*3.4. Initial Working Conditions*

The outdoor relative humidity range is 45.45% to 87.89%.

The range of relative humidity is simulated by changing the water vapor mass fraction, with a gradient of 0.02%. The effects of ground soil relative humidity, outdoor ambient temperature, and wall relative humidity on indoor relative humidity are investigated. The boundary conditions are set as follows:


#### **4. Results and Discussion**

#### *4.1. Mathematical Model Accuracy Verification*

According to the relevant standards [28], the indoor area is less than 30 m2, the measurement points should be placed on a plane of (1.3 ± 0.1) m height, and the humidity measurement points should be no less than three. In this paper, six relative humidity measurement points are set up, and the measurement points are indicated by the numbers 1–6. The locations of the indoor relative humidity measurement points are shown in Figure 5a, and the coordinates of the measurement points are 1 (−1.2 m, −1.6 m, −1.5 m), 2 (−1.2 m, −3.2 m, −1.5 m), 3 (−1.2 m, −1.6 m, −3 m), 4 (−1.2 m, −3.2 m, −3 m), 5 (−1.2 m, −1.6 m, −4.5 m), and 6 (−1.2 m, −1.6 m, −4.5 m). At this point, multiple measurements are taken at each measurement point on a particular day in summer, and the average is taken as the actual indoor RH data. The model's accuracy is verified by simulating relative humidity at each measurement point. A comparison graph of measured and simulated data is shown in Figure 5b.

**Figure 5.** Location of measurement points and data map. (**a**) Location of indoor relative humidity measurement points and (**b**) comparison chart of measured and simulated data.

As seen from Figure 5b, the measured and simulated interior average relative humidity at each measurement point ranged from 90% to 100%. Clearly, the relative humidity is large. The maximum relative error between measured and simulated data was calculated to be 6%, and the minimum relative error was 1.2%. The results show that the data from the simulation are consistent with the measured data. The accuracy of the simulation results is verified based on the comparison of the measured and simulated data.

#### *4.2. The Indoor Temperature and Humidity Distribution in Initial Working Conditions*

In this work, under the initial working conditions of ancient buildings (outdoor temperature of 26.3 ◦C and outdoor relative humidity of 67.17%), the indoor temperature and humidity distribution of ancient buildings are simulated. For the purpose of the following analysis, detailed cross-sections in the horizontal and vertical directions are shown in Figure 6 below.

**Figure 6.** Cross-sectional view in different directions. (**a**) Cross-section in the vertical direction and (**b**) cross-section in the horizontal direction.

The distribution of temperature and relative humidity at Z = 0 m, Z = −3 m, and Z = −5 m in the vertical direction are shown in Figure 7, respectively. As seen in Figure 7a,d, the temperature and relative humidity distribution atZ=0m (east wall) remain essentially constant. This is due to the fact that there are no windows in the east wall, and there is no heat dissipation to dissipate humidity. However, there are smaller temperature and humidity fluctuations at ground level. This is due to the fact that the wall root zone is less exposed to sunlight, which causes its humidity to rise slightly. The temperature was around 24.5 ◦C, and the relative humidity was 90.2%.

As shown in Figure 7b,e, the temperature and relative humidity in the middle part of the room remain more or less constant at Z = −3 m. The temperature is 24.5 ◦C, and the relative humidity is about 84.3%, mainly due to its more even distribution of moisture content. Fluctuations in temperature and humidity occur on the lower side (floor) and the right side (around the south window). The relative humidity is lower near walls and the ground than inside, mainly because sunlight in summer and poor heat storage capacity of windows can make the part near windows and walls warmer than inside and contain less moisture.

As shown in Figure 7c,f, at Z = −5 m (west wall), fluctuations in temperature and humidity occur mainly in the west window. The temperature and relative humidity at the west window are lower than at the same vertical plane, and the temperature and relative humidity gradually increase from the middle of the window to the surrounding area. This is due to the fact that the windows are wooden and will have gaps, resulting in infiltration and moisture dispersion, resulting in low moisture content. The overall temperature is at 24.4 ◦C–24.7 ◦C, and the relative humidity is at 75.9–85.8%.

**Figure 7.** Indoor temperature and relative humidity distribution in the vertical direction. (**a**) Indoor temperature distribution at Z = 0 m, (**b**) indoor temperature distribution at Z = −3 m, (**c**) indoor temperature distribution at Z = −5 m, (**d**) indoor relative humidity distribution at Z = 0 m in the vertical direction, (**e**) indoor relative humidity distribution at Z = −3 m, and (**f**) indoor relative humidity distribution at Z = −5 m.

The distribution of temperature and relative humidity in the horizontal direction at X = 0 m, X = −2 m, and X = −4 m are shown in Figure 8, respectively. Analysis of Figure 8a–c above shows that the room temperature is maintained at 23.3 ◦C and remains the same. From Figure 8d, it can be seen that the relative humidity of the ground remains unchanged at 91.7%. This is mainly due to the presence of a moat on the ground, which makes its moisture content evenly distributed. From Figure 8e, it can be seen that the relative humidity values of the south and west windows are larger than those of the rest of the plane, which is due to the infiltration effect of the windows that makes their humidity greater. From Figure 8f, it can be seen that the relative humidity on the roof remains constant, and the indoor relative humidity value is higher.

The comprehensive analysis reveals that the indoor average temperature is 24.5 ◦C, and the indoor relative humidity range is between 87.4% and 92.4%. Overall, the temperature fluctuations in the interior of the ancient building are small, while the relative humidity fluctuates widely. Therefore, the following section focuses on the effect of each factor on indoor humidity. The control variate method is taken to investigate changes in humidity.

**Figure 8.** Indoor temperature and humidity distribution in the horizontal direction. (**a**) Indoor temperature distribution at X = 0 m, (**b**) indoor temperature distribution at X = −2 m, (**c**) indoor temperature distribution at X = −4 m, (**d**) indoor relative humidity distribution at X = 0 m in the vertical direction, (**e**) indoor relative humidity distribution at X = −2 m, and (**f**) indoor relative humidity distribution at X = −4 m.

### *4.3. Effect of Outdoor Humidity on Indoor Moisture Transfer*

The humidity of the soil and walls is set as the initial state. With the difference in outdoor humidity, the indoor humidity is shown in Figure 9a,b. Due to the ancient age of this historic building, outdoor air enters the interior through windows, which are made of a paper material and have a significant degree of damage. Thus, the outdoor humid environment is an important factor affecting the indoor humidity of ancient buildings.

**Figure 9.** Effect of outdoor humidity on the humidity in the horizontal and vertical direction of the room. (**a**) Trends in the effect of outdoor ambient relative humidity on average relative humidity in the vertical direction inside the room and (**b**) trends in the effect of outdoor ambient relative humidity on average relative humidity in the horizontal direction of the room.

As seen from Figure 9a, under a given outdoor humidity, the indoor relative humidity is observed to change in the vertical direction from east to west (Z = 0 m to Z = −5 m). When the outdoor humidity is less than 75.6%, the average indoor relative humidity shows a trend of gradual decrease. And when the outdoor humidity is greater than 75.6%, the average indoor relative humidity shows a gradually increasing trend. When located in the same vertical plane, with the increase in outdoor humidity, the average indoor relative humidity increases significantly at Z = −5 m. At Z = −3 m, the trend of the average indoor relative humidity increases more slowly than that at Z = −5 m. At Z = 0 m, the average indoor relative humidity remains unchanged.

As seen from Figure 9b, under a given outdoor humidity, the change in indoor relative humidity in the horizontal direction from the ground to the roof (X = 0 m to X = −4 m) is observed. When the outdoor humidity is less than 75.6%, the average indoor relative humidity shows a trend of first decreasing and then gradually increasing, and the change in decreasing is larger. At outdoor humidity greater than 75.6%, the average indoor relative humidity showed a trend of first increasing and then gradually decreasing. Therefore, it was concluded that the average relative humidity at ground level was the highest. When located in the same horizontal plane, with the increase in outdoor humidity, the average indoor relative humidity is the highest and remains the same at X = 0 m. At X = −2 m, the average indoor relative humidity increases significantly. At X = −4 m, the average indoor relative humidity shows a slowly increasing trend.

#### *4.4. Effect of Soil Moisture on Moisture Transfer*

Xu et al. [22] carried out experiments on the effect of coupled heat and moisture transfer on soil heat storage systems and confirmed that ignoring moisture migration and temperature dependence of soil thermal conductivity would lead to a low predicted value of the numerical model, and the influence of initial soil moisture on coupled heat and moisture transfer should be considered. In this paper, the influence of soil moisture on the humidity in different directions in the room was simulated by changing the mass fraction of groundwater vapor (soil moisture).

As seen from Figure 10a, under a given soil moisture, changes in indoor relative humidity in the vertical direction from east to west (Z = 0 m to Z = −5 m) are observed. The average indoor relative humidity decreases gradually, but the decrease is small. When located in the same vertical plane, the average indoor relative humidity gradually increased with the increase in soil moisture, and the trend of the increase was almost the same on each plane.

**Figure 10.** Effect of soil moisture on the humidity in the horizontal and vertical direction of the room. (**a**) Trends in the effect of soil moisture on average relative humidity in the vertical direction inside the room and (**b**) trends in the effect of soil moisture on average relative humidity in the horizontal direction of the room.

As seen from Figure 10b, under a given soil moisture, the average indoor temperature shows a first decreasing and then increasing trend when observing the change in indoor temperature and humidity in the horizontal direction from ground to roof (X = 0 m to X = −4 m), but the change is smaller. When located in the same horizontal plane, the average indoor relative humidity increases gradually with the increase in soil humidity.

#### *4.5. Effect of Wall Moisture on Indoor Humidity Transfer*

Over time, the porosity of the ancient building envelope will become larger, and its moisture storage capacity will also be enhanced. In addition, excessive humidity in the building envelope can lead to damage to building materials and mold growth [29]. It is also a factor that produces wall mold, as it migrates into the indoor environment. Therefore, the influence of wall humidity on the humidity in different directions of the room was simulated by changing the water vapor mass fraction (changing wall moisture) of the wall.

As seen from Figure 11a, the indoor relative humidity values on different planes are the same, so the relative humidity of the whole room can be analyzed by the above figure. From Figure 11a,b, it can be seen that as the humidity of the walls increases, the relative humidity in the room also gradually increases. This is due to the moisture transfer from the walls, which makes the humidity in the room also increase gradually.

**Figure 11.** Effect of wall humidity on the average humidity in the horizontal and vertical direction of the room. (**a**) Trends in the effect of wall humidity on average relative humidity in the vertical direction inside the room and (**b**) trends in the effect of wall humidity on average relative humidity in the horizontal direction of the room.

From the analysis of indoor relative humidity law in 4.4 and 4.5, it can be seen that when the ground or wall water vapor mass fraction decreases (ground soil or wall moisture decreases), the average indoor relative humidity decreases when the conditions of building protection and maintaining the original appearance of the building can be met. Therefore, the relative humidity of the indoor environment can be reduced by lowering the ground soil moisture or wall moisture.

#### *4.6. The Sensitivity of Factors*

While the effect patterns of outdoor environmental humidity, soil moisture, and wall humidity on indoor relative humidity have been obtained via simulation, the sensitivity of each factor requires correlation analysis that takes statistical methods [30], with indoor relative humidity as the target (significant test level of 0.01). Outdoor ambient relative humidity, soil moisture, and wall moisture are set as the reference series *X*<sup>0</sup> and the indoor ambient relative humidity is set as the comparison series *Xi*(*k*), respectively. Based on the existing correlation empirical equations [31,32], the calculation steps for correlation analysis are as follows.

Relation coefficient:

$$\gamma\_i(k) = \frac{\min\_i \min\_k \Delta\_i(k) + \mathfrak{J} \max\_i \max\_k \Delta\_i(k)}{\Delta\_i(k) + \mathfrak{J} \max\_i \max\_k \Delta\_i(k)} \tag{8}$$

where Δ*i*(*k*) = *X* <sup>0</sup>(*k*) <sup>−</sup> *<sup>X</sup> <sup>i</sup>*(*k*) , *<sup>ξ</sup>* <sup>∈</sup> (0, 1) is the resolution factor, which usually takes the value of 0.5.

Correlation degree:

$$R\_i = \frac{1}{n} \sum\_{k=1}^{n} \gamma\_i(k), i = 1, 2, 3, \dots, m; k = 1, 2, 3, \dots, n \tag{9}$$

From Table 6, it can be seen that the correlation between outdoor ambient humidity to indoor relative humidity is weak; while the correlation between soil humidity and wall humidity to indoor relative humidity is strong, and the correlation between wall and indoor relative humidity is lower than that of soil by 0.002. This paper mainly focuses on the problem of wet building floors and high indoor relative humidity. Therefore, it can be concluded that soil moisture and wall moisture are the main factors affecting indoor relative humidity.

**Table 6.** Correlation analysis result.


#### *4.7. Indoor Temperature and Humidity Distribution after Moisture-Proof Treatment*

According to related studies [33–35], antimicrobial and hydrophobic coatings can be used to reduce room humidity by coating and protecting moldy areas of bricks without affecting the appearance of ancient buildings, such as SiO2-TiO2 hybrid fluorinated B-72, lime putty mortar (ASPL and ASPL/PP series), etc. This coating has better resistance to acid, alkali, salt, and UV light as well as the inhibition of damp proofing. Ground and walls are as examples of wet sources, obtained from Figure 12. When the water vapor mass fraction is 0.0105% (ground soil relative humidity of 59.02%) and the wall water vapor mass fraction is 0.0107% (wall relative humidity of 60%), the relative humidity of the ancient building interior is 60.2% to 78.8%, in line with the requirements of indoor relative humidity under summer working conditions. Indoor ground temperature and humidity distribution are shown in Figure 12, and the temperature at the ground is 23.3 ◦C, with an average relative humidity of 60.32%. As seen in Figure 12a, after the damp-proofing treatment, the relative humidity of the ancient building interior was reduced from 90.9% to 94.0% to 60.2% to 78.8%, and the relative humidity decreased and met the requirements of indoor relative humidity under summer working conditions.

**Figure 12.** Indoor ground temperature and humidity distribution picture: (**a**) Relative humidity distribution at ground level and (**b**) temperature distribution at ground level.
