The Effect of Smart Colored Windows on Visual Performance of Buildings

: The photochromic coating is a promising smart technology that provides different optical properties in response to daylight variations. The application of photochromic coatings with various colors/shades on window glass is one of the current research approaches for ﬁnding better energy saving techniques. The aim of this study was to develop a series of photochromic coatings for window glass and measure the impact of such smart technologies on occupants’ visual comfort. This paper examines the visual performance of building facades that utilize windows with different photochromic-coated glass. The visual performance data of three window types coated with nine different photochromic color shades were considered and compared to determine the best photochromic shades and window types that provide optimum visual metrics for the inside of the building. The results show that compared to no-coating glass, both the Daylight Glare Probability and the Useful Daylight Illuminance could be improved by using multi-color coatings that contain equal or different color proportions for photochromic window glass. From an energy-saving point of view, the results indicate that the windows coated with photochromic materials provide a better alternative to the no-coating window products.


Introduction
Materials that are able to significantly alter one or more of their inherent properties with the application of external stimuli such as stress, temperature, moisture, pH, electrical fields, and magnetic field, in a controlled fashion, are known as smart materials [1]. Applying smart materials as a smart coating on windows can improve energy efficiency, user comfort and well-being, and decrease CO 2 emissions in built environments [2]. Different types of smart coatings, such as electrochromic [3][4][5], thermochromic [6], gasochromic [7], and liquid crystal [8] have been utilized to develop smart windows [9][10][11]. The coating of photochromic materials can be applied on the surface of window glass as a thin film to provide a capability for the glass to dynamically adjust its own color, transparency, and consequently, its reflective properties upon exposure to various intensities of sunlight over a day [12]. It needs to be noted that the dynamic behavior of photochromic coatings is reversible and by dimming or blocking the sunlight the glass will revert to its initial optical properties [10]. As a result, the optical properties of photochromic coated windows countinouselly move between bleached phase and colored phase [13]. The dynamic behavior in response to sunlight intensities caused by such photochromic coatings could be a promising replacement for implemented mechanical and electro-mechanical technologies in the design and development of responsive facades [14].
A literature review of the most recent studies on smart windows is summarized in Table 1  . Although the majority of studies examine the influence of thermochromic [19][20][21][22][23][24][25][26], electrochromic [27][28][29][30], and gasochromic coatings [31][32][33] on building energy consumption, CO 2 emission, heading, and cooling load [34][35][36], only a few studies has focused on the photochromic coating and its application in the built environment [14][15][16][17][18]. Additionally, among studies of smart windows with photochromic coatings, the effect of such coating on occupants' visual comfort has not been adequately explored. In addition, only three colors/shades of gray, blue, and green have been investigated and no investigation has focused on combinations of different photochromic colors/shades and their visual performance in buildings. mance in a building environment. The main colors that were developed for photochromic coatings included red, medium blue, yellow, and their dual and triple combinations. To assess the visual performance of window glass substrates, the Red-Green-Blue (RGB) values determination test was utilized to determine the optical properties of photochromic glass. Then, the obtained optical propertie's data were used to simulate the smart coated windows using validated daylight simulator software. Three smart window types were designed including one-layer photochromic glass, two-layer photochromic glass, and onelayer of low-e glass with one-layer of photochromic glass. The visual performance of the photochromic windows was evaluated using Daylight Glare Probability (DGP) and Useful Daylight Illuminance (UDI) [37]. An office room with a smart window as a facade was parametrically simulated to test the developed smart coated windowpanes for different color scenarios. The visual performance evaluations were repeated for south, east, north, and west orientations as the main facade directions during different hours and days. Then, to identify the best photochromic colors and windowpane types, the results were compared with a no-coating glass window.

Smart Color Coated Windowpane
The smart coatings were created by using photochromic dyes of red, medium blue, and yellow colors. Each dye solution was added to the mixture of thermoplastic acrylic resin and leveling agent additive. Table 2 lists the formulations of each coating color that was used. The coating materials were applied to the degreased glass plates and pre-coated low-carbon steel panels with a wet film thickness of 4 mils (100 µm) using a film applicator. The glass plates were exposed to a UV LED light lamp to check the photochromic activity of coatings. The applied coating materials were then left at ambient conditions for 24 h to dry. The photochromic coatings have reversible properties that adapt to glass light transmittance based on the amount of solar irradiance received [38,39]. Thus, to determine the light transmittance of the coated glass plates over time, the direct photographic technique was used to measure the RGB values of the coated glass plates. The direct photography was conducted for the two days of 25 May and 16 September at the two different times of 12:00 p.m. and 6:00 p.m., because the maximum solar radiation occurrs at 12:00 p.m. and the minimum happens at 6:00 p.m. [40,41]. Accordingly, the coated glass plates were initially exposed to direct sunlight for 60 s, before being placed in the gap between the diffuser and the guiding camera lens, and were instantly photographed. The RGB values of the coated glass were acquired after uploading the photographs to Adobe Photoshop. The photochromic coatings applied to the glass plates showed high light transmittance at the bleached condition and significant low light transmittance at the colored conditions. Figure 1 demonstrates the glass plates coated with red, medium blue, and yellow colors with four different exposure times of 0, 10, 30, and 60 s. plates were initially exposed to direct sunlight for 60 s, before being placed in the gap between the diffuser and the guiding camera lens, and were instantly photographed. The RGB values of the coated glass were acquired after uploading the photographs to Adobe Photoshop. The photochromic coatings applied to the glass plates showed high light transmittance at the bleached condition and significant low light transmittance at the colored conditions. Figure 1 demonstrates the glass plates coated with red, medium blue, and yellow colors with four different exposure times of 0, 10, 30, and 60 s.

Simulation of the Building Smart with Color Coated Windowpane
A simple office room with the dimensions of 4.0 m wide, 9.0 m deep, and 3.0 m high was designed. A shoebox office model was chosen because the results are easily read and interpreted, and the effect of design parameters such as colored glass type, facade type, and window size can quickly be analyzed [40].The depth of the room was chosen to be larger than the typical depth so that the effect of daylight remains visible for all variants [41]. Natural light was considered the only light source in the office room with no artificial lighting. This simulated office room was designed to have a 2.6 m width and 3.6 m length window. A responsive facade system with a window was parametrically modeled and applied to the office room using the Grasshopper modeling tool. The simulated room could be rotated to face N, W, S, and E as the four main cardinal directions.
The office was assumed to be located in the city of Ann Arbor in Michigan and to be occupied daily from 8:00 a.m. to 6:00 p.m. outside of daylight savings time. The occupancy schedule was in agreement with IESNA's new Lighting Measurement IES LM-83-12 [41]. During occupancy hours, it was assumed that six workspaces were occupied, and occupants were performing regular office work, including working on a computer. The clear sky with the sun was considered as the sky conditions. The weather data for the office location was obtained from the U.S. Department of Energy that provides typical annual meteorological data as an EnergyPlus Weather File (EPW).
For the office room, a Grasshopper plug-in for Rhinoceros software was utilized to simulate one-pane and two-pane photochromic coated glass windows. The data obtained from the RGB determination test was used by the Honeybee Legacy plug-in for

Simulation of the Building Smart with Color Coated Windowpane
A simple office room with the dimensions of 4.0 m wide, 9.0 m deep, and 3.0 m high was designed. A shoebox office model was chosen because the results are easily read and interpreted, and the effect of design parameters such as colored glass type, facade type, and window size can quickly be analyzed [40].The depth of the room was chosen to be larger than the typical depth so that the effect of daylight remains visible for all variants [41]. Natural light was considered the only light source in the office room with no artificial lighting. This simulated office room was designed to have a 2.6 m width and 3.6 m length window. A responsive facade system with a window was parametrically modeled and applied to the office room using the Grasshopper modeling tool. The simulated room could be rotated to face N, W, S, and E as the four main cardinal directions.
The office was assumed to be located in the city of Ann Arbor in Michigan and to be occupied daily from 8:00 a.m. to 6:00 p.m. outside of daylight savings time. The occupancy schedule was in agreement with IESNA's new Lighting Measurement IES LM-83-12 [41]. During occupancy hours, it was assumed that six workspaces were occupied, and occupants were performing regular office work, including working on a computer. The clear sky with the sun was considered as the sky conditions. The weather data for the office location was obtained from the U.S. Department of Energy that provides typical annual meteorological data as an EnergyPlus Weather File (EPW).
For the office room, a Grasshopper plug-in for Rhinoceros software was utilized to simulate one-pane and two-pane photochromic coated glass windows. The data obtained from the RGB determination test was used by the Honeybee Legacy plug-in for Grasshopper to characterize each of the ten color shades used in photochromic glass windows. The honeybee Legacy is one of Grasshopper's plug-ins, which assists Grasshopper to conduct sustainability simulations, such as daylight analysis using Radiance engine. Radiance is software that was numerously validated previously by other researchers [42][43][44][45]. Reinhart and Walkenhorst [42] have shown that Radiance-based simulation methods "are able to efficiently and accurately model complicated daylighting elements such as Venetian blind system". Additionally, Reinhart and Andersen [43] have shown that translucent materials "can be modeled in Radiance with an even higher accuracy than what was demonstrated in the earlier studies". Statistic software R and Microsoft Excel were utilized for the management, visualization and analysis of the data.
The Honeybee Legacy plug-in was utilized to measure DGP and hourly usable daylight illuminance (UDI h ). As a grid-based metric, UDI h was measured by defining 900 sensors located over a horizontal grid surface with a height of 0.83 m from the office floor, which was within the standard of the height for work-plane surfaces in an office area. The sensors were spaced approximately every 0.2 m from each other in both surface directions. The interior of the office room was simulated with standard radiance materials that included a generic floor with 20% reflectance, a generic ceiling with 70% reflectance, generic interior walls with 50% reflectance, and generic furniture with 50% reflectance to allow indirect illumination.
DGP is classified in four ranges of 0-35 (imperceptible), 35-40 (perceptible), 40-45 (disturbing), and 45-100 (intolerable) [46]. To calculate DGP, a camera needs to be located in the simulated office at the eye level of an assumed occupant seated behind a workstation working with a computer. In this study, the camera was located at the first workstation on the right side of the window facing the cardinal directions. It needs to be noted that the DGP calculations are based on a formula developed by Wienold and Christofferen as follows [46]: where E ν is the vertical eye illuminance (Lux), constant c 1 = 5.87 × 10 −5 ; L S is the luminance of the source (cd/m 2 ), constant c 2 = 9.18 × 10 −2 , w s is the solid angle of the source, constant c 3 = 0.16; P is the position index, and constant a 1 = 1.87. UDI h is an indicator for evaluating the hourly light amount that exists in a specific interior space, which includes lower and upper thresholds and an acceptable range as UDI underlit (300 Lux < E), UDI overlit (E > 1000 Lux), and UDI useful (300 Lux < E < 1000 Lux), respectively [47][48][49][50][51][52]. Calculating UDI h can be considered as an attempt to integrate the measurement of indoor illuminance level and discomfort glare in one scheme [53,54]. In general, UDI h is defined as a weighted average as follows [49]: where t i is the time when the illuminance E is calculated, and wf i is the weighting factor, which depends on the range of the calculated illuminance E. It should be noted that wf i weighting factor is selected based on the range of the calculated illuminance E. For instance, as shown below, for the upper threshold, UDI overlit is calculated as below after wf i is selected depending on how the illuminance E value is compared to the upper limit of illuminance specified in standards [49]: In a similar way, the lower threshold UDI underlit is calculated as: Similarly, UDI useful is calculated as:

Experiment Setting
The DGP and UDI h are considered as the two main metrics of visual comfort of a building. The visual performance data of each photochromic color coated windows were studied and compared to determine the best photochromic shades for managing daylight inside the simulated office. To determine these metrics, three types of windows and ten different color coatings were utilized. The types of windows considered for testing were: a Type A window, which consists of a one-layer photochromic glass, b Type B window, which consists of two-layer photochromic glass, c Type C window, which consists of one-layer of photochromic glass in interior and one-layer of Low-E glass in the exterior.
The architectural sketches of the color shades are presented in Figure 2. It needs to be noted that grasshopper scripts were utilized to randomly distribute the selected colors of R, MB, Y, and MBY on the surface of the windowpane with and without color proportions in order to create MCP and MCPs scenarios. Similarly, UDIuseful is calculated as:

Experiment Setting
The DGP and UDIh are considered as the two main metrics of visual comfort of a building. The visual performance data of each photochromic color coated windows were studied and compared to determine the best photochromic shades for managing daylight inside the simulated office. To determine these metrics, three types of windows and ten different color coatings were utilized. The types of windows considered for testing were: a. Type A window, which consists of a one-layer photochromic glass, b. Type B window, which consists of two-layer photochromic glass, c. Type C window, which consists of one-layer of photochromic glass in interior and one-layer of Low-E glass in the exterior.
The color shades considered for each window types were: The architectural sketches of the color shades are presented in Figure 2. It needs to be noted that grasshopper scripts were utilized to randomly distribute the selected colors of R, MB, Y, and MBY on the surface of the windowpane with and without color proportions in order to create MCP and MCPs scenarios.  By using Honeybee software, DGP and UDI h for all three window types with each of the ten color shades, for two days of 25 May and 16 September at two times of 12:00 p.m. and 6:00 p.m. were computed and reapeated for each of the four (N, S, W, and E) facade directions. Figures 3 and 4 show the computed DGPs for 25 May and 16 September at noon, respectively. In comparison with a no-coating glass, all scenarios of photochromic coated glass significantly influenced DGP. As Figures 3 and 4 illustrate, DGPs are reduced considerably by utilizing Type A, Type B, and Type C windows. The glare occurrence in the south oriented office room happened more frequently in early spring and late fall when the incidence angle was small due to low solar altitude and high intensity [55]. So, using photochromic glass in window types A, B, and C can dramatically reduce glare in the south facade during 25 May at noon, as demonstrated in Figure 3. On the other hand, as Figure 4 shows the application of photochromic glass in window types A, B, and C leads to a decrease in the negative effect of glare during 16 September at noon. However, the glare reduction is not as significant as on 25 May. In fact, sun in September would be more hamful for occupants' eyes in May since its location would be lower in the sky and at different angles that may expose the occupants to additional discomfort glare [56]. By using Honeybee software, DGP and UDIh for all three window types with each of the ten color shades, for two days of 25 May and 16 September at two times of 12:00 p.m. and 6:00 p.m. were computed and reapeated for each of the four (N, S, W, and E) facade directions. Figures 3 and 4 show the computed DGPs for 25 May and 16 September at noon, respectively. In comparison with a no-coating glass, all scenarios of photochromic coated glass significantly influenced DGP. As Figures 3 and 4 illustrate, DGPs are reduced considerably by utilizing Type A, Type B, and Type C windows. The glare occurrence in the south oriented office room happened more frequently in early spring and late fall when the incidence angle was small due to low solar altitude and high intensity [55]. So, using photochromic glass in window types A, B, and C can dramatically reduce glare in the south facade during 25 May at noon, as demonstrated in Figure 3. On the other hand, as Figure 4 shows the application of photochromic glass in window types A, B, and C leads to a decrease in the negative effect of glare during 16 September at noon. However, the glare reduction is not as significant as on 25 May. In fact, sun in September would be more hamful for occupants' eyes in May since its location would be lower in the sky and at different angles that may expose the occupants to additional discomfort glare [56].   Additionally, the intensity of sunlight received by west facade is in its maximum amounts during late afternoon [55]. The measurements at 6:00 p.m. on 25 May and 16 September reveal that the photochromic glass used in window types can significantly control discomfort glare in comparison with no-coating glass. Utilizing photochromic glass in all of the window types can effectively reduce glare more at 6:00 p.m. in 16 September compared to 25 May.

UDI Analysis
As well as DGP, UDIh was also calculated for different color shades of different window types. The data was obtained on 25 May and 16 September at 12:00 p.m. and 6:00 p.m. for four cardinal orientations (N, W, S, E). Then, three ranges of UDIhs were determined and recorded for further analysis. As an example, Figure 5 shows the UDIunderlit, UDIoverlit, and UDIuseful of all color shades in three window types on 25 May at noon in the South facade. In comparison with no-coating glass, using photochromic glass can increase UDIuseful percentage, decrease UDIoverlit, and increase UDIunderlit percentage. It should be noted that decreasing UDIoverlit can lead to less discomfort glare and increasing UDIunderlit can lead to more of a need to use artificial light at the end of the office room [57]. Figure 5 demonstrates the useful range on 25 May at noon in a type A window with blank glass is 33, which means 33% of the working space area had useful indoor illuminance. If the R color shade was utilized, the working space area with useful indoor illuminance could increase to 44%. As a result, UDIuseful relatively increased by 30%. On the other hand, using the R color shade in type A can decrease UDIoverlit and increase UDIunderlit percentage. Additionally, the intensity of sunlight received by west facade is in its maximum amounts during late afternoon [55]. The measurements at 6:00 p.m. on 25 May and 16 September reveal that the photochromic glass used in window types can significantly control discomfort glare in comparison with no-coating glass. Utilizing photochromic glass in all of the window types can effectively reduce glare more at 6:00 p.m. in 16 September compared to 25 May.

UDI Analysis
As well as DGP, UDI h was also calculated for different color shades of different window types. The data was obtained on 25 May and 16 September at 12:00 p.m. and 6:00 p.m. for four cardinal orientations (N, W, S, E). Then, three ranges of UDI hs were determined and recorded for further analysis. As an example, Figure 5 shows the UDI underlit , UDI overlit , and UDI useful of all color shades in three window types on 25 May at noon in the South facade. In comparison with no-coating glass, using photochromic glass can increase UDI useful percentage, decrease UDI overlit , and increase UDI underlit percentage. It should be noted that decreasing UDI overlit can lead to less discomfort glare and increasing UDI underlit can lead to more of a need to use artificial light at the end of the office room [57]. Figure 5 demonstrates the useful range on 25 May at noon in a type A window with blank glass is 33, which means 33% of the working space area had useful indoor illuminance. If the R color shade was utilized, the working space area with useful indoor illuminance could increase to 44%. As a result, UDI useful relatively increased by 30%. On the other hand, using the R color shade in type A can decrease UDI overlit and increase UDI underlit percentage.  Figures 6 and 7, respectively. As Figure 6 shows, the UDIh acceptable of south facade is lower than other facade directions in type A. Additionally, in type B the UDIh acceptable for R and RMB color shades was lower than the other color shades for all directions. As it is shown in Figure 6, there is a lower variation for different color shades and orientations in type C compared to type A and type B. As illustrated in Figure 7, the value for west oriention in all color shades and window types were higher compared to other facade orientations. In addition, big differences were observed in type C for the no-coating and MB color shade in west facade. On the other hand, the overall UDIh acceptable stands higher in type A for all color shades and orientations compared to type B and type C.   Figures 6 and 7, respectively. As Figure 6 shows, the UDI h acceptable of south facade is lower than other facade directions in type A. Additionally, in type B the UDI h acceptable for R and RMB color shades was lower than the other color shades for all directions. As it is shown in Figure 6, there is a lower variation for different color shades and orientations in type C compared to type A and type B. As illustrated in Figure 7, the value for west oriention in all color shades and window types were higher compared to other facade orientations. In addition, big differences were observed in type C for the no-coating and MB color shade in west facade. On the other hand, the overall UDI h acceptable stands higher in type A for all color shades and orientations compared to type B and type C.  Figures 6 and 7, respectively. As Figure 6 shows, the UDIh acceptable of south facade is lower than other facade directions in type A. Additionally, in type B the UDIh acceptable for R and RMB color shades was lower than the other color shades for all directions. As it is shown in Figure 6, there is a lower variation for different color shades and orientations in type C compared to type A and type B. As illustrated in Figure 7, the value for west oriention in all color shades and window types were higher compared to other facade orientations. In addition, big differences were observed in type C for the no-coating and MB color shade in west facade. On the other hand, the overall UDIh acceptable stands higher in type A for all color shades and orientations compared to type B and type C.

A Comparison of Color Shades and Window Types
To identify the most effective window type and color shade in various facade orientations, the type A window was selected as a baseline for determining the average improvement rate of type B and type C by using Equations (6) and (7): × 100 Average Improvement rate of window Type (j) = ∑ ( , ) where j represents either type B or type C window, k is the corresponding color shade, and x denotes either DGP or UDIh value. A sample of DGP improvement rate and its average is shown in Table 3.  Table 3 shows that type C yields better results for all color shades in all facade orientations, and also DGPs are reduced considerably by utilizing type A, type C, and type B, respectively.

A Comparison of Color Shades and Window Types
To identify the most effective window type and color shade in various facade orientations, the type A window was selected as a baseline for determining the average improvement rate of type B and type C by using Equations (6) and (7): Average Improvement rate of window Type (j) = ∑ k Improvement rate (j, k) 10 (7) where j represents either type B or type C window, k is the corresponding color shade, and x denotes either DGP or UDIh value. A sample of DGP improvement rate and its average is shown in Table 3.  Table 3 shows that type C yields better results for all color shades in all facade orientations, and also DGPs are reduced considerably by utilizing type A, type C, and type B, respectively.
Next, no-color shade was selected as a baseline to determine the improvement rate of each color shades by using Equations (8) and (9): Improvement rate of color shade (i, k) = y (i, k) − y(no − color Type A, k) y (no − color Type A, k) × 100 (8) Improvement rate (i) = ∑ k Improvement rate of color shade (i, k) 9 (9) where i represents a color shade, k is the corresponding window type, and y denotes either the DGP or UDI h value. A sample of the DGP improvement rate for different color shades and its average is shown in Table 4. As shown in Table 4, type B in north direction presented the most significant improvement in DGP with color shades of MB, R, MCP, and MCPs, respectively. However, the most significant improvement in DGP in type C was observed in south with color shades of R, RMB, MCPs, MBY, respectively. The same order of DGP improvement occurred in the east and west facade directions.
Visual performance of various window types with different color shades and different facade orientations are compared in Tables 5 and 6. Table 5 presents the color shades with the highest improvement rates of DGP on 25 May and 16 September, respectively.
On 16 September at noon, type C obtained better results for all color shades in all facade orientations. DGP improved effectively in south with color shades of R, MCPs, RMB, and MCP, respectively. In north, the most significant improvement in DGP was for Type C with color shades of R, RMBY, Y, and MCPs, respectively. A similar order of DGP improvement was observed for east and west as well. Table 5 shows the highest improvement rates of UDI h on 25 May and 16 September. On average the acceptable UDI h decreased for all color shades in different facade orientations if either type B or Type C were used on 25 May at 6:00 p.m., as Table 5 shows. Additonally, Type B had the maximum improvement rate with color shades of MB, RMB, CMP and CMPs in south façade direction, respectively. However, the pattern of improvement rate in the south changed when type C was used.

Discussion
This study showed that the application of photochromic coated glass in proposed window types can control daylight discomfort effects such as glare and exceeded indoor illuminance.
Due to the smart nature of the photochromic glass, UDI h underlit , UDI h acceptable , UDI h overlit can be meaningfully controlled in order to provide maximum office area with less discomfort glare and less over lited/overheated conditions, along with more comfort in indoor illuminance for daily office activities, which can lead to increased occupant productivity [58]. The depth of the simulated office room was chosen to be larger than the typical depth; therefore, complementary artificial lights might be needed at the office areas far from the window, since the photochromic glass is in the opaque/colored phase at noon with high solar radiation [59].
Haghshenas et. al. [60] have suggested that by using a combination of fixed/static colored glass in windows, one can control the depth of daylight penetration in buildings. The result of this study showed that the proposed smart coated glass with real-time adaptation not only can control daylight penetration in response to daylight intensity but also can allow daylight in without blocking the view whenever it is needed. Furthermore, as it was shown in [61], applying photochromic coatings such as the proposed smart colored window types can protect interior materials and furnishings from the ultraviolet (UV) and Infrared (IR) wavelengths, which are the main reasons of discoloration and degradation.
In view of the existing drawbacks of responsive facades such as the complexity of heavy mechanical parts [62], high potential failure of material fatigue and friction [63], difficulty in parts replacement, high costs in maintenance and repairing [64], limited components durability [65], and dependency on electrical powers [64], this study suggests that a chemical-based responsive facade by using photochromic materials can overcome some of these drawbacks. The approach presented in this study could be used in early phases of practical design settings. It was shown how different color shades could be chemically formulated and evaluated from the optical characteristic perspective. Additionally, it was demonstrated that how the formulated color glasses should be evaluated based on occupants' visual comfort metrics. This study could support future researchers and designers by illustrating a full process of photochromic glass design from chemical lab experiments and optical characteristics to visual performance evaluation. The results of this study reveal that the smart window technology with photochromic coatings can be an alternative to the current products in the market.

Conclusions
This paper assessed the visual performance of buildings containing windows with various smart photochromic color coated glass. The colors considered were red, medium blue, yellow, and their dual and triple combinations. Three window types were designed to evaluate the performance of various color shades based on their DGP and UDI metrics.
Among different color shades, MB and its combinations such as RMB, MBY, RMBY showed the highest percentage of UDI useful . The optimum performance of photochromic glass occurred in the windowpanes with MCP and MCPs colors presenting the high percentage of UDI useful and the low percentage UDI overlit . The performance of yellow photochromic glass in all window types was identical to glass with no coating.
Furthermore, all photochromic color shades had a major impact on decreasing discomfort glare by reducing the percentage of DGP values in comparison with no-coated glass. Among different color shades, R, MB, and its combinations such as RMB and RMBY had the maximum influence on controlling discomfort glare in different façade orientations, respectively. Considering both DGP and UDI metrics, colored-glass windowpanes with MCP and MCPs colors had the optimum performance in increasing useful illuminance and decreasing discomfort glare. Additonally, colored-glass windowpanes with MCP and MCPs colors have better performance in increasing useful illuminance compared to controlling discomfort glare. It needs to be mentioned that the findings of this study can open up a venue toward the applications of multi-color windowpanes such as MCP and MCPs and their possible potential in increasing visual comfort of users in various design scenarios. It needs to be noted that the optimum distributions of colors and optimum colors proportions in multi-color windowpanes must be investigated further in the future study.