A quantitative evaluation method for uniformity of heat flux distribution in the parabolic trough collector

Abstract

The parabolic trough collector (PTC) is one of the most mature technologies to harvest solar energy for heat applications. However, the non-uniform heat flux distribution on the outer surface of absorber tube can lead to a high local temperature and a large temperature gradient on the tube wall, thus resulting into many issues, such as the degradation of the selective coating, the vacuum loss, the deformation of the absorber tube, and even the breakage of the glass envelope. These issues pose great challenges for the safety and high-efficiency operation of PTC systems. The corresponding effective solution is to increase the uniformity of the heat flux distribution on the absorber tube. Based on this purpose, how to quantify the uniformity of heat flux distribution is of great significance for the design of the parabolic trough collector. In this work, the existing uniformity indexes in engineering are summarized and compared. It is found that there are three problems in the related studies: (1) Some indexes are unbounded, which makes it difficult to compare uniformity of different distribution types; (2) some indexes are dimensioned, and its difficult to compare uniformity of different physical quantities distribution; (3) for most of the existing indexes, only the value of physical quantity is considered, while the spatial distribution characteristic of physical quantity is ignored. This phenomenon makes the description of uniformity incomprehensive. In view of this, a new uniformity index is proposed to consider both the value and spatial position of physical quantity by decoupling uniformity index into uniformity index of value and uniformity index of spatial position. The uniformity index of value is to quantify the dispersion degree of a set of data values from the average, and the uniformity index of spatial position is to quantify the amount of dispersion of data values in different spatial zones. The effectiveness of the proposed uniformity index is verified by evaluating the uniformity of three different distributions. Compared with existing uniformity indexes, the proposed index has a better ability to distinguish the uniformity of the distribution. Thereafter, the proposed uniformity index is employed to evaluate the uniformity of heat flux distribution in four typical types of PTC. The obtained results show that the proposed uniformity index can quickly and accurately evaluate the uniformity of heat flux distributions in PTC. Furthermore, due to the characteristics of strict boundedness and dimensionless, the proposed index can be easily applied as the guidance of PTC design and optimization.