1. Introduction
A fundamental objective of building enclosures is to protect occupants from weather effects. Therefore, each part of a building envelope needs to meet certain thermal requirements in order to create a comfortable interior environment. A good thermal performance of building envelopes is very important in order to minimize overall energy consumption. Besides industry and transportation, residential households are one of the largest energy consumers in the European Union (EU). According to an EU report [
1], 25.4% of total energy is consumed by residential houses and 70% of that amount is represented by heating energy [
2]. This means that significant energy savings can be achieved by improving the effectiveness of heating systems or thermal insulating capabilities of building envelopes, which are required by national thermal standards.
Currently, when a building envelope is being designed or assessed, the U-value (thermal transmittance) is mostly used to indicate its insulating capabilities. It is a basic quantity describing the thermal insulating capability of building constructions; its required values are prescribed for each part of a building in any European country [
3,
4,
5]. The U-value calculation is based on steady-state loading conditions and mostly comes from laboratory measurements [
6,
7,
8,
9]. However, there are several drawbacks to its laboratory methods. First, the accuracy is not always sufficient, as the effect of moisture on thermal conductivity of building materials is often neglected [
10,
11,
12]. Although the national standards define design values of thermal conductivity and assume a certain level of operational moisture content, the thermal conductivity of building materials can significantly differ in the real conditions due to weather effects and presence of liquid moisture. Second, external thermal loads on building walls in real conditions are not steady. This may be due to changing outdoor conditions, such as temperature, relative humidity, wind speed, precipitation, and/or solar radiation.
Since the climate is comprehended as a local variable, it is apparent that geographical location affects significantly the thermal performance of individual wall assemblies. For that reason, many research studies have been aimed at the investigation of differences between laboratory and on-site thermal performance of building materials, components, or whole buildings. Byrne et al. [
13] pointed out that predicted values of heat loss using standardized assumed material properties of the existing structure do not reflect the actual values achieved in situ. Marchio and Rabl [
14] compared the predicted and observed performance of selected houses and apartments in France. Branco et al. [
15] compared predicted and performed heat consumption of low energy family house in Switzerland. Roels et al. [
16] provided an extensive comparison of various assessment methods for on-site characterization of the overall heat loss coefficient. Ficco et al. [
17] conducted experimental measurement of in situ U-values and compared them against the estimated ones from design data and field analyses. The traditional empirical rules or standardized methods for U-value calculation were thus found not to work effectively, which was due to the high variability of the environmental and material properties or insufficient quality of input data. For a more proper assessment of thermal performance of building enclosures, more advanced techniques were supposed to be incorporated. Therefore, some new approaches for determination of thermal performance were suggested. For example, Robinson et al. [
18] outlined a new transient, straightforward, and low-cost method for estimating the thermal properties of wall structures. Byrne at al. [
19] designed a facility for testing the thermal properties of wall samples under both steady and transient conditions. Perilli et al. [
20] performed a numerical analysis of thermophysical behavior of cork insulation based on in situ experimental data. Some other advanced techniques were applied, for example, for the analysis of the effect of wind velocity on quantification of heat losses through building envelope thermal bridges [
21], the estimation of overall heat loss coefficient [
22], convective heat transfer coefficient of exterior surface of building walls [
23], or the prediction of residential heating demands [
24].
In this paper, a method for rapid quantification of thermal performance of exterior wall systems is designed, which is intended to provide the designers and engineers with a fast and efficient tool for thermal design of residential buildings. The approach is based on the development of formulas for the calculation of monthly energy balances that only use monthly averages of temperature and relative humidity and the elevation of building’s location as input parameters, but can achieve similar accuracy as advanced computational methods utilizing robust finite-element simulation tools and hourly climatic data. At the development of the calculation formulas, climatic data for 50 locations across the Czech Republic are used as a training set. The data for other 14 Czech locations are utilized as a testing set in the first step of the verification procedure. Another set of weather data for 10 randomly selected European locations are obtained from the Meteonorm software [
25] and is used in the second verification step. The application of the method is presented for nine common wall systems, but it can be extended to any other type of building wall.
4. Discussion
The results presented in
Figure 1,
Figure 2 and
Figure 3 show a good agreement between the data simulated using an advanced hygrothermal model and predicted by the proposed approach based on the knowledge of monthly temperature, relative humidity, and elevation. This means that in a real application the knowledge of commonly available weather statistics for a given location, together with a unique combination of
c0–
c3 coefficients from Equation (7) allows to produce a set of monthly energy balances capable of assessing the thermal performance of a wall assembly with a sufficient accuracy. Although for each wall assembly it takes 80 h of computational time to identify and verify obtained correlation coefficients, this method can be quite effective as the outputs can be used in simple algebra to obtain results that are comparable with those from sophisticated computational models. Moreover, the presented method can be extended to any kind of wall assembly or any other part of building envelope, such as glazing or roofs, providing the users with a tool that can produce results with research-like quality. However, it is important to say that finding those coefficients might be time-consuming and requires expert or research skills. The obtained U-values or heat fluxes can be used for fast assessment in such cases, where 1-D analysis is needed or requested. Moreover, the effective U-values (changing with time) can be used in advanced BIM models instead of standard U-values obtained from theoretical calculations (see below).
The presented analysis was done for continuous wall assemblies only as they are most typical structures in the Central Europe. However, the method can be extended to cavity/frame assemblies as well. In case that ventilated cavity or air gap need to be modelled, it will be necessary to replace the Künzel’s mathematical model or to couple it with some other CFD model. Basically, this method should be comprehended as tailor-made, which is primarily dedicated to the very same wall assemblies as presented in this paper or for their very slight modifications. If an application on different kind of building envelope is needed, it is recommended rather to perform the simulation and optimization procedure from scratch than to approximate the results from available outputs. On the other hand, the presented method can be used to create input parameters for some approximation models, that will produce final and accurate outputs for various types of wall assemblies.
From the point of view of selected time-frame, the monthly averages seem to be most suitable choice for several reasons. First, the weather data are usually available for free without any additional costs, which is a good precondition for application of this method in practice. Second, considering the fact that national standards define only one value of thermal transmittance that is not changing over time, choosing monthly values gives a reasonable resolution for classifying building performance during the year. Additionally, lower time-frame would bring high fluctuations to the obtained results. Although the accuracy will be higher, it will be not suitable for practical applications.
The monthly values of energy balance may be effectively used for design of buildings’ heating and cooling components or as advanced input parameters in more complex models used, e.g., for the assessment of energy efficiency of buildings or overall U-value.
Since the U-value is defined as the heat flux density through a given structure divided by the difference in environmental temperatures on either side of the structure in steady state conditions, the monthly energy balances can be simply used for calculation of equivalent or apparent U-values. When average monthly temperatures are known, each month can be considered as a steady-state period. Then, an apparent U-value can be calculated from monthly energy balance and used as a more accurate parameter describing the insulation capabilities of building elements. The apparent U-value can be calculated as:
where
Uapp (W·m
−2·K
−1) is the apparent U-value,
EBi (W·h·m
−2·month
−1) is the monthly energy balance calculated from Equation (7),
Ti,int (K) is the interior temperature (294.15 K), and
Ti,ext (K) is the average monthly exterior temperature. Since all the computational simulations in this research were conducted using an advanced hygrothermal model, the calculated outputs include the effect of moisture content on heat transport through the materials involved. This provides a higher accuracy than some common laboratory experiments or calculations done by more simplified techniques.
As an example of utilization of the proposed approach, a comparison between standardized and apparent U-value is provided below. In this example the wall assembly made of ceramic brick and polystyrene is chosen (building envelope 2, see
Table 2), which is subjected to the effect of two environmental loads: Prague, Karlov, and Šerák (locations 24 and 29, see
Table 1). The standardized procedure defines U-value as:
where
R (m
2·K·W
−1) is thermal resistance of the construction,
Rsi and
Rse (m
2·K·W
−1) are external surface and internal surface resistances defined by the standards (according to [
6],
Rsi = 0.13 m
2·K·W
−1 and
Rse = 0.04 m
2·K·W
−1). The R-value is calculated as:
where
di (m) is the thickness of individual layer in the composition of wall assembly and
λi (W·m
−1·K
−1) is the thermal conductivity of the material involved in that layer. The U-value for building envelope 1 calculated according to (10) is equal to 0.258 W·m
−2·K
−1. The apparent value calculated from (9) using (7) and data from
Table 6,
Tables S1 and S2 is equal to 0.205 W·m
−2·K
−1 for Prague and 0.246 W·m
−2·K
−1 for Šerák. Although the standard U-value is on the safe side in this case, as it claims higher (i.e., worse) U-value than the apparent U-value approach, when individual months are analyzed in detail, it can be different in some other cases. Looking at
Figure 4 showing apparent U-values during individual months, it is obvious that the construction will not meet the criteria given by standards during winter periods. The brick wall located in Prague will not stand the comparison in months December to March, while the same wall located in Šerák will not meet the criteria from November to March.
The analysis of solar radiation and precipitation and wall orientation was performed on wall assemblies made of ceramic brick both insulated and non-insulated (building envelopes 1 and 2). For that analysis, a location of Velké Meziříčí (location 37) was selected. The monthly heat fluxes for different wall orientations are depicted in
Figure 5.
The highest differences in simulated energy balances can be observed during summer period especially when non-insulated walls (building envelope #2) are considered. The differences in non-insulated walls (building envelope #1) range from 0.55% in winter (December) to more than 100% in summer (July). In absolute numbers, the differences are up to 1.050 kW·h·m−2·month−1 (August). The differences in case of insulated brick wall are significantly less when speaking of absolute numbers. The highest difference in heat fluxes of north and south orientation can be observed in the same month of August, but the difference is only 0.269 kW·h·m−2·month−1, which is given by the insulation capability of expanded polystyrene. Such inaccuracies should be considered when using this method in the practice.
The effect of solar radiation (SR) and precipitation (PP) on monthly heat fluxes is shown in
Figure 6. Similarly, to results shown in
Figure 4, the highest differences can be observed in case of a non-insulated wall. The effects of solar radiation and precipitation contribute to the overall energy balance by approximately 2% in winter periods, but more significantly in summer. In case of non-insulated wall, the sun radiation can change the overall heat balance from negative to positive, which may be a very significant factor. For that reason, the effects of solar radiation and precipitation should be included in the computational model in order to produce satisfactory results. The fact that the presented method allows for the prediction of thermal performance of wall assembly including the effects of solar radiation and precipitation only from the knowledge of average monthly values temperature and relative humidity together with the elevation makes the method very useful. Since there can be found some level of correlation between temperature and solar radiation, or relative humidity and precipitation, the knowledge of limited weather data could be sufficient to bring relatively accurate predictions.
5. Conclusions
In this study, we introduced a method suitable for rapid evaluation of thermal performance of building walls, which needs only monthly averages of temperature and relative humidity for a given location and its elevation as input data. The proposed approach was successfully tested for nine different types of wall assemblies. The results showed a good accuracy of the method; the average prediction error for tested wall assemblies was ranging between 1.63 and 6.43%.
The proposed approach can be considered as very time-saving, as compared with the methods that involve utilization of robust models. On the other hand, since the effect of moisture content is included in the model outputs, this approach outperforms more simplified models and methods. As a result, it offers a solution, which is neither too simple nor too complex. The presented method can be used for any location across Europe and can also be easily extended to any kind of wall assembly or building envelope component. Since the utilization of the proposed method is demonstrated on nine different wall assemblies only, the method should be extended to a broader range of wall assemblies or building components. In this way, a catalogue or database for civil engineers and designers can be generated, facilitating the thermal design of building structures or fast pre-assessment of wall assemblies from several points of view, e.g. predispositions to frost-induced damage, biofilms growth conditions or salt attack.