INTRODUCTION

The purpose of this functionality is to calculate the optimal diameter of a cylindrical receiver, vertically oriented and centered at the user-defined point of interest, to intersect a large fraction of a given set of rays. Particularly, FluxTracer conducts a parametric study along various diameters and receiver heights. It finds the optimal pair of these parameters, which achieve the maximum intersection of rays.

The cylinder analysis functionality of FluxTracer is operated by the user by specifying a set of parameters needed to perform the cylindrical receiver size optimization analysis based on a given heliostat field. These parameters include the minimum (dMin) and maximum (dMax) diameters as well as the minimum (hMin) and maximum (hMax) heights that constitute the design optimization space. For each combination of diameter and height, the cylindrical surface of the receiver is divided into cylindrical surface bins, based on the number of circumferential (hDivs) and height (dDivs) values which are set as input parameters by the user. The last parameter that the user sets is the coordinates of the focal point of the optical system of the plant, which is usually located along the center axis of the receiver. These coordinates are consistent with the coordinates of the focal point as set in the ray-tracing software. Unlike other optimization tools, FluxTracer does not need estimation of good initial conditions to ensure the calculation of the optimum solution. Rays generated from the ray tracing software for a given heliostat field are fed into FluxTracer, and the cylinder analysis functionality starts exploring the design optimization space for the optimal sizing of the cylindrical receiver. It should be mentioned here that the ray tracing scene within the ray tracer (Tonatiuh or Tonatiuh++ for this case) includes only the heliostat field without the presence of any receiver at the focal point of the optical system. Instead, in order for FluxTracer to find the optimal receiver size, the whole photon data map that passes through the region of the three-dimensional space around the focal point is saved in the ray tracing software and it is then passed to FluxTracer for post processing.

GENERATION OF THE INTERSECT FACTOR MATRIX

The cylindrical analysis functionality can be either run for annual simulations, or for single sun position simulations. The output of the functionality is a two dimensional matrix in .csv file format. The annual or single point intercept factor matrix is a two-dimensional matrix representing the variation of the annual intersect factor of the cylindrical receiver as a function of its height and diameter. To generate the annual intersect factor matrix, the user should provide the following information to the program:

• The interval (dMin, dMax) of diameters of the cylindrical receivers to be analyzed
• The interval (hMin, hmax) of heights of the cylindrical receivers to be analyzed
• The number of divisions of the interval of diamaters (dDivs) to be considered.
• The number of divisions of the interval of heights (hDivs) to be considered.
• The coordinates of the focal point of the optical system of the plant, which is usually located along the center axis of the receiver. (These coordinates should be identical to the coordinates of the focal point defined in the ray-tracing software.

The coordinates of the focal point of the optical system of the plant to be provided to FluxTracer is usually located along the center axis of the receiver. These coordinates should be identical to the coordinates of the focal point defined in the ray-tracing software. To build the annual intersect factor matrix FluxTracer computes the intersection points of each one of the rays in the annual set of rays with the cylindrical surface of the receiver as it is described in the section that follows.

INTERSECTION OF CYLINDRICAL RECEIVER WITH RAY

The points on cylindrical surface can be described by the following equation

where the radius ρ, azimuth φ and height z are the cylindrical coordinates. The points on a ray are described as

where r0 is the origin, d is the direction of propagation, and t is the distance from the origin. The intersection points of cylinder and ray satisfy a quadratic equitation for t

It can be rewritten in a standard form

In general, there can be two roots. The smaller root t1 corresponds to the first intersection with the surface. The height of the intersection point is

The root should be within the length of the ray segment 0≤t1≤tmax. Otherwise, the ray should be excluded from consideration. The case when dx^2+dy^2=0 corresponds to rays which are parallel to cylindrical surface and can be neglected. The intersections with bottom and top cap of cylinder are excluded.

The functionality within FluxTracer investigates the design space by using cylinders of fixed diameter and explores all combinations of the set cylinder heights due to the fact that if a ray intersects a smaller in height cylinder, it will always intersect a larger in height cylinder of the same diameter. In contrary, if a ray intersects a smaller in diameter cylinder, it does not necessarily intersect a larger in diameter cylinder of the same height (see Figure 2). Finally, as output, the program provides a table with the amount of energy captured by the bins which is then post-processed accordingly.

Based on the above, to build the two dimensional (hDivs, dDivs) annual intersect factor matrix, FluxTracer only needs to process the rays in the annual set of rays dDivs times, and not hDivs x dDivs times, which typically is a significant reduction in the computational effort.