For the comparison the geometry of the greenhouse-environment system shown in figure 1 was taken into consideration.

Fig. 1. Sunspace-environment system and schematization of solar heat gains. Te external air temperature, Ta air temperature in the airconditioned environments, Ts air temperature in the sunspace.

The sunspace, measuring 6^3×3 m in dimension, borders with the outside by means of three vertical walls and the roof, and is separated from the airconditioned environment by a wall that is part glazed and part opaque; furthermore it borders with an underlying environment that is also airconditioned. The glazed surfaces are formed by a clear double glass 4-12-4 with thermal transmittance Ug = 2,88 W/m2K and solar gain coefficient gi = 0,747. The internal opaque wall and the floor of the sunspace have a respective thermal transmittance of Uw = 0,55 W/m2K and Uf= 0,57 W/m2K. The other walls of the airconditioned environments are considered internal walls, adiabatic in corrispondence with the symmetry axis.

The overall heat transfer coefficients by ventilation between the greenhouse and the outside, and between the airconditioned environment and the greenhouse were placed equal to 18 W/K and correspond to an air change equal to 1 volume/h. The coefficient of surface thermal exchange of the sunspace floor hf was set equal to 10 W/(m2K) and that of the opaque dividing wall hw = 7,7 W/m2K [7]. In the evaluation of the thermal coupling coefficient between the airconditioned volumes and the sunspace, through the vertical wall and the floor, the effects of thermal bridges were not taken into consideration. Furthermore for the glazed surfaces corrective factors due to shading, to curtains and to the frame were considered unitary.

With reference to figure 1, the total solar contribution through the vertical separation wall QW and through the greenhouse floor Qf were obtained by adding the respective direct Qd and indirect Qt contributions

Qw = Qd, g + Qd, w + Q w (1)

Qf = Qd, f + Qf (2)

Indirect contributions require the evaluation of the net energy absorbed by the sunspace Qa

Qa = Qw + QaJ — Qd, w — Qdf (3)

and are calculable with the relations

with Hw and H f heat loss coefficients between the airconditioned spaces and the greenhouse, through the mixed vertical wall and the floor, and He loss coefficient between the greenhouse and the external environment [8].

With the considered outlined conditions, the average monthly temperature within the greenhouse is given by the relation

Qa

(Hw + Hf + He )At

with Ta the temperature of the adjacent airconditioned environments, set at 20°C during the heating period and at 26°C during the cooling period, and At the number of seconds in a month.

With reference to two Italian localities characterised by different climatic conditions, Milan (Lat. 45°27’, Long 9°11’) and Cosenza (Lat. 39°18’, Long 16°15’), direct, indirect and global solar contributions were compared with a variation: of the glass fraction f of the greenhouse — environment separating wall f = 20%, 60%, 100%); of the orientation of the greenhouse (South, East, West); of the optical properties of the opaque surfaces, the absorption coefficient of the solar band was presumed to be identical for the different surfaces of the greenhouse and the environment, and was made to vary between a=0,2 (highly reflecting environment) and a=0,5 (moderately absorbing environment). Furthermore, the solar contribution obtained in the airconditioned environment in the absence and presence of the greenhouse was evaluated.

2. Comparison results

The monthly direct, indirect and total solar heat gain, through the separation wall and the floor obtained with the simulation code and the Standard were compared. The direct contribution through the glazed surface for Milan and Cosenza, with a variation of the glass fraction f, for a = 0,20 and for its Southern exposure are reported in figures 2 and 3.

The results of the comparison depend on the glass fraction, in particular for glass fractions of 20% the Standard underestimates with greater deviation in the summer period (23% for Cosenza, 17% for Milan) and is more contained during winter months (less than 10%). Instead, for 100% solar fractions, the Standard leads to a significant overestimation in winter months for both locations, with deviations of 43%. During summer months such a percentage is reduced to 13% for Cosenza and to 20% for Milan. For Eastern exposure, the previous trends remain confirmed with reduced deviations which do not exceed 17% for f = 20%, and 33% for f = 100%. For an absorption coefficient value of the greenhouse-environment system equal to 0,50, the Standard provides evaluation in good agreement with the code, with deviations which does not exceed 17%.

For the comparison of the indirect contribution through the separation elements between the greenhouse and the airconditioned environments, the comparison of the temperature increase of the air within the sunspace is significant, as a consequence of solar absorption and exchange through the shell. In figures 4 and 5, for Milan and Cosenza, the monthly trends of the increase in temperature in the greenhouse relative to its Southern exposure are reported for environments with a = 0,20.

Fig. 4. Increase in sunspace air temperature 4 Fig. 5. Increase in sunspace air temperature consequent to consequent to solar absorption, varying the glass 4 solar absorption, varying the glass fraction f. Cosenza, fractionf. Milan, South, a=0,20. S Standard, C code. South, a=0,20. S Standard, C code.

The Standard underestimates the increase in temperature with variations between 1,0 °C in January and 4,5°C in July for Milan, and between 2,5°C and 5,3°C for Cosenza, for the different glass fractions. The increase in the absorption coefficient (a = 0,50) gave rise to a more contained underestimation of the increases, with deviations that for Milan do not exceed 3,0°C in July for f= 100%, and 3,7°C for Cosenza. For Eastern exposure similar variances were found.

The solar heat gains obtained as the sum of direct contribution through the opaque surfaces and the indirect contributions consequent to the heating of the greenhouse, evaluated with the Standard, are compared with the contributions in the environment adjacent through the separation wall, evaluated with the code. It can be observed that the Standard gives rise to a systematic underestimation of such contributions. In figures 6 and 7 the values of the previous contributions for a = 0,20, southern exposure, for the considered localities are reported.

The Standard provides trends which vary slightly with the glass fraction, since, with an increase in the glass surface, the thermal coupling coefficient between the greenhouse and the adjacent environment increases while the energy absorbed by the opaque walls diminishes as demonstrated by the equation (4). Significant variations produced by the different evaluations of the increase in temperature between the greenhouse and the environment are highlighted, which increase with the glass fraction and are between 33% (f = 20%) and 84% (f = 100%) inclusive. For more absorbent environments, it is ascertainable that for contained glass fractions, the Standard gives rise to an overestimation, attributable to the evaluation of the direct contribution through the opaque wall, with deviations varying between 10% and 33%. Instead, for glass fractions f = 100%, the Standard leads to an underestimation with deviations between 23% and 55% inclusive. For Eastern exposure, similar trends are recorded with more contained deviations. The comparison of the contributions through the sunspace floor leads to considerations similar to the previous ones, in particular for a = 0,20 the Standard underestimates in a proportion increasing with the glass fraction, with variations between 24% and 58% inclusive.

For a = 0,50 the Standard overestimates in the summer months and underestimates in the winter months with deviations that do not exceed 24%. Finally, the comparison of total solar heat gains for the adjacent environment, the sum of the direct and indirect contributions, is reported for case a=0,20 and for Southern exposure in figures 8 and 9. For such configurations, the Standard underestimates the solar contribution with deviations which diminish with the increase of the glass fraction, and do not exceed 28%. Fore more absorbent environments and reduced glass fractions (a=0,50 ed f=20%), for both the localities the Standard underestimates the contribution in a measure less than 18%, while for the glass fractions it is higher (60%, 100%) [9].

The results provided by the two calculation procedures appear to be in agreement, as an effect of the compensation between the underestimation of indirect contributions and the overestimation of direct contributions.

3. Considerations

In light of the simplifications hypothesised by EN ISO 13790, the results obtained with the code were used for quantitative evaluations on the direct and indirect solar heat gains for the adjacent airconditioned environment. Furthermore, the solar contribution of the sunspace — environment system obtained with the code was compared with those calculated by applying the Standard to the environment lacking a greenhouse in front of it.

The indirect contribution was generally lower than the direct contribution, but they can also result as being greater in the case of absorbent environments with reduced glass fractions. Their relationship is a function of the glass fraction, of the absorption coefficient of the spaces, of the exposure and of the locality. In figures 10 and 11 the results obtained for Southern exposure for Milan and Cosenza are reported.

It should be immediately highlighted that the indirect contributions are not negligible in any case compared to the direct contributions, even when the increases in the temperature of the greenhouse are modest. With the same glass fractions, the indirect solar heat gain increases in a significant manner with the absorption coefficient since, in comparison with a modest increase of the direct contribution, the indirect contribution increases in a considerable way due to the greater absorption of the sunspace. It should be highlighted that the greater total contribution is obtained by configurations which ensure maximum direct and indirect solar heat gain, with prevalence over
direct contribution (f=100%). The previous trends with a lesser monthly variability remain confirmed for Eastern exposure.

In figures 12 and 13 the total solar heat gains for the sunspace-environment system, with a = 0,20 and Southern exposure, calculated with the code are compared with those evaluated by the Standard for the same windowed environment.

In Milan the sunspace gives rise to increases in contributions that, for a glass fraction of 20%, result as being hardly variable with the absorption coefficient and being between 25% and 35% inclusive during summer and between 11% and 19% during winter.

For Cosenza the percentages are between 21%-43% during summer, and between 12%-20% during winter. If the glass fraction increases, the solar contributions undergo variations during winter which differ to those during summer. In particular, during the winter months the presence of the sunspace gives rise to a reduction of the contributions, which results as being less than 17% for f = 60%, and less than 49% for f = 100%. The reduction of the direct solar heat gains linked to the presence of the greenhouse does not appear to be compensated by the indirect contributions.

During summer, viceversa, the greenhouse determines an increase in contributions which do not exceed 21%. For environments which are more absorbent the previous variances undergo an attenuation during winter, while during summer they remain substantially unaltered. For Eastern exposure, poor monthly variability was observed for f = 20%, with values between 24% and 31% inclusive for both the localities and optical configurations. For higher glass fractions an invariance in solar contribution in the case of f = 60% was observed, and a significant reduction for f = 100% that is equal to 28% for Milan and a = 0,20. More contained variations were recorded for Cosenza.

Fig. 13. Solar heat gain for sunspace-adjacent environment systems and for windowed environments, varying the glass fraction f. Cosenza, South, a=0,20.

4. Conclusions

For a system comprising of a sunspace bordering airconditioned environments, the solar heat gain calculated by the simplified calculation procedure of the EN ISO 13790 Standard was compared with those obtained by means of a dynamic calculation code that accurately calculates the interaction between solar radiation and the glazed spaces adjacent to airconditioned rooms. The analysis, carried out for different climatic conditions, geometries and optical configurations, permitted the evaluation of direct solar contribution, through glazed and opaque surfaces, and indirect due to heating of the greenhouse, and the total contributions.

The different modelling of the absorption of solar radiation leads to different increases in air temperature in the greenhouse which lead to considerable underestimation of the indirect contributions on behalf of the Standard. For configurations with a solar fraction of 100% the variances reach 80%. Furthermore, it is possible to observe that, for such configurations, the direct contributions result as being overestimated by 40%. With regards to total contributions, the results provided by the two calculation procedures appear to be in greater agreement: deviations of less

than 28% are recorded for environments with a = 0,20 and lower than 18% for more absorbent environments.

With the aim of evaluating applicability, for the climatic conditions considered, the simplified hypothesis proposed by EN ISO 13790 (do not compute the indirect contributions, ignore the presence of a glass shell) the direct and indirect contributions obtained with the code were compared, and the solar heat gain for a windowed environment was calculated with the Standard. The indirect solar contributions, compared to direct contributions, result as being significant in percentage and variable according to the locality, the glass fraction, the absorption coefficient of the environments and the exposure. Therefore, the indirect contributions are in no case negligible even in the presence of contained increases in the sunspace temperature.

To the South, for reduced glass fractions (f=20%), the greenhouse gives rise to an increase in solar heat gain that is more accentuated in summer, and which reaches 35% for Milan and 43% for Cosenza. For greater glass fractions the greenhouse leads to a reduction in solar gain in winter, for f=100% it results as being equal to 49%, and increases of less than 21% during summer. For Eastern exposure the effects of the greenhouse appear to be more contained, for f=100% the increase of solar contribution does not exceed 31% for both localities.

References

[1] De Simone M. , Oliveti G. , Ruffolo S. , " EVALUATION OF THE ABSORPTION COEFFICIENT FOR SOLAR RADIATION IN SUNSPACES AND WINDOWED ROOMS". Solar Energy, Vol. 82, pp. 212-219, 2008.

[2] EN ISO 13790. Energy performance of buildings. Calculation of energy use for space heating and cooling, 2008.

[3] UNI EN 832. Thermal performance of buildings. Calculation of energy use for heating. Residential buildings, 2001.

[4] DEROB-LTH v1.0. User’s Manual. Division of Energy and Building Design, Lund Institute of Technology, Sweden, 2004.

[5] Arumi-Noe, F. The DEROB System, Volume II, Explanatory Notes and Theory. Numerical Simulation Laboratoty, School of Architecture, University of Texas Austin, 1979.

[6] UNI 10349. Heating and cooling of buildings. Climatic data, 1994.

[7] UNI EN ISO 6946. Building components and building elements. Thermal resistance and thermal transmittance, 1999.

[8] EN ISO 13789.Thermal performance of buildings. Transmission and ventilation heat transfer coefficients. Calculation method, 2007.

[9] De Simone M. , Oliveti G. , Arcuri N. , Bruno R. , " RADIAZIONE SOLARE NEGLI AMBIENTI ADIACENTI A SPAZI SOLEGGIATI. UNA VERIFICA DELLA PROCEDURA DI CALCOLO PREVISTA DALLA NORMATIVA". Book proceedings of the "46° International Conference AICARR", Milan, Vol. I, pp. 1009-1023, 12-13 March, 2008.