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A simplified calculation method for seasonal accumulated solar heat gain through windows.

Article Excerpt
Abstract: To estimate the energy performance of windows, the seasonal accumulated solar heat gain through the windows has to be calculated. A simplified method for calculating seasonal accumulated solar heat gain through windows with arbitrary azimuth and tilt angle is proposed. The method was tested using weather data from seven locations in Japan. The proposed simplified method provided good simulations of detailed hourly calculations.

Keywords: Energy performance, Glazing, Heating and cooling load, Solar heat gain, Thermal performance, Windows

Introduction

Of all building skin components, windows most affect the energy used to heat and cool buildings. Generally, the thermal performance of windows is expressed using thermal performance values such as the thermal transmittance (U-value), the solar heat gain coefficient (SHGC) and the air-leakage rate. However, in recent years the importance of integrating thermal performance values in terms of total heating and cooling loads has been recognized for energy rating of windows. Several different energy performance measures have already been introduced, such as European (EWERS, 2000), the ISO (2002) and Canadian (CSA, 1998) standards.

One of the difficulties in calculating the energy performance of windows is that the seasonal accumulated solar heat gain for the location, azimuth and tilt angle is required. In this study to determine the seasonal accumulated solar heat gain, detailed calculations using daily and hourly weather data from seven locations throughout Japan were conducted. In addition, a simplified calculation method to determine the seasonal accumulated solar heat gain was developed and tested. Results confirm that the simplified method is suitable.

Equations for the Energy Performance of Windows

The energy performance of a window is defined as the energy requirements for heating and cooling through the unit area of the window. It is expressed using the following equations (CSA, 1998; EWERS, 2000; ISO, 2002):

E[P.sub.h] = [[eta].sub.h,G] * [G.sub.h] (1)

E[P.sub.h] = [G.sub.c] * [[eta].sub.c,L] * [L.sub.c], (2)

where:

E[P.sub.h], E[P.sub.c]: Energy performance values of the window [Wh/[m.sup.2]]

[L.sub.h], [L.sub.c]: Heat loss through the window [Wh/[m.sup.2]]

[G.sub.h], [G.sub.c]: Heat gain through the window [Wh/[m.sup.2]]

[[eta].sub.h,G]: Gain utilisation factor [-]

[[eta].sub.c,L]: Loss utilisation factor [-].

Subscripts h and c denote heating and cooling periods, and G and L denote heat gain and loss, respectively. Here, heat loss through the window consists of seasonal accumulated heat loss due to heat transmission and air leakage, whereas heat gain through the window is the seasonal accumulated solar heat gain. The gain utilisation factor corresponds to the reduction in energy required to heat the building because of the total seasonal heat gain. Similarly, the loss utilisation factor corresponds to the reduction in energy required to cool the building because of seasonal heat transfer from the building. The values change depending on the building specifications (ISO, 2007; Saito, Akasaka, Nimiya, Soga, & Kinoshita, 2007). Therefore, according to Equations (1) and (2), the smaller the values of E[P.sub.h] and E[P.sub.c], the better is the thermal energy performance of the window.

Here, we show seasonal accumulated heat loss and gain through the window in the following equations (CSA, 1998), where the integral range is for either the heating period or the cooling period:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (3)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (4)

where:

t : Time [h]

U : Thermal transmittance (U-value) [W/[m.sup.2] K]

[rho] : Air density [kg/[m.sup.3]]

c : Specific heat of air [J/kg K]

V : Air leakage volume [[m.sup.3]/h]

A : Area of...

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