## 5 Results and Discussions  
* Thermal Performance of VSW with airflow rate  
The outlet air temperature values from the CFD model and the two simplified models are provided by Figure 14. They correspond to the values calculated at the exit of the VSW. The figure also represents the heat gain obtained with the VSW for the three cases. The outlet air temperature appears to evolve according to a decreasing exponential.  
Figure 13: Modelica model for the VSW.  
To evaluate the results, the relative error was used as an indicator. The RE between CFD and the analytical results was calculated by:  
\[RE=\left|\frac{X_{CFD}-X_{SM}}{X_{CFD}}\right|\]  
The outlet air temperature values predicted by the first simplified model were extremely close to those obtained by the CFD study (\(\Delta T\) < 0.4 \({}^{\circ}\)C). The difference in heat gain values between the two models was less than 1%.  
The results from the CFD model are in good agreement with those from the simplified models. Moreover, SM1 is more accurate than SM2. However, a single CFD simulation can provide only one result under a given condition. It would thus be necessary to perform a CFD simulation each time a wall parameter is modified and recalculate the corresponding convective heat transfer coefficients. Therefore, it is more convenient to work with SM2. In the next sections, the SM2 is tested under different solar radiation conditions.  
* Thermal Performance of VSW with Solar Irradiation  
Figure 15 presents the simulation results for the heat balance as a function of incident solar radiation for both systems. Good agreement was found between the CFD model and SM2. The relative error for heat gain between the two models was less than 10%.  
Figure 14: Variation in the temperature and heat gain of the air at the outlet with mass flow rate.  
Figure 15: Variation in the temperature and heat gain of the air at the outlet with incident solar radiation.  
* No solar radiation The comparison indicates that the simulated results agree well with the CFD results, and their variation tendencies are consistent, which means that the simulation model has acceptable and reasonable accuracy for evaluating the thermal performance and calculating the annual energy consumption of the VSW. The model is a little less accurate when there is no solar radiation (see Figure 16): the relative error increased from 15% to 25% as the air mass flow rate increased from 0.01 kg/s to 0.018 kg/s, but this remains acceptable.  
* Contribution of each air gap to the heat gain The contribution of each of the two air gaps to the preheating of the fresh ventilation air is given in Figure 17. The results indicate that the heat flux gained by the air occurred mainly in the second air gap, and as the airflow rate increased, this effect became more apparent. Approximately, the first air gap accounted for only one-third of the recovered heat flow.  
* Performance of the VSW The thermal efficiency of the VSW is calculated as the ratio of the useful heat gain to the global solar power received by the solar facade (see Equation (2)). This is valid because it is considered that the wall is insulated and therefore that the flow recovered through the insulation is almost zero.  
Figure 16: Variation in the temperature and heat gain of the air at the outlet with mass flow rate (no solar radiation).  
Figure 17: Contribution of air gaps in air preheating.  
As mentioned before, the simulations were carried out under steady-state conditions.  
At this stage of the investigation, numerical modeling showed a promising potential for the ventilated solar wall studied. The thermal efficiency of the wall increased with a mass flow rate between 55% and 70% (Figure 18). It was very effective compared to other kinds of solar walls (see Table 1).  
At this level, this modeling demonstrated that VSW can provide much energy to a building. System performance may be accurately assessed by evaluating its thermal efficiency throughout the heating season when the model is integrated into a building energy simulation.