Foulaadvand M Ebrahim, Aghamohammadi Amir, Karimi Parvin, Borzouei Hadi
Department of Physics, Faculty of Science, University of Zanjan, Zanjan, PC, 45371-38791, Iran.
Department of Physics, Faculty of Physics and Chemistry, Alzahra University, Tehran, Iran.
Sci Rep. 2021 Dec 28;11(1):24474. doi: 10.1038/s41598-021-03768-w.
We analytically, experimentally and computationally explore the solar radiation flux distribution in the interior region of a spherical mirror and compare it to that of a paraboloidal one with the same aperture area. Our investigation has been performed in the framework of geometrical optics. It is shown that despite one can assign a quasi focus, at half the radius, to a spherical mirror, the light concentration occurs as well on an extended line region which starts at half-radius on the optical axis. In contrast to a paraboloidal concentrator, a spherical mirror can concentrate the radiation parallel to its optical axis both in a point-focus and in a line-focus manner. The envelope of the reflected rays is also obtained. It is shown that the flux distribution has an axial symmetry. The radial dependence of the flux on a flat circular receiver is obtained. The flux longitudinal dependence is shown to exhibit three distinctive regions in the interval [0, R] (R is mirror radius). We obtain the radiational (optical) concentration ratio characteristics and find the optimal location of the flat receiver of a given size at which the concentration ratio is maximised. In contrast to a parabolic mirror, it is shown that this location depends on the receiver size. Our findings offers that in spherical mirrors one can alternatively use a line receiver and gains a considerable thermal energy harvest. Our results are supported by Monte Carlo ray tracing performed by Zemax optical software. Experimental validation has been performed in lab with a silver-coated lens as the spherical mirror.
我们通过分析、实验和计算的方法，探究了球面镜内部区域的太阳辐射通量分布，并将其与具有相同孔径面积的抛物面镜的辐射通量分布进行了比较。我们的研究是在几何光学框架内进行的。结果表明，尽管可以将球面镜半径一半处的准焦点赋予球面镜，但光的聚集也发生在从光轴上半径一半处开始的扩展线区域。与抛物面聚光器不同，球面镜可以以点聚焦和线聚焦的方式聚集与其光轴平行的辐射。还得到了反射光线的包络线。结果表明，通量分布具有轴对称性。得到了平面圆形接收器上通量的径向依赖性。通量的纵向依赖性在区间[0, R]（R为镜面半径）内表现出三个不同的区域。我们得到了辐射（光学）聚光比特性，并找到了给定尺寸的平面接收器的最佳位置，在该位置聚光比最大。与抛物面镜不同的是，结果表明这个位置取决于接收器的尺寸。我们的研究结果表明，在球面镜中可以使用线接收器，并获得可观的热能收获。我们的结果得到了Zemax光学软件进行的蒙特卡罗光线追踪的支持。在实验室中使用镀银透镜作为球面镜进行了实验验证。
