Factored approximations for biaxial incident angle modifiers

Abstract

Solar collectors using various types of nonimaging concentrators have optical efficiencies which are not symmetrical about the collector normal. To fully specify the optical efficiency for a given sun angle, more details of the collector orientation and incident angle modifier are needed than for flat plate collectors. This could lead to the need for extensive collector test data. Fortunately, for reflecting concentrators, the detailed incident angle modifier, K ατ ( θ l , θ t ), can be approximated accurately by the product K ατ ( θ l , 0) K ατ (0, θ t ), where θ t and θ l are projected angles between the sun's position vector and the collector normal. Ray-trace calculations of the various optical effects which result in biaxial incident angle modifiers show the accuracy of the approximation. Since the various optical effects for reflecting concentrators can be represented separately by products of two projected angle factors, extension of the approximation to the general case of low concentration collectors is valid. Measurements and/or calculations need be made only for incident angles in two well-defined orthogonal planes to obtain information sufficient to approximate K ατ ( θ l , θ t ) for any projected angles of interest for solar collectors.