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An accurate calculation model of solar heat gain through glazed surfaces
Energy and Buildings 43 (2011) 269–274
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Review
An accurate calculation model of solar heat gain through glazed surfaces Giuseppe Oliveti ∗ , Natale Arcuri, Roberto Bruno, Marilena De Simone Mechanical Engineering Department, University of Calabria, V. P. Bucci 44/C, 87036 Rende (CS), Italy
a r t i c l e
i n f o
Article history: Received 19 August 2010 Received in revised form 11 October 2010 Accepted 5 November 2010 Keywords: Building energy performances Heat gains Simplified methods Technical standards
a b s t r a c t A model for the calculation of solar heat gain through glazed surfaces, to be used in the simplified calculation of thermal energy requirements in air-conditioned buildings, is proposed. The model uses the effective absorption coefficient of the indoor environment to take into account that the entering energy is in part absorbed by the surfaces of the cavity and in part is dispersed outwards, through the same glazed surfaces. The effective absorption coefficient is calculated by means of a correlation, and is made to depend on the average absorption coefficient of the internal opaque surfaces of the environment, on the glazed fraction and on the transmission coefficient of diffuse radiation of the glazed system. This coefficient permits a more accurate evaluation of solar heat gain through glazed surfaces, obtained adding: the direct optical contribution, produced by solar radiation absorbed by the indoor environment, the direct secondary contribution, produced by external solar radiation absorbed by the glazed surfaces, the indirect secondary contribution, produced by the absorption of reflected radiation exiting the indoor environment. The model, validated by means of comparisons with the TRNSYS 16 code, was used for the verification of the monthly solar heat gain calculation procedure of EN ISO 13790:2008. © 2010 Elsevier B.V. All rights reserved.
Contents 1. 2. 3. 4. 5.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effective cavity absorption coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A more accurate calculation model of solar heat gains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Energy comparisons With En Iso 13790 monthly method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Introduction In putting into effect Directive 2002/91/CE [1] the CEN, following mandate 343 “Energy Performance of Buildings Directive” (E.P.B.D.), prepared the EN ISO 13790:2008 Standard [2] which represents one of the most important documents for the calculation of energy performance of residential and non-residential buildings. The Standard permits identification of the energy required for heating and cooling by means of three different calculation methods of differing complexity. The first is a quasi steady state monthly method, acknowledged with the Italian UNI TS 11300-1:2008 Standard [3], the second is a simplified dynamic hourly method and the third is a detailed dynamic simulation method of the building described in EN 15265:2007 [4]. In the first and second methods, the dynamic aspects linked to the variability of weather data are cal-
∗ Corresponding author. Tel.: +39 0984 494605; fax: +39 0984 494673. E-mail address: [email protected] (G. Oliveti). 0378-7788/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2010.11.009
269 270 272 272 273 274
culated differently. In the first, by means of corrective coefficients, denominated gain utilisation factor in winter, and loss utilisation factors in summer. In the second, thermal behaviour of the building is described by some simplifications of heat transmission mechanisms between indoor and outdoor environments, which lead to an electrical network equivalent to three nodes, five resistances and a representative capacity of the thermal mass of the structures. All three models are based on the energy balance formulated considering the thermal zones of the building, in order to attain utilised energy requirements and, successively, for the determination of primary energy requirements by the plants. Energy use and primary requirement values are used for building energy classification and their evaluation must be as accurate as possible. In the energy balance of the building, a significant contribution is represented by solar heat gain by means of glazed surfaces. In dynamic simulation models, absorbed solar power is calculated by resolution of the radiant field in the solar band, obtained through the determination of solar irradiance of the opaque and glazed surfaces which delimit the spaces. Such evaluations are usually carried
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out presuming that solar irradiation transmitted by the glazed surfaces is just diffused [5], in such a way as to eliminate entering radiation directional properties, or rather such properties can be taken into account, considering incident irradiation subdivided into beam and diffuse radiation, and distinguishing between areas illuminated directly by beam radiation and not-illuminated areas, by means of meshing of the internal surfaces of the environment [6,7]. In simplified models, entering solar radiation through glazed surfaces is commonly held to be completely absorbed by the cavity surfaces (black body cavity hypothesis). This formulation overlooks the solar irradiation fraction which is reflected outside by the internal surfaces of the cavity through the same irradiated glazed surfaces, and other possible glazed surfaces present. Absorbed solar radiation is calculated by means of an optical and thermal parameter of the transparent system denominated total solar energy transmittance for normal incidence g, modified with correction factor Fw to take into account glazed system optical properties variability with the direction of solar radiation. This parameter is used to identify solar performance of the glazed system, and does not depend on the geometrical and optical properties of the indoor environment. Due to the low thermal heat loss coefficient values required by the building shell to limit winter losses due to transmission, the evaluation of solar contribution through glazed surfaces assumes great importance for the correct determination of thermal energy requirements. Moreover, in the quasi steady state method, the incorrect estimation of solar contribution, both in winter and summer, leads to an erroneous determination of monthly utilisation factors, which also depend upon the ratio between solar energy absorbed by the environments, increased by possible endogenous energy, and the thermal energy exchange with the outdoor environment. The utilisation factors introduced in the energy balance, in order to take the dynamic behaviour of the building into account, require a correct evaluation of solar heat gains. Consequently the hypothesis, commonly adopted and present in recent works [8,9], of considering completely absorbed solar energy in the balance equation and determination of utilisation factors, appears criticisable. In such a case, utilisation factors assume the role of corrective factors as reported in Annex I EN ISO 13790, having to take into account both the incorrect evaluation of solar heat gains, as well as dynamic phenomena. Furthermore, in the evaluation of cooling energy requirements, an overestimation of solar heat gains leads to an increase in the cooling period, with a consequent thermal energy increase. The evaluation of solar heat gains in sunspaces adjoining airconditioned environments is addressed by the formulation of simplified models which estimate the effective absorption coefficient [10]. An approximate equation obtained in the hypothesis that solar radiation on internal environment surfaces is both constant and equal to the average value, is provided by Duffie and Beckman [5], who evaluate the solar absorption coefficient as the ratio between absorbed and entering energy, which is equal to the sum between absorbed and lost energy. In this work a method for the calculation of solar heat gains, through glazed surfaces to be used in simplified evaluation procedures of building thermal energy requirements, is proposed. It uses the entering solar radiation effective absorption coefficient, evaluated with a correlation created by the authors, which depends upon the optical and geometrical properties of the indoor environment and the transmission coefficient of the diffuse radiation of the transparent surfaces. Solar energy absorbed by the indoor environment is calculated as the sum of three contributions: the first optical, produced by solar radiation transmitted by glazed surfaces, the second direct convective-radiative, which evaluates the fraction of solar radiation absorbed and provided to the indoor envi-
ronment by the glazed surface which is radiated directly by the sun, the third indirect convective-radiative, produced by solar radiation reflected by internal surfaces and absorbed by glazed surfaces. The proposed calculation method permits the accurate evaluation of solar contributions, in particular in environments with several glazed surfaces with differing exposures, such as buildings with a glazed external shell and environments with large glazed surfaces used for exhibitionsetc. The calculation method was validated with reference to parallelepiped environments with one or more glazed surfaces with differing exposure, by means of a comparison of solar heat gain obtained with the model implemented in Type 56 of TRNSYS 16 code [11], which uses data from the software WINDOW 5.2 in order to evaluate the optical properties of transparent surfaces [12]. Successively, a critical comparison was developed between the results obtained applying the proposed calculation methodology and those determined applying the EN ISO 13790 Standard. 2. Effective cavity absorption coefficient The effective absorption coefficient of the indoor environment is defined as the ratio between absorbed solar energy and entering solar energy. Absorbed energy is calculated as the difference between the solar energy entering through the glazed surfaces Qsol,in and that reflected out of the cavity Qsol,out ˛cav =
Qsol,in − Qsol,out Qsol,in
(1)
Entering radiation directional properties render the optical field within the environments highly complex. A considerable simplification is obtained considering entering solar radiation, which goes beyond the glazed surface, as uniformly diffuse radiation. The hypothesis is acceptable if one considers that, usually, beam radiation reflection phenomena are evaluated considering indoor environments without furnishings and internal shading devices, situations which are not commonly encountered. A widespread simulation campaign carried out with the TRNSYS code, with reference to parallelepiped shaped environments with different ratios between plant linear dimensions, with one or more glazed surfaces with differing exposures, has highlighted that the effective absorption coefficient of the cavity ˛cav can be made to depend upon: - the average absorption coefficient in the solar band of the opaque internal surfaces of the environment
˛ · Ai i i ˛m =
(2)
A i i
- the glazed fraction of the air-conditioned space, by the ratio Agl,j and the opaque one of the cavity
between the glazed area
j
Ai
j
A j gl,j = A i i
(3)
- the optical properties of the glazed system defined by the diffuse solar radiation transmission coefficient d . In the simulations ˛m was made to vary between 0.20, very light smooth surfaces, and 0.80, dark and rough surfaces. For each wall, the glazed fraction varied between 25% and 100%, in such a way as
G. Oliveti et al. / Energy and Buildings 43 (2011) 269–274
Fig. 1. Cavity absorption coefficient in relation to the glazed fraction for three values of the average absorption coefficient of the indoor environment. Double glazing.
Fig. 2. Cavity absorption coefficient in relation to the ratio between the effective absorption area of the indoor environment, for the considered glass systems.
to obtain different values of the geometrical index . Three glazed systems were considered: 4 mm clear single glass, double glazing with 4 mm clear glass and an air gap of 16 mm, and triple glazing with 2.5 mm clear glass and an air gap of 12 mm. The corresponding transmission coefficient values d are equal to 0.79, 0.59 and 0.51. In Fig. 1 cavity absorption coefficient values ˛cav are reported, which were obtained with the TRNSYS code in relation to the ratio , for three values of the average absorption coefficient of the internal surfaces, and for a clear double glazing. In Fig. 2 ˛cav values were diagrammed relating to the ratio ˛m / , which represents the effective absorption area of the indoor environment, per glazed square meter, for the three considered glazed systems. The figures highlight how the absorption coefficient varies with an increase of the glazed fraction and a decrease of the absorption capacity of the opaque walls, and also the importance of the parameter ˛m / for the environment on which the cavity absorption coefficient can be made to depend. The least squares criterion was used to interpolate the ˛cav values obtained with the simulation programme. This procedure permitted the obtainment of an accurate expression of the cavity
271
Fig. 3. Reduction of the cavity absorption coefficient with an increase of the glazed fraction for indoor environments with ˛m = 0.20.
Fig. 4. Reduction of the cavity absorption coefficient with an increase of the glazed fraction for indoor environments with ˛m = 0.50.
absorption coefficient, which can be expressed as:
˛cav = 1 − a · Exp · −b ·
˛ c m
(4)
with coefficients a, b and c quadratic functions of the transmission coefficient of the diffuse radiation of the glazed system d , calculable with the relations: a = 3.500 − 5.453 · d + 4.516 · d2 b = 3.700 − 5.388 · d + 3.462 · d2
(5)
c = 0.124 + 0.545 · d − 0.355 · d2 The statistical comparison between the values calculated with TRNSYS and those obtained with the preceding correlation present a correlation index r = 0.999, an average relative percentage error ε = 0.11% and a maximum error εmax = 1.2%. In Figs. 3 and 4, the reduction of the cavity absorption coefficient upon the increase of the glazed fraction , calculated with the correlation in the case of ˛m = 0.20 and ˛m = 0.50, is reported. In the same figures, trend of ˛cav in the absence of a glazed system, or rather d = 1, is reported to highlight the increase of the absorp-
Table 1 Optical and thermal characteristics of the considered glazed surfaces. Glazed system
ggl,n [–]
b,n [–]
d [–]
˛b,n1 [–]
˛b,n2 [–]
˛b,n3 [–]
12 [W/m2 K]
23 [W/m2 K]
qi [–]
qe [–]
Single Double Triple
0.857 0.761 0.705
0.830 0.693 0.624
0.749 0.590 0.512
0.095 0.101 0.084
– 0.080 0.069
– – 0.055
– 5.03 5.46
– – 5.46
0.027 0.068 0.081
0.068 0.113 0.127
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G. Oliveti et al. / Energy and Buildings 43 (2011) 269–274
tion coefficient produced by the presence of the glazed system. Such a growth increases with the glazed fraction, and for environments with ˛m = 0.50 does not exceed 20%, while for reflective environments (˛m = 0.20) it is more significant and reaches 76%. The simplified model reported in [5] was also verified by means of a comparison of the results obtained with the TRNSYS code. The hypothesis of believing radiation to be constant on internal opaque surfaces and equal to the average value, is held to have been verified in the case of reflective environments (˛m = 0.20) with very contained glazed fractions = 0.033, in such a case the relative deviation between the values does not exceed 6%; while for non-reflective environments with high glazed fractions (˛m = 0.80, = 0.600), the deviation for single pane reaches 38%. 3. A more accurate calculation model of solar heat gains The removal of the hypothesis that the environment behaves like a black cavity with regards to entering solar radiation, led to a model which is closer to the effective optical behaviour of the cavity. Solar heat gains through glazed surfaces are evaluable with the relation: Qsol =
Fsh,k · Fsh,gl,k · (1 − FF,k ) · Aw,k · Isol,k · Fw,k · [b,n · ˛cav
k
+ qi + b,n · (1 − ˛cav ) · qe ],k · t
(6)
Fsh and Fsh,gl are reduction factors for shading produced by external elements and for the presence of mobile shading devices which are relative to the surface k, FF area reduction factor relative to the frame, Aw,k gross window area, Isol,k average solar irradiance, Fw,k average corrective factor, e,n beam solar transmission coefficient for normal incidence, qi secondary internal radiative-convective heat transfer factor, qe secondary external radiative-convective heat transfer factor and t the time step. In relation (6), in square brackets, the first term b,n ˛cav represents the direct optical fraction of solar radiation absorbed by the indoor environment, the second term, the secondary fraction produced by absorption of incident external solar radiation by the glazed system and the third term the secondary indirect fraction, generated by the fraction reflected by internal surfaces b,n (1 − ˛cav ), exiting the indoor environment through the glazed surfaces. In the case of black cavity (˛cav = 1) the term linked to the secondary indirect contribution is annulled. While the effective absorption coefficient ˛cav characterises the indoor environment with reference to energy entering through the glazed surface, the parameter gn,eff = b,n · ˛cav + qi + b,n · (1 − ˛cav ) · qe
(7)
characterises the absorption of solar radiation in the system constituted by the indoor environment and glazed surfaces, with reference to incident solar energy. It is possible to give it the name of effective solar heat gain coefficient of the environment comprehensive of glazed surfaces, and it is a function of the optical and thermal properties of the glazed surfaces and of the optical properties and geometrical characteristics of the indoor environment. The use of the relation (7) requires the determination of the parameters e,n , qi and qe obtainable from the EN 410 Standard [13]. Given the total solar energy transmittance for normal incidence of the glazed system ggl,n , the relation ggl,n = b,n + qi
(8)
permits calculation of the transmission coefficient e,n , expressions of the secondary heat transfer factor qi for single, double and triple glazing being known. The external secondary heat transfer factor qe is calculable, for example for a transparent system with three
panes, with the relation: qe + qi = ˛b,n1 + ˛b,n2 + ˛b,n3
(9)
with ˛b,n1 , ˛b,n2 and ˛b,n3 direct absorption coefficients for normal incidence respectively of the first, second and third pane of the glazed system. Validation of the calculation model was obtained with the TRNSYS simulation code, considering a reference environment 6 m × 6 m in plant dimension and 3 m in height, with vertical dispersive walls facing south, east and west, and the remaining vertical and horizontal opaque walls neighbouring air-conditioned environments. The opaque surfaces were presumed to be light with a solar band absorption coefficient equal to 0.30. The glazed systems considered are those defined previously, with air gap thermal resistance equal to 0.190 m2 K/W for double glazing, and 0.173 m2 K/W for triple glazing. In Table 1 the following optical parameters for normal incidence are reported: total solar energy transmittance ggl,n , beam solar transmission coefficient e,n , diffuse radiation transmission coefficient d ; direct absorption factors of the panes ˛e ; thermal conductance between the panes ; and the internal qi and external qe secondary heat transfer factors. With an increase in the number of panes which constitute the glazed system, optical parameters ggl,n , e,n , d , are reduced, while the internal qi and external qe heat transfer factors increase. In order to verify the results provided by the calculation model, with reference to the considered indoor environment, several optical configurations were evaluated, obtained by varying the glazed areas, their exposure, and the radiated glazed surfaces. The following parameters were evaluated: cavity absorption coefficients ˛cav and the three contributions of solar heat gain, represented by the optical fraction absorbed by the cavity b,n · ˛cav , by the direct secondary fraction qi and the indirect secondary fraction b,n · (1 − ˛cav ) · qe . In the investigation, it was presumed that shading reduction factors Fsh and Fsh,gl were equal to one, and the area reduction factor FF equal to zero, perpendicular incident solar irradiation Isol that provides a correction factor Fw = 1, since in this evaluation phase the directional effects of solar radiation are not involved. Table 2 reports the values presumed by the absorption coefficient and the three solar gain fractions, direct optical, direct secondary and indirect secondary, the sum of the three fractions and the relative percentage weight, as well as the sum of the three fractions calculated with the TRNSYS code and the error percentage between the total fractions calculated with the code and the model. The new calculation procedure provides accurate estimations, with a deviation which does not exceed 1%. The cavity absorption coefficient varies in a significant manner with the glazed area, with values between 0.93 and 0.44 for single glass, between 0.94 and 0.52 for double glazing, and between 0.95 and 0.56 for triple glazing. The direct optical fraction varies between 96%, for an environment with single glazing and = 0.033, and 75% for an environment with triple glazing and = 0.600. The indirect secondary contribution produced by reflected radiation, becomes, in percentage, significant in environments with > 0.230 for which values comprising between 3.4% and 8.0% are obtained. 4. Energy comparisons With En Iso 13790 monthly method Countries of the European Economic Community, in procedures adopted for building energy certification, have prevalently acknowledged the energy requirement monthly calculation method of EN ISO 13790 [14]. This method considers solar radiation entering glazed surfaces to be completely absorbed. The adopted hypothesis appears plausible for indoor environments with a ratio
0.36 −0.33 −0.41 −0.34 −0.01 0.41 1.00 0.03 0.29 −0.24 −0.34 −0.29 −0.06 0.24 0.61 0.18 0.29 −0.13 −0.28 −0.22 −0.05 0.11 0.51 0.21 0.799 0.747 0.700 0.658 0.620 0.584 0.495 0.425 0.724 0.690 0.658 0.630 0.604 0.579 0.517 0.466 0.676 0.649 0.624 0.601 0.580 0.561 0.509 0.466 0.0323 0.0667 0.1034 0.1429 0.1852 0.2308 0.3913 0.6000 0.0323 0.0667 0.1034 0.1429 0.1852 0.2308 0.3913 0.6000 0.0323 0.0667 0.1034 0.1429 0.1852 0.2308 0.3913 0.6000 4.5 9 13.5 18 22.5 27 40.5 54 4.5 9 13.5 18 22.5 27 40.5 54 4.5 9 13.5 18 22.5 27 40.5 54
0.929 0.855 0.793 0.740 0.693 0.650 0.538 0.441 0.942 0.881 0.829 0.784 0.743 0.706 0.608 0.521 0.950 0.895 0.849 0.808 0.770 0.736 0.645 0.563
0.771 0.710 0.658 0.614 0.575 0.540 0.447 0.366 0.653 0.611 0.575 0.543 0.515 0.489 0.421 0.361 0.593 0.559 0.530 0.504 0.481 0.459 0.402 0.351
0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.081 0.081 0.081 0.081 0.081 0.081 0.081 0.081
0.004 0.008 0.012 0.015 0.017 0.020 0.026 0.032 0.005 0.009 0.013 0.017 0.020 0.023 0.031 0.037 0.004 0.008 0.012 0.015 0.018 0.021 0.028 0.035
0.802 0.745 0.697 0.656 0.619 0.586 0.500 0.425 0.726 0.688 0.656 0.628 0.603 0.580 0.520 0.467 0.678 0.648 0.623 0.600 0.580 0.561 0.511 0.467
96.1 95.3 94.5 93.6 92.8 92.0 89.4 86.2 90.0 88.8 87.6 86.5 85.4 84.3 81.0 77.4 87.5 86.2 85.1 84.0 82.9 81.8 78.7 75.2
3.4 3.6 3.9 4.1 4.4 4.6 5.4 6.4 9.4 9.9 10.4 10.8 11.3 11.7 13.1 14.6 12.0 12.5 13.0 13.5 14.0 14.4 15.8 17.4
0.5 1.1 1.7 2.2 2.8 3.4 5.2 7.4 0.6 1.4 2.0 2.7 3.3 4.0 5.9 8.0 0.6 1.3 1.9 2.5 3.1 3.7 5.5 7.4
Deviation [%] qi /qsol,tot [%] ( b,n · ˛cav )/qsol,tot [%] corr gn,eff [–]
b,n (1 − ˛cav ) qe [–] qi [–] b,n · ˛cav [–] ˛cav [–] [–] Agl [m2 ]
273
Fig. 5. Comparison between the average monthly contributions calculated with the TRNSYS code, those obtained with the EN ISO 13790 Standard and the proposed model.
between glazed and opaque area that is very limited, while it does not appear justified for environments with large glazed surfaces in which part of the entering solar radiation is discharged. In order to investigate the accuracy of the results obtained from the application of simplified models, monthly solar heat gains were determined by applying the EN ISO 13790 procedure, the proposed model, which uses the effective radiation absorption coefficient, and the TRNSYS simulation code. It was presumed that in the considered indoor environment the internal opaque surfaces present an absorption coefficient ˛i = 0.30 and that the glazed surfaces are situated on external walls, each one with an area varying between 4.5 m2 and 18 m2 . The considered solar radiation data are relative to Palermo (lat. 38.2◦ N), a locality with a Mediterranean climate. With the aim of evaluating the effective absorption of solar radiation by the cavity, the directional properties of incident radiation were evaluated by means of factor Fw , whose average values were calculated as the ratio between the monthly energy transmitted through the glazed surfaces, considering beam, diffuse and reflected radiation, and that transmitted in the hypothesis that the three components of solar radiation have a normal incidence. The results of the comparison for the considered glazed systems are reported in Fig. 5, for varying between 0.033 and 0.600. The average monthly values of the percentage relative error, calculated according to the values provided by TRNSYS, demonstrate that EN ISO 13790 overestimates monthly solar heat gains in a growing measure upon the increase of ratio between the glazed area and the opaque area. For a value of = 0.033, corresponding to a glazed area of 4.5 m2 , overestimation does not exceed 7%; for a glazed area of 13.5 m2 ( = 0.103), the increases for single glazing are 22.5%, for double glazing 16.8%, and for triple glazing 14.6%; for a glazed area of 54 m2 ( = 0.600), for single glazing 105%, for double glazing 62.9%, and for triple glazing 49.1%. In the same figure, the results obtained for monthly solar heat gains calculated with the new calculation procedure and those obtained with TRNSYS are also reported: the relative error percentages are very contained and fall within the band ±2 % Further evaluations for indoor environments having parallelepiped plant and different shapes have provided relative percentage errors in the same band.
Triple
Double
Single
5. Conclusions Glazed system
Table 2 Comparison between the specific solar contributions calculated with the proposed model and with the TRNSYS code. Indoor environments with ˛m = 0.30.
( b,n · (1 − ˛cav ) · qe )/qsol,tot [%]
trn gn,eff [–]
G. Oliveti et al. / Energy and Buildings 43 (2011) 269–274
The problem of evaluating solar heat gains through glazed surfaces of air-conditioned environments, by means of the creation of a calculation correlation which estimates the effective absorption coefficient of solar radiation, was approached. This allowed for the
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G. Oliveti et al. / Energy and Buildings 43 (2011) 269–274
formulation of a more accurate simplified calculation model which takes into account all the absorption phenomena which are to be found within the indoor environment. The results obtained can be summarised as follows: 1) Believing solar radiation entering through glazed surfaces to be completely absorbed by the indoor environment, as hypothesized in EN ISO 13790 simplified models, setting aside the geometry and optical properties of the walls, is not always physically correct. The effective absorption coefficient is in relation to the average absorption coefficient of the opaque surfaces of the cavity, of the ratio between the glazed area and the opaque area, of the diffuse solar radiation transmission coefficient of the glazed surfaces. For environments with smooth and light internal surfaces, the effective absorption coefficient assumes values which, with an increase of the glazed fraction, are reduced in a significant manner from 0.93 to 0.44 for clear single glass, from 0.94 to 0.52 for clear double glazing and from 0.95 to 0.56 for clear triple glazing. 2) A calculation correlation was obtained which estimates the effective absorption coefficient of the environments with an error which does not exceed 1%, applicable to environments with clear glazed systems with variable glazed fractions from 0.033 to 0.600. 3) In the new proposed model, solar heat gains through glazed surfaces are evaluated by summing three contributions: the direct optical contribution, the secondary direct contribution, and the indirect secondary contribution due to the radiation reflected internally which is discharged. The latter contribution becomes significant in environments with glazed fractions greater than 0.230, and varies from 3.4% to 8.0%. 4) The new calculation procedure of solar heat gains allows for more accurate monthly evaluations, with deviations which do not exceed 2% in comparison with the TRNSYS code.
References [1] European Union, Directive 2002/91/EC of the European Parliament and of the Council of December 16th 2002 on the energy performance of buildings, Official Journal of the European Communities, January 4th 2003, replaced by Directive 2010/31/UE of May 19th 2010 of European Council and Parliament, on Official Gazette No 153 of June 18th, 2010. [2] ISO, Thermal Performance of Buildings – Calculation of Energy Use for Space Heating and Cooling, ISO/DIS 13790:2008, International Organization for Standardization, Geneva, 2008. [3] UNI, Energy Performances of Buildings – Part 1: Evaluation of Energy Need for Space Heating and Cooling, UNI Italian Company for Standardization, 2008, May. [4] CEN, Thermal Performance of Buildings – Calculation of Energy Use for Space Heating and Cooling – General Criteria and Validation Procedures, En15265:2007, European Committee For Standardization, Brussels, 2007. [5] J.A. Duffie, W.A. Beckman, Solar Engineering of Thermal Processes, third ed., Wiley, New York, 2006. [6] M. Cucumo, D. Kaliakatsos, V. Marinelli, Estimating effective solar absorbance in rooms, Energy and Buildings 23 (1995) 117–120. [7] Jin Wen, F. Theodore, Smith, Absorption of solar energy in a room, Solar Energy 72 (2002) 283–297. [8] J. Jokisalao, J. Kurnitski, Performance of EN ISO 13790 utilisation factor heat demand calculation method in a cold climate, Energy and Buildings 39 (2007) 236–247. [9] V. Corrado, E. Fabrizio, Assessment of building cooling energy need through a quasi-steady state model: simplified correlation for gain–loss mismatch, Energy and Buildings 39 (2007) 569–579. [10] G. Oliveti, M. De Simone, S. Ruffolo, Evaluation of the absorption coefficient for solar radiation in sunspaces and windowed rooms, Solar Energy 82 (2008) 212–219. [11] TRNSYS Program Manual Ver. 16, Solar Energy Laboratory, University of Wisconsin, Madison, USA, 2005. [12] WINDOW 5.2, PC Program for Analyzing Window Thermal Performances in Accordance with Standard NFRC Procedures, Windows and Day lighting Group, Building technologies Program, Energy and Environment Division, Lawrence Berkeley Laboratory, CA 94729, USA, 2005. [13] CEN, Glass in Building – Determination of Luminous and Solar Characteristics of Glazing, EN 410:1998, European Committee for Standardization, Brussels, 1998, April. [14] IEE SAVE ASIEPI Report, International Workshop on Impact, Compliance and Control of Legislation: Collection of the 14 Country Reports and 4 Synthesis Reports, Brussels, September, 2009. Available from: www. buildingsplatform.eu.
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Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
Review
An accurate calculation model of solar heat gain through glazed surfaces Giuseppe Oliveti ∗ , Natale Arcuri, Roberto Bruno, Marilena De Simone Mechanical Engineering Department, University of Calabria, V. P. Bucci 44/C, 87036 Rende (CS), Italy
a r t i c l e
i n f o
Article history: Received 19 August 2010 Received in revised form 11 October 2010 Accepted 5 November 2010 Keywords: Building energy performances Heat gains Simplified methods Technical standards
a b s t r a c t A model for the calculation of solar heat gain through glazed surfaces, to be used in the simplified calculation of thermal energy requirements in air-conditioned buildings, is proposed. The model uses the effective absorption coefficient of the indoor environment to take into account that the entering energy is in part absorbed by the surfaces of the cavity and in part is dispersed outwards, through the same glazed surfaces. The effective absorption coefficient is calculated by means of a correlation, and is made to depend on the average absorption coefficient of the internal opaque surfaces of the environment, on the glazed fraction and on the transmission coefficient of diffuse radiation of the glazed system. This coefficient permits a more accurate evaluation of solar heat gain through glazed surfaces, obtained adding: the direct optical contribution, produced by solar radiation absorbed by the indoor environment, the direct secondary contribution, produced by external solar radiation absorbed by the glazed surfaces, the indirect secondary contribution, produced by the absorption of reflected radiation exiting the indoor environment. The model, validated by means of comparisons with the TRNSYS 16 code, was used for the verification of the monthly solar heat gain calculation procedure of EN ISO 13790:2008. © 2010 Elsevier B.V. All rights reserved.
Contents 1. 2. 3. 4. 5.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effective cavity absorption coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A more accurate calculation model of solar heat gains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Energy comparisons With En Iso 13790 monthly method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Introduction In putting into effect Directive 2002/91/CE [1] the CEN, following mandate 343 “Energy Performance of Buildings Directive” (E.P.B.D.), prepared the EN ISO 13790:2008 Standard [2] which represents one of the most important documents for the calculation of energy performance of residential and non-residential buildings. The Standard permits identification of the energy required for heating and cooling by means of three different calculation methods of differing complexity. The first is a quasi steady state monthly method, acknowledged with the Italian UNI TS 11300-1:2008 Standard [3], the second is a simplified dynamic hourly method and the third is a detailed dynamic simulation method of the building described in EN 15265:2007 [4]. In the first and second methods, the dynamic aspects linked to the variability of weather data are cal-
∗ Corresponding author. Tel.: +39 0984 494605; fax: +39 0984 494673. E-mail address: [email protected] (G. Oliveti). 0378-7788/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2010.11.009
269 270 272 272 273 274
culated differently. In the first, by means of corrective coefficients, denominated gain utilisation factor in winter, and loss utilisation factors in summer. In the second, thermal behaviour of the building is described by some simplifications of heat transmission mechanisms between indoor and outdoor environments, which lead to an electrical network equivalent to three nodes, five resistances and a representative capacity of the thermal mass of the structures. All three models are based on the energy balance formulated considering the thermal zones of the building, in order to attain utilised energy requirements and, successively, for the determination of primary energy requirements by the plants. Energy use and primary requirement values are used for building energy classification and their evaluation must be as accurate as possible. In the energy balance of the building, a significant contribution is represented by solar heat gain by means of glazed surfaces. In dynamic simulation models, absorbed solar power is calculated by resolution of the radiant field in the solar band, obtained through the determination of solar irradiance of the opaque and glazed surfaces which delimit the spaces. Such evaluations are usually carried
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G. Oliveti et al. / Energy and Buildings 43 (2011) 269–274
out presuming that solar irradiation transmitted by the glazed surfaces is just diffused [5], in such a way as to eliminate entering radiation directional properties, or rather such properties can be taken into account, considering incident irradiation subdivided into beam and diffuse radiation, and distinguishing between areas illuminated directly by beam radiation and not-illuminated areas, by means of meshing of the internal surfaces of the environment [6,7]. In simplified models, entering solar radiation through glazed surfaces is commonly held to be completely absorbed by the cavity surfaces (black body cavity hypothesis). This formulation overlooks the solar irradiation fraction which is reflected outside by the internal surfaces of the cavity through the same irradiated glazed surfaces, and other possible glazed surfaces present. Absorbed solar radiation is calculated by means of an optical and thermal parameter of the transparent system denominated total solar energy transmittance for normal incidence g, modified with correction factor Fw to take into account glazed system optical properties variability with the direction of solar radiation. This parameter is used to identify solar performance of the glazed system, and does not depend on the geometrical and optical properties of the indoor environment. Due to the low thermal heat loss coefficient values required by the building shell to limit winter losses due to transmission, the evaluation of solar contribution through glazed surfaces assumes great importance for the correct determination of thermal energy requirements. Moreover, in the quasi steady state method, the incorrect estimation of solar contribution, both in winter and summer, leads to an erroneous determination of monthly utilisation factors, which also depend upon the ratio between solar energy absorbed by the environments, increased by possible endogenous energy, and the thermal energy exchange with the outdoor environment. The utilisation factors introduced in the energy balance, in order to take the dynamic behaviour of the building into account, require a correct evaluation of solar heat gains. Consequently the hypothesis, commonly adopted and present in recent works [8,9], of considering completely absorbed solar energy in the balance equation and determination of utilisation factors, appears criticisable. In such a case, utilisation factors assume the role of corrective factors as reported in Annex I EN ISO 13790, having to take into account both the incorrect evaluation of solar heat gains, as well as dynamic phenomena. Furthermore, in the evaluation of cooling energy requirements, an overestimation of solar heat gains leads to an increase in the cooling period, with a consequent thermal energy increase. The evaluation of solar heat gains in sunspaces adjoining airconditioned environments is addressed by the formulation of simplified models which estimate the effective absorption coefficient [10]. An approximate equation obtained in the hypothesis that solar radiation on internal environment surfaces is both constant and equal to the average value, is provided by Duffie and Beckman [5], who evaluate the solar absorption coefficient as the ratio between absorbed and entering energy, which is equal to the sum between absorbed and lost energy. In this work a method for the calculation of solar heat gains, through glazed surfaces to be used in simplified evaluation procedures of building thermal energy requirements, is proposed. It uses the entering solar radiation effective absorption coefficient, evaluated with a correlation created by the authors, which depends upon the optical and geometrical properties of the indoor environment and the transmission coefficient of the diffuse radiation of the transparent surfaces. Solar energy absorbed by the indoor environment is calculated as the sum of three contributions: the first optical, produced by solar radiation transmitted by glazed surfaces, the second direct convective-radiative, which evaluates the fraction of solar radiation absorbed and provided to the indoor envi-
ronment by the glazed surface which is radiated directly by the sun, the third indirect convective-radiative, produced by solar radiation reflected by internal surfaces and absorbed by glazed surfaces. The proposed calculation method permits the accurate evaluation of solar contributions, in particular in environments with several glazed surfaces with differing exposures, such as buildings with a glazed external shell and environments with large glazed surfaces used for exhibitionsetc. The calculation method was validated with reference to parallelepiped environments with one or more glazed surfaces with differing exposure, by means of a comparison of solar heat gain obtained with the model implemented in Type 56 of TRNSYS 16 code [11], which uses data from the software WINDOW 5.2 in order to evaluate the optical properties of transparent surfaces [12]. Successively, a critical comparison was developed between the results obtained applying the proposed calculation methodology and those determined applying the EN ISO 13790 Standard. 2. Effective cavity absorption coefficient The effective absorption coefficient of the indoor environment is defined as the ratio between absorbed solar energy and entering solar energy. Absorbed energy is calculated as the difference between the solar energy entering through the glazed surfaces Qsol,in and that reflected out of the cavity Qsol,out ˛cav =
Qsol,in − Qsol,out Qsol,in
(1)
Entering radiation directional properties render the optical field within the environments highly complex. A considerable simplification is obtained considering entering solar radiation, which goes beyond the glazed surface, as uniformly diffuse radiation. The hypothesis is acceptable if one considers that, usually, beam radiation reflection phenomena are evaluated considering indoor environments without furnishings and internal shading devices, situations which are not commonly encountered. A widespread simulation campaign carried out with the TRNSYS code, with reference to parallelepiped shaped environments with different ratios between plant linear dimensions, with one or more glazed surfaces with differing exposures, has highlighted that the effective absorption coefficient of the cavity ˛cav can be made to depend upon: - the average absorption coefficient in the solar band of the opaque internal surfaces of the environment
˛ · Ai i i ˛m =
(2)
A i i
- the glazed fraction of the air-conditioned space, by the ratio Agl,j and the opaque one of the cavity
between the glazed area
j
Ai
j
A j gl,j = A i i
(3)
- the optical properties of the glazed system defined by the diffuse solar radiation transmission coefficient d . In the simulations ˛m was made to vary between 0.20, very light smooth surfaces, and 0.80, dark and rough surfaces. For each wall, the glazed fraction varied between 25% and 100%, in such a way as
G. Oliveti et al. / Energy and Buildings 43 (2011) 269–274
Fig. 1. Cavity absorption coefficient in relation to the glazed fraction for three values of the average absorption coefficient of the indoor environment. Double glazing.
Fig. 2. Cavity absorption coefficient in relation to the ratio between the effective absorption area of the indoor environment, for the considered glass systems.
to obtain different values of the geometrical index . Three glazed systems were considered: 4 mm clear single glass, double glazing with 4 mm clear glass and an air gap of 16 mm, and triple glazing with 2.5 mm clear glass and an air gap of 12 mm. The corresponding transmission coefficient values d are equal to 0.79, 0.59 and 0.51. In Fig. 1 cavity absorption coefficient values ˛cav are reported, which were obtained with the TRNSYS code in relation to the ratio , for three values of the average absorption coefficient of the internal surfaces, and for a clear double glazing. In Fig. 2 ˛cav values were diagrammed relating to the ratio ˛m / , which represents the effective absorption area of the indoor environment, per glazed square meter, for the three considered glazed systems. The figures highlight how the absorption coefficient varies with an increase of the glazed fraction and a decrease of the absorption capacity of the opaque walls, and also the importance of the parameter ˛m / for the environment on which the cavity absorption coefficient can be made to depend. The least squares criterion was used to interpolate the ˛cav values obtained with the simulation programme. This procedure permitted the obtainment of an accurate expression of the cavity
271
Fig. 3. Reduction of the cavity absorption coefficient with an increase of the glazed fraction for indoor environments with ˛m = 0.20.
Fig. 4. Reduction of the cavity absorption coefficient with an increase of the glazed fraction for indoor environments with ˛m = 0.50.
absorption coefficient, which can be expressed as:
˛cav = 1 − a · Exp · −b ·
˛ c m
(4)
with coefficients a, b and c quadratic functions of the transmission coefficient of the diffuse radiation of the glazed system d , calculable with the relations: a = 3.500 − 5.453 · d + 4.516 · d2 b = 3.700 − 5.388 · d + 3.462 · d2
(5)
c = 0.124 + 0.545 · d − 0.355 · d2 The statistical comparison between the values calculated with TRNSYS and those obtained with the preceding correlation present a correlation index r = 0.999, an average relative percentage error ε = 0.11% and a maximum error εmax = 1.2%. In Figs. 3 and 4, the reduction of the cavity absorption coefficient upon the increase of the glazed fraction , calculated with the correlation in the case of ˛m = 0.20 and ˛m = 0.50, is reported. In the same figures, trend of ˛cav in the absence of a glazed system, or rather d = 1, is reported to highlight the increase of the absorp-
Table 1 Optical and thermal characteristics of the considered glazed surfaces. Glazed system
ggl,n [–]
b,n [–]
d [–]
˛b,n1 [–]
˛b,n2 [–]
˛b,n3 [–]
12 [W/m2 K]
23 [W/m2 K]
qi [–]
qe [–]
Single Double Triple
0.857 0.761 0.705
0.830 0.693 0.624
0.749 0.590 0.512
0.095 0.101 0.084
– 0.080 0.069
– – 0.055
– 5.03 5.46
– – 5.46
0.027 0.068 0.081
0.068 0.113 0.127
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G. Oliveti et al. / Energy and Buildings 43 (2011) 269–274
tion coefficient produced by the presence of the glazed system. Such a growth increases with the glazed fraction, and for environments with ˛m = 0.50 does not exceed 20%, while for reflective environments (˛m = 0.20) it is more significant and reaches 76%. The simplified model reported in [5] was also verified by means of a comparison of the results obtained with the TRNSYS code. The hypothesis of believing radiation to be constant on internal opaque surfaces and equal to the average value, is held to have been verified in the case of reflective environments (˛m = 0.20) with very contained glazed fractions = 0.033, in such a case the relative deviation between the values does not exceed 6%; while for non-reflective environments with high glazed fractions (˛m = 0.80, = 0.600), the deviation for single pane reaches 38%. 3. A more accurate calculation model of solar heat gains The removal of the hypothesis that the environment behaves like a black cavity with regards to entering solar radiation, led to a model which is closer to the effective optical behaviour of the cavity. Solar heat gains through glazed surfaces are evaluable with the relation: Qsol =
Fsh,k · Fsh,gl,k · (1 − FF,k ) · Aw,k · Isol,k · Fw,k · [b,n · ˛cav
k
+ qi + b,n · (1 − ˛cav ) · qe ],k · t
(6)
Fsh and Fsh,gl are reduction factors for shading produced by external elements and for the presence of mobile shading devices which are relative to the surface k, FF area reduction factor relative to the frame, Aw,k gross window area, Isol,k average solar irradiance, Fw,k average corrective factor, e,n beam solar transmission coefficient for normal incidence, qi secondary internal radiative-convective heat transfer factor, qe secondary external radiative-convective heat transfer factor and t the time step. In relation (6), in square brackets, the first term b,n ˛cav represents the direct optical fraction of solar radiation absorbed by the indoor environment, the second term, the secondary fraction produced by absorption of incident external solar radiation by the glazed system and the third term the secondary indirect fraction, generated by the fraction reflected by internal surfaces b,n (1 − ˛cav ), exiting the indoor environment through the glazed surfaces. In the case of black cavity (˛cav = 1) the term linked to the secondary indirect contribution is annulled. While the effective absorption coefficient ˛cav characterises the indoor environment with reference to energy entering through the glazed surface, the parameter gn,eff = b,n · ˛cav + qi + b,n · (1 − ˛cav ) · qe
(7)
characterises the absorption of solar radiation in the system constituted by the indoor environment and glazed surfaces, with reference to incident solar energy. It is possible to give it the name of effective solar heat gain coefficient of the environment comprehensive of glazed surfaces, and it is a function of the optical and thermal properties of the glazed surfaces and of the optical properties and geometrical characteristics of the indoor environment. The use of the relation (7) requires the determination of the parameters e,n , qi and qe obtainable from the EN 410 Standard [13]. Given the total solar energy transmittance for normal incidence of the glazed system ggl,n , the relation ggl,n = b,n + qi
(8)
permits calculation of the transmission coefficient e,n , expressions of the secondary heat transfer factor qi for single, double and triple glazing being known. The external secondary heat transfer factor qe is calculable, for example for a transparent system with three
panes, with the relation: qe + qi = ˛b,n1 + ˛b,n2 + ˛b,n3
(9)
with ˛b,n1 , ˛b,n2 and ˛b,n3 direct absorption coefficients for normal incidence respectively of the first, second and third pane of the glazed system. Validation of the calculation model was obtained with the TRNSYS simulation code, considering a reference environment 6 m × 6 m in plant dimension and 3 m in height, with vertical dispersive walls facing south, east and west, and the remaining vertical and horizontal opaque walls neighbouring air-conditioned environments. The opaque surfaces were presumed to be light with a solar band absorption coefficient equal to 0.30. The glazed systems considered are those defined previously, with air gap thermal resistance equal to 0.190 m2 K/W for double glazing, and 0.173 m2 K/W for triple glazing. In Table 1 the following optical parameters for normal incidence are reported: total solar energy transmittance ggl,n , beam solar transmission coefficient e,n , diffuse radiation transmission coefficient d ; direct absorption factors of the panes ˛e ; thermal conductance between the panes ; and the internal qi and external qe secondary heat transfer factors. With an increase in the number of panes which constitute the glazed system, optical parameters ggl,n , e,n , d , are reduced, while the internal qi and external qe heat transfer factors increase. In order to verify the results provided by the calculation model, with reference to the considered indoor environment, several optical configurations were evaluated, obtained by varying the glazed areas, their exposure, and the radiated glazed surfaces. The following parameters were evaluated: cavity absorption coefficients ˛cav and the three contributions of solar heat gain, represented by the optical fraction absorbed by the cavity b,n · ˛cav , by the direct secondary fraction qi and the indirect secondary fraction b,n · (1 − ˛cav ) · qe . In the investigation, it was presumed that shading reduction factors Fsh and Fsh,gl were equal to one, and the area reduction factor FF equal to zero, perpendicular incident solar irradiation Isol that provides a correction factor Fw = 1, since in this evaluation phase the directional effects of solar radiation are not involved. Table 2 reports the values presumed by the absorption coefficient and the three solar gain fractions, direct optical, direct secondary and indirect secondary, the sum of the three fractions and the relative percentage weight, as well as the sum of the three fractions calculated with the TRNSYS code and the error percentage between the total fractions calculated with the code and the model. The new calculation procedure provides accurate estimations, with a deviation which does not exceed 1%. The cavity absorption coefficient varies in a significant manner with the glazed area, with values between 0.93 and 0.44 for single glass, between 0.94 and 0.52 for double glazing, and between 0.95 and 0.56 for triple glazing. The direct optical fraction varies between 96%, for an environment with single glazing and = 0.033, and 75% for an environment with triple glazing and = 0.600. The indirect secondary contribution produced by reflected radiation, becomes, in percentage, significant in environments with > 0.230 for which values comprising between 3.4% and 8.0% are obtained. 4. Energy comparisons With En Iso 13790 monthly method Countries of the European Economic Community, in procedures adopted for building energy certification, have prevalently acknowledged the energy requirement monthly calculation method of EN ISO 13790 [14]. This method considers solar radiation entering glazed surfaces to be completely absorbed. The adopted hypothesis appears plausible for indoor environments with a ratio
0.36 −0.33 −0.41 −0.34 −0.01 0.41 1.00 0.03 0.29 −0.24 −0.34 −0.29 −0.06 0.24 0.61 0.18 0.29 −0.13 −0.28 −0.22 −0.05 0.11 0.51 0.21 0.799 0.747 0.700 0.658 0.620 0.584 0.495 0.425 0.724 0.690 0.658 0.630 0.604 0.579 0.517 0.466 0.676 0.649 0.624 0.601 0.580 0.561 0.509 0.466 0.0323 0.0667 0.1034 0.1429 0.1852 0.2308 0.3913 0.6000 0.0323 0.0667 0.1034 0.1429 0.1852 0.2308 0.3913 0.6000 0.0323 0.0667 0.1034 0.1429 0.1852 0.2308 0.3913 0.6000 4.5 9 13.5 18 22.5 27 40.5 54 4.5 9 13.5 18 22.5 27 40.5 54 4.5 9 13.5 18 22.5 27 40.5 54
0.929 0.855 0.793 0.740 0.693 0.650 0.538 0.441 0.942 0.881 0.829 0.784 0.743 0.706 0.608 0.521 0.950 0.895 0.849 0.808 0.770 0.736 0.645 0.563
0.771 0.710 0.658 0.614 0.575 0.540 0.447 0.366 0.653 0.611 0.575 0.543 0.515 0.489 0.421 0.361 0.593 0.559 0.530 0.504 0.481 0.459 0.402 0.351
0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.081 0.081 0.081 0.081 0.081 0.081 0.081 0.081
0.004 0.008 0.012 0.015 0.017 0.020 0.026 0.032 0.005 0.009 0.013 0.017 0.020 0.023 0.031 0.037 0.004 0.008 0.012 0.015 0.018 0.021 0.028 0.035
0.802 0.745 0.697 0.656 0.619 0.586 0.500 0.425 0.726 0.688 0.656 0.628 0.603 0.580 0.520 0.467 0.678 0.648 0.623 0.600 0.580 0.561 0.511 0.467
96.1 95.3 94.5 93.6 92.8 92.0 89.4 86.2 90.0 88.8 87.6 86.5 85.4 84.3 81.0 77.4 87.5 86.2 85.1 84.0 82.9 81.8 78.7 75.2
3.4 3.6 3.9 4.1 4.4 4.6 5.4 6.4 9.4 9.9 10.4 10.8 11.3 11.7 13.1 14.6 12.0 12.5 13.0 13.5 14.0 14.4 15.8 17.4
0.5 1.1 1.7 2.2 2.8 3.4 5.2 7.4 0.6 1.4 2.0 2.7 3.3 4.0 5.9 8.0 0.6 1.3 1.9 2.5 3.1 3.7 5.5 7.4
Deviation [%] qi /qsol,tot [%] ( b,n · ˛cav )/qsol,tot [%] corr gn,eff [–]
b,n (1 − ˛cav ) qe [–] qi [–] b,n · ˛cav [–] ˛cav [–] [–] Agl [m2 ]
273
Fig. 5. Comparison between the average monthly contributions calculated with the TRNSYS code, those obtained with the EN ISO 13790 Standard and the proposed model.
between glazed and opaque area that is very limited, while it does not appear justified for environments with large glazed surfaces in which part of the entering solar radiation is discharged. In order to investigate the accuracy of the results obtained from the application of simplified models, monthly solar heat gains were determined by applying the EN ISO 13790 procedure, the proposed model, which uses the effective radiation absorption coefficient, and the TRNSYS simulation code. It was presumed that in the considered indoor environment the internal opaque surfaces present an absorption coefficient ˛i = 0.30 and that the glazed surfaces are situated on external walls, each one with an area varying between 4.5 m2 and 18 m2 . The considered solar radiation data are relative to Palermo (lat. 38.2◦ N), a locality with a Mediterranean climate. With the aim of evaluating the effective absorption of solar radiation by the cavity, the directional properties of incident radiation were evaluated by means of factor Fw , whose average values were calculated as the ratio between the monthly energy transmitted through the glazed surfaces, considering beam, diffuse and reflected radiation, and that transmitted in the hypothesis that the three components of solar radiation have a normal incidence. The results of the comparison for the considered glazed systems are reported in Fig. 5, for varying between 0.033 and 0.600. The average monthly values of the percentage relative error, calculated according to the values provided by TRNSYS, demonstrate that EN ISO 13790 overestimates monthly solar heat gains in a growing measure upon the increase of ratio between the glazed area and the opaque area. For a value of = 0.033, corresponding to a glazed area of 4.5 m2 , overestimation does not exceed 7%; for a glazed area of 13.5 m2 ( = 0.103), the increases for single glazing are 22.5%, for double glazing 16.8%, and for triple glazing 14.6%; for a glazed area of 54 m2 ( = 0.600), for single glazing 105%, for double glazing 62.9%, and for triple glazing 49.1%. In the same figure, the results obtained for monthly solar heat gains calculated with the new calculation procedure and those obtained with TRNSYS are also reported: the relative error percentages are very contained and fall within the band ±2 % Further evaluations for indoor environments having parallelepiped plant and different shapes have provided relative percentage errors in the same band.
Triple
Double
Single
5. Conclusions Glazed system
Table 2 Comparison between the specific solar contributions calculated with the proposed model and with the TRNSYS code. Indoor environments with ˛m = 0.30.
( b,n · (1 − ˛cav ) · qe )/qsol,tot [%]
trn gn,eff [–]
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The problem of evaluating solar heat gains through glazed surfaces of air-conditioned environments, by means of the creation of a calculation correlation which estimates the effective absorption coefficient of solar radiation, was approached. This allowed for the
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formulation of a more accurate simplified calculation model which takes into account all the absorption phenomena which are to be found within the indoor environment. The results obtained can be summarised as follows: 1) Believing solar radiation entering through glazed surfaces to be completely absorbed by the indoor environment, as hypothesized in EN ISO 13790 simplified models, setting aside the geometry and optical properties of the walls, is not always physically correct. The effective absorption coefficient is in relation to the average absorption coefficient of the opaque surfaces of the cavity, of the ratio between the glazed area and the opaque area, of the diffuse solar radiation transmission coefficient of the glazed surfaces. For environments with smooth and light internal surfaces, the effective absorption coefficient assumes values which, with an increase of the glazed fraction, are reduced in a significant manner from 0.93 to 0.44 for clear single glass, from 0.94 to 0.52 for clear double glazing and from 0.95 to 0.56 for clear triple glazing. 2) A calculation correlation was obtained which estimates the effective absorption coefficient of the environments with an error which does not exceed 1%, applicable to environments with clear glazed systems with variable glazed fractions from 0.033 to 0.600. 3) In the new proposed model, solar heat gains through glazed surfaces are evaluated by summing three contributions: the direct optical contribution, the secondary direct contribution, and the indirect secondary contribution due to the radiation reflected internally which is discharged. The latter contribution becomes significant in environments with glazed fractions greater than 0.230, and varies from 3.4% to 8.0%. 4) The new calculation procedure of solar heat gains allows for more accurate monthly evaluations, with deviations which do not exceed 2% in comparison with the TRNSYS code.
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