Determination of the Distribution of Incident Solar Radiation in Cavity Receivers With Approximately Real Parabolic Dish Collectors

The absorption of solar heat and the attendant thermal and mechanical loadings on the tubes of cavity receivers depend predominantly on the flux distribution of the incident solar radiation. For an axially symmetric cavity receiver with a parabolic dish collector, it is simple to determine the insulation pattern on the receiver internal surfaces if the system is ideal. In such a system the surface of the dish is perfectly parabolic (no contour flaws are present), and the sun’s central ray impinges on the dish surface parallel to the focal axis (no sun tracking flaws are present). These two conditions cannot be achieved in practice, and therefore the feasible parabolic dish system is referred to as a “real” system although, in actual fact, it is only an approximation to any actual system. The purpose of this paper is to devise calculation principles which permit analysis of a receiver designed for ideal conditions (Bammert and Seifert, 1983; Bammert and Hegazy, 1984; Johanning, 1987) to verify its structural adequacy under the nonideal conditions to be expected in reality. Of the many possible imperfections in real collectors, two were selected which increase the loadings sustained. The first case concerns flaws in the contour of the dish surface. These locally increase the radiation concentration on the receiver inside walls and tubing. In the second case, sun-tracking errors give rise to axially asymmetric radiation distributions. In both examples, greater than design basis loadings will occur in the receiver tubing. Both kinds of flaws considered in this paper are of a purely deterministic nature. Other flaws statistically distributed on the dish surface (Kohne and Kleih, 1987, Guven, Bannerot, and Mistree, 1983; O’Neill and Hudson, 1978; Ratzel et al., 1987) do not cause structural overloading but must be taken into account in thermal performance analysis. The paper presents a method of analyzing the flux distribution on the internal surfaces of a cavity receiver with an approximately real parabolic dish collector. After a discussion of the theoretical principles, the effects of the collector contour and sun tracking errors on the insulation pattern are described with reference to an example.