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Simulations and quantitative data analytic interpretations of indoor-outdoor temperatures in a high thermal mass structure
Author’s Accepted Manuscript Quantitative data analytic interpretation of indooroutdoor temperatures in a high thermal mass structure Wael A. Yousef Mousa, Werner Lang, Waleed A. Yousef www.elsevier.com/locate/jobe
PII: DOI: Reference:
S2352-7102(17)30155-9 http://dx.doi.org/10.1016/j.jobe.2017.05.007 JOBE265
To appear in: Journal of Building Engineering Received date: 15 March 2017 Accepted date: 6 May 2017 Cite this article as: Wael A. Yousef Mousa, Werner Lang and Waleed A. Yousef, Quantitative data analytic interpretation of indoor-outdoor temperatures in a high thermal mass structure, Journal of Building Engineering, http://dx.doi.org/10.1016/j.jobe.2017.05.007 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Quantitative data analytic interpretation of indoor-outdoor temperatures in a high thermal mass structure Wael A. Yousef Mousa¹*, Werner Lang¹, Waleed A. Yousef² ¹Technische Universität München, Germany ²Helwan University, Egypt *Corresponding author: [email protected]
Abstract The present paper investigates the impact of thermal mass on indoor temperature and reduction of cooling loads in summer. The major contribution of this paper is providing an objective assessment and a quantitative data analytic interpretation from the pattern recognition literature for the reported findings. The experimental study adopted one of the traditional stone structures of medieval Cairo. The house was monitored during summer days for Indoor and outdoor temperatures. Further data for local climate were obtained and given to TRNSYS 17 in which simulations were generated and validated against measured data. The absolute deviance error between simulated and measured indoor temperatures was 0.3 °C for a couple of monitored spaces. Data visualization and regression analysis of indoor temperature on two values of outdoor temperature show a relative stability of the indoor temperature, a direct result of the heat storage capacity of the stone walls. A quantitative interpretation of the regression equation tells that the indoor temperature increases by merely 1 °C if the outdoor temperature increased by 11.5 °C. Upon ambient-temperature-responsive natural ventilation, the maximum indoor temperatures were reduced, in average of 5.5 °C and 4.2 °C below ambient for two different spaces. A comparative analysis took place then between the base case and a modified model were the walls’ material was substituted with hollow red bricks. For the two rooms, the energy demand for cooling was found to be as less as 72 % and 56 % in the base case than the brick-walls model. Keywords: Thermal mass; indoor temperature; energy efficiency; thermal simulations, data analysis; pattern recognition
1. Introduction In hot and arid climates where daily temperature fluctuations are found, the thermal mass is effective in improving thermal comfort, as a major method in passive building design. Walls with sufficient amount of thermal mass, with low surface absorptivity, are recommended to be used in places where there is considerable diurnal temperature variation around design indoor condition [2]. To describe differences of thermal mass in construction, the terms heavy weight and light weight are correspondent to high and low thermal mass. The rate of heat transfer and the effectiveness of thermal mass are determined by various parameters; material thermal properties; location and distribution of the thermal mass in the building; insulation portion; ventilation and the occupancy pattern [3]. The use of thermal mass can be more effective with a significant diurnal variation of ambient temperature and/or diurnal variation in solar radiation intensity [21]. In the night-time cooling the gained heat is to be released to the outdoor space when it has lower temperature [4].
In addition to enhancement of the indoor air quality and providing cooling to the inhabitants, ventilation can be used for cooling the thermal mass of the building [12]. Thermal mass was also found to be more effective in reducing the rise of indoor temperature caused by heat gain through the external walls than that caused by penetrating solar radiation. The shading of the window has reduced the indoor average temperature by about 1 °C [8]. Measurements showed that in a hot and arid climate it is possible to achieve a reduction between 3 and 6 °C in a heavy constructed building without operating an air conditioning unit. The anticipated reduction depends on the amount of thermal mass, the ventilation rate, and temperature swing [11]. In hot climate, night ventilation is based on the principle that thermal mass can be cooled by night air and then acts as a heat sink to reduce cooling loads in the daytime [19]. A study has developed a simple model coupling thermal mass and natural ventilation. The experiments showed that the internal thermal mass affects the time lag of indoor air temperature. By comparing six different external walls it is found that the use of heavy wall with external insulation is predicted to have the lowest amplitude of indoor air temperature and hence the heavy walls with external insulation are suitable for naturally ventilation [23]. Pre-cooling attempts to remove some of the increased peak demand on the electricity grid by shifting the cooling load. The cooling thermostat set points are reduced in the period preceding the peak period to force the air-conditioner to operate [18]. Various researches investigated the potential of higher thermal mass for energy savings. Hypothetical modules of different types of Australian residential constructions were numerically analyzed. The analysis showed that the heavier mass constructions were found to be the most effective walling systems which offer the least energy consumption and indoor temperature fluctuations, especially when protected within the insulation portion [7]. As a result of optimizing thermal mass, different study concluded that the maximum savings in yearly transmission loads are about 17% for cooling and 35% for heating [1]. In cold climates, however, minimal mass is required to deliver warm air to adjacent spaces during daytime [13]. A study investigated the effect of thermal mass on annual heat load of buildings. The results indicated that increased thermal mass is not effective for decreasing annual heat demand in typical residential buildings [16]. The present paper departs from the fact that indoor air temperature changes periodically as outdoor temperatures, but with different phase shift and fluctuation amplitude [20]. The study investigates the correlation between indoor and outdoor temperatures. To objectively quantify the relationship between the ambient temperature and the temperature inside the building, a first order regression analysis is carried out and an equation is provided. The difference in temperatures is measured in terms of t-test and showed statistical significance. In addition to this qualitative measures, these relationships and findings was demonstrated using data visualization methods, e.g., matrix plot, and time series plots, for more comprehension and interpretation. Another set of objective-assessment is carried out for comparing the two wall materials, brick and stone. The correlation coefficient between the temperatures outside and inside the building in case of brick walls is much higher than the correlation coefficient for the case of stone walls. This shows the stabilizing effect of the stone’s heat storage capacity. The analysis also shows the increased efficacy of the thermal mass by adopting an ambient-temperaturedependent ventilation schedule. A comparative analysis of energy demands shows that a higher thermal mass can contribute to up of 72% savings in cooling demands.
2. Case Study and Validation of the Simulation Model This study adopts a traditional courtyard house built during the 15th century in Cairo (fig. 1). The walls are constructed of limestone in thicknesses between 60 and 80 cm. A couple of large halls in the first floor were monitored. The grand hall (GH), north-east oriented, has a large opening on the northwestern wall overlooking the courtyard and a couple of windows on the northeastern wall. The secondary hall (SH) occupies the northeastern
wing and overlooks the courtyard through several windows on southwestern wall, in addition to a window on the upper level of the southeastern wall. Each hall has a roof skylight. Indoor and outdoor temperatures were measured during August. The data loggers used are HOBO U12-012. According to the manufacturer, the measurement range of the loggers are -20° to 70° C and 5% to 95% RH. The accuracy of the loggers is ± 0.35° C from 0° to 50° and ± 2.5% from 10% to 90% RH. The loggers were set to continuously take readings each 30 minute. Table 1 describes the installation of the sensors in both halls and in the courtyard. The lowest indoor temperatures were recorded in the grand hall. The average maximum is found to be lower than that of the courtyard with 2.2 °C. The average maximum temperature was 35.2 °C. The average minimum was 28.6 °C. Generally, the grand hall (GH) showed a slight better performance than the secondary one (SH) with average difference of 1.1 °C and 1 °C for maximum and minimum temperature respectively. A simulation model has been created in TRNSYS 17. Further climatic data was collected on daily basis from the NOAA (National Oceanic and Atmospheric Administration). The recorded data includes hourly records for air temperature, dew point, relative humidity, wind velocity, and air pressure. The data collected for a time spanned from August 7 2014, one week before measurements, until September 8. The weather data file used in TRNSYS is the type TM2 which includes more extensive details adopted from the test reference file. However, data for ambient air temperature were replaced by records obtained in site; courtyard temperature. Figure 2 is a 3D model of the building (monitored spaces are shaded). Surrounding buildings were modeled as shading groups. Window screens were designed with modular sections of 5x5 cm. with ratio between the width and the depth 1:1 and 50% perforation, and modeled as shading groups in TRNSYS3d. All windows were set into the condition, no window, corresponding to the condition of being opened along the measurement period. Material thermal properties, as shown in table 2, were given to TRNBuild. Initial values for indoor temperature was set to 21° C and relative humidity to 50%. The solar radiation distribution mode was set into a detailed model. 3 values for air change rates (ACH) were defined to the simulation model, 6, 8, and 10/h. Simulations ran for annual round and results for the measurement periods were extracted. Results for Indoor temperature showed remarkable conformity in both spaces, GH and SH; high proximity was found between results upon all presumed values of air change rates. However, it is found that ACH 6/h achieved the highest level of conformity with measured indoor temperature for both halls. The absolute deviance error between simulated and measured indoor temperatures was 0.3 °C. Figures 3-6 demonstrate the validation of the simulation results against measured data and average indoor temperatures for both halls. The absolute deviance error (ADE) was calculated as: ∑ where,
and
(1)
are the simulated and experimentally measured temperatures respectively at a time step i.
3. Data Analysis and Quantitative Interpretation In this section, the relationship between indoor and outdoor temperatures is investigated upon an objective assessment and quantitative measures. A regression analysis is carried out for the base case, stone walls and a modified model where the lime stone wall material was substituted with hollow red brick and cement mortar, with the same thermal properties of materials used in modern building practices in Cairo. The mathematical treatment of regression analysis and linear models can be found in many texts, e.g., [5, 14, 15]. However, a practical approach associated with good rigorous foundation is portrayed in their seminal work Hastie, et. al. [9].
Thermal properties of the brick walls are shown in table 3. A data visualization of indoor and outdoor temperatures for the data acquired during the last two weeks of August, which fall into the measurement period, can illustrate the relationship between indoor and outdoor temperatures in the grand hall (GH) in both cases. As for the base case, stone walls, figure 7 is a matrix-plot of three variables; outdoor temperature ( ); indoor temperature with no ventilation ( ), and in-door temperature with ventilation and air change rate ACH of 6/hour ( ). The three subplots on the diagonal, from top left to bottom right, are histograms of the three variables , and respectively. The pair-wise plot of each of the three variables results in the six subplots located off diagonal of the figure, (with obvious symmetry). For example, the subplot on the first column and second row is a plot of , vs. ; while vs. is located on second column and first row. From the histograms, it is obvious that and have very similar distributions, a direct consequence of the air flow and exposure to the ambient temperature. In contrast, the distributions of , indoor temperature with no ventilation, and are dissimilar in two aspects. First, the temperature range (31 to 33.5 °C) vs. (29 to 40 °C); this conveys the effect of the wall material in stabilizing the temperature inside. Second, and very interestingly, the shape of the distribution, where has a bi-modal shape (at temperatures 29 and 37 °C) and has a uni-modal shape (at temperature 32.5 °C). In the vernacular, this means that even when the ambient temperature frequently occurs at 29 °C and 37 °C (with variation), the indoor temperature frequently occurs only at 32.5 °C (with variation). This is another stabilizing effect of the wall material. By applying the same visualization for the brick-walls case (fig. 8) the temperature inside the brick building with is almost the same pattern as the temperature outside with just a scaling factor. However, it is evident that there is a phase-shift between and for the brick-walls case of almost 7 hours. For more objective assessment, a correlation analysis between and for both brick and stone cases is investigated (fig. 9). It revealed that the maximum correlation between and for the case of brick is occurred at 7 hours of delay; this correlation is 0.88. The interpretation of this strong correlation, yet delayed, is that the temperature pattern inside the building follows, almost linearly (as high correlation coefficient always means) the temperature outside but with a delay of 7 hours. This delay is caused by the brick thermal properties. On the other hand, the maximum correlation between and is 0.96 and occurs at 0 phase-shift, which means that the temperature inside the brick building with ventilation is almost the same pattern as the temperature outside with just a scaling factor. This was already clear from the previous matrix plot. For a clearer blueprint, table 4 reports the maximum correlations, along with the corresponding phase-shift, for four cases; each is between on a hand and the inside temperate with/without ventilation for brick/stone cases. Interestingly, the stone case has almost a constant correlation with regardless to the phase-shift; and this correlation is smaller than that of the brick case. This is an evidence of the stabilizing effect of the stone case. It is more illustrative now to re-draw the matrix plot for the brick case but with replacing with a 7-hour phaseshifted version. The new matrix plot is displayed in figure 10. The strong correlation between (7-hour phaseshifted) and is obvious now. The histogram of , if compared with its analogue of the stone case, is more spread. This is another evidence for the stabilizing effect of the stone walls. The data visualization for the high thermal mass (stone case) conveys the relationship between outdoor and indoor temperatures qualitatively. A quantitative description however can be provided using regression analysis to estimate the linear relationship that appears in the figures. A straight forward first order regression analysis gives: Mean of
(2)
Figure 11 is a plot of this regression line equation (in black), where the blue points are the actual readings appearing on the matrix plot discussed above. The regression line comes in-between the data points to show the
average trend of the relationship between these two variables. The root-mean-square-error (RMSE) of this line is 0.37 degree, which shows accurate regression. The quantitative interpretation of this regression equation says that an increase of 1 degree in the ambient temperature results in an increase of only 0.087 degree inside. Said differently, the inside temperature will increase by 1 degree only if the outside temperature increases by (1/0.087 = 11.5) degree. This emphasizes quantitatively the stabilizing effect of the wall material that is observed above from reading the histograms in the data visualization step. When the regression above is repeated on the whole period of summer time (June-August); it gives the following equation: Mean of (3) Figure 12 is an analogue for figure 11. The RMSE of this equation is 1.3 degree, obviously larger than the RMSE obtained for regression during only the last two weeks of Aug. This is foreseeable since more explanatory variables (than merely ) will be needed to model the relationship when the period extends and hence more factors interact. In the equation above, the variable is called "predictor" and the variable is called "response"; this terminology is borrowed from the literature of statistics. From the physics of the current problem it can be anticipated that depends, in parallel to , on the temperature outside the building hours earlier, a direct result of the capacitance effect of building material (Limestone). Accordingly, a table of 13 columns is formulated; the first column includes the outdoor temperature at a moment and the other 12 columns are the temperature each preceding hour. The correlation coefficient was calculated and the smallest correlation was with the temperature outside 12 hours earlier ( ). Then is regressed on and , and obtained the equation: = 15.1313+ 0.2979
+ 0.2056
(4)
Figure 13 is the 3D analogue to figures 11-2. The RMSE of this equation is 1.05 degree, a 19% reduction when compared to the 1.3 mentioned above. Obviously, when is replaced by any other temperature that is more correlated with , i.e. , a higher regression error will be obtained. The interpretation of this regression equation is of interest. The coefficients of both and are close to each other, which means that the temperature outside now and 12 hours ago are almost equally important in predicting the temperature inside, which can be attributed to the heat storage capacity of the walls’ material However, the reduction in error is not very significant; only 19% as indicated above. More elaborate regression methods can be employed to reduce the error and to better formalize in terms of outdoor temperature. For example, slicing the data, as it appears from figures 12-3 then building a regression model for each slice will build a more accurate equation. However, this regression analysis is carried out to demonstrate the efficacy of the thermal mass of the building material, since the prediction of indoor temperature is already carried out in TRNSYS. It should be noted that employing the two-explanatory variable ( and ) for the data of the last two weeks of August does not help in reducing the RMSE below the 0.37 degree mentioned upfront. Moreover the coefficient of for this data is almost zero, producing a very similar equation to equation (4).
4. Indoor Temperature and Energy Demand upon Weather Responsive Ventilation schedule The use of thermal mass can reduce peak heating or cooling load and hence the energy consumption, especially when it is integrated with night ventilation [22]. In order to understand the correlation between indoor
and outdoor temperatures, different ventilation conditions were applied; closed and opened windows. For the open window condition, it is applied for both daylong schedule and for a more weather responsive schedule between 8 pm and 12 pm so the interior space could be protected against overheating through the hot air during daytime. The average diurnal differences significantly vary when ventilation is active along the day where higher correlation between indoor and ambient temperature takes place. The heat loss through ventilation (convective heat loss) is in proportion to the air exchange rate, difference in temperature between the inside and the outside, and the capacity of air. Despite the high heat storage capacity of the stone walls, a higher correlation with ambient temperature occurs with significant temperature fluctuation between day and night temperatures. When an air change rate value is defined, the indoor temperatures change dramatically as the heat flux increases according to the equation: (5) where is the heat capacity of air (1006 J/kgK), is density of air (1.2 kg/m³ for dry air), is air volume flow (m³/s), is the inside air temperature (°C), and is the ambient air temperature (°C). Real values of air change rates, in both halls of the building adopted in this study, were predicted from numerous CFD simulations which are described in detail in Ref. [10]. The values were given to TRNSYS as an equation for the function of ACH as an output; while the variables; wind direction; velocity; and time of the date were defined as inputs from the weather data file. According to the psychometric chart of Cairo, the accepted range of temperature is between 20 °C and 26 °C. To set the ventilation schedule during summer to correspond to the ambient temperatures, a conditional function is added to the ACH equation statement. Thus, ventilation schedule was assigned according to this condition: , where and stand for greater than or equal, and less than respectively, and is the ambient temperature. This means that windows will be opened only when ambient temperature ranges between 20 and 26 °C. Figure 14 shows the simulation results for indoor temperatures for both halls GH and SH during summer, June-August, upon ambient temperature-dependent ventilation schedule. The maximum indoor temperatures were remarkably reduced, in average of 5.5 °C and 4.2 °C below ambient for GH and SH respectively. The highest maximum values for GH and SH are found to be 31.1 °C and 32.7 during August. These values remain quite acceptable in as much as being 11.9 °C and 10.3 °C below ambient temperature which reaches 43 °C. The wide difference here is attributed to the capacitance of the wall material thermal mass as previously explained. The average minimum however was 1.4 °C and 2 °C above ambient for GH and SH respectively (fig. 15). The average maximum values for GH and SH were 28.8 °C and 30.1 °C.
4.2 Indoor temperature The hollow bricks, due to the lower storage capacity, absorb and release heat much faster than the stones do and thus are more influenced by the ambient temperature fluctuations. This behavior can be more tangible in the grand hall than in the secondary hall where the south-west wall is more exposed to solar radiation, in terms of time span, and the secondary hall hence has higher temperatures than the grand hall within all conditions yearround. On the contrary the indoor temperature variation between the two cases in winter is not as wide as in summer, though the energy demand for heating significantly differs due to the lower thermal capacity of the brick walls. Figure 16 shows the indoor temperatures during summer, June-August, for both the base case and brickwalls model. As shown in figure 17 for an average summer day (Jun-Aug), the base case had a maximum temperature as lower as 1.8 °C than the brick-wall model. The difference in minimum temperatures, however, is
comparatively smaller, 0.7 °C. Expectedly, the base case showed less correlation to the outdoor temperature fluctuation than the other case. This can be explained considering the stone’s higher thermal mass which keeps the indoor temperature more stable when compared to the brick-walls case where the indoor temperature keeps to increase until night time as the heat being transferred to the indoor space rather than to the outside. In average the base case achieved 1.4 °C lower than the brick-walls model. For two different cases, (stones) and (bricks), are computed, which equals to: average of , where is an index running over all readings. Statistical significance of this difference is then tested. Statistical significance confirms whether the calculated temperature difference occurs only by coincidence or a consequence of the corresponding design. The statistical test used in this analysis is the two-sided t-test, a standard test in statistics literature to measure the difference between the means of two populations (a population here in this context is the readings of indoor temperature for a particular design). The hypothesis is tested that the means of the two populations are the same; then the hypothesis either accepted or rejected at some level of significance. For example, at summer time (June-Aug), the first row of average difference in the table reads as follows: The average difference between the indoor temperature for the base case and the brick-walls model is -1.4 degrees; and a two-sided t-test that tests the hypothesis that "the two populations of temperature have the same mean value" is rejected at 0.05 level. The 0.05 level means a confidence level of 95% (= 100 x (1-0.05)) that what has been concluded about the temperature difference is correct and statistically significant (referred to as 1.0). 4.3 Energy demand In naturally ventilated buildings people generally accept greater climate variability [6] and the indoor temperatures achieved by adopting the weather responsive ventilation schedule might be accepted in this context. However, it remains subject to the inhabitants’ culture and behavior In such a relatively harsh hot climate, it remains expected to adopt mechanical cooling devices, if they are available, in response to even slight overheating. Moreover, the ambient temperatures, and hence indoor temperatures, significantly drop during winter time which causes states of dissatisfaction. The energy performance of the base case was hence compared against the brick-walls model to demonstrate the impact of the thermal mass in relation to the quantitative analysis and interpretation previously described. As considered for the ventilation schedule, a temperature between 20 and 26 °C is adopted as an accepted range. The simulation model was adapted in TRNBuild for both cooling and heating types which would be operated for an indoor temperature above 26 °C and below 20 °C respectively. The ventilation schedule and hence the ACH condition were in reverse disabled. As the windows would be closed during cooling and heating times, a conditional statement was hence added to the ventilation schedule as: ( ). Figures 18-9 show the monthly energy demand for cooling (+) and heating (-) for both halls to keep the indoor temperature between 20 and 26 °C in the base case and the modified model respectively. For the brickwalls model, the energy needed for both cooling and heating is found to be significantly higher than in the base case which can be simply understood in light of the thermal capacity of the wall material. In winter time, the indoor temperature variation between this model and the base case is not as wide as in summer. However, the energy needed to keep the indoor environment within the required range is much higher than in the base case as the walls do not reserve the heat as much as in the stone case and hence the indoor space would not be protected against temperature fluctuations. The lower heat storage capacity of the hollow bricks will result in more indoor temperature fluctuation Considering the relatively low density of the hollow red bricks, the role of the stone’s higher thermal mass can hence be evident through its ability to store the absorbed heat, which results in less temperature fluctuation along the day. According to equation (5), the energy intake ( ) required to heat up 1 m² of the stone wall is C. However, for the brick wall ( ) is C
However, the differences in energy demand between the base case and the modified model do not proportionally correspond to the differences in indoor temperatures. In other words, the stone walls store the heat during daytime and release it at night to the cooler outdoor. The indoor temperature therefore can significantly drop during nighttime, and therefore mechanical cooling will be switched off. The time-shifting accomplished by the thermal mass can move the energy demand for cooling or heating from the peak hours [17]. On the contrary, in the brick-walls model, the wall material keeps transferring the heat to the indoor environment, which results in the temperature rising continuously even in night-time. Therefore, the temperature along the day remains higher than the level needed to keep the indoor temperature within the accepted range. Thus, more operation hours are demanded to cool down the space. The same interpretation can conversely be valid for the heating process. Figure 20 shows a comparison between the annual energy demand of cooling and heating between the base case and the modified model for both halls GH and SH. From the figure it can be concluded that the grand hall (GH) in the base case demands energy as less as 72 % and 49 % than the brick-walls model for cooling and heating respectively. This can obviously reflect the impact of the wall material thermal mass on the energy efficiency of the building, especially in hot weather conditions. This gap between the energy demands for both cases significantly narrows down in the secondary hall to 56 % for cooling. However, the difference in energy demand for heating remains too close, 45%, as the secondary hall has higher temperature degrees during winter in both cases due to the higher amounts of solar radiation transmitted through the south-west windows. Conclusion Simulation model was validated against real measured data for indoor temperature in a traditional stone structure. The time shifting due to the high thermal mass of the walls achieved a statistically significant reduction of indoor temperature with an average of 1.4 °C, when compared to a brick-walls model. Upon ambient-temperaturedependent natural ventilation, the maximum indoor temperature in the base case was reduced, in average of 5.5 °C and 4.2 °C below ambient in two different spaces. On the contrary, the brick walls keep transferring the heat to the indoor environment along the day, which results in the temperature rising continuously even during nighttime, and hence more active cooling is needed. In terms of energy demand the base case reduced up to 72% and 49% for cooling and heating respectively. Although both acquired and simulated data may deliver some known information, the present paper stresses on the objective assessment and quantitative measures, borrowed from the field of pattern recognition and statistical analysis. Assessment of the relationship between indoor and outdoor temperatures is provided in terms of regression analysis, statistical tests, and correlation measures. A regression of indoor temperature on simultaneous outdoor temperature and before 12 hours shows that indoor temperature does not exceed 32.5 °C even when the outdoor temperature reaches 40 °C. The method can draw better understanding of the relationship between building design parameters (inputs) and indoor temperature and energy consumption (outputs). This can be adopted in multi-objective optimization studies for estimating the unknown input-output dependency using a limited number of observations. Acknowledgment The study is a part of a research work financed by the German Academic Exchange Service (DAAD).
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Figures
Figure 1: External view of the south west facade
Figure 2: TRNSYS 3D model
Figure 3: GH, simulation results for indoor temperature against measured data
Figure 5: SH, simulation results for indoor temperature against measured data.
Figure 4: GH, average day temperature, simulation results against measured data. ADE ± 0.3 °C
Figure 6: SH, average day temperature, simulation results against measured data. ADE ± 0.3 °C
Figure 7: GH, matrix-plot of outdoor and indoor temperatures, stone
Figure 8: GH, matrix-plot of outdoor and indoor temperatures, hollow red bricks
Figure 9: GH-time-series plot of , for brick design, and for the stone design, all versus the sampling hour (time step) across the two weeks.
Figure 10: GH, matrix-plot of outdoor and indoor temperatures, hollow red bricks, replacing with a 7-hour phase-shifted version.
Figure 11: GH, regression of indoor temperature on outdoor temperature, 17-31 Aug.
Figure 12: GH, regression of indoor temperature on outdoor temperature, Jun.-Aug.
Figure 13: GH, regression of indoor temperature on simultaneous outdoor temperature and before 12 hours, Jun.Aug.
Figure 14: GH-SH, simulation results for indoor temperatures with ambient temperature-dependent ventilation, Jun-Aug.
Figure 16: GH, indoor temperature, base case vs. modified/brick-walls model. June-August
Figure 15: GH-SH, average summer day indoor temperatures with ambient temperature-dependent ventilation
Figure 17: GH, indoor temperature, base case vs. modified/brick-walls model, average summer day
Figure 18: GH-SH, monthly energy demand (kW/h) for cooling and heating, operation on 26 and 20 °C respectively, base case (stone walls)
Figure 19: GH-SH, monthly energy demand (kW/h) for cooling and heating, operation on 26 and 20 °C respectively, modified model (brick walls)
Figure 20: GH-SH, total annual energy demand (kw/h) for cooling (+) and heating (-), base case vs. modified/brick-wall model.
Tables Table 1: Sensors installation Space Grand hall
Secondary hall Courtyard
Sensor GH1 GH2 GH3 SH1 SH2 CRT
Position Ceiling-hanged at 2.5 m from F.F.L. ceiling-hanged at 9 m from F.F.L. Mounted on window at 2.5 m from F.F.L Ceiling-hanged at 2.5 m from F.F.L Mounted on window screen at 4 m Hanged at 4 m from G.F.L
Table 2: Construction material and thermal properties
Component
Material
External walls Internal walls Ground floor Flat roof
Limestone Lime mortar Limestone Lime mortar Limestone
Internal floor Windows
Limestone Sand Wood Limestone Sand Wood Glass Frames
Thermal conductivity (kJ/hmK) 4.68 3.13 4.68 3.13 4.68
Capacity (kJ/kg K)
Density (kg/m³)
1.0 1.0 1.0 1.0 1.0
2200 1800 2200 1800 2200
Total thickness U-value (m) (W/m²K)
0.85
1.19
0.65 0.3
1.45 2.47
4.68 1.0 2200 2.52 1.0 1800 0.35 0.72 2 800 4.68 1.0 2200 2.52 1.0 1800 0.35 0.72 2 800 3.6 0.75 2400 Wooden screen lattice work added as shading 0.11 groups in simulation model
1.25
1.25
5.8
Table 3: Thermal properties of the brick walls Component
External walls Internal walls
Hollow red brick Cement mortar Hollow red brick Cement mortar
Thermal conductivity (kJ/hmK) 2.10 5.04 2.10 5.04
Capacity (kJ/kg K)
Density (kg/m³)
Total thickness U-value (m) (W/m²K)
0.84 1.0 0.84 1.0
1790 2000 1790 2000
0.25
1.82
0.15
2.65
Table 4: Maximum correlations with corresponding phase-shift Variable correlated with brick brick stone
Correspondence 0.88 0.96 0.61
Phase-shift in hours 7 0 const.
brick
0.97
const.
Highlights
The impact of thermal mass on indoor temperatures is examined through data interpretation from the field of statistical learning. For the high-mass model, regression analysis concluded that 11.5 °C increase in outdoor temperature results in 1 °C in indoor temperature. The energy demand for cooling for the high-mass model reduced with up to 72 %, when compared to the low-mass model.
PII: DOI: Reference:
S2352-7102(17)30155-9 http://dx.doi.org/10.1016/j.jobe.2017.05.007 JOBE265
To appear in: Journal of Building Engineering Received date: 15 March 2017 Accepted date: 6 May 2017 Cite this article as: Wael A. Yousef Mousa, Werner Lang and Waleed A. Yousef, Quantitative data analytic interpretation of indoor-outdoor temperatures in a high thermal mass structure, Journal of Building Engineering, http://dx.doi.org/10.1016/j.jobe.2017.05.007 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Quantitative data analytic interpretation of indoor-outdoor temperatures in a high thermal mass structure Wael A. Yousef Mousa¹*, Werner Lang¹, Waleed A. Yousef² ¹Technische Universität München, Germany ²Helwan University, Egypt *Corresponding author: [email protected]
Abstract The present paper investigates the impact of thermal mass on indoor temperature and reduction of cooling loads in summer. The major contribution of this paper is providing an objective assessment and a quantitative data analytic interpretation from the pattern recognition literature for the reported findings. The experimental study adopted one of the traditional stone structures of medieval Cairo. The house was monitored during summer days for Indoor and outdoor temperatures. Further data for local climate were obtained and given to TRNSYS 17 in which simulations were generated and validated against measured data. The absolute deviance error between simulated and measured indoor temperatures was 0.3 °C for a couple of monitored spaces. Data visualization and regression analysis of indoor temperature on two values of outdoor temperature show a relative stability of the indoor temperature, a direct result of the heat storage capacity of the stone walls. A quantitative interpretation of the regression equation tells that the indoor temperature increases by merely 1 °C if the outdoor temperature increased by 11.5 °C. Upon ambient-temperature-responsive natural ventilation, the maximum indoor temperatures were reduced, in average of 5.5 °C and 4.2 °C below ambient for two different spaces. A comparative analysis took place then between the base case and a modified model were the walls’ material was substituted with hollow red bricks. For the two rooms, the energy demand for cooling was found to be as less as 72 % and 56 % in the base case than the brick-walls model. Keywords: Thermal mass; indoor temperature; energy efficiency; thermal simulations, data analysis; pattern recognition
1. Introduction In hot and arid climates where daily temperature fluctuations are found, the thermal mass is effective in improving thermal comfort, as a major method in passive building design. Walls with sufficient amount of thermal mass, with low surface absorptivity, are recommended to be used in places where there is considerable diurnal temperature variation around design indoor condition [2]. To describe differences of thermal mass in construction, the terms heavy weight and light weight are correspondent to high and low thermal mass. The rate of heat transfer and the effectiveness of thermal mass are determined by various parameters; material thermal properties; location and distribution of the thermal mass in the building; insulation portion; ventilation and the occupancy pattern [3]. The use of thermal mass can be more effective with a significant diurnal variation of ambient temperature and/or diurnal variation in solar radiation intensity [21]. In the night-time cooling the gained heat is to be released to the outdoor space when it has lower temperature [4].
In addition to enhancement of the indoor air quality and providing cooling to the inhabitants, ventilation can be used for cooling the thermal mass of the building [12]. Thermal mass was also found to be more effective in reducing the rise of indoor temperature caused by heat gain through the external walls than that caused by penetrating solar radiation. The shading of the window has reduced the indoor average temperature by about 1 °C [8]. Measurements showed that in a hot and arid climate it is possible to achieve a reduction between 3 and 6 °C in a heavy constructed building without operating an air conditioning unit. The anticipated reduction depends on the amount of thermal mass, the ventilation rate, and temperature swing [11]. In hot climate, night ventilation is based on the principle that thermal mass can be cooled by night air and then acts as a heat sink to reduce cooling loads in the daytime [19]. A study has developed a simple model coupling thermal mass and natural ventilation. The experiments showed that the internal thermal mass affects the time lag of indoor air temperature. By comparing six different external walls it is found that the use of heavy wall with external insulation is predicted to have the lowest amplitude of indoor air temperature and hence the heavy walls with external insulation are suitable for naturally ventilation [23]. Pre-cooling attempts to remove some of the increased peak demand on the electricity grid by shifting the cooling load. The cooling thermostat set points are reduced in the period preceding the peak period to force the air-conditioner to operate [18]. Various researches investigated the potential of higher thermal mass for energy savings. Hypothetical modules of different types of Australian residential constructions were numerically analyzed. The analysis showed that the heavier mass constructions were found to be the most effective walling systems which offer the least energy consumption and indoor temperature fluctuations, especially when protected within the insulation portion [7]. As a result of optimizing thermal mass, different study concluded that the maximum savings in yearly transmission loads are about 17% for cooling and 35% for heating [1]. In cold climates, however, minimal mass is required to deliver warm air to adjacent spaces during daytime [13]. A study investigated the effect of thermal mass on annual heat load of buildings. The results indicated that increased thermal mass is not effective for decreasing annual heat demand in typical residential buildings [16]. The present paper departs from the fact that indoor air temperature changes periodically as outdoor temperatures, but with different phase shift and fluctuation amplitude [20]. The study investigates the correlation between indoor and outdoor temperatures. To objectively quantify the relationship between the ambient temperature and the temperature inside the building, a first order regression analysis is carried out and an equation is provided. The difference in temperatures is measured in terms of t-test and showed statistical significance. In addition to this qualitative measures, these relationships and findings was demonstrated using data visualization methods, e.g., matrix plot, and time series plots, for more comprehension and interpretation. Another set of objective-assessment is carried out for comparing the two wall materials, brick and stone. The correlation coefficient between the temperatures outside and inside the building in case of brick walls is much higher than the correlation coefficient for the case of stone walls. This shows the stabilizing effect of the stone’s heat storage capacity. The analysis also shows the increased efficacy of the thermal mass by adopting an ambient-temperaturedependent ventilation schedule. A comparative analysis of energy demands shows that a higher thermal mass can contribute to up of 72% savings in cooling demands.
2. Case Study and Validation of the Simulation Model This study adopts a traditional courtyard house built during the 15th century in Cairo (fig. 1). The walls are constructed of limestone in thicknesses between 60 and 80 cm. A couple of large halls in the first floor were monitored. The grand hall (GH), north-east oriented, has a large opening on the northwestern wall overlooking the courtyard and a couple of windows on the northeastern wall. The secondary hall (SH) occupies the northeastern
wing and overlooks the courtyard through several windows on southwestern wall, in addition to a window on the upper level of the southeastern wall. Each hall has a roof skylight. Indoor and outdoor temperatures were measured during August. The data loggers used are HOBO U12-012. According to the manufacturer, the measurement range of the loggers are -20° to 70° C and 5% to 95% RH. The accuracy of the loggers is ± 0.35° C from 0° to 50° and ± 2.5% from 10% to 90% RH. The loggers were set to continuously take readings each 30 minute. Table 1 describes the installation of the sensors in both halls and in the courtyard. The lowest indoor temperatures were recorded in the grand hall. The average maximum is found to be lower than that of the courtyard with 2.2 °C. The average maximum temperature was 35.2 °C. The average minimum was 28.6 °C. Generally, the grand hall (GH) showed a slight better performance than the secondary one (SH) with average difference of 1.1 °C and 1 °C for maximum and minimum temperature respectively. A simulation model has been created in TRNSYS 17. Further climatic data was collected on daily basis from the NOAA (National Oceanic and Atmospheric Administration). The recorded data includes hourly records for air temperature, dew point, relative humidity, wind velocity, and air pressure. The data collected for a time spanned from August 7 2014, one week before measurements, until September 8. The weather data file used in TRNSYS is the type TM2 which includes more extensive details adopted from the test reference file. However, data for ambient air temperature were replaced by records obtained in site; courtyard temperature. Figure 2 is a 3D model of the building (monitored spaces are shaded). Surrounding buildings were modeled as shading groups. Window screens were designed with modular sections of 5x5 cm. with ratio between the width and the depth 1:1 and 50% perforation, and modeled as shading groups in TRNSYS3d. All windows were set into the condition, no window, corresponding to the condition of being opened along the measurement period. Material thermal properties, as shown in table 2, were given to TRNBuild. Initial values for indoor temperature was set to 21° C and relative humidity to 50%. The solar radiation distribution mode was set into a detailed model. 3 values for air change rates (ACH) were defined to the simulation model, 6, 8, and 10/h. Simulations ran for annual round and results for the measurement periods were extracted. Results for Indoor temperature showed remarkable conformity in both spaces, GH and SH; high proximity was found between results upon all presumed values of air change rates. However, it is found that ACH 6/h achieved the highest level of conformity with measured indoor temperature for both halls. The absolute deviance error between simulated and measured indoor temperatures was 0.3 °C. Figures 3-6 demonstrate the validation of the simulation results against measured data and average indoor temperatures for both halls. The absolute deviance error (ADE) was calculated as: ∑ where,
and
(1)
are the simulated and experimentally measured temperatures respectively at a time step i.
3. Data Analysis and Quantitative Interpretation In this section, the relationship between indoor and outdoor temperatures is investigated upon an objective assessment and quantitative measures. A regression analysis is carried out for the base case, stone walls and a modified model where the lime stone wall material was substituted with hollow red brick and cement mortar, with the same thermal properties of materials used in modern building practices in Cairo. The mathematical treatment of regression analysis and linear models can be found in many texts, e.g., [5, 14, 15]. However, a practical approach associated with good rigorous foundation is portrayed in their seminal work Hastie, et. al. [9].
Thermal properties of the brick walls are shown in table 3. A data visualization of indoor and outdoor temperatures for the data acquired during the last two weeks of August, which fall into the measurement period, can illustrate the relationship between indoor and outdoor temperatures in the grand hall (GH) in both cases. As for the base case, stone walls, figure 7 is a matrix-plot of three variables; outdoor temperature ( ); indoor temperature with no ventilation ( ), and in-door temperature with ventilation and air change rate ACH of 6/hour ( ). The three subplots on the diagonal, from top left to bottom right, are histograms of the three variables , and respectively. The pair-wise plot of each of the three variables results in the six subplots located off diagonal of the figure, (with obvious symmetry). For example, the subplot on the first column and second row is a plot of , vs. ; while vs. is located on second column and first row. From the histograms, it is obvious that and have very similar distributions, a direct consequence of the air flow and exposure to the ambient temperature. In contrast, the distributions of , indoor temperature with no ventilation, and are dissimilar in two aspects. First, the temperature range (31 to 33.5 °C) vs. (29 to 40 °C); this conveys the effect of the wall material in stabilizing the temperature inside. Second, and very interestingly, the shape of the distribution, where has a bi-modal shape (at temperatures 29 and 37 °C) and has a uni-modal shape (at temperature 32.5 °C). In the vernacular, this means that even when the ambient temperature frequently occurs at 29 °C and 37 °C (with variation), the indoor temperature frequently occurs only at 32.5 °C (with variation). This is another stabilizing effect of the wall material. By applying the same visualization for the brick-walls case (fig. 8) the temperature inside the brick building with is almost the same pattern as the temperature outside with just a scaling factor. However, it is evident that there is a phase-shift between and for the brick-walls case of almost 7 hours. For more objective assessment, a correlation analysis between and for both brick and stone cases is investigated (fig. 9). It revealed that the maximum correlation between and for the case of brick is occurred at 7 hours of delay; this correlation is 0.88. The interpretation of this strong correlation, yet delayed, is that the temperature pattern inside the building follows, almost linearly (as high correlation coefficient always means) the temperature outside but with a delay of 7 hours. This delay is caused by the brick thermal properties. On the other hand, the maximum correlation between and is 0.96 and occurs at 0 phase-shift, which means that the temperature inside the brick building with ventilation is almost the same pattern as the temperature outside with just a scaling factor. This was already clear from the previous matrix plot. For a clearer blueprint, table 4 reports the maximum correlations, along with the corresponding phase-shift, for four cases; each is between on a hand and the inside temperate with/without ventilation for brick/stone cases. Interestingly, the stone case has almost a constant correlation with regardless to the phase-shift; and this correlation is smaller than that of the brick case. This is an evidence of the stabilizing effect of the stone case. It is more illustrative now to re-draw the matrix plot for the brick case but with replacing with a 7-hour phaseshifted version. The new matrix plot is displayed in figure 10. The strong correlation between (7-hour phaseshifted) and is obvious now. The histogram of , if compared with its analogue of the stone case, is more spread. This is another evidence for the stabilizing effect of the stone walls. The data visualization for the high thermal mass (stone case) conveys the relationship between outdoor and indoor temperatures qualitatively. A quantitative description however can be provided using regression analysis to estimate the linear relationship that appears in the figures. A straight forward first order regression analysis gives: Mean of
(2)
Figure 11 is a plot of this regression line equation (in black), where the blue points are the actual readings appearing on the matrix plot discussed above. The regression line comes in-between the data points to show the
average trend of the relationship between these two variables. The root-mean-square-error (RMSE) of this line is 0.37 degree, which shows accurate regression. The quantitative interpretation of this regression equation says that an increase of 1 degree in the ambient temperature results in an increase of only 0.087 degree inside. Said differently, the inside temperature will increase by 1 degree only if the outside temperature increases by (1/0.087 = 11.5) degree. This emphasizes quantitatively the stabilizing effect of the wall material that is observed above from reading the histograms in the data visualization step. When the regression above is repeated on the whole period of summer time (June-August); it gives the following equation: Mean of (3) Figure 12 is an analogue for figure 11. The RMSE of this equation is 1.3 degree, obviously larger than the RMSE obtained for regression during only the last two weeks of Aug. This is foreseeable since more explanatory variables (than merely ) will be needed to model the relationship when the period extends and hence more factors interact. In the equation above, the variable is called "predictor" and the variable is called "response"; this terminology is borrowed from the literature of statistics. From the physics of the current problem it can be anticipated that depends, in parallel to , on the temperature outside the building hours earlier, a direct result of the capacitance effect of building material (Limestone). Accordingly, a table of 13 columns is formulated; the first column includes the outdoor temperature at a moment and the other 12 columns are the temperature each preceding hour. The correlation coefficient was calculated and the smallest correlation was with the temperature outside 12 hours earlier ( ). Then is regressed on and , and obtained the equation: = 15.1313+ 0.2979
+ 0.2056
(4)
Figure 13 is the 3D analogue to figures 11-2. The RMSE of this equation is 1.05 degree, a 19% reduction when compared to the 1.3 mentioned above. Obviously, when is replaced by any other temperature that is more correlated with , i.e. , a higher regression error will be obtained. The interpretation of this regression equation is of interest. The coefficients of both and are close to each other, which means that the temperature outside now and 12 hours ago are almost equally important in predicting the temperature inside, which can be attributed to the heat storage capacity of the walls’ material However, the reduction in error is not very significant; only 19% as indicated above. More elaborate regression methods can be employed to reduce the error and to better formalize in terms of outdoor temperature. For example, slicing the data, as it appears from figures 12-3 then building a regression model for each slice will build a more accurate equation. However, this regression analysis is carried out to demonstrate the efficacy of the thermal mass of the building material, since the prediction of indoor temperature is already carried out in TRNSYS. It should be noted that employing the two-explanatory variable ( and ) for the data of the last two weeks of August does not help in reducing the RMSE below the 0.37 degree mentioned upfront. Moreover the coefficient of for this data is almost zero, producing a very similar equation to equation (4).
4. Indoor Temperature and Energy Demand upon Weather Responsive Ventilation schedule The use of thermal mass can reduce peak heating or cooling load and hence the energy consumption, especially when it is integrated with night ventilation [22]. In order to understand the correlation between indoor
and outdoor temperatures, different ventilation conditions were applied; closed and opened windows. For the open window condition, it is applied for both daylong schedule and for a more weather responsive schedule between 8 pm and 12 pm so the interior space could be protected against overheating through the hot air during daytime. The average diurnal differences significantly vary when ventilation is active along the day where higher correlation between indoor and ambient temperature takes place. The heat loss through ventilation (convective heat loss) is in proportion to the air exchange rate, difference in temperature between the inside and the outside, and the capacity of air. Despite the high heat storage capacity of the stone walls, a higher correlation with ambient temperature occurs with significant temperature fluctuation between day and night temperatures. When an air change rate value is defined, the indoor temperatures change dramatically as the heat flux increases according to the equation: (5) where is the heat capacity of air (1006 J/kgK), is density of air (1.2 kg/m³ for dry air), is air volume flow (m³/s), is the inside air temperature (°C), and is the ambient air temperature (°C). Real values of air change rates, in both halls of the building adopted in this study, were predicted from numerous CFD simulations which are described in detail in Ref. [10]. The values were given to TRNSYS as an equation for the function of ACH as an output; while the variables; wind direction; velocity; and time of the date were defined as inputs from the weather data file. According to the psychometric chart of Cairo, the accepted range of temperature is between 20 °C and 26 °C. To set the ventilation schedule during summer to correspond to the ambient temperatures, a conditional function is added to the ACH equation statement. Thus, ventilation schedule was assigned according to this condition: , where and stand for greater than or equal, and less than respectively, and is the ambient temperature. This means that windows will be opened only when ambient temperature ranges between 20 and 26 °C. Figure 14 shows the simulation results for indoor temperatures for both halls GH and SH during summer, June-August, upon ambient temperature-dependent ventilation schedule. The maximum indoor temperatures were remarkably reduced, in average of 5.5 °C and 4.2 °C below ambient for GH and SH respectively. The highest maximum values for GH and SH are found to be 31.1 °C and 32.7 during August. These values remain quite acceptable in as much as being 11.9 °C and 10.3 °C below ambient temperature which reaches 43 °C. The wide difference here is attributed to the capacitance of the wall material thermal mass as previously explained. The average minimum however was 1.4 °C and 2 °C above ambient for GH and SH respectively (fig. 15). The average maximum values for GH and SH were 28.8 °C and 30.1 °C.
4.2 Indoor temperature The hollow bricks, due to the lower storage capacity, absorb and release heat much faster than the stones do and thus are more influenced by the ambient temperature fluctuations. This behavior can be more tangible in the grand hall than in the secondary hall where the south-west wall is more exposed to solar radiation, in terms of time span, and the secondary hall hence has higher temperatures than the grand hall within all conditions yearround. On the contrary the indoor temperature variation between the two cases in winter is not as wide as in summer, though the energy demand for heating significantly differs due to the lower thermal capacity of the brick walls. Figure 16 shows the indoor temperatures during summer, June-August, for both the base case and brickwalls model. As shown in figure 17 for an average summer day (Jun-Aug), the base case had a maximum temperature as lower as 1.8 °C than the brick-wall model. The difference in minimum temperatures, however, is
comparatively smaller, 0.7 °C. Expectedly, the base case showed less correlation to the outdoor temperature fluctuation than the other case. This can be explained considering the stone’s higher thermal mass which keeps the indoor temperature more stable when compared to the brick-walls case where the indoor temperature keeps to increase until night time as the heat being transferred to the indoor space rather than to the outside. In average the base case achieved 1.4 °C lower than the brick-walls model. For two different cases, (stones) and (bricks), are computed, which equals to: average of , where is an index running over all readings. Statistical significance of this difference is then tested. Statistical significance confirms whether the calculated temperature difference occurs only by coincidence or a consequence of the corresponding design. The statistical test used in this analysis is the two-sided t-test, a standard test in statistics literature to measure the difference between the means of two populations (a population here in this context is the readings of indoor temperature for a particular design). The hypothesis is tested that the means of the two populations are the same; then the hypothesis either accepted or rejected at some level of significance. For example, at summer time (June-Aug), the first row of average difference in the table reads as follows: The average difference between the indoor temperature for the base case and the brick-walls model is -1.4 degrees; and a two-sided t-test that tests the hypothesis that "the two populations of temperature have the same mean value" is rejected at 0.05 level. The 0.05 level means a confidence level of 95% (= 100 x (1-0.05)) that what has been concluded about the temperature difference is correct and statistically significant (referred to as 1.0). 4.3 Energy demand In naturally ventilated buildings people generally accept greater climate variability [6] and the indoor temperatures achieved by adopting the weather responsive ventilation schedule might be accepted in this context. However, it remains subject to the inhabitants’ culture and behavior In such a relatively harsh hot climate, it remains expected to adopt mechanical cooling devices, if they are available, in response to even slight overheating. Moreover, the ambient temperatures, and hence indoor temperatures, significantly drop during winter time which causes states of dissatisfaction. The energy performance of the base case was hence compared against the brick-walls model to demonstrate the impact of the thermal mass in relation to the quantitative analysis and interpretation previously described. As considered for the ventilation schedule, a temperature between 20 and 26 °C is adopted as an accepted range. The simulation model was adapted in TRNBuild for both cooling and heating types which would be operated for an indoor temperature above 26 °C and below 20 °C respectively. The ventilation schedule and hence the ACH condition were in reverse disabled. As the windows would be closed during cooling and heating times, a conditional statement was hence added to the ventilation schedule as: ( ). Figures 18-9 show the monthly energy demand for cooling (+) and heating (-) for both halls to keep the indoor temperature between 20 and 26 °C in the base case and the modified model respectively. For the brickwalls model, the energy needed for both cooling and heating is found to be significantly higher than in the base case which can be simply understood in light of the thermal capacity of the wall material. In winter time, the indoor temperature variation between this model and the base case is not as wide as in summer. However, the energy needed to keep the indoor environment within the required range is much higher than in the base case as the walls do not reserve the heat as much as in the stone case and hence the indoor space would not be protected against temperature fluctuations. The lower heat storage capacity of the hollow bricks will result in more indoor temperature fluctuation Considering the relatively low density of the hollow red bricks, the role of the stone’s higher thermal mass can hence be evident through its ability to store the absorbed heat, which results in less temperature fluctuation along the day. According to equation (5), the energy intake ( ) required to heat up 1 m² of the stone wall is C. However, for the brick wall ( ) is C
However, the differences in energy demand between the base case and the modified model do not proportionally correspond to the differences in indoor temperatures. In other words, the stone walls store the heat during daytime and release it at night to the cooler outdoor. The indoor temperature therefore can significantly drop during nighttime, and therefore mechanical cooling will be switched off. The time-shifting accomplished by the thermal mass can move the energy demand for cooling or heating from the peak hours [17]. On the contrary, in the brick-walls model, the wall material keeps transferring the heat to the indoor environment, which results in the temperature rising continuously even in night-time. Therefore, the temperature along the day remains higher than the level needed to keep the indoor temperature within the accepted range. Thus, more operation hours are demanded to cool down the space. The same interpretation can conversely be valid for the heating process. Figure 20 shows a comparison between the annual energy demand of cooling and heating between the base case and the modified model for both halls GH and SH. From the figure it can be concluded that the grand hall (GH) in the base case demands energy as less as 72 % and 49 % than the brick-walls model for cooling and heating respectively. This can obviously reflect the impact of the wall material thermal mass on the energy efficiency of the building, especially in hot weather conditions. This gap between the energy demands for both cases significantly narrows down in the secondary hall to 56 % for cooling. However, the difference in energy demand for heating remains too close, 45%, as the secondary hall has higher temperature degrees during winter in both cases due to the higher amounts of solar radiation transmitted through the south-west windows. Conclusion Simulation model was validated against real measured data for indoor temperature in a traditional stone structure. The time shifting due to the high thermal mass of the walls achieved a statistically significant reduction of indoor temperature with an average of 1.4 °C, when compared to a brick-walls model. Upon ambient-temperaturedependent natural ventilation, the maximum indoor temperature in the base case was reduced, in average of 5.5 °C and 4.2 °C below ambient in two different spaces. On the contrary, the brick walls keep transferring the heat to the indoor environment along the day, which results in the temperature rising continuously even during nighttime, and hence more active cooling is needed. In terms of energy demand the base case reduced up to 72% and 49% for cooling and heating respectively. Although both acquired and simulated data may deliver some known information, the present paper stresses on the objective assessment and quantitative measures, borrowed from the field of pattern recognition and statistical analysis. Assessment of the relationship between indoor and outdoor temperatures is provided in terms of regression analysis, statistical tests, and correlation measures. A regression of indoor temperature on simultaneous outdoor temperature and before 12 hours shows that indoor temperature does not exceed 32.5 °C even when the outdoor temperature reaches 40 °C. The method can draw better understanding of the relationship between building design parameters (inputs) and indoor temperature and energy consumption (outputs). This can be adopted in multi-objective optimization studies for estimating the unknown input-output dependency using a limited number of observations. Acknowledgment The study is a part of a research work financed by the German Academic Exchange Service (DAAD).
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Figures
Figure 1: External view of the south west facade
Figure 2: TRNSYS 3D model
Figure 3: GH, simulation results for indoor temperature against measured data
Figure 5: SH, simulation results for indoor temperature against measured data.
Figure 4: GH, average day temperature, simulation results against measured data. ADE ± 0.3 °C
Figure 6: SH, average day temperature, simulation results against measured data. ADE ± 0.3 °C
Figure 7: GH, matrix-plot of outdoor and indoor temperatures, stone
Figure 8: GH, matrix-plot of outdoor and indoor temperatures, hollow red bricks
Figure 9: GH-time-series plot of , for brick design, and for the stone design, all versus the sampling hour (time step) across the two weeks.
Figure 10: GH, matrix-plot of outdoor and indoor temperatures, hollow red bricks, replacing with a 7-hour phase-shifted version.
Figure 11: GH, regression of indoor temperature on outdoor temperature, 17-31 Aug.
Figure 12: GH, regression of indoor temperature on outdoor temperature, Jun.-Aug.
Figure 13: GH, regression of indoor temperature on simultaneous outdoor temperature and before 12 hours, Jun.Aug.
Figure 14: GH-SH, simulation results for indoor temperatures with ambient temperature-dependent ventilation, Jun-Aug.
Figure 16: GH, indoor temperature, base case vs. modified/brick-walls model. June-August
Figure 15: GH-SH, average summer day indoor temperatures with ambient temperature-dependent ventilation
Figure 17: GH, indoor temperature, base case vs. modified/brick-walls model, average summer day
Figure 18: GH-SH, monthly energy demand (kW/h) for cooling and heating, operation on 26 and 20 °C respectively, base case (stone walls)
Figure 19: GH-SH, monthly energy demand (kW/h) for cooling and heating, operation on 26 and 20 °C respectively, modified model (brick walls)
Figure 20: GH-SH, total annual energy demand (kw/h) for cooling (+) and heating (-), base case vs. modified/brick-wall model.
Tables Table 1: Sensors installation Space Grand hall
Secondary hall Courtyard
Sensor GH1 GH2 GH3 SH1 SH2 CRT
Position Ceiling-hanged at 2.5 m from F.F.L. ceiling-hanged at 9 m from F.F.L. Mounted on window at 2.5 m from F.F.L Ceiling-hanged at 2.5 m from F.F.L Mounted on window screen at 4 m Hanged at 4 m from G.F.L
Table 2: Construction material and thermal properties
Component
Material
External walls Internal walls Ground floor Flat roof
Limestone Lime mortar Limestone Lime mortar Limestone
Internal floor Windows
Limestone Sand Wood Limestone Sand Wood Glass Frames
Thermal conductivity (kJ/hmK) 4.68 3.13 4.68 3.13 4.68
Capacity (kJ/kg K)
Density (kg/m³)
1.0 1.0 1.0 1.0 1.0
2200 1800 2200 1800 2200
Total thickness U-value (m) (W/m²K)
0.85
1.19
0.65 0.3
1.45 2.47
4.68 1.0 2200 2.52 1.0 1800 0.35 0.72 2 800 4.68 1.0 2200 2.52 1.0 1800 0.35 0.72 2 800 3.6 0.75 2400 Wooden screen lattice work added as shading 0.11 groups in simulation model
1.25
1.25
5.8
Table 3: Thermal properties of the brick walls Component
External walls Internal walls
Hollow red brick Cement mortar Hollow red brick Cement mortar
Thermal conductivity (kJ/hmK) 2.10 5.04 2.10 5.04
Capacity (kJ/kg K)
Density (kg/m³)
Total thickness U-value (m) (W/m²K)
0.84 1.0 0.84 1.0
1790 2000 1790 2000
0.25
1.82
0.15
2.65
Table 4: Maximum correlations with corresponding phase-shift Variable correlated with brick brick stone
Correspondence 0.88 0.96 0.61
Phase-shift in hours 7 0 const.
brick
0.97
const.
Highlights
The impact of thermal mass on indoor temperatures is examined through data interpretation from the field of statistical learning. For the high-mass model, regression analysis concluded that 11.5 °C increase in outdoor temperature results in 1 °C in indoor temperature. The energy demand for cooling for the high-mass model reduced with up to 72 %, when compared to the low-mass model.