A note on design of linear dielectric compound parabolic concentrators

In this communication, three-dimensional radiation transfer within linear dielectric compound parabolic concentrators (DCPC) is investigated based on vector algebra and solar geometry, and the design of DCPC oriented in east-west direction is addressed. The analysis shows that, the projected incident and refractive angles of solar rays on the cross-section of DCPC are not subjected to the correlation as Snell law except for incident rays on the cross-section, hence, the acceptance half-angle (θa) of DCPC should be determined based on time variations of projected refractive angle and minimum time (2tc) required to concentrate direct sunlight in all days of a year. It is also found that, to make all refractive radiation within θa are totally internally reflected onto the absorber, DCPC with a restricted exit angle (DCPC-θa/θe should be employed, and solar leakage from walls of DCPC-θa/90 can be avoided or reduced by increasing θa and number of periodical tilt-angle adjustment in a year. Calculations show that, the minimum θa of DCPC depends on tc and strategy of tilt-angle adjustment; and for a given tc, the ratio (Rc) of maximum geometric concentration of DCPC to that of reflective CPC (n = 1) is dependent on number of periodical tilt-angle adjustment in a year, but always larger than refractive index (n) of dielectric. Calculations also indicate that, for DCPCs with n > 1.4, when solar rays incident towards onto right/left wall, the radiation incident on its opposite wall (left/right) will be totally internally reflected, and multiple reflections of solar rays on way to the absorber will also be total internal reflection for radiation within its acceptance angle.