INTRODUCTION

By point analysis we mean the capability of FluxTracer, given a set of rays and a reference point, to compute the shortest distances from the rays to the point and to compute the points on the rays at which this shortest distance is achieved. In this analysis, FluxTracer computes the minimum distance from each ray, within the large set of rays generated by the Monte Carlo ray tracer, to a user-defined point within the region of interest. It provides information regarding the minimum distances of the rays to the point, and the position of the points on the rays corresponding to those minimum distances.

To carry out the point analysis, the user should specify to FluxTracer the following information:

The size and location of the region of three-dimensional space of interest, as in the radiant density analysis. How the region of interest shall be voxelized, as in the radiant density analysis. The point of interest in regard to which the analysis should be carried out, specified by its coordinates (x, y, z). The set of rays generated by the Monte Carlo ray tracer to be processed by FluxTracer. Since, as stated earlier, the number of rays processed by FluxTracer is relatively large, it is not usually practical to provide for each ray its closest distance to the point of interest and the coordinates of the points of closest distance. Because of this, by default, FluxTracer provides instead the probability distribution of distances of the rays to the point of interest and the radiant density of this points in three-dimensional space using a similar voxelisation of the region of interest than in the radiant energy analysis.

Since the point analysis provides information regarding the minimum distances of the rays to a point of interest defined by the user, this type of analysis can be used to get an idea of the minimum region that should be analysed around the point of interest to get insight on the distribution of radiant energy around that point. If the point of interest defined by the user is the focal point of the solar concentrator being analysed, this type of analysis could provide insight on how to define a sensible region for the radiant density analysis or insight on what should be the dimensions and shape of a receiver to capture a given fraction of all the solar energy sent by the solar concentrator to the receiver. It could also facilitate the resolution of specific receiver related optimization problems without the need to run again the Monte Carlo ray tracer or of generating new sets of rays.

COMPUTATION OF THE MINIMUM DISTANCE FROM A RAY TO A POINT

The shortest distance to the point rC can be found via cross product

p=|(rC−r0)×d|.(1)

The corresponding point on the ray rP has

t=(rC−r0# )⋅d.(2)

The ray is described as

r=r0+td,(3)

where r0 is the origin of the ray, d is the unit vector in the direction of propagation, and t is the distance from the origin.

ANALYSIS OF INTEREST

Adding to FluxTracer the capability of computing the shortest distances from a set of rays to a user defined point and to compute the position or points on the rays at which this shortest distance is achieved will allow the following types of analysis:

Set of shortest distances from the rays to the point:

• Compute the cumulative distribution function providing the number of rays (or the percentage of total rays) as a function of the shortest distance to the point.
• From the cumulative function compute its derivative, i.e., the density function providing the probability that a ray be at a given shortest distance from the reference point

Cloud of 3D-points which are at the shortest distances from the rays to the point:

• Transform the cloud of 3D-points into a voxelized energy density in 3D-space.
• Compute the minimum enclosure containing the cloud of 3D-points.
• Compute the center of gravity and the axis of inertia of the 3D-point cloud. The analysis of the distances may be useful to determine the minimum radius of a sphere, which has its center at the user defined point, and which will intersect a given fraction of rays.

The analysis of the cloud of 3D-points may be useful to determine the shape of the minimum size receiver which will intersect a given fraction of rays. To some extent the analysis of the voxelized energy density obtained from the cloud of 3D-points may also provide insight into the shapes of potential receiver geometries of interest.

If the interest is to gain insight regarding the possible shape of receivers that will intersect a given fraction of the concentrated solar radiant energy delivered by the solar concentrating system (e.g., the heliostat field) in a given period of time, then:

• The analysis of shortest distances from the rays to the user defined point will allow the user to determine the radius of a sphere centered at the point of interest (typically the focal point of the solar concentrating system) that will intersect a given fraction of rays.
• The analysis of the cloud of 3D-points which are the shortest distance from the rays to the user defined point will allow the user to determine accurately the shape of the receiver envelop that will intersect the given fraction of rays.

Obviously, the analysis of the cloud of 3D-point, while computationally more expensive, have the potential to provide more valuable insight regarding novel receiver designs, as illustrated in the following picture, drawn in two dimensions just for the sake of illustration.