Natural Ventilation Strategy in a Social Housing with Sub-humid Warm Climate Based on Thermal Comfort


 Natural ventilation was analysed in a low-income dwelling to control open or closed windows according to a dynamic simulation process in sub-humid warm climate. A selective algorithm to control natural ventilation was determined in an annual period per hour with the following findings: a) an algorithm to select open or closed windows was determined, b) comfort hours per year were evidenced with open, closed windows and selective algorithm to operate natural ventilation, and c) the schedule and periods of ventilation control were presented. Meteonorm® data were used on an hourly basis in Design Builder® simulations and the Meteorological System data based on 30 years of measurements were used to determine the comfort range. Conclusions: the potential benefits to be obtained by applying this ventilation strategy with a selective algorithm are observed in sub-humid warm climate.


INTRODUCTION
Generally, social housing has the minimum dimensions established by local and federal regulations [1], these characteristics limit ventilation in spaces with reduced volumes. Selecting when open or closed the windows on an hourly basis in one year represents a natural

METHODS
To achieve the primary objective of this study, a quantitative study was conducted [13]. The process of obtaining the results followed the correlational method steps [14] between the operative temperature and the time-dependent adaptive comfort range from the ASHRAE Standard 55 thermal comfort model [15] for natural ventilation. The data analysis used the Auliciem's equation [16] and the amplitude comfort range was determined by Szokolay's equation [17] considering the adaptation of users to low occupancy housing.

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510 As the first step, the average air temperature of the Climatological Normals from 1981 to 2010 of the National Meteorological System (SMN by its Spanish acronym) was compared [18] to the interpolated data from Meteonorm version 7.3 in sub-humid warm climate (Fig. 1). As a result, there was a difference between 1 °C and 2 °C. To evaluate the correlation between Meteonorm v7.3 data and the observed dry-bulb temperature taken from the SMN data, the statistical method of the Percent Mean Absolute Relative Error (PMARE) was used, which is represented in Eq. (1) [19]. The PMARE validation results were acceptable, indicating a good performance rating for the model.
Once the similarities between the different climate file providers were established, the following steps were carried out: 1. Case study and boundary conditions. 2. Adaptive comfort range. 3. Dynamic Thermal Simulation: open windows (ow) and closed windows (cw). 4. Selective Algorithm (sa), to control natural ventilation. 5. Results and discussion. 6. Conclusions.

Benchmark Case and boundary conditions
The benchmark case was a social housing in the central region of Mexico with sub-humid warm climate; based on climatic characterization by the National Meteorological System and the Köppen-Geiger classification modified by García to adapt them to the climatic conditions of Mexico [19], [20].
In the benchmark case, the main façade faces north. For the simulation process, two virtual scenarios were used: open windows (ow) and closed windows (cw) with cross ventilation as shown in Fig. 2. The simulation process was carried out in Design Builder® software version 4.7. The influence area or selected space to perform the simulation analysis was Bedroom 1 (B1) with measurements of 2.81 m × 2.83 m to axes, indicated with a dotted line in Fig. 2.
Bedroom 1 was selected as a representative space because the low-income housing belongs to the working class with regular 8-hour workdays; therefore, the place where users spend the longest amount of time in their own house corresponds to the bedrooms, while they are sleeping.  512 Calculated natural ventilation was selected to allow the windows to be open and closed in the one-year simulation process and an excellent infiltration model was used, according to the recommendations of the applicable regulations [15], [16]. A 50 % opening was considered concerning the windows' dimensions and the temperature control was done with air temperature. The 50 % selection aperture with respect to the whole window area complies with ANSI / ASHRAE Standard 62.2-2019 recommendations [2].
The heat gains in the simulation process were calculated as follows: ̶ A dynamic calculation was selected where the occupancy was based on internal temperatures and metabolic rate (value 1 in Design Builder v4.7). ̶ Computer: it was selected a value of 0.1, which means that the heat is transferred to the air node in the simulation (convective and radiative).

Adaptive comfort model
To obtain the adaptive comfort model, the average air temperature from the Climatological Normals per month (1981-2010) was taken as a basis [18], the Auliciems's equation was used together with the Szokolay's amplitude range for the adaptation of users to social housing [16], [17]. Table 2 shows the amplitude range results per month.

Selective Algorithm
The 'selective algorithm (sa)' consisted of determining, between ow and cw simulations at hourly intervals, which scenario remained or was closer to the established adaptive comfort model, according to the selective algorithm in Table 3.
The selection criterion corresponds to the control that the users have over opening or closing their windows manually and without the use of active controls, which are hardly ever bought by users of social dwellings.
The comfort range from month 11 in Table 2 was used as an example in Table 3 and seven possible cases were established. The results obtained were integrated into a matrix to quantify

Representative Day
To determine the representative day, the dry-bulb temperature data from the Meteorological System and the climatic characterization by Gómez-Azpeitia were used [17], [20]. The representative day was firstly estimated from the analysis of the 12 months of the year divided by two seasons, which resulted in one representative month per season; then, using the representative month of each season, the representative day was obtained.
The climatic characterization developed by Gómez-Azpeitia presented an evaluation of the drybulb temperature and relative humidity according to Köppen climate classification for Mexican localities. As a result, this locality had characteristics of a sub-humid warm climate throughout the year, with the two and representative seasons shown in Table 4. A representative month (or day) is that in which the temperature behaviour is the closest to the behaviour of a given season, and the difference in its thermal oscillation is the closest to ____________________________________________________________________________ 2021 / 25 514 zero. The representative month was estimated using Eq. (2) in both established seasons [24]. In other words, the representative month does not necessarily correspond to the hottest month in Season A (March to September) or the coldest month in Season B (January, February, October, November and December); but to the month that in each season reflected the behaviour of the whole season.
where: RD = Representative Day; Adt = Average daily dry -bulb temperature; Ads = Average season dry -bulb temperature; OSCTdt = Average Oscillation daily dry -bulb temperature; OSCTds = Average Oscillation season dry -bulb temperature. As a result, Table 5 shows for Season A the month of March as the representative month, and for Season B, the month of October.  Figure 3 shows the comfort hours in one year according to the simulation with ow, cw and sa. The results tended to keep open windows during the warm season from June to October. April and May presented similar comfort hours quantification between cw and ow. November presented greater comfort hours and the biggest difference between keeping ow and cw occurred in October.

Windows opening schedule
According to the representative month results, the operative temperature behaviour (resulting from sa) for sub-humid warm climate varies not only throughout the same day, but also throughout the whole month. Due to the thermal characteristics, the analysis of schedules to keep ow or cw for the representative day was proposed, as well as for two additional days that represented the thermal needs of the entire season.  Fig. 5, the operative temperature behaviour for ow, cw and sa is indicated. According to the results, heating needs are observed from 3 h to 11 h, while the cooling needs appear between 17 h and 18 h. In order to stay more time in the comfort zone, the selective algorithm indicated a tendency to keep ow from 18 h to 3 h, while this trend is reversed to keep cw from 4 h to 11 h.   4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 (Fig. 6).

March 31.
It is not recommended to keep cw throughout the day and night at the end of Season A, as indicated in Fig. 7. During this representative day, a clear tendency to cool the indoor air volume was observed. Finally, when analysing the three representative days for Season A, a tendency to keep ow on day 16 and 31 was observed. However, a heating task (cw) was performed at the beginning 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 11 h, as the season progresses, it is recommended to close the windows only from 5 h to 9 h and, finally to keep ow throughout the day and night at the end of the Season A. During cw, it is recommended to ow for at least 5 min every 2 hours to ensure air exchange and the minimum recommended ventilation rate [2]. Season B. In Fig. 8, the operative temperature behaviour in °C according to the representative day on October 23 corresponding to the coldest period (Season B) for a sub-humid warm climate is presented. To analyse this season, two more days were chosen: October 7 and 29 because this Season presented variations throughout the period.  October 7. At the beginning of Season B, a clear trend toward cooling is observed, so it is recommended to keep ow day and night (Fig. 9). October 23. In this case, the cooling trend remained in a lower proportion than the observed in Fig. 9, and a tendency to increase the temperature was observed with cw ( Fig. 10).  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 (Fig. 11).

DISCUSSION
In the following discussion, perspectives of previous studies were interpreted according to the object of this study: natural ventilation and thermal comfort. Furthermore, directions for future investigations are recommended.

Natural ventilation
The current study analysed a low-income dwelling in the central region of Mexico with sub-humid warm climate to establish an algorithm with the main aim to control windows (open or closed) at hourly intervals and generate a strategy according to an adaptive comfort model. The adaptive comfort model correctly operates in dwellings with natural ventilation [21]- [24].
The main condition for using natural ventilation was the low occupancy in social housing due to the fact that users belong to the working class with 8-hour or more workdays. Carlton et al. found that in low-income urban houses, high ventilation rates are associated with increases in chronic cough, asthma and asthma-like symptoms [28]. It is recommended that one air change per Hour (ACH) during the occupancy time. ANSI/ASHRAE recommended 14 L/s using the Eq. (3).
where Qtot = total required ventilation rate, L/s; Afloor = dwelling -unit floor area, m 2 ; Nbr = number of bedrooms. This study showed limitations in the use of closed windows since there was a risk of noncompliance with the minimum ventilation rate of air change per Hour during the occupancy time. It is recommended to open windows periodically during the cw strategy if it indicates more than 2 h consecutively. However, it is recommended to expand the area of knowledge of the air change rates in sub-humid warm climate, as well as the variation of indoor air temperature when opening the windows to renew the air during the closed windows strategy.

Thermal comfort
Deng Xiang et al. [26] used the adaptive comfort model ASHRAE 55 [29] to analyse an advanced natural ventilation supplemented by a survey on the thermal sensation of the occupants carried out for the summer period, during the season with the greatest need for cooling. Knowledge on thermal comfort does not necessarily imply the implementation of mechanical controls, but rather having tools that allow the dwellers to expand the permanence of the comfort range and reduce the electrical consumption of active systems. It shows, in natural ventilation strategy, a possibility to save energy and increase the comfort hours.
The adaptive comfort model used by Bienvenido-Huertas et al. [25] was established in three ranges according to the metabolic rates of the occupants. The study used a comfort temperature with an amplitude range due to the user's adaptability in the selected location. Sung-Kyung Kim et al. found that temperature and humidity controlled by HVAC system usage may be reduced due to human ability to thermally adapt after reaching the thermal comfort range [30].
Utkucu et al. [31] analysed the window openings in two levels dwelling under four scenarios, and they found that the open windows scenario in both levels favoured the thermal comfort conditions, but the scenario with closed windows in the second level and open windows in the first level favoured energy consumption. Control of natural ventilation was dominant to maintain thermal comfort with an adaptive model, using residual active systems in summer [27]. Figure 12 shows the selective algorithm results for the month with the highest cooling requirement (May) and the month with the highest heating requirement (March) for Season A. The comfort range determined for each month is included. The cooling needs reach 4 °C during the month of May while in the month of March these needs are halved. The heating needs for the month of March were during the first days, while for the month of May they are practically null. There was a greater oscillation in the cooling needs during the month of May. Due to the temperature variation from March to May, and the variation of the oscillation, it is recommended to use night ventilation during the months of April, May and June and to decrease the opening of windows during the following months. Figure 13 presents selective algorithm results for the month with the highest heating (January) and cooling (October) requirements for Season B. In contrast to Season A, and due to the temperature variation observed in Figs. 8-11, in Season B the cooling requirements decrease significantly from October to January. In mid-January, heating requirements of less than 2 °C were observed. It is recommended to reduce night ventilation, and to keep windows closed during November, December and January.
The selective algorithm is a tool for manual control of a natural ventilation system, aimed at users with social housing who cannot invest in their own thermal comfort.

CONCLUSIONS
This study adheres to the effort of different authors to find natural ventilation control strategies that increase the permanence of the thermal comfort with the potential to reduce electricity consumption in houses.
Due to the characteristics of this study, it covers two types of contribution: 1) An adequate method was presented to users of low-income housing in the central region of Mexico with a subhumid warm climate and 2) an adaptive comfort model was used due to the low occupancy of users of this type of housing.
However, the analysis was performed on an hourly basis because the possibility of using natural ventilation throughout the day was presented, and an algorithm that allowed manual selection between open or closed windows in sub-humid warm climate with possibilities to understand the indoor environmental performance of a social housing was also found.
The analysis of adaptive thermal comfort ranges for social housing occupants allows for insights the natural ventilation strategies with greater precision and their effect on the thermal environment.
In order to reach or stay longer in the comfort range, the selection algorithm between open or closed windows in sub-humid warm climate showed the following results: it is recommended during the months of February, March and April to close windows from 4 h to 11 h and during the months of May and June only from 5 h to 9 h. It is recommended to keep open windows day and night from July to October and to keep closed windows day and night during November, December and January. The selection algorithm allows low-income users to control their ventilation by passive systems. To enhance the findings, the following research directions are recommended: 1) to analyse the selective algorithm effect on humid and dry climates and determine the air rates and the indoor air quality according to international standards for social housing in developing countries; 2) to compare global simulation providers and compare results according to the National Climatological Service.