.71% 4 18.10 18.11 17.97 0.05% 0.80% 0.01% 0.11% 2.31% 5 17.07 17.07 16.70 0.04% 2.19% 0.01% 0.31% 2.62% 6 16.75 16.77 16.40 0.09% 2.22% 0.01% 0.32% 2.70% 7 17.98 17.92 17.70 0.31% 1.27% 0.04% 0.18% 2.36% 8 17.15 17.12 16.86 0.16% 1.52% 0.02% 0.22% 2.65% 9 16.89 16.87 16.52 0.10% 2.10% 0.01% 0.30% 2.82% 10 11.07 11.15 11.08 0.70% 0.60% 0.08% 0.09% 7.41% 11 17.22 16.94 16.53 1.63% 2.46% 0.19% 0.35% 2.72% 12 16.64 16.45 16.07 1.18% 2.35% 0.14% 0.33% 2.97%

*Necessary parameters used for the calculation of the GCI during the grid refinement process (example for*

*3D cell grid used for medium mesh. Cross-section at the measurement plane.*

*p* <sup>21</sup> � *s r p* <sup>32</sup> � *s*

*Calibration Methodology for CFD Models of Rooms and Buildings with Mechanical Ventilation…*

where ∅*<sup>i</sup>* is the variable of interest (sensor temperature), *εij* is the error between

!

j j *ln* j j *ε*32*=ε*<sup>21</sup> þ *q p*ð Þ (6)

(8)

**bias error (%)**

*ε*<sup>32</sup> ¼ ∅<sup>3</sup> � ∅2; *ε*<sup>21</sup> ¼ ∅<sup>2</sup> � ∅<sup>1</sup> (7)

*s* ¼ *sgn* ð Þ *ε*32*=ε*<sup>21</sup> (9)

The second step entails calculating the refinement degree of the grid "r" using the relationship between the number of the elements of the studied mesh and the number of elements of the refined mesh. According to the cited methodology by Celik [15], the recommended value for this refinement factor needs to be lower than 1.3. With this criteria, the number of elements of the finer and the basic mesh can be calculated having the number of elements of the coarse mesh using Eq. (3) and Eq. (4), where rij is the refinement degree, hi is the cell size, and N is the number of grid cells [16]. Finally, the selected meshes are shown in **Table 3**.

$$r\_{21} = \frac{h\_2}{h\_1} = \left(\frac{N\_1}{N\_2}\right)^{1/3} \tag{3}$$

$$r\_{32} = \frac{h\_3}{h\_2} = \left(\frac{N\_2}{N\_3}\right)^{1/3} \tag{4}$$

The grid quantitative verification was completed using the grid convergence index (GCI) and based on the Richardson extrapolation formula [17]. These methods are helpful to estimate the grid convergence error. The formula is developed as follows:

$$GCI^{21} = \frac{\mathbf{1.25} \cdot e\_{21}}{r\_{21}^p - \mathbf{1}} \tag{5}$$

#### **Figure 9.**

*Trend line of wall surface temperature vs. room height. Wall 3 in Experiment 1 (blue) and 2 (red).*


**Table 3.**

*Selected grids for the grid refinement study.*

*Calibration Methodology for CFD Models of Rooms and Buildings with Mechanical Ventilation… DOI: http://dx.doi.org/10.5772/intechopen.89848*

$$p = \frac{1}{\ln\left(r\_{21}\right)} |\ln\left|e\_{32}/e\_{21}\right| + q(p)|\tag{6}$$

$$
\varepsilon\_{32} = \mathcal{Q}\_3 - \mathcal{Q}\_2; \varepsilon\_{21} = \mathcal{Q}\_2 - \mathcal{Q}\_1 \tag{7}
$$

$$q(p) = \ln\left(\frac{r\_{21}^p - s}{r\_{32}^p - s}\right) \tag{8}$$

$$\mathfrak{s} = \mathfrak{sgn}\left(\mathfrak{e}\_{\mathfrak{Y}2}/\mathfrak{e}\_{\mathfrak{Y}1}\right) \tag{9}$$

where ∅*<sup>i</sup>* is the variable of interest (sensor temperature), *εij* is the error between i and j mesh, *eij* is the error between i and j mesh (%), and *p*, *q p*ð Þ and *s* are the


#### **Table 4.**

*<sup>h</sup>* <sup>¼</sup> <sup>1</sup> *N* X *N*

*Computational Fluid Dynamics Simulations*

grid cells [16]. Finally, the selected meshes are shown in **Table 3**.

developed as follows:

**Figure 9.**

**Table 3.**

**16**

*Selected grids for the grid refinement study.*

*<sup>r</sup>*<sup>21</sup> <sup>¼</sup> *<sup>h</sup>*<sup>2</sup> *h*1

*<sup>r</sup>*<sup>32</sup> <sup>¼</sup> *<sup>h</sup>*<sup>3</sup> *h*2

*i*¼1

The second step entails calculating the refinement degree of the grid "r" using the relationship between the number of the elements of the studied mesh and the number of elements of the refined mesh. According to the cited methodology by Celik [15], the recommended value for this refinement factor needs to be lower than 1.3. With this criteria, the number of elements of the finer and the basic mesh can be calculated having the number of elements of the coarse mesh using Eq. (3) and Eq. (4), where rij is the refinement degree, hi is the cell size, and N is the number of

> <sup>¼</sup> *<sup>N</sup>*<sup>1</sup> *N*<sup>2</sup> � �1*=*<sup>3</sup>

> <sup>¼</sup> *<sup>N</sup>*<sup>2</sup> *N*<sup>3</sup> � �<sup>1</sup>*=*<sup>3</sup>

The grid quantitative verification was completed using the grid convergence index (GCI) and based on the Richardson extrapolation formula [17]. These methods are helpful to estimate the grid convergence error. The formula is

> *GCI*<sup>21</sup> <sup>¼</sup> <sup>1</sup>*:*<sup>25</sup> � *<sup>e</sup>*<sup>21</sup> *r p*

*Trend line of wall surface temperature vs. room height. Wall 3 in Experiment 1 (blue) and 2 (red).*

**Grid Number of elements Refining degree** Grid 1 (fine) 1,151,812 1.37 Grid 2 (medium) 442,939 — Grid 3 (coarse) 181,938 1.34

<sup>21</sup> � <sup>1</sup> (5)

ð Þ *ΔVi* " #1*=*<sup>3</sup>

(2)

(3)

(4)

*Necessary parameters used for the calculation of the GCI during the grid refinement process (example for experiment n. 2).*

**Figure 10.** *3D cell grid used for medium mesh. Cross-section at the measurement plane.*

auxiliary parameters. In **Table 4**, all the necessary variables for the calculation of the GCI for the 12 temperature sensors are shown. The table shows the values of the GCI12, the GCI23 indexes and the temperature sensor measurement bias error (0.5 error sensor, divided by measurement temperature sensor in percent). The small values for GCI confirm that the solution is grid independent. On the other hand, high GCI values confirm a larger relative error close to the sensor error. However, in this case the values of the GCI12 are low, and therefore the relative errors are far away from the values of the sensor error. It was concluded that mesh number 2 is the option that provides an optimum equilibrium between accuracy and computational cost, and therefore it was the author's choice for the CFD model developed. **Figure 10** shows a cross-section at the measurement plane of the 3D grid generated.

and causes the air temperature variation. This behaviour was present in all the tests and was more pronounced during the daytime, where more thermal load is experienced. Due to the short period of this fluctuation, only the mean temperature of the refrigeration cycles was considered. The steady-state conditions were reached at the end of the measurement campaign, where the sensor temperature was stable and

*Calibration Methodology for CFD Models of Rooms and Buildings with Mechanical Ventilation…*

The CFD simulation results are represented in **Figure 4**; this set of 2D graphs show a vertical view of the measurement plane. The variable displayed is the contour air temperature and is plotted according to a colour scale; the different colour areas are delimited by isotherm lines. The red point is the sensor position and

In order to facilitate the comparison between the CFD and the experimental results, **Table 5** shows the value of (1) measured sensor temperature once the steady-state condition is reached including the mentioned and (2) temperature simulated produced by the CFD models of the position. In Experiment 1, **Table 5** has shown a good fit of the CFD results, being the larger differences in sensors S1, S4 and S7, near to the room ceiling, and in sensors S12 and S9, near the floor surface closed to the HVAC equipment. However, in the central space, the results of the CFD match closely the experimental measurements. Experiment 2 differs from Experiment 1 in the fan speed of the HVAC unit. The shortened cooling cycle effect explained previously makes the air to circulate at a higher rate around the room, thus producing a sustained cooling effect. In Experiments 3 and 4, Wall 3 (opposite

the measured values in the experiment. It is worth to notice that, due to the precision error of the temperature sensors, the temperatures measured during the experiments could vary within 0.5°C. In **Figure 4a** and **b**, it can be appreciated that in both experiments, there is a clear temperature stratification. The difference between experiments 1 and 2 relies mainly in the A/C fan speed. The fan speed at the Experiment 1 was set to "low", while the fan was set to "high" speed at Experiment 2. In the latest case, the temperatures reached within the room were lower due to shortened cooling cycles of the A/C unit. On the other hand, the differences between experiments 3 and 4 rely on the surface temperature of Wall 3, opposite to the A/C unit (Wall 1). In these experiments, the adjacent rooms are heated to warm the cited Wall 3 and analyse the effect on the room air temperature of the test room. The isotherm contour plots corresponding to Experiments 3 and 4 are shown in **Figure 4c** and **d**, respectively. In **Figure 4**, a stratification of the room air is also clearly noticeable. Likewise in Experiments 1 and 2 (**Figure 4a** and **b**), the fan speed of the A/C unit is a very important factor in the average temperature of the internal air. In Experiment 3, the fan speed is set to "high" (2.7 m/s), and the average air temperature reached is 19.8°C, while in Experiment 4 (**Figure 4d**) the fan speed was set to "low" (2.2 m/s), and the average room air temperature was 22.8°C. It can be concluded that the differences in fan speed and consequently the changes in cooling cycles of the A/C unit can result on average thermal differences of 3°C. Summarising, there is a general good agreement between the experimental results and the CFD models. The stratification phenomenon caused by the fluid natural buoyancy is also clearly reflected in the results, with cool air near to the room floor surface and the hot air at the room upper zones. In the model analysed, the natural convection is also enhanced by the position of the HVAC unit. This device takes the room air through its inlet located in the top part, cools it passing it through the coil and discharges it through the outlet pointing downwards direction, hence working in favour of the natural buoyancy flow and causing and increased temperature gradient. It can be concluded that the complexity of modelling the HVAC unit plus the uncertainty of the surface temperature measurements can be considered the two main causes of discrepancy between CFD model results and

maintained during a certain period of time.

*DOI: http://dx.doi.org/10.5772/intechopen.89848*

experimental results.

**19**

### **3. Results and discussion**

The experiment performed is aimed at measuring the temperature distribution of the air in the internal environment of a 3D test room equipped with an air conditioning device. The measurements were taken with 12 temperature sensors, 1 thermocouple sensor and 1 anemometer. The test room was emptied for the experiment, so no people or furniture was considered in order to simplify the airflow trajectory and to ease the CFD modelling efforts. Regarding the boundary conditions, the intention of the authors was to create big temperature gradients that minimise relative errors. The available sensors were installed in a two-dimensional grid contained in an orthogonal plane positioned perpendicularly to the A/C equipment outlet direction; this arrangement was chosen to better capture the fluid stratification. **Figure 6** shows the location of the surface temperature measurement points. The temperature sensors readings were gathered for 24-hour periods for each test. An example of the sensor measurements gathered in test n. 2 is shown in the time series of **Figure 11**. It can be noticed that sensor n.10 register periodical fluctuations. This sensor is located at the A/C outlet, being approximately sinusoidal fluctuations of 4-minute period. This phenomenon was found to be caused by the specific behaviour of the VRV inverter A/C unit which varies the refrigerant flow

**Figure 11.** *Air temperature measurements of Experiment 2 during 24 h.*

#### *Calibration Methodology for CFD Models of Rooms and Buildings with Mechanical Ventilation… DOI: http://dx.doi.org/10.5772/intechopen.89848*

and causes the air temperature variation. This behaviour was present in all the tests and was more pronounced during the daytime, where more thermal load is experienced. Due to the short period of this fluctuation, only the mean temperature of the refrigeration cycles was considered. The steady-state conditions were reached at the end of the measurement campaign, where the sensor temperature was stable and maintained during a certain period of time.

The CFD simulation results are represented in **Figure 4**; this set of 2D graphs show a vertical view of the measurement plane. The variable displayed is the contour air temperature and is plotted according to a colour scale; the different colour areas are delimited by isotherm lines. The red point is the sensor position and the measured values in the experiment. It is worth to notice that, due to the precision error of the temperature sensors, the temperatures measured during the experiments could vary within 0.5°C. In **Figure 4a** and **b**, it can be appreciated that in both experiments, there is a clear temperature stratification. The difference between experiments 1 and 2 relies mainly in the A/C fan speed. The fan speed at the Experiment 1 was set to "low", while the fan was set to "high" speed at Experiment 2. In the latest case, the temperatures reached within the room were lower due to shortened cooling cycles of the A/C unit. On the other hand, the differences between experiments 3 and 4 rely on the surface temperature of Wall 3, opposite to the A/C unit (Wall 1). In these experiments, the adjacent rooms are heated to warm the cited Wall 3 and analyse the effect on the room air temperature of the test room. The isotherm contour plots corresponding to Experiments 3 and 4 are shown in **Figure 4c** and **d**, respectively. In **Figure 4**, a stratification of the room air is also clearly noticeable. Likewise in Experiments 1 and 2 (**Figure 4a** and **b**), the fan speed of the A/C unit is a very important factor in the average temperature of the internal air. In Experiment 3, the fan speed is set to "high" (2.7 m/s), and the average air temperature reached is 19.8°C, while in Experiment 4 (**Figure 4d**) the fan speed was set to "low" (2.2 m/s), and the average room air temperature was 22.8°C. It can be concluded that the differences in fan speed and consequently the changes in cooling cycles of the A/C unit can result on average thermal differences of 3°C.

Summarising, there is a general good agreement between the experimental results and the CFD models. The stratification phenomenon caused by the fluid natural buoyancy is also clearly reflected in the results, with cool air near to the room floor surface and the hot air at the room upper zones. In the model analysed, the natural convection is also enhanced by the position of the HVAC unit. This device takes the room air through its inlet located in the top part, cools it passing it through the coil and discharges it through the outlet pointing downwards direction, hence working in favour of the natural buoyancy flow and causing and increased temperature gradient. It can be concluded that the complexity of modelling the HVAC unit plus the uncertainty of the surface temperature measurements can be considered the two main causes of discrepancy between CFD model results and experimental results.

In order to facilitate the comparison between the CFD and the experimental results, **Table 5** shows the value of (1) measured sensor temperature once the steady-state condition is reached including the mentioned and (2) temperature simulated produced by the CFD models of the position. In Experiment 1, **Table 5** has shown a good fit of the CFD results, being the larger differences in sensors S1, S4 and S7, near to the room ceiling, and in sensors S12 and S9, near the floor surface closed to the HVAC equipment. However, in the central space, the results of the CFD match closely the experimental measurements. Experiment 2 differs from Experiment 1 in the fan speed of the HVAC unit. The shortened cooling cycle effect explained previously makes the air to circulate at a higher rate around the room, thus producing a sustained cooling effect. In Experiments 3 and 4, Wall 3 (opposite

auxiliary parameters. In **Table 4**, all the necessary variables for the calculation of the GCI for the 12 temperature sensors are shown. The table shows the values of the GCI12, the GCI23 indexes and the temperature sensor measurement bias error (0.5 error sensor, divided by measurement temperature sensor in percent). The small values for GCI confirm that the solution is grid independent. On the other hand, high GCI values confirm a larger relative error close to the sensor error. However, in this case the values of the GCI12 are low, and therefore the relative errors are far away from the values of the sensor error. It was concluded that mesh number 2 is the option that provides an optimum equilibrium between accuracy and computational cost, and therefore it was the author's choice for the CFD model developed. **Figure 10** shows a cross-section at the measurement plane of the 3D grid generated.

The experiment performed is aimed at measuring the temperature distribution

of the air in the internal environment of a 3D test room equipped with an air conditioning device. The measurements were taken with 12 temperature sensors, 1 thermocouple sensor and 1 anemometer. The test room was emptied for the experiment, so no people or furniture was considered in order to simplify the airflow trajectory and to ease the CFD modelling efforts. Regarding the boundary conditions, the intention of the authors was to create big temperature gradients that minimise relative errors. The available sensors were installed in a two-dimensional grid contained in an orthogonal plane positioned perpendicularly to the A/C equipment outlet direction; this arrangement was chosen to better capture the fluid stratification. **Figure 6** shows the location of the surface temperature measurement points. The temperature sensors readings were gathered for 24-hour periods for each test. An example of the sensor measurements gathered in test n. 2 is shown in the time series of **Figure 11**. It can be noticed that sensor n.10 register periodical fluctuations. This sensor is located at the A/C outlet, being approximately sinusoidal fluctuations of 4-minute period. This phenomenon was found to be caused by the specific behaviour of the VRV inverter A/C unit which varies the refrigerant flow

**3. Results and discussion**

*Computational Fluid Dynamics Simulations*

**Figure 11.**

**18**

*Air temperature measurements of Experiment 2 during 24 h.*


shown satisfactory results, finding a maximum error of 9% between the CFD model and the experimental model. In this work it has been shown that the CFD model calibrated can be used to predict the air temperature distribution at any point of the room. Validated 3D models can be a useful tool to assess multiple changes in boundary conditions that would be otherwise very difficult to reproduce in experimental test due to limitations in the number of sensor available and uncertainty and the complexity of changing boundary conditions in a real physical facility. The biggest difficulty encountered in the CFD model is the modelling of the HVAC split unit, where the inner conduit shape showed satisfactory results with respect to the experimental results. It is worth to highlight the difficulties experienced at collecting reliable surface temperature measurements in the experimental tests. The surface temperatures collected were taken when the steady state was reached at the end of the experiments. As previous authors have [4], inaccurate results at some specific points of the model were to be expected. In the experiments performed, these differences were more remarkable in zones where the temperature gradient was higher, like in the areas closer to the walls, floor and ceiling

*Calibration Methodology for CFD Models of Rooms and Buildings with Mechanical Ventilation…*

Summarising the methodology it is necessary to first consider the geometry of the computational domain, where it is advisable to eliminate obstacles and elements to simplify the calibration of the CFD model. Subsequently the meshing, which must be optimised by the GCI method, and find the mesh with a balance between precision and computational cost. Another important aspect is the turbulence model and the wall function chosen, presenting the k-ɛ model with scalable wall function and y + 11.25 satisfactory results. Regarding the solver of ANSYS CFX, in the method based on pressure and using air as the ideal gas, good results are obtained. Another important aspect is to monitor the variables of interest to be studied, such as the temperature of certain points within a 2D plane. The boundary conditions must be measured when the experimental test reaches the steady state, and in case of stratification, the variable temperature conditions with the height present better results. Finally, in the case of bad convergence, the transient model can be used

The highlight of this work is the methodology carried out to calibrate the CFD model with experimental results. The methodology is useful for other researchers to calibrate the CFD model of building rooms. In addition, the calibrated CFD model can be used to study the effect of different boundary conditions on comfort or energy demand. CFD analysis reveals as a powerful technique to overcome the limitations of physical experiments where only few sensors can be installed and the

As future direction of this work is to reduce the computational cost and simulation time. The calculation of the complete building or the annual simulation for the evaluation of demand or comfort is a procedure that is very computationally expensive. For this, it is necessary to use reduced and simplified CFD solver, oriented specifically to buildings. This simplified programme can be implemented in thermal building simulation programmes and can be very useful for design

surfaces and also in the zones near the HVAC equipment.

*DOI: http://dx.doi.org/10.5772/intechopen.89848*

with a small time step until reaching the steady state.

boundary conditions cannot be changed easily.

engineers.

**21**

#### **Table 5.**

*Air temperature comparison of CFD results and experimental measurements.*

to the HVAC unit) was maintained at a warmer temperature by heating the adjacent room using heaters. The warm surface temperature of this wall directly influences the average temperature of the internal environment of the test room. Again, the maximum divergences are in the near-ceiling and near-floor locations and closed to the HVAC unit. In this experiment, sensor S2 indicates a larger deviation than in previous experiments due fundamentally to the warm surface effect that produced a larger temperature gradient between the wall and the room air. The difference between Experiments 3 and 4 is the higher fan speed of Experiment 3 versus the one of Experiment 4. This variation makes the cooling cycles of the HVAC units in Experiment 4 fewer than in Experiment 3. Therefore, the average room temperature reached in this example is higher than in the previous experiment. The stratification phenomenon is similar as in Experiment 3, although the temperatures registered are higher due to the lower HVAC fan speed. The error in the temperature prediction of line 4 (Sensors S1, S2 and S3) is quite higher than in Experiment 3.

In general terms, the results show that the CFD model and the test results agree at predicting the stratification effect and the temperature trend distribution inside the room air. In the central space of the room, the temperature is similar across the room air. Temperature increases steadily when approaching the ceiling and diminishes when moving towards the floor surface. For most of the measurement points, the CFD results fell inside the error threshold of the sensor measurements, except for some of the sensors located near the ceiling, floor and Wall 3 surfaces, which registered larger differences. Therefore, it can be stated that the CFD is less accurate at predicting air temperatures in the zones with larger temperature gradients, in contrast with the central spaces, where temperature gradients are of smaller extent and the CFD predictions were more accurate.

### **4. Conclusions**

A methodology has been developed for the calibration of CFD models of rooms and buildings from experimental results. The application of the methodology has

#### *Calibration Methodology for CFD Models of Rooms and Buildings with Mechanical Ventilation… DOI: http://dx.doi.org/10.5772/intechopen.89848*

shown satisfactory results, finding a maximum error of 9% between the CFD model and the experimental model. In this work it has been shown that the CFD model calibrated can be used to predict the air temperature distribution at any point of the room. Validated 3D models can be a useful tool to assess multiple changes in boundary conditions that would be otherwise very difficult to reproduce in experimental test due to limitations in the number of sensor available and uncertainty and the complexity of changing boundary conditions in a real physical facility.

The biggest difficulty encountered in the CFD model is the modelling of the HVAC split unit, where the inner conduit shape showed satisfactory results with respect to the experimental results. It is worth to highlight the difficulties experienced at collecting reliable surface temperature measurements in the experimental tests. The surface temperatures collected were taken when the steady state was reached at the end of the experiments. As previous authors have [4], inaccurate results at some specific points of the model were to be expected. In the experiments performed, these differences were more remarkable in zones where the temperature gradient was higher, like in the areas closer to the walls, floor and ceiling surfaces and also in the zones near the HVAC equipment.

Summarising the methodology it is necessary to first consider the geometry of the computational domain, where it is advisable to eliminate obstacles and elements to simplify the calibration of the CFD model. Subsequently the meshing, which must be optimised by the GCI method, and find the mesh with a balance between precision and computational cost. Another important aspect is the turbulence model and the wall function chosen, presenting the k-ɛ model with scalable wall function and y + 11.25 satisfactory results. Regarding the solver of ANSYS CFX, in the method based on pressure and using air as the ideal gas, good results are obtained. Another important aspect is to monitor the variables of interest to be studied, such as the temperature of certain points within a 2D plane. The boundary conditions must be measured when the experimental test reaches the steady state, and in case of stratification, the variable temperature conditions with the height present better results. Finally, in the case of bad convergence, the transient model can be used with a small time step until reaching the steady state.

The highlight of this work is the methodology carried out to calibrate the CFD model with experimental results. The methodology is useful for other researchers to calibrate the CFD model of building rooms. In addition, the calibrated CFD model can be used to study the effect of different boundary conditions on comfort or energy demand. CFD analysis reveals as a powerful technique to overcome the limitations of physical experiments where only few sensors can be installed and the boundary conditions cannot be changed easily.

As future direction of this work is to reduce the computational cost and simulation time. The calculation of the complete building or the annual simulation for the evaluation of demand or comfort is a procedure that is very computationally expensive. For this, it is necessary to use reduced and simplified CFD solver, oriented specifically to buildings. This simplified programme can be implemented in thermal building simulation programmes and can be very useful for design engineers.

to the HVAC unit) was maintained at a warmer temperature by heating the adjacent room using heaters. The warm surface temperature of this wall directly influences the average temperature of the internal environment of the test room. Again, the maximum divergences are in the near-ceiling and near-floor locations and closed to the HVAC unit. In this experiment, sensor S2 indicates a larger deviation than in previous experiments due fundamentally to the warm surface effect that produced a larger temperature gradient between the wall and the room air. The difference between Experiments 3 and 4 is the higher fan speed of Experiment 3 versus the one of Experiment 4. This variation makes the cooling cycles of the HVAC units in Experiment 4 fewer than in Experiment 3. Therefore, the average room temperature reached in this example is higher than in the previous experiment. The stratification phenomenon is similar as in Experiment 3, although the temperatures registered are higher due to the lower HVAC fan speed. The error in the temperature prediction of

**Experiment 1 Experiment 2 Experiment 3 Experiment 4**

**Texp (°C)**

**Tsim (°C)**

**ΔT (°C)** **Texp (°C)**

**Tsim (°C)**

**ΔT (°C)**

**ΔT (°C)**

S1 22.3 21.0 1.3 22.0 20.7 1.3 24.0 22.5 1.6 27.1 25.3 1.9 S2 19.9 19.6 0.3 19.5 19.3 0.2 21.2 20.3 0.9 24.3 23.2 1.0 S3 19.0 18.8 0.2 18.4 18.4 0.0 19.6 19.2 0.4 23.1 22.2 0.8 S4 21.9 21.1 0.8 21.7 20.9 0.7 23.3 22.8 0.5 26.4 25.4 1.0 S5 19.5 19.6 0.1 19.1 19.1 0.1 20.5 20.2 0.3 23.7 23.2 0.5 S6 19.1 19.0 0.1 18.5 18.5 0.0 19.6 19.3 0.3 22.9 22.4 0.5 S7 21.2 20.7 0.5 21.2 20.5 0.7 22.7 22.4 0.3 25.9 25.3 0.6 S8 19.4 19.6 0.2 18.9 19.2 0.3 20.1 20.1 0.0 23.4 23.2 0.2 S9 18.3 19.2 0.9 17.7 18.8 1.1 18.8 19.6 0.8 22.0 22.6 0.5 S10 7.3 7.9 0.6 6.7 7.5 0.8 6.9 7.0 0.1 11.2 10.9 0.3 S11 18.9 19.7 0.7 18.4 18.7 0.3 19.3 19.8 0.5 22.7 22.8 0.1 S12 17.4 18.7 1.3 16.8 18.2 1.4 17.7 19.2 1.5 21.5 22.3 0.8

In general terms, the results show that the CFD model and the test results agree at predicting the stratification effect and the temperature trend distribution inside the room air. In the central space of the room, the temperature is similar across the room air. Temperature increases steadily when approaching the ceiling and diminishes when moving towards the floor surface. For most of the measurement points, the CFD results fell inside the error threshold of the sensor measurements, except for some of the sensors located near the ceiling, floor and Wall 3 surfaces, which registered larger differences. Therefore, it can be stated that the CFD is less accurate at predicting air temperatures in the zones with larger temperature gradients, in contrast with the central spaces, where temperature gradients are of smaller extent

A methodology has been developed for the calibration of CFD models of rooms and buildings from experimental results. The application of the methodology has

line 4 (Sensors S1, S2 and S3) is quite higher than in Experiment 3.

and the CFD predictions were more accurate.

**4. Conclusions**

**20**

**Sensor Texp (°C)**

**Table 5.**

**Tsim (°C)**

*Computational Fluid Dynamics Simulations*

**ΔT (°C)** **Texp (°C)**

*Air temperature comparison of CFD results and experimental measurements.*

**Tsim (°C)**

*Computational Fluid Dynamics Simulations*
