Anna Werner, Arne Roos, The Angstrom Laboratory, Department of Engineering Science, Uppsala, Sweden

Introduction

Solar radiation reaches the windowpane from many angles simultaneously. Most of the radiation, however, is direct radiation, coming from the direction of the sun. The incidence angle of this radiation varies from one moment to the other. Radiation coming from different directions are affected differently by the windowpane. The absorptance for instance, is typically lower at an incidence angle close to 90° than at an incidence angle close to 0°. This angle dependence is useful in some applications (angular selective windows), but it might also pose a geometrical problem. To calculate the instantaneous overall absorptance (integrated over all incidence angles), one needs to know how much radiation comes from each angle at each moment [3]. In this study, we have focused on the maximum power absorbed in a windowpane from different angles. The reason for this limited analysis, is that we want an empirical model for the angular variation of the solar absorptance that gives as accurate estimations as possible for these extreme values that are crucial when evaluating thermal stress on a windowpane and surface temperatures [1].

If there were no (refraction in the) atmosphere, 1367 W/m2 would reach a pane perpendicular to the sun at our distance1. In the atmosphere, radiation is scattered and absorbed so that less power actually reaches the Earth. We have focused on Stockholm data. Approximately, 1000 kWh a year reaches a horizontal surface of one square meter in Sweden. If, instead, the surface is tilted 45° with respect to the horizontal, 1150 kWh will be captured, and if the pane follows the sun, 1450 KWh can be collected. These are experimental values. Climate files exist with the direct and diffuse irradiation on a horizontal surface for different locations and years. The calculations of the irradiation on a vertical surface were based on these data. We used data from 1982. Figure 1 shows the maximum solar power in our test year (W/m2) for each angle of incidence for a north facing window, an east facing window, a south facing window and a west facing window.

The solar constant, as used by the World Radiaion Center and in [3] with an error estimate of ±1%

Figure 1 Maximum directly irradiated power versus angle of incidence for four differently oriented windows in Stockholm in 1982.

Table 1 shows that a window facing the north never is hit by radiation from an incidence angle lower than about 40°. It also shows that for windows facing one of the other three major orientations, the highest (hourly) power is attained at incidence angles around 20°. Table 1 shows when each of these maximas occurs (month of the year, day of the month, hour of the day). In five cells no figures are shown, since according to our simulations a north facing window in Stockholm never receives direct sunradiation from an angle below 40°.

Some of the irradiated power will be absorbed by the window. It is possible with Fresnel calculations to find out exactly how much solar power is absorbed in each pane.

Different windows have different properties at different angles of incident. We studied 27 different windows, with 62 panes altogether. Not only the level of solar absorptance is different for each pane, but also the angular variation of this solar absorptance. It would be impossible to show all the angular properties of all panes here. Instead, we show only one example in Figure 2. It shows how much solar power is absorbed in the outer pane in a double pane window where the inner glass is a 4 mm clear float glass and the outer is a 4 mm grey float glass. By comparing figure 2 with figure 1, it is realized that radiation coming with one angle of incidence is not affected in the same way by the pane as radiation coming from another angle.

•North……………. East -8— South -*-West |

Figure 2 Maximum power absorbed versus angle of incidence for one of 62 studied panes; the outer pane in a double pane window where the outer pane is a grey 4 mm float glass and the inner pane is a clear 4 mm float glass, no coatings applied. The climatic data used for producing the diagram are the ones shown in Figure 1 and multi-Fresnel formalism was used to calculate the pane optical data.