Incident Angle Modifiers for Flat-Plate Solar Collectors: Analysis of Measurement and Calculation Procedures

Existing test procedures for measuring and rating thermal performance require the determination of the angular response of collectors in order to account for non-normal incident beam irradiance. Angular response measurements for four different types of collectors, each type tested by three different laboratories, are presented and analyzed. Substantial differences, both within and between laboratories, are reported for the same type collectors. An analysis of the measurement procedure shows that experimentally determined angular response parameters are subject to relatively large uncertainties. The problem results to a large extent from measuring collector efficiencies at non-normal incident angles where measurement uncertainty is of the same order of magnitude as the efficiency reduction attributable to these off-normal angles. Other factors which can affect angular response measurements and the method of correlating results are also discussed. A theoretical analysis shows that shading of the absorber by the collector air space side- and end-walls for non-normal incident angles can be of the same order of importance as the decrease in the transmittance of the cover assembly. While this situation complicates an analytical approach, it is concluded that calculations are adequate to depict the angular response of conventional flat-plate tube-in-sheet collector designs. A simplified analytical procedure and nomographs are presented for rapid calculation of incident angle modifiers. The predicted seasonal performance of solar energy systems and clear-day ratings of typical flat-plate collectors are shown to be relatively insensitive to large uncertainties in incident angle modifiers. Typically, the values of these calculated quantities could be affected by approximately five percent as a result of uncertainty in the test-derived angular response parameter.