Influence of Roof Windows Area Changes on the Classroom

sustainability

Article Inﬂuence of Roof Windows Area Changes on the Classroom Indoor Climate in the Attic Space: A Case Study

Erika Dolnikova * , Dusan Katunsky , Marian Vertal and Marek Zozulak

Institute of Architectural Engineering, Faculty of Civil Engineering, Technical University of Kosice, 042 00 Kosice, Slovakia; [email protected] (D.K.); [email protected] (M.V.); [email protected] (M.Z.) * Correspondence: [email protected]; Tel.: +421-055-602-4162

Received: 28 April 2020; Accepted: 17 June 2020; Published: 20 June 2020

Abstract: Windows are a complex part of building design and provide a considerable benefit, including to school buildings. For the evaluation of the daylighting conditions prevailing in classrooms, the daylight factor (DF) was considered as the most appropriate parameter for indicating the quantity of admitted daylight. The DF values and CIE overcast sky were calculated using Velux Daylight Visualizer 3 software. The task of the paper is to compare various roof window openings in relation to the level of daylight in the attic, looking to optimize the use of the attic for teaching. The indoor air temperature has a general influence on comfort in the interior, in addition to daylight. In winter, the situation is not critical. The thermal insulation properties of packaging structures are sufficient. The situation is worse in summer, due to the fact that the heat-storage properties are undersized and there is excessive overheating of the indoor air. Four variants of roof windows and their influence on the overall microclimate in the attic are compared. The variant without roof windows is a suitable solution with regard to minimum overheating, but the worst situation for daylight. In order to receive even more light from the window (by moving windows to the top of the roof), we can use variant 2. Based on a combination of daylight calculations and summer temperature, a graphical dependence on window size prediction in terms of top and combined lighting is derived. This was hypothesized without shading the windows. Of course, the shading elements of these windows or cooling are expected in the summer. Finally, the energy required for cooling is compared depending on the size of the windows and achievement of the permissible temperature.

Keywords: roof windows; daylighting; attic space; simulation program; school building

1. Introduction Daylight systems should provide a sufficient level of daylight in the classroom for activities, such as reading and writing. The level and quality of daylight in the classroom is important for the health of students, and it also affects their academic performance and participation in the teaching process. Daylight is a critical design factor for those interested in global warming, carbon emissions and sustainable design—in addition to visual comfort. Creating an ideal classroom environment depends on so many different factors (see Figure1), including the structure of the building, classroom size, windows, orientation to the cardinal, glare protection, interior equipment, color of surfaces, etc. [1].

Sustainability 2020, 12, 5046; doi:10.3390/su12125046 www.mdpi.com/journal/sustainability Sustainability 2020, 12, x FOR PEER REVIEW 2 of 24 subjectiveSustainability 2020perception, 12, 5046 of space, and ensures an adequate level of vision with good uniformity2 of of 24 lighting. Its application also saves energy on artificial lighting [2].

Windows and View

Productivity and Human Factors Satisfaction in Daylight Design Controlling Daylight in Interior Spaces

Minimize Glare

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Proper daylighting in a school environment is very complex task. The energy consumption of . Better utilization of daylight accompanied with proper management; classroom lighting can reach up to 50% of the school’s total electricity costs—this is because the energy . Regular cleaning of windows and bulbs from dust; this can save energy in light; used for lighting is consumed at a daily rate, and is expensive [9,10]. Adequate and high-quality . Incorrect lamp maintenance can absorb up to 50% of light through a thick layer of dust; lighting is a very important part of our daily activities. . When leaving the room, the last obligation is always to turn off the light. Energy saving options without cost include [11,12]: The level of light incidences from above is higher. Lighting and brightness increases from Better utilization of daylight accompanied with proper management; horizon to zenith. Therefore, roof windows provide at least twice as much light as vertical windows of Regularthe same cleaning size, and of three windows times and that bulbs of dormers from dust; of the this same can save size energy(see Figure in light; 2). The roof window provides Incorrect a greater lamp maintenance possibility of can combining absorb up lighting to 50% levels of light [13–15]. through The a thickdaylight layer level of dust; is described by the When daylight leaving factor the (see room, equation the last 5). obligation is always to turn off the light. The minimum and average daylight factors are defined in the standard [16], STN 730580; The level of light incidences from above is higher. Lighting and brightness increases from horizon Daylighting in buildings, Part-1 Basic requirements, and the standard [17] EN 12464-1:2012. Light to zenith. Therefore, roof windows provide at least twice as much light as vertical windows of the and Lighting; Lighting of Work Places-Part 1: Indoor Work Places. Several practical exercises have same size, and three times that of dormers of the same size (see Figure2). The roof window provides been carried out to assess the impact of external outlook on well-being. The standard level was a greater possibility of combining lighting levels [13–15]. The daylight level is described by the daylight assessed through the analysis of many classes [18]. The quality of lighting assessment in university factor (see equation 5). classrooms is the subject of [19]. The uniformity of lighting plays a very important role in regulations, Sustainability 2020, 12, x FOR PEER REVIEW 3 of 24

Sustainabilityand should2020 be, 12clear, 5046 in every country. This has been performed, for example, through a standard3 of 24 design for classrooms at public schools in Malaysia [20].

10 vertical window 8 roof window 6

Daylight factor DF (%) DF factor Daylight 2

0 0.5 1 1.5 2 2.5 3 Distance from peripheral wall (m)

Figure 2. Lighting efficiency eﬃciency of the vertical window and roof window at a distance from the peripheral wallwall (source(source author,author, processedprocessed accordingaccording toto[ 15[15]).]).

TheRecently minimum published and contributions average daylight included factors several are definedaspects of in school the standard light analysis, [16], STN such 730580; as the Daylightingdaily intensity in buildings,of high school Part-1 buildings Basic requirements, [21], the impact and the of standard glazing [17and] EN window 12464-1:2012. configuration Light and on Lighting;comfort and Lighting energy of efficiency Work Places-Part [22], daylight 1: Indoor levels Work in classrooms Places. Several adjacent practical to covered exercises and have exposed been carriedcourtyards out tounder assess clear the impactskies [23], of external ways of outlook using onlight well-being. in Portuguese The standard school buildings, level was assessedand the throughperception the of analysis user comfort of many [24]. classes [18]. The quality of lighting assessment in university classrooms is the subjectIt is possible of [19]. to The design uniformity an integrated of lighting daylight plays asystem, very important a combination role in regulations,of top and side and lighting should bein clearthe classroom, in every country. using the This DaySim has been simulation performed, tool for [2 example,5]. When through creating a standard the architecture design for of classroomsthe school atbuilding, public schoolsit is possible in Malaysia to use [ 20simulation]. tools when designing daylight. In some schools it is also possibleRecently to consider published top contributionslighting. For example, included several[26] assesses aspects the of sustainability school light analysis, characteristics such as theof a daily new intensityskylight type of high when school designing. buildings [21], the impact of glazing and window configuration on comfort andIn the energy case of effi windowciency [ 22structures,], daylight adjustments levels in classrooms are important adjacent to ensure to covered the lowest and exposed possible courtyards economic undercost of clearimproving skies [ the23], physical ways of conditions using light of in the Portuguese indoor environment school buildings, of school and buildings the perception [27]. Optimal of user comfortconditions [24 ].of the indoor climate at school can be designed by modeling the physical characteristics of theIt indoor is possible environment, to design anincluding integrated daylight daylight [28]. system, a combination of top and side lighting in the classroom,The orientation using theof the DaySim classroom simulation to the toolcardinal [25]. influences When creating the results the architecture of such modeling. of the school It is building,always necessary it is possible to seek to usea compromise simulation between tools when daylight designing and daylight.heat gain Inin somesummer schools [29]. itIt is alsoalso possibleimportant to to consider optimize top the lighting. design For of example,the school [26 bu] assessesilding geometry the sustainability in terms of characteristics daylight and of energy a new skylightefficiency type in winter when designing.[30]. It all depends on different daylighting techniques, depending on the climate (latitude)In the and case various of window complex structures, shading adjustments systems [31]. are importantThis is describe to ensured in a the project lowest to possible assess the economic energy costefficiency of improving and comfort the physical of school conditions buildings of the [32]. indoor The environment principles and of school implem buildingsentation [27 of]. daylight Optimal conditionssystems in ofclassrooms, the indoor climatein the field at school of energy can be ma designednagement, by modeling with the theimpact physical of noise characteristics from urban of thetransport indoor and environment, transport facilities including are daylight outlined [28 in]. [33]. For the overall assessment of the quality of the environmentThe orientation in the auditoriums of the classroom of the touniversity the cardinal building influences [34], the the relationship results of suchbetween modeling. the physical It is alwaysconditions necessary of the toschool seek abuilding compromise and betweenthe orga daylightnizational and commitment heat gain in according summer [29 to]. teachers’ It is also importantperception to[35] optimize can be taken the design into account. of the school building geometry in terms of daylight and energy efficiencyLast but in winter not least, [30]. this It all affects depends the health on diff erentand co daylightingmfort of students. techniques, Such depending an impact on on the the climate health (latitude)of schoolchildren and various in complex54 classes shading of 21 systems Dutch [31school]. This buildings is described was in apublished project to in assess Building the energy and eEnvironmentfficiency and comfort[36]. A comparative of school buildings study [of32 comfort]. The principles indicators and for implementation school buildings of daylightin sustainability systems inmethodologies classrooms, in in the the field Amazon of energy and management, South-East Braz withilian the impactregions of was noise also from conducted urban transport [37]. Here, and transportoptimum facilitiesglazing areconfigurations outlined in [for33]. visual For the performance overall assessment are very of important the quality [38]. of the If these environment proposals in thedo not auditoriums meet the requirements, of the university additional building daylight [34], the methods relationship should between be used the as physical a tool to conditions improve the of theprovision school of building daylight and in theexisting organizational education commitmentareas [39]. according to teachers’ perception [35] can be taken into account. Sustainability 2020, 12, 5046 4 of 24

Last but not least, this affects the health and comfort of students. Such an impact on the health of schoolchildren in 54 classes of 21 Dutch school buildings was published in Building and Environment [36]. A comparative study of comfort indicators for school buildings in sustainability methodologies in the Amazon and South-East Brazilian regions was also conducted [37]. Here, optimum glazing configurations for visual performance are very important [38]. If these proposals do not meet the requirements, additional daylight methods should be used as a tool to improve the provision of daylight in existing education areas [39]. Currently, the focus is on intelligent methods of managing intelligent daylighting using artificial neural networks [40]. Given the higher demands on cooling compared to heating, emphasis is placed on reducing the energy efficiency of the school building in a hot environment [41] as well as the optimum window to wall ratio. Part of this work also deals with this issue. At present, attention is paid to the shading of transparent surfaces and also to the design of dynamic façade elements. The effect of two motion types on solar transmittance and daylight on dynamic facades is found in [42]. The impact of building accumulation in energy-efficient school buildings is significant [43]. One of the newest articles on classrooms is “Studying the Light Environment with the Phenomenon of Redirection of Daylight Prisms in Classrooms” published in Indoor and Build Environment [44]. K. Kondas dealt with the lighting of the attic space and ideas of designing new lighting technical standards in the laboratories of the Institute of Civil Engineering and Architecture of the Slovak Academy of Sciences, under the leadership of Dr. Darula [45]. The authors of [46,47] also dealt with the properties of sloping windows, i.e., roof windows, as well as the transmission of sunlight through the windows and the optical properties of glazing systems [46,47]. Pitched roofs have insufficient heat accumulation, which results in overheating in the attic space [48]. Skylights also create visual discomfort. The authors of this article have addressed similar issues in the past [49–51]. Computational procedures, needed to determine the lighting conditions in the outdoor environment, are included in the literature [52,53]. Recent research from 2020 examining daylight levels in terms of functional needs is described in [54]. In source [55], there is information about dimming daylight lighting through interior shading devices and the effects on the energy performance of buildings. Several authors deal with the overheating of school buildings in the summer. An analysis of summer overheating in an elementary school building is shown in [56]. There are several regulations for determining suitable temperatures for different rooms [57,58]. It can be said that these are different in each country. Many literary sources deal with various problems of overheating. Problems with indoor temperatures in new buildings, retrofitted and existing British dwellings are reported [59]. Problems related to the summer season in the UK are reported in several articles [60–62]. Overheating caused by passive solar elements in Tunisia is demonstrated in [63]. The use of phase change materials [64], shielding devices [65], and heat adaptation in hot and humid outdoor conditions [66] have also been demonstrated. In the next part of the article, the authors would like to expand this knowledge by focusing on the current assessment of daylight and overheating of classes in the attic.

2. Materials and Methods The subject of the paper is a classroom located in a school building. The school is in the northern part of Kosice, in Slovakia (see Figure 5). Although this is not a custom, the classroom is located in the attic. The intention behind this was to expand the teaching space and the reconstruct the attic, creating new possibilities. Due to the fact that there are roof windows in the attic, there is excessive lighting and the possibility of glare. The subject, goal and methodology of the research can be seen in Figure3. Sustainability 2020, 12, x FOR PEER REVIEW 5 of 24 Sustainability 2020, 12, 5046 5 of 24

Creation of an optimal indoor climate of the classroom in the attic space in terms of daylight and overheating in summer

Optimal values Optimal values DFaverage, DFmin (normed) θai,max θai,max,N (normed)

Calculation only with roof windows with Calculation with roof and vertical strip of varying windows area combined windows (varying windows area)

Choice of solution variants with changing WFR and WWR values (equations 7 and 8)

Boundary conditions for simulations— Boundary conditions for simulations— light climate indoor thermal climate in summer

Selection of a suitable period for Selection of an unfavorable period, the measurement uniform outdoor highest outdoor temperature θae, max illumination approximately in summer 5500–7000 lx

Illumination measurement in situ Preparation of summer forecast (June, July 2020) data year IWEC

Evaluation of daylighting in a cloudy sky Evaluation of overheating in summer

Input data for evaluation, climatic data, description of building structures, roof, wall, windows, partitions

Choice of classroom in the attic with combined lighting (roof windows, windows in vertical position)

Figure 3. The subject, goal and methodology of the research. Figure 3. The subject, goal and methodology of the research.

TheThe aim aim is is to to find find the the optimal optimal ratioratio ofof roofroof window area area to to floor floor ar areaea (WFR), (WFR), or or the the ratio ratio of ofroof roof windowwindow area area to to surrounding surrounding wall wall areaarea (WWR).(WWR). This WFR or or WWR WWR ratio ratio affects affects the the level level ofof daylight, daylight, a reduction in the possibility of overheating but also a reduction in the level of glare. a reduction in the possibility of overheating but also a reduction in the level of glare. The methodology is focused on in-situ measurements, calculations, the confrontation of The methodology is focused on in-situ measurements, calculations, the confrontation of measured measured and calculated facts, simulation of the whole process of classroom lighting, and prediction and calculated facts, simulation of the whole process of classroom lighting, and prediction of overheating. of overheating. The tested classrooms are illuminated by side windows and roof windows. As The tested classrooms are illuminated by side windows and roof windows. As already mentioned, already mentioned, in this article, the following methodology is applied: in this article, the following methodology is applied: . Measurement of daylight value, Daylight Factor; .Measurement Prediction ofof daylightsummer value,overheating; Daylight Factor; .Prediction Calculated of summer on the basis overheating; of simulation tools based on measured or predicted data; Calculated on the basis of simulation tools based on measured or predicted data; Search for optimization of indoor light and thermal climate. Sustainability 20202020,, 1212,, 5046x FOR PEER REVIEW 66 of of 24

Further measurements and calculations are performed according to WFR and WWR factors, whichIn express this study, the four ratio design of the variants area of were the tested:windows the to basic the modelfloor area (real or situation), to the area a model of the without walls roof(Formulas windows, (7) and and (8)). two models with roof windows with diﬀerent conﬁgurations (see Figure4).

(a) variant 0—real, basic model (b) variant 1—without roof windows

Figure 4. Schematic modelsmodels descriptions, descriptions, variants variants 0 and 0 and 1, variants 1, variants 2 and 2 3 (roofand 3 view (roof from view above, from theabove, area the of area the roof of the windows roof windows is highlighted). is highlighted).

2.1. DaylightFigure4 aMetrics shows the current situation, (b) shows the illumination only using the strips of the associated windows in a vertical plane (without the roof windows). Configuration (c) shows the Daylighting on the working plane in oriented attic classroom under overcast and clear sky was illumination only using skylights in one plane next to each other, and (d) shows the illumination by determined. skylights in two planes. The mentioned configurations were chosen only on the basis of the design The investigation of the effects of direct sunlight and diffuse light on the size of the windows in possibilities of the classroom in the attic space. the attic was carried out using a simulation program Velux Daylight Visualizer 3. It is a simple tool Further measurements and calculations are performed according to WFR and WWR factors, for designing and analyzing daylight under various standard conditions. It is designed to support which express the ratio of the area of the windows to the floor area or to the area of the walls the use of daylight in buildings and to help predict and document daylight and the appearance of the (Formulas (7) and (8)). space before the construction project. The simulation program offers many outputs: surface 2.1.brightness, Daylight illuminance Metrics values, and the distribution of the daylight factor on the reference plane as well as the animation of daylight/sunlight. Calculation of all radiations, globally, direct and scattered, Daylighting on the working plane in oriented attic classroom under overcast and clear sky at solar altitude on the ground γ, by the diffusion ratio Evd/Evoh and the luminous turbidity factor T wasused, determined. can usually be expressed as [52,53]: The investigation of the effects of direct sunlight and diffuse light on the size of the windows in 𝐸 =𝐸 +𝐸 (𝑙𝑥) the attic was carried out using a simulation, program, Velux Daylight Visualizer 3. It is a simple tool(1) for designingwhere and analyzing daylight under various standard conditions. It is designed to support the use of daylight in buildings and to help predict and document daylight and the appearance of the 𝐸 —is the global external horizontal illuminance [lx]; space, before the construction project. The simulation program offers many outputs: surface brightness, 𝐸 —is the direct external illuminance, recalculated on the horizontal plane [lx]; illuminance, values, and the distribution of the daylight factor on the reference plane as well as the 𝐸 —is the diffuse external horizontal illuminance [lx]. animation of daylight/sunlight. Calculation of all radiations, globally, direct and scattered, at solar altitudeTo calculate on the ground the directγ, bycomponent the diffusion of the ratio externalEvd/E illuminance,voh and the luminousthe next ex turbidityponential factor formula,T used, also canrecommended usually be expressedby [52,53], ascan [52 be,53 used:]: Ev,g = Ev,s + Evd(lx) (1) 𝐸, =𝐸.𝑒^(−𝛼.𝑚.𝑇)(𝑙𝑥) (2) where where

Ev,g—is the global external horizontal illuminance [lx]; 𝐸—is the extraterrestrial illuminance expressed on the horizontal plane [lx]; 𝛼—is the luminous extinction coefficient [-]; Sustainability 2020, 12, 5046 7 of 24

Ev,s—is the direct external illuminance, recalculated on the horizontal plane [lx]; Evd—is the diﬀuse external horizontal illuminance [lx].

To calculate the direct component of the external illuminance, the next exponential formula, also recommended by [52,53], can be used:

Ev,s = E eˆ( αV m TV)(lx) (2) voh · − · · where

Evoh—is the extraterrestrial illuminance expressed on the horizontal plane [lx]; αV—is the luminous extinction coeﬃcient [-]; m—is the optical relative air mass of the atmosphere [-];

TV—is the luminous turbidity factor (TV = 4 representing ISO/CIE Type 12 clear sky standard conditions and the environment in common cities areas).

The north-facing classroom was selected to demonstrate the optimization of interior lighting depending on the size of the windows in the roof plane. Direct radiation only falls into a certain part of the room. If we want to determine the total internal light intensity at the table plane, we must calculate the direct light intensity by the indirect internal light intensity obtained using a computer program. The direct illumination was calculated from the external direct illumination reduced by the loss of light transmission through the glazing material and impurities on the inner and outer glazing surfaces. The formula for calculating the contribution of sunlight to the internal light intensity Ei on the working plane for orientation is as follows: ( ) τs,ϕ Ev,si = Ev,s τs,nor(τz,e τz,i)(lx) (3) τs,nor ·

where

τz,ϕ—is the factor of light transmission at angle ϕ from the window normal [-]; τs,nor—is the factor of light transmission in normal direction [-]; τz,e—is the factor of dirt reduction for the outer side of the glass [-]; τz,i—is the factor of dirt reduction for the inner side of the glass [-].

The following daylight metrics are used in the study: lighting, daylight factor, and uniformity. Illuminance is the amount of light falling on a surface per unit area, measured in lux. The recommended average value is 500 lux.

∅ lm E = (lx) (4) A → m2 → where

∅—is luminous ﬂux [lm]; A—is area [m2].

Daylight factor DF (%) is the simplest and the most common metric to quantity the daylight allowed by a window. Minimum and average daylight factor for classroom has been deﬁned as 1.5% and 5%, respectively [16,17]. E DF = internal 100 (%) (5) Eexternal · where

Einternal—illuminance of internal horizontal plane (lx); Sustainability 2020, 12, 5046 8 of 24

Eexternal—illuminance of external horizontal plane (lx). Uniformity—is deﬁned as the ratio of the minimum DF to the average DF within the space. Standards require a uniformity of 0.2.

DFmin U0 = ( ) (6) DFaverage −

where

DFmin—is minimum of daylight factor [%], DFaverage—is average value of daylight factor [%]. Window–Floor Ratio A WFR = WINDOW 100(%) (7) AFLOOR · Window–Wall Ratio A WWR = WINDOW 100(%) (8) AWALL · where

2 AWINDOW—is area of windows [m ]; 2 AFLOOR—is area of ﬂoor [m ]; 2 AWALL—is area of walls [m ].

2.2. Summer Overheating Let us take an example from measurements made in the attic when the temperature was measured at more than + 40.0 ◦C. The roof (according to the official methodology) heated the interior to a passive level only with low intensity. However, when the sun heats the dark roof to 80 ◦C, the actual influx of heat into the interior is significantly higher. The room air temperature will be higher than the outside temperature. According to the Stefan–Boltzmann law, the radiant heat flux between a dark roof heated by the sun (80 ◦C) and safety waterproofing (40 C) is 880 550 = 230 W/m2 (for comparison: solar radiation intensity) is ◦ − about 1000 W/m2). Just as the outside air cannot cool the glazed roof to “its” temperature by flow, the air flow in the gap cannot cool the safety waterproofing of the roof to the outside air temperature. Thus, in practice, the safety waterproofing is rapidly heated to a temperature of about 60 ◦C. The optimal indoor temperature for a person depends on individual needs and other factors. According to these facts, the standard parameters of the indoor climate for classrooms are:

In summer—from + 24 to 28 C; • ◦ In winter—from + 22 to 24 C. • ◦ The regulation states the requirement should exceed the standard indoor air temperature (27 ◦C in non-production areas) in the Czech Republic. Exceeding this value is by maximum of 2 ◦C for a maximum of 2 h is standardly permitted, though only for residential buildings and with the consent of the investor. Air conditioning, which is highly debatable from a health point of view, will help reduce the temperature in the attic. While cooling the room protects the body from overheating and subsequent nausea and exhaustion, on the other hand, the temperature in the air conditioner should be set to a maximum of six degrees below the outside temperature. Therefore, if it is 35 degrees, it is recommended to set the internal temperature to 29 degrees from a health point of view. Computer programs for the energy assessment of buildings have long been one of the important tools that can facilitate the work of designing optimizations of project solutions. They can be divided into two main groups: programs using correlation methods and simulation programs. While correlation Sustainability 2020, 12, 5046 9 of 24 methods work with average data over a long period of time, the simulation works with dynamically changing boundary conditions, as it is in real life. Simulation methods are based on solving more or less accurate physical models in short time intervals. One of the ﬁrst widely used joint air ventilation models comes from the Lawrence Berkeley National Laboratories. This model, like others in its time, used the relationship between air exchange and the pressure diﬀerence on the building envelope. Its current form is as follows (ASHRAE 2005): q Ae 2 V = ct ( θ θa,e) + cv v (9) 1000 · a,i − · where

V—is the volume of infiltrated air [m3 /s]; 2 Ae—is the effective area of the orifice through which air can flow [m ]; ct and cv are the outflow factors for the pressure difference caused by gravity and wind.

The effluent coefficients are taken from the table. These simple equations are suitable for the first estimate in a simple space (one zone) with an opening with bidirectional air flow. However, calculating the natural ventilation of interconnected spaces, where a much more complex airflow is created, requires more complex equations, or the use of a simulation tool such as multi-zone network models or CFD models. Multi-zone network models solve the equation of conservation of mass, energy and concentration based on several approximations. The most commonly used types of multi-zone network models use Bernoulli’s equations. Perfect mixing of the air within the zone is assumed. The model consists of nodal points and connections (airflow components) that create airflow in one direction for small openings, or both in the case of large ones. Then, in a multi-zone network model, the mass, energy and concentration conservation equations for each zone are solved in order to obtain a solution for specific boundary conditions. This is essential when selecting and using weather data to simulate a proper understanding of the nature climate data. This fact shows considerable variability within individual hours, with the following characteristics:

- The air temperature changes relatively slowly, rarely rising or falling by more than a few degrees in an hour; - In the case of sunlight, large and rapid changes in values can occur within a few minutes. This is due to the very sensitive connection to cloudy skies; - The wind speed can take on multiple values in a few minutes. The record of this quantity is very variable, although it is possible to notice a certain character of increase or decrease during the day. Simplifying such a course of climatic factors into hourly values requires aggregation, which must necessarily omit a large number of sometimes very diﬀerent records.

As for the number of hours the window is open, it increases signiﬁcantly from the ambient temperature. Statistics show that at an outside air temperature of 20 ◦C, the windows open for 6 h, at 26 ◦C for 13 h. The increase in the opening time of the tv (h) window here has an almost linear dependence on the outside air temperature θa,e (◦C) according to the relation:

tv = 0.44 θa,e + 0.62 (10) · where tv—is opening time of windows [h]; θa,e—is outside air temperature [◦C]. Sustainability 2020, 12, 5046 10 of 24

3. Case Study—Classroom in Attic of School Building The school building that was elected is located in the city of Kosice, north (see Figure4a,b). The proposed attic of the school used in the case study is located on the fourth ﬂoor of this selected building.

3.1. Context The situation of the selected case study building as well as views of the building from the exterior side and classroom spaces in the interior of the attic space can be found in Figure5. Sustainability 2020, 12, x FOR PEER REVIEW 10 of 24

(a) (b)

(e) (f)

FigureFigure 5. Situation, 5. Situation, external external and and internal internal view viewof of selectedselected school school building building and and selected selected classroom classroom in in the attic.the attic. (a,b )(a the,b) situationthe situation of aof casea case study; study; ( c()c) external external view of of school school building; building; (d) (internald) internal view view of of coridor;coridor; (e) internal (e) internal view view of roofof roof windows; windows; (f ()f) internal internal viewview of of school school room. room.

3.2. Daylight Rating Measurements were performed in a classroom in school building in Kosice (see Figure 5e,f). A fourth floor north facing tested room was selected with interior dimensions 10.77 × 4.36 m × 3.03 m, and the height of the parapet was 900 mm. The area of the room was 46.96 m2. The side windows had dimensions of 900 mm × 860 mm, and the roof windows of 780 mm × 1180 mm. The window–wall ratio ranged from 0.05 (without roof windows) to 0.12 (see Table 1 and Figure 6). Sustainability 2020, 12, x FOR PEER REVIEW 11 of 24

The fenestration systems are created using plastic frames and double glass. For the calculations, the following coefficients were considered: transmittance coefficient 0.8, maintenance factor of glazing on the exterior surface 0.9, maintenance factor of glazing on the interior surface 0.85, reflectance factor of ground 0.15 (dark ground). The walls and the ceiling were white in color with a reflectance factor of 0.7, and the floor had a reflectance factor of 0.45. The working plane was 0.80 m high (desk height). Light loss coefficient due to window Sustainability 2020, 12, 5046 11 of 24 construction was τ = 0.64. The neighboring objects at a distance did not shade the room. The classroom is usually occupied from 8:00 a.m. to 17:00 p.m. 3.2. DaylightThe room Rating being used for medium-precision activity was classified in III. Light—technical class. With the given lighting system, at the critical point of the functional place on the Measurements were performed in a classroom in school building in Kosice (see Figure5e,f). horizontal plane, the following values are required: minimum standard value of daylight factor A fourth ﬂoor north facing tested room was selected with interior dimensions 10.77 4.36 m 3.03 m, DFmin = 1.5%, average daylight factor Daverage = 5%, and uniformity of the illumination× more× than and the height of the parapet was 900 mm. The area of the room was 46.96 m2. The side windows had 0.3 for a given visual task [16,17]. dimensions of 900 mm 860 mm, and the roof windows of 780 mm 1180 mm. The window–wall × × ratio ranged from 0.05Table (without 1. Window–Wall roof windows) Ratio WRW to 0.12 and (see Wi Tablendow–Floor1 and FigureRatio WFR.6).

Table 1. Window–WallArea (m Ratio2) WRWArea and Window–Floor (m2) Ratio WFR. Area (m2) Side Area (m2) WWR WFR Roof Windows (Side + AreaWindows (m2) Side Area (m2) Area (m2) Areawall (m2) WWR(%) WFR(%) Windows RoofLights Windows (SideRoof)+ Roof) Wall (%) (%) VariantVariant 0 9.3 9.3 9.20 9.20 18.5 18.5 171 171 11 11 39 39 VariantVariant 1 9.3 9.3 - - 9.3 9.3 171 171 5 5 20 20 VariantVariant 2 9.3 9.3 5.50 5.50 14.8 14.8 171 171 9 9 32 32 Variant 3 9.3 11.0 20.3 171 12 43 Variant 3 9.3 11.0 20.3 171 12 43

0.43 0.39 0.4 WWR 0.32 0.3

0.2 0.2 0.11 0.12 0.09 WWR and WFR (-) WFR and WWR 0.1 0.05

0 variant 0 variant 1 variant 2 variant 3

Figure 6.6. DeterminationDetermination of of coefficient coeﬃcient of window–w window–wallall ratio and window–ﬂoorwindow–floor ratio WWRWWR/100,/100, WFRWFR/100./100.

TheAn illumination fenestration systemsof minimum are created 300 lx usingis recomme plasticnded frames for and most double of the glass. room For area, the calculations,meeting the thetarget following climate-based coefficients daylight were factor considered: and 500 transmittance lx for the areas coe wherefficient productive 0.8, maintenance work is factor performed. of glazing On onthe the selected exterior day, surface the 0.9,value maintenance of the outside factor light of glazing ranged on from the interior5500–7000 surface lx in 0.85, February reflectance this factoryear. ofMeasurement ground 0.15 was (dark performed ground). Theat nine walls control and the points ceiling simultaneously were white in with color two with lux a reflectance meters (see factor Figure of 0.7,7). An and exterior the floor horizontal had a reflectance illumination factor of 5000 of 0.45. lx was The considered working plane for the was simulation 0.80 m high program (desk height).[16,17]. Light loss coefficient due to window construction was τ = 0.64. The neighboring objects at a distance did not shade the room. The classroom is usually occupied from 8:00 a.m. to 17:00 p.m. The room being used for medium-precision activity was classified in III. Light—technical class. With the given lighting system, at the critical point of the functional place on the horizontal plane, the following values are required: minimum standard value of daylight factor DFmin = 1.5%, average daylight factor Daverage = 5%, and uniformity of the illumination more than 0.3 for a given visual task [16,17]. An illumination of minimum 300 lx is recommended for most of the room area, meeting the target climate-based daylight factor and 500 lx for the areas where productive work is performed. On the selected day, the value of the outside light ranged from 5500–7000 lx in February this year. Measurement was performed at nine control points simultaneously with two lux meters (see Figure7). An exterior horizontal illumination of 5000 lx was considered for the simulation program [16,17]. Sustainability 2020, 12, 5046 12 of 24 Sustainability 2020, 12, x FOR PEER REVIEW 12 of 24

Figure 7.Figure Situation—floorplan 7. Situation—ﬂoorplan of classroom,classroom, measured measured points. points. 3.3. Daylight Measurement and Daylight Simulation 3.3. Daylight MeasurementDaylight measurements and Daylight were Simulation performed according to the Slovak standard “Measurements of day lighting.” The instruments used were two data loggers, ALMEMO 2690-10A, and illuminance sensor Daylight ALMEMOmeasurements FLA 623VL were with the performed production number accordin 15061543,g to with the an Slovak accuracy ofstandard 5%. “Measurements of day lighting.” TheDaylighting instruments simulations used were were performed two da withta Veluxloggers, windows ALMEMO with the model 2690-10A, of the tested and illuminance classroom and 3 variants. The measurement was performed similarly to the method of the authors sensor ALMEMOin [54 ],FLA who performed623VL with measurements the production of illuminance number (lx) in various 15061543, historic buildings with in an situ. accuracy The results of 5%. Daylightingof DF simulations and other results were can be performed seen in Figures with 9 and Velux 10. The resultswindows of the measuredwith the values model and of the tested classroom andsimulated 3 variants. values The of DF measurement (in points according was to Figure performed7) can be seen similarly in Table2 andto the Figure method8. of the authors in [54], who performedTable 2.measurementsResults of DF measured of and illuminance simulated values—variant (lx) in 0 (real various situation), historic validation of buildings model. in situ. The results of DF and other results canDaylight be seen Factor (%)—Measuredin Figures Values9 and in the10. Points The results of the measured values and simulated values of PointDF (in points 1according to 2 Figure 7) can 3 be seen Uin0 (-) Table 2 and Figure 8. A 12.2 5.4 2.3 B 12.7 5.0 2.8 Table 2. Results of DF measuredC and10.6 simulated values—variant 3.1 1.8 0 (real situation), validation of model. 0.29 DaylightDaylight Factor Factor (%)—Measur (%)—Simulateded Values values in the in Points the points Validation—According to Boundary Conditions Obtained from the Measurement Point 1 2 3 U0 (-) 1 2 3 U0 (-) A 12.2 5.4 2.3 A 12.3 4.9 2.0 B B 12.7 12.15.0 4.7 2.5 2.8 C 9.7 2.8 1.5 C 10.6 3.1 1.8 0.26 0.29 Daylight Factor (%)—Simulated values in the points Validation—according to boundary conditions obtained from the measurement 1 2 3 U0 (-) A 12.3 4.9 2.0 B 12.1 4.7 2.5 C 9.7 2.8 1.5 0.26 Sustainability 2020, 12, 5046 13 of 24 Sustainability 2020, 12, x FOR PEER REVIEW 13 of 24

Sustainability 2020, 12, x FOR PEER REVIEW 13 of 24 7 6.53 5.78 6 7 6.53 5555 5 6 5.78 4.31 5555 4 5 4.31 % 4 3 %

Daylight Factor Daylight 2.1 3 2 Daylight Factor Daylight 1.52.1 1.5 1.5 1.5 2 1.5 1.5 1.5 1.5 1 1 0.2 0.1 0.16 0.24 0 0.2 0.1 0.16 0.24 basic variant 1 variant 2 variant 3 variant0 basic variant 1 variant 2 variant 3 variant DF min DF average standardized min standardized average DF min DF average standardized min standardized average

Figure 8. Comparison of DF calculated and standardized values. Figure 8. Comparison of DF calculated and standardized values.

DiDifferencesﬀerencesDifferences betweenbetween between variantsvariants variants with with with roof roof roof windows windows windows and andand without without roof roof roof windows windows windows can can canbe beseen be seen seen in Table in in Table Table 3. 3. 3. Table 3. Diﬀerences between variants with and without roof windows.

TableTable 3. Differences3. DifferencesDF between between variantsvariantsDF withwith and and withoutDF without roof roof windows. windows.U DF min max average 0 (%) (%) (%) (-) DFDFminmin DFmax DFDFaverageaverage U0 U0 DF DF Variant 0(%) 50 47(%) 64(%) 67 (-) (%) (%) (%) − (-) VariantVariant Variant0 0 1 50primary 50 primary 47 primary 64 64 primary−67 −67 VariantVariant 1 2primary 38 primary 41 primary 51 25primary − Variant Variant1 3primary 58 primary 48 68primary 25 primary Variant 2 38 41 51 − −25 VariantVariant 2 3 38 58 4148 68 51 −25 −25 Variant 3 58 48 68 −25 The results of the variant calculations of the daylight factor DF can be seen in Figure9. The results of the variant calculations of the daylight factor DF can be seen in Figure 9. The results of the variant calculations of the daylight factor DF can be seen in Figure 9.

Variant 0 Variant 1

Figure 9. Cont. Variant 0 Variant 1 Sustainability 2020, 12, 5046 14 of 24

Sustainability 2020, 12, x FOR PEER REVIEW 14 of 24 Sustainability 2020, 12, x FOR PEER REVIEW 14 of 24

Variant 2 Variant 3

Variant 2 Variant 3 FigureFigure 9. 9.Results Results of of daylightdaylight factor DF DF (%) (%) for for chosen chosen variants. variants. Figure 9. Results of daylight factor DF (%) for chosen variants. The resultsThe results of luminance of luminance (brightness) (brightness) for for considered considered variantsvariants can be be seen seen in in Figure Figure 10. 10 The. The glare glare of the eyesof the isThe noteyes results high is not in of high the luminance view in the of view(brightnes the window of thes) windowfor glass considered from glass the from variants classroom the canclassroom be in seen the cloudyin in the Figure cloudy sky. 10. The Thesky. brightness glare The 2 of thebrightnessof glazing the eyes is of is about thenot glazing high 279 cdin /is mthe about2 inview each 279 of case.cd/mthe window Thein each di ﬀglass erencescase. from The between differencesthe classroom the between brightness in the the cloudy ofbrightness the sky. background The of the background and the glazing are not large.2 and thebrightness glazing of are the not glazing large. is about 279 cd/m in each case. The differences between the brightness of the background and the glazing are not large.

Variant 0 Variant 1 Variant 0 Variant 1

Variant 2 Variant 3 Variant 2 Variant 3

Figure 10. Results of luminance cd/m2. Sustainability 2020, 12, x FOR PEER REVIEW 15 of 24

Figure 10. Results of luminance cd/m2. Sustainability 2020, 12, 5046 15 of 24 Figure 11 shows the situation of how the DF factor changes depending on the individual variants. In Figure 11a, the decreasing of the DF factor as a function of the distance from the windows, Figure 11 shows the situation of how the DF factor changes depending on the individual variants. which are vertical, i.e., a distance from the perimeter wall, can be seen. Option 3 is the best, and it In Figure 11a, the decreasing of the DF factor as a function of the distance from the windows, which should be noted that all situations are better with respect to the minimum value of the DF factor. are vertical, i.e., a distance from the perimeter wall, can be seen. Option 3 is the best, and it should There will be a much higher DF value at all points. Even at the farthest points from the perimeter be noted that all situations are better with respect to the minimum value of the DF factor. There will wall, there is a sufficient degree of illumination, unless the DF drops sharply to the minimum value. be a much higher DF value at all points. Even at the farthest points from the perimeter wall, there DF values can be found in parts (b) and (c) if we move the roof windows closer to the top of the is a suﬃcient degree of illumination, unless the DF drops sharply to the minimum value. DF values sloping roof; i.e. they are shifted by a distance of 0.5 m; 1.0 m; 1.5 m; 2.0 m and 2.5 m in variants 2 can be found in parts (b) and (c) if we move the roof windows closer to the top of the sloping roof; (part b) and in variants 3 (part c). It can be clearly seen that the DF value decreases at the perimeter i.e., they are shifted by a distance of 0.5 m; 1.0 m; 1.5 m; 2.0 m and 2.5 m in variants 2 (part b) and in wall, but vice versa at the top of the roof, i.e. in distant places from the perimeter wall DF grows. variants 3 (part c). It can be clearly seen that the DF value decreases at the perimeter wall, but vice Here, too, it is necessary to state that it is necessary to find a compromise and the geometry of the versa at the top of the roof, i.e., in distant places from the perimeter wall DF grows. Here, too, it is shape of the roof, to adjust the size of the windows so that we may approach the uniform lighting in necessary to state that it is necessary to ﬁnd a compromise and the geometry of the shape of the roof, the classroom. The higher the windows, the more discomfort there is, and it is necessary to pay to adjust the size of the windows so that we may approach the uniform lighting in the classroom. attention to glare reduction using internal shading devices [55]. The higher the windows, the more discomfort there is, and it is necessary to pay attention to glare It is also important to defend against high heat input in the summer. The heat gains are such reduction using internal shading devices [55]. that internal discomfort arises.

(a) (b) (a) Differences DF for variants 0 to 3 of the roof windows in distance from peripheral wall. (b) Differences DF for variant 2 in points from the perimeter wall if the roof windows move from the peripheral wall 0.2, 0.5, 1.0, 1.5, 2.0, 2.5 meters. (c) Differences DF for variant 3 in points from the perimeter wall if the roof windows move from the perimeter wall 0.2, 0.5, 1.0, 1.5, 2.0 meters.

(c)

Figure 11. Dependencies of changes of the daylight factor (DF) (%) in different diﬀerent alternatives to the use of roof windows.

3.4. PredictionIt is also importantof Indoor Climate to defend in Summer against Period high heat input in the summer. The heat gains are such that internal discomfort arises. We addressed the issue of overheating in the summer not only for all considered variants 3.4.(0,1,2,3), Prediction but also of Indoor for cases Climate without in Summer a vertical Period window strip (Figure 12) and for variable sizes of windows and variable distances from the window sill (peripheral wall). As only informative measurementWe addressed was performed the issue of in overheating the attic space, in the the summer situation not can only only for allbe consideredconsidered variants as a prediction. (0,1,2,3), butThe alsomeasurement for cases without of daylight a vertical was performed window strip in February (Figure 12 under) and a for cloudy variable sky. sizes There of was windows excessive and variablelighting during distances thefrom measurements the window and sill also (peripheral during th wall).e simulations As only (not informative glare). It was measurement stated that was the performeddaylight will in be the fine, attic but space, it will the result situation in excessive can only heat be considered gains through as a prediction.the skylights The and measurement at the same oftime daylight through was the performed roof covering, in February which has under small a cloudy (not suitable) sky. There heat was accumulation. excessive lighting The evaluation during the of measurements and also during the simulations (not glare). It was stated that the daylight will be ﬁne, but it will result in excessive heat gains through the skylights and at the same time through the roof Sustainability 2020, 12, x FOR PEER REVIEW 17 of 24

Material/Layer Nr ρ c λ Thickness (from Outside to Inside) (kg/m³) (J/kgK) (W/mK) (m) 1 Cement lime Plaster 2000 850 1.2 0.01 2 Steel-Concrete slab 2300 850 1.6 0.25 3 Mineral Insulation Board 115 850 0.043 0.06 4 Air Layer 70 mm 1.3 1000 0.4 0.07 5 Oriented Strand Board 630 1400 0.13 0.02 6 Oriented Strand Board 630 1400 0.13 0.02

Table 7. Composition of the partition structure.

Material/Layer ρ c λ Thickness Nr (kg/m³) (J/kgK) (W/mK) (m) Sustainability 2020, 12,(from 5046 Outside to Inside) 16 of 24 1 Gypsum Board 850 850 0.2 0.013 Sustainability 22020 , Air 12, xLayer FOR PEER 120 REVIEWmm 1.3 1000 0.723 0.12 16 of 24 covering, which3 Mineral has small Insulation (not suitable) Board heat accumulation. 115 850 The evaluation 0.043 of the 0.04 overheating of thethe presentedoverheating4 buildingGypsum of the presented wasBoard realized building by the was simulation realiz 850ed toolby the WUFI 850 simulation Plus. Boundary 0.2tool WUFI conditions0.013 Plus. Boundary were consideredconditions were as for considered daylight—only as for the daylight—only date was changed. the date We was considered changed. the We warmest considered months the warmest of June andmonths JulyFrom 2020of Junethe according temperatures,and July to the2020 IWEC accordingyou forecast.can see to Thisthehow IW prediction theEC accumulationforecast. contains This “typical” capacityprediction weather manifests contains ﬁles, itself.“typical” suitable The forweathermaximum use in files, simulating temperature suitable energy for inuse the einﬃ ciencysimulatingoutdoor which environment energy can alsoefficiency beis usedreached which as a oncan prediction June also be19, ofused but people’s asinside a prediction thermalit is the sensations.ofmaximum people’s thermalOutdooruntil June sensations. temperatures, 20, there isOutdoor an globaleffect temperatur of solar the radiationaccumulationes, global and solar behavior indoor radiation temperature of the and envelope indoor over and temperature the its selected impact twooveron monthsthe the indoor selected can environment be two seen months in Figure of can the 13be attic.. seen in Figure 13. It can be seen from the above that the temperature maximum in the indoor environment of the classroom is reached on June 20 for Variant 0 (real situation) 39.20 °C; for Variant 1 (without roof windows) 31.58 °C; for Variant 2 (one row of windows) 37.01 °C; and for Variant 3 (two rows of windows) 40.19 °C. The difference between these variants is about 8 K. When the facade is oriented to the north, the effect of vertical windows on overheating in summer is irrelevant. Temperatures are simulated for individual variants—Variant (0), (2), (3) = (38.80 °C); (36.01 °C); and (40.10 °C). This means that without vertical windows, the resulting temperature in summer will be reduced by only about 0.5 K. Variant 2 (one strip of windows) seems (toa) bevariant most 0— suitable basic model for optimal (b) variant lighting 2—one and row small roof overheating. windows (c) variant 3—two rows roof windows

FigureFigure 12.12. Variants 0,0, 2,2, 33 onlyonly withwith roofroof windows,windows, withoutwithout aa verticalvertical one.one.

The analyzed time of maximum overheating was selected from 7 to 21 June 2020, which is 15 days. The composition of individual types of attic packaging structures can be seen in Tables 4–7 (three-zone model). It was a north-facing classroom, a corridor, and a south-facing classroom. Occupancy in the simulated zones was determined for 20 adults with easy work activity. Classrooms were staffed Monday through Friday from 7 a.m. to 6 p.m. with an hour-long break during lunch. Considering the expected occupancy, this would mean a large increase in CO2, which would be 750 ppm (1350 mg/m3), which is a lot. The air exchange rate was therefore set at 50 m3/h of fresh air per person. The IWEC weather limit was used to predict the simulation of the indoor climate in the Kosice Region for 2020. The simulation model prepared for this calculation was divided into three zones. There are two classrooms with north and south orientation and a corridor between of them, see Figures 4 and 12. The maximal internal superheat temperature must not exceed a value of 27 °C indoors according to prescription. The time period selected for the calculation represents the warmest weather, including days with high temperatures (day/night) combined with high sunlight.

Table 4. Composition of the structure—parapet masonry as a perimeter wall.

Material/Layer ρ c λ Thickness Nr (a) (b) (from Outside to Inside) (kg/m³) (J/kgK) (W/mK) (m) Figure 13. Results of summer overheating for variants 0 and 1 in 60 days from 1 June 2020 – 31 July 2020 Figure1 13. CementResults of lime summer Plaster overheating for variants 2000 0 and 1 in 850 60 days from 1.2 1 June 2020–31 0.02 July 2020 (simulated time) and in analyzed time 7 June – 21 June, 14 days. (simulated2 Solid time) Brick and in Masonry analyzed time 7 June–21 1900June, 14 days. 850 0.6 0.45 3 Mineral Insulation Board 115 850 0.043 0.1 The analyzed time of maximum overheating was selected from 7 to 21 June 2020, which is 15 days. 4 Air Layer 50 mm 1.3 1000 0.28 0.05 The composition5 Gypsum of individual Board types of attic packaging 850 structures 850 can be seen 0.2 in Tables 0.0134–7 (three-zone model). It was a north-facing classroom, a corridor, and a south-facing classroom. Occupancy in the simulated zones was determinedTable 5. for Composition 20 adults withof the easy roof workstructure. activity. Classrooms were staﬀed Monday through Friday from 7 a.m. to 6 p.m. with an hour-long break during lunch. Material/Layer Nr ρ c λ Thickness (from Outside to Inside) (kg/m³) (J/kgK) (W/mK) (m) 1 Roofing 2400 1000 0.5 0.0001 2 Air Layer 100 mm Low ventilated 1.3 1000 0.59 0.1 3 Mineral Insulation Board 113 850 0.040 0.18 4 Vapour retarder 130 2300 2.3 0.0001 5 Air Layer 50 mm 1.3 1000 0.28 0.05 6 Gypsum Board 850 850 0.2 0.013

Table 6. Composition of the ceiling structure. Sustainability 2020, 12, 5046 17 of 24

Table 4. Composition of the structure—parapet masonry as a perimeter wall.

Material/Layer % c λ Thickness Nr (from Outside to Inside) (kg/m3) (J/kgK) (W/mK) (m) 1 Cement lime Plaster 2000 850 1.2 0.02 2 Solid Brick Masonry 1900 850 0.6 0.45 3 Mineral Insulation Board 115 850 0.043 0.1 4 Air Layer 50 mm 1.3 1000 0.28 0.05 5 Gypsum Board 850 850 0.2 0.013

Table 5. Composition of the roof structure.

Material/Layer % c λ Thickness Nr (from Outside to Inside) (kg/m3) (J/kgK) (W/mK) (m) 1 Rooﬁng 2400 1000 0.5 0.0001 2 Air Layer 100 mm Low ventilated 1.3 1000 0.59 0.1 3 Mineral Insulation Board 113 850 0.040 0.18 4 Vapour retarder 130 2300 2.3 0.0001 5 Air Layer 50 mm 1.3 1000 0.28 0.05 6 Gypsum Board 850 850 0.2 0.013

Table 6. Composition of the ceiling structure.

Material/Layer % c λ Thickness Nr (from Outside to Inside) (kg/m3) (J/kgK) (W/mK) (m) 1 Cement lime Plaster 2000 850 1.2 0.01 2 Steel-Concrete slab 2300 850 1.6 0.25 3 Mineral Insulation Board 115 850 0.043 0.06 4 Air Layer 70 mm 1.3 1000 0.4 0.07 5 Oriented Strand Board 630 1400 0.13 0.02 6 Oriented Strand Board 630 1400 0.13 0.02

Table 7. Composition of the partition structure.

Material/Layer % c λ Thickness Nr (from Outside to Inside) (kg/m3) (J/kgK) (W/mK) (m) 1 Gypsum Board 850 850 0.2 0.013 2 Air Layer 120 mm 1.3 1000 0.723 0.12 3 Mineral Insulation Board 115 850 0.043 0.04 4 Gypsum Board 850 850 0.2 0.013

Considering the expected occupancy, this would mean a large increase in CO2, which would be 750 ppm (1350 mg/m3), which is a lot. The air exchange rate was therefore set at 50 m3/h of fresh air per person. The IWEC weather limit was used to predict the simulation of the indoor climate in the Kosice Region for 2020. The simulation model prepared for this calculation was divided into three zones. There are two classrooms with north and south orientation and a corridor between of them, see Figures4 and 12. The maximal internal superheat temperature must not exceed a value of 27 ◦C indoors according to prescription. The time period selected for the calculation represents the warmest weather, including days with high temperatures (day/night) combined with high sunlight. From the temperatures, you can see how the accumulation capacity manifests itself. The maximum temperature in the outdoor environment is reached on June 19, but inside it is the maximum until June 20, there is an eﬀect of the accumulation behavior of the envelope and its impact on the indoor environment of the attic. Sustainability 2020, 12, 5046 18 of 24

It can be seen from the above that the temperature maximum in the indoor environment of the classroom is reached on June 20 for Variant 0 (real situation) 39.20 ◦C; for Variant 1 (without roof Sustainabilitywindows) 2020 31.58, 12,◦ xC; FOR for PEER Variant REVIEW 2 (one row of windows) 37.01 ◦C; and for Variant 3 (two rows 18 of 24of windows) 40.19 ◦C. The diﬀerence between these variants is about 8 K. When the facade is( orienteda) to the north, the eﬀect of vertical windows(b on) overheating in summer Figureis irrelevant. 13. Results Temperatures of summer overheating are simulated for forvariants individual 0 and 1 variants—Variant in 60 days from 1 (0),June (2), 2020 (3) – =31(38.80 July 2020◦C); (simulated(36.01 ◦C); time) and and (40.10 in analyzed◦C). This time means 7 June that – 21 without June, 14 days. vertical windows, the resulting temperature in summer will be reduced by only about 0.5 K. Variant 2 (one strip of windows) seems to be most suitable for optimalThe results lighting for the and considered small overheating. two months are shown in Figure 13a, and those for the selected 15-dayThe interval results for(7–21 the June considered 2020) are two shown months in are Figure shown 13b. in FigureTaking 13 intoa, and account those forthe the boundary selected conditions15-day interval as well (7–21 as Juneadjusting 2020) arethe shownair exchange in Figure to 13n b.= 6 Taking h−1 and into orientation account the to boundarythe cardinal conditions south– 1 north.as well as adjusting the air exchange to n = 6 h− and orientation to the cardinal south–north. TheThe calculation calculation of of the the need need for for air air cooling cooling was was performed performed (see (see Figure Figure 14)14) to to achieve achieve the the optimal optimal (permissible)(permissible) indoorindoor air air temperature temperature of 27of ◦27C in°C the in summerthe summer for the for analyzed the analyzed basic simulation basic simulation variants variants(according (according to Figure 4to). Figure Based on4). the Based calculation, on the calculation, it can be stated it can that be reducing stated that the areareducing of roof the windows area of roofto the windows visual optimum to the visual (Variant optimu 2)m will (Variant reduce 2) the will need reduce for suppliedthe need energyfor supplied for cooling energy by for a cooling quarter bycompared a quarter to compared the original to solutionthe original (Variant solution 0). (Variant 0).

Figure 14. The cooling demand calculation for basic variants with indoor temperature setting on 27 C. Figure 14. The cooling demand calculation for basic variants with indoor temperature setting on ◦27 4. Discussion°C.

4. DiscussionThis case study examines the effect of the size of skylights to maximize the use of daylight in an attic. It is used to find solutions to maximize the use of daylight, reduce the cost of artificial lighting,This andcase minimizestudy examines overheating. the effect Real of measurementsthe size of skylights and a to series maximize of computer the use simulations of daylight usingin an attic.a simulation It is used tool to fromfind solutions Velux Daylight to maximize Visualizer the use 3 and of WUFIdaylight, plus reduce served the as cost tools of for artificial determining lighting, the andsize ofminimize windows. overheating. Real measurements and a series of computer simulations using a simulationThe results tool from were Velux evaluated Daylight in Visualizer terms of daylight 3 and WUFI and plus classroom served lightingas tools for levels determining according the to sizedaylight of windows. standards. TheThe daylightresults were factor evaluated is the basis in for terms assessing of daylight the illuminance and classroom in cloudy lighting sky. Results levels obtainedaccording were to daylightcompared standards. to a standard DF value. TheThe daylight degree of factor illumination is the basis at points for assessing at distances the illuminance of 1 m, 2 m andin cloudy 3 m from sky. the Results window obtained sill is wereshown compared in Figure to 11 ab,c. standard Here a DF decrease value. and increase in the DF factor at a distance from the perimeter wallThe can bedegree seen. of As illumination the roof windows at points are at moved distances to the of top 1 m, of the2 m slope and roof,3 m from the level the ofwindow illumination sill is shownincreases in Figure and the 11b,c. uniformity Here a of decrease the lighting and increase in the classroom in the DF also factor improves. at a distance from the perimeter wall can be seen. As the roof windows are moved to the top of the slope roof, the level of illumination increases and the uniformity of the lighting in the classroom also improves. Shifting the windows to the top does not affect the resulting temperature in summer or the energy for cooling the indoor air, but it improves the visual conditions presented by the level of daylight DFaverage. If we were to move this strip of windows to the center of the roof, i.e., at its top, the most suitable situation is when this strip is at a distance of about 2 m from the window sill—from the perimeter Sustainability 2020, 12, 5046 19 of 24

Shifting the windows to the top does not aﬀect the resulting temperature in summer or the energy for cooling the indoor air, but it improves the visual conditions presented by the level of daylight DFaverage. If we were to move this strip of windows to the center of the roof, i.e., at its top, the most suitable Sustainabilitysituation is 2020 when, 12, x this FOR strip PEER isREVIEW at a distance of about 2 m from the window sill—from the perimeter 19 of 24 wall, (see Figure 15). In this case, the highest DFaverage value is reached. An interesting result is that if wall, (see Figure 15). In this case, the highest DFaverage value is reached. An interesting result is that if the window strip moves more than 2 m away from the window sill, the average DF value decreases the window strip moves more than 2 m away from the window sill, the average DF value decreases (see Figure 15b). (see Figure 15b).

(a)

(b)

FigureFigure 15. 15.Results Results ofof (a(a)) DF DFminmin and (b) DFaverage forfor combined combined and and top top lighting. lighting.

These results results show show that that skylights skylights successfully successfully bring bring light light deeper deeper into into the theroom. room. However, However, the numberthe number of light of light intensity intensity levels levels is still is still below below normal normal in in some some places. places. Good Good lighting lighting intensity intensity was analyzed based on class requ requirementsirements for Slovak standards. The highest internal light intensity at the farthest point point of of the the class class is is 160–200 160–200 lx, lx, which which is is below below the the standard standard value value of of 500 500 lx. lx. Skylights Skylights have have a significanta signiﬁcant effect eﬀect on on daylight daylight where where the the WFR WFR va valuelue is is exceeded exceeded and and the the WWR WWR value value is is close close to the required level (see Figure6 6).). WFRWFR valuesvalues reachreach aa levellevel higherhigher thanthan 10%10% inin almostalmost allall variants.variants. A number of window resizing calculations were performed, as shown in Figure 16. This figure contains a graph from which it is possible to predict the size of the windows (relative to the floor), the WFR, and to find out what the level of daylight (DF%) and summer overheating (indoor air temperature °C) is predicted to be. In a very simple way, we can preliminarily determine the size of windows under top and combined lighting. Based on the WFR from the graph in Figure 16, not only the value of DF (daylight Sustainability 2020, 12, 5046 20 of 24

A number of window resizing calculations were performed, as shown in Figure 16. This figure Sustainability 2020, 12, x FOR PEER REVIEW 20 of 24 contains a graph from which it is possible to predict the size of the windows (relative to the floor), thefactor) WFR, can and be to read, find but out at whata given the value level of of WFR daylight (window–floor (DF%) and ratio), summer the temperature overheating of the (indoor indoor air temperatureair during ◦overheatingC) is predicted in summer to be. also.

FigureFigure 16. 16.Resulting Resulting graphical graphical dependence dependence of of DF DF andand indoorindoor temperatures to to using using top top and and combined combined lightinglighting according according to to WFR WFR (window-ﬂoor-ratio). (window-floor-ratio).

5. InConclusions a very simple way, we can preliminarily determine the size of windows under top and combined lighting.Students Based on spend the WFRmore from time the at graphschool inthan Figure anywhere 16, not else. only Of the this value time, of DFabout (daylight 70% is factor) spent canin beclassrooms. read, but at Daylight a given valuehas a ofsignific WFRant (window–floor impact on students’ ratio), educational the temperature outcomes. of the The indoor proper air use during of overheatingdaylight can in summerimprove also.the indoor environment and reduce energy consumption. Windows allow natural light to penetrate to the interior. In the vertical plane of the perimeter 5. Conclusions cladding, in the window sill, they allow a visual connection with the external environment. Energy savingsStudents in daylighting spend more are time achieved at school by reducing than anywhere the use of else. electric Of lighting. this time, Daylight about 70%also isimproves spent in classrooms.passenger Daylightsatisfaction has and a significant comfort. Windows impact on are students’ a complex educational part of building outcomes. design The and proper provide use of daylightsignificant can improvebenefits to the school indoor buildings. environment The aim and of reducethe study energy is to evaluate consumption. the availability of daylight in Windowsthe attic, which allow is natural used for light teaching. to penetrate The article to thecompares interior. three In thealternatives vertical planeto skylights. of the Skylights perimeter cladding,are definitely in the needed window to sill, provide they allowmore light a visual for remote connection areas. with It is theinteresting external that environment. the movement Energy of savingsthe roof in daylightingwindow strip are achieves achieved maximum by reducing uniformity the use ofand electric achieves lighting. the required Daylight levels, also improveseven at passengerdistances satisfaction from the perimeter and comfort. walls. Windows are a complex part of building design and provide significantIn this benefits study, to schoolsimulation buildings. programs The were aim of used the studyfor model is to evaluatewindow thesituations. availability Based of daylighton the performed DF simulations and superheat predictions, the results were integrated closer to the in the attic, which is used for teaching. The article compares three alternatives to skylights. Skylights optimal state. The results of this study show recommendations for the appropriate design of roof are definitely needed to provide more light for remote areas. It is interesting that the movement of the windows in the attic and their uses for similar studies. The whole process was realized in cooperation roof window strip achieves maximum uniformity and achieves the required levels, even at distances with light and thermal conditions. The measurement results show that the levels of interior lighting from the perimeter walls. in the basic variant are below the level of the standard. Information measurements of the indoor In this study, simulation programs were used for model window situations. Based on the temperature in the summer show that a high indoor air temperature has been reached, which causes performeddiscomfort. DF Daylight simulations was and not superheat enough to predictions, ensure good the lighting results and were the integrated lighting was closer not to distributed the optimal state.evenly, The and results the oftemperature this study was show excessive recommendations despite the forincreased the appropriate amount of design ventilation. of roof The windows analysis in theshowed attic and that their there uses are for many similar alternatives studies. regarding The whole the process location was of realizedopenings in to cooperation improve daylight with light in andthe thermal classroom. conditions. It was found The measurement that the combination results show of facade that theand levels roof windows of interior (combined lighting in lighting) the basic varianthas better are below results, the as levelwell as of the the fact standard. that vertic Informational windows measurements are not very important of the indoor for calculating temperature the in thetemperature summer rise show in thatsummer. a high indoor air temperature has been reached, which causes discomfort. DaylightThe was attic not space enough is not to common ensure good for use lighting in the andteaching the lighting process. was Only not a few distributed classrooms evenly, are located and the in attics. The article shows such a case study, in which the school expanded the teaching space by raising the roof and creating new teaching spaces. There is an excessive amount of light in the classrooms; the problem is overheating in the summer. The prediction of the indoor climate in the Sustainability 2020, 12, 5046 21 of 24 temperature was excessive despite the increased amount of ventilation. The analysis showed that there are many alternatives regarding the location of openings to improve daylight in the classroom. It was found that the combination of facade and roof windows (combined lighting) has better results, as well as the fact that vertical windows are not very important for calculating the temperature rise in summer. The attic space is not common for use in the teaching process. Only a few classrooms are located in attics. The article shows such a case study, in which the school expanded the teaching space by raising the roof and creating new teaching spaces. There is an excessive amount of light in the classrooms; the problem is overheating in the summer. The prediction of the indoor climate in the summer showed that it is not possible to achieve the prescribed well-being with the proposed design solution. The shielding elements help to reduce overheating and reduce the indoor temperature, but not below the prescribed maximum indoor air temperature. The design solution will not solve the problem; cooling must be designed. For the evaluated period (June, July) in the given case, cooling is proposed, which will ensure a sufficient degree of reduction in the internal temperature in summer to the required level. The graphical dependence derived in the paper serves to predict similar spaces in conjunction with the achievement of the required DF and the estimation of the achievement of the indoor temperature in summer.

Author Contributions: Conceptualization, E.D.; Data curation, M.Z.; Formal analysis, D.K. and M.V.; Investigation, M.Z.; Methodology, E.D.; Project administration, D.K.; Resources, M.V.; Software, M.Z.; Supervision, D.K.; Visualization, E.D.; Writing—original draft, E.D. and D.K.; Writing—review and editing, M.V. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Acknowledgments: This paper was elaborated with the financial support of the research project VEGA 1/0674/18 and VEGA 2/0017/20 of the Scientific Grant agency, the Ministry of Education, Science, Research, and Sport of the Slovak Republic and the Slovak Academy of Sciences. Conflicts of Interest: The authors declare no conflict of interest.

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