In this paper the features of using a geometrical involute method for calculating of the conical concentrators are discussed. The
conditions for the passage of rays through the focon are analyzed. Working formulas are presented.
Among the optical elements used for the concentration of solar
energy, focons are widely used. The simplest focus is an optical
element with a cone-shaped reflective surface. Currently, methods
for calculating optical fibers have been developed in sufficient detail
[1,2] and can be successfully applied to the calculation of a certain
type of solar collectors, namely for conical focons. Note that the main
difference between the fiber and the focon is the great value of the
parametric angle of the latter. In optical fibers, this angle is small.
Let us consider the case of multiple reflection of rays in a conical
focon (Figure 1).
Figure 1: Multiple reflection of rays in the focus.
To calculate the optical parameters of the focon, it is
convenient to use the geometric scanning method. In this
case, it is convenient to consider the ray path in the scan of
the focon (Figure 2). We introduce the following notation:
R is the radius of the input end of the focon;
r is the radius of the output end of the focon;
γ is the parametric focal angle;
L is the length of the focon;
α is the angle of incidence of the beam into the focal area.
Consider the triangle AOW. We have
Figure 2: Geometric scan of focus.
According to the sine theorem
The length of the focon, beginning with which the beam returns
back, can be found from the condition that the angle of incidence ψ
on the focon wall is zero, i.e. sin (90 + ψ) = 1. We have
from here
Knowing L0, we can determine r
A numerical analysis using the formulas obtained showed that
the passage of rays through a focal glass with multiple reflections is
possible only at small values of the parametric angle γ. This fact is
the biggest drawback of the conical focus. For this reason, together
with the conical focon, despite the difficulties of manufacture,
parabolotoric focons are used [3,4].
In conclusion, we note that using the ratio of the areas of the
input and output ends of the focus as an optical concentration
coefficient is incorrect due to the presence of multiple reflections.
To do this, use the following expression
Where Rs is the reflection coefficient, is the percentage of the
number of reflection of rays (transmitted and non-transmitted rays),
i is the multiplicity of reflections. In this case, the normalization
condition must be observed.