Scientific Visualisation for Solar Concentrating Systems

Dr. Baum Research e.K.
Pfitznerweg 20, D-74523 Schwäbisch Hall, Germany

www.drbaumresearch.com

Presented at the National Solar Energy Conference, April 13-18, 1996, Asheville, NC, USA

SCIENTIFIC VISUALIZATION FOR SOLAR CONCENTRATING SYSTEMS:

COMPUTER SIMULATION PROGRAM FOR VISUAL & NUMERICAL ANALYSIS

Igor V. Baum

ABSTRACT -- The Computer Simulation Program for Visual & Numerical Analysis of Solar Concentrators (VNASC) and specific scientific visualization methods for computer modeling of solar concentrating systems are described. The program has two code versions (FORTRAN and C++). It visualizes a concentrating process and takes into account geometrical factors and errors, including Gauss errors of reflecting surfaces, facets' alignment errors, and sun-tracking errors.

1. INTRODUCTION

Computer calculations of solar concentrators mostly are devoted to investigation of the final output characteristic of a concentrating system, a concentrated flux density distribution on a receiver surface. Since the distribution is a result of an interaction of all kinds of geometrical features of a solar concentrator, it is very difficult to separate a contribution of any one certain factor from this “mixture”. The VNASC program also provides calculations of flux density distributions. But in addition, it allows to analyze how the distribution is configured by the optical system’s geometry. The program uses specific scientific visualization methods that are developed just for these purposes.

The concentrated flux density in any point on a receiver surface is equal to an integral of an incoming radiation flux brightness that is a function of angular coordinates. The brightness is a brightness of objects that are seen at a receiver viewpoint. In the case of a solar concentrator the term "objects" means the solar disk image reflected from the concentrator surface. The image is transformed and increased by the concentrator’s optical elements. The integral value depends on the area that is occupied by the sun image. The greater are angular dimensions of the sun image, the greater is the concentration ratio.

Usually, the brightness function is implicitly used as an intermediate hidden value within a calculation procedure. The main idea of the VNASC visualization method is to store the intermediate information about the brightness distribution and to display it on a computer screen. Our natural capability to analyze and interpret visual images is rather more powerful than our capability to interpret abstract mathematical equation or numerical information. It is the main argument to use the computer simulated sun image technique for analysis & design of solar concentrators.

The general mathematical description of the solar concentrator optics used in the program was developed by the author in (1,4). It was applied to inverse problems of solar concentrators in (2), and to the solar power plant optical system’s design in (3,5). Data of the Solar Furnace of DLR (Köln), which is described in (6,7), are used in this paper as an example to demonstrate the VNASC methods' application to a particular solar concentrating system.

2. VISUALIZATION TECHNIQUE

The standard methods for calculations of a concentrated flux density distribution on a receiver surface usually use the ray tracing technique. There are many versions of such an approach so we mention here a general scheme only to use it as a background for explanation of the visualization technique specific.

Two coordinate grids are needed to organize the calculation process. First one is a coordinate grid on a receiver surface that serves to describe a 2D distribution of the flux density as a set of values of the density function. It serves for a result representation only so it does not concern to the ray tracing itself. The second one is a coordinate grid on the concentrators reflecting surface. We should scan the reflecting surface along with this grid to calculate the photometric integral for each certain point of the receiver surface. Just this scanning is associated with images of the solar disk in the reflecting surface that could be observed at a receiver point.

The VNASC program invites a user to "walk" along the receiver surface to observe images from several viewpoints and to understand better how the concentrator does work, what part of its reflecting surface is responsible for providing a flux concentration in each certain receiver point. The sequence of such pictures that is managed by a user's choice provides a very new impression that serves to improve a 3D imagination in solar optics problems. This method is very intuitive and very useful for the evaluation of the efficiency of solar concentrator elements. It is applicable both for a design and improvement of new concentrators and for an interpretation of measurements and experiments on existing ones.

The ray tracing technique allows to determinate which point of the solar disk (if any) is seen in a certain point of the concentrator surface from a chosen viewpoint on the receiver. To answer this question we should trace the ray trajectory in a direction just opposite to the solar flux. Because it is not known is any valid solar beam associated with this particular direction or not, we should simply use the vector equation of the reflectance law.

The ray tracing comes to the following. First, the program calculates the area of the concentrator image that is displayed on the screen according to a scale ratio of the picture and a viewpoint that are chosen by a user. The concentrator surface image depends on the type of projection (Cartesian or spherical) that a user chose. Then the program scans the concentrator image pixel by pixel. For each pixel the same sequence of the ray tracing steps are repeating. The 3D coordinates of a corresponding concentrator surface point and a vector of the normal of the surface in this point are calculated. The direction of an inverse ray is determined by the pair of points (one point on the concentrator and another point on the receiver). It is used in the reflecting equation to obtain a direction of a solar beam that comes to the concentrator point. If the concentrating system has only one reflecting surface and has no heliostats, then the obtained beam direction is compared with angular coordinates of the sun to calculate which point of the solar disk (if any) corresponds this beam. Depending on this, the pixel is switched to a "sun" or to a "sky" color. The calculation of the corresponding contribution in the photometric integral is implemented according to the brightness distribution over the solar disk. If the concentrating system has more than one reflecting surface or has heliostats then the ray tracing includes some additional steps.

There are two possibilities to take several errors of the optical system into account. First, the degraded sun brightness distribution could be recalculated before the implementation of the ray tracing according to Gauss errors of reflecting surfaces. Second way is to simulate errors inside the ray tracing by a random correction of normal vectors. The VNASC program uses the second way, but it is opened for the first one too.

3. SOURCE CODE STRUCTURE AND REALIZATION

The VNASC program is developed as a specific library of functions and subroutines that is supplied by a flexible main program that organizes a user’s interface in a convenient menu system. There are two versions of the main program and library source codes, one as the MS FORTRAN 5.1 code and the second as the Borland C++ 4.5 (including OWL 2.5) code for Windows programming.

There are also several realizations of these two versions for separate research and design tasks. So the main program could be adjusted for a computer modeling of any particular solar concentrating system.

4. SAMPLE REALIZATION OF FORTRAN VERSION

The user's menu of the FORTRAN version of the program that is applied to case of the DLR Solar Furnace is organized as it is shown on Fig. 1.

A user can set and change several parameters like a date and a time of a day, the intensity of the solar beam radiation, Gauss errors of the concentrator’s and heliostat’s reflecting surfaces, alignment errors of the concentrator’s facet array, sun-tracking errors of the heliostat control system, etc.

To get first experience with the images displayed by the program and to consider the concentrating effect itself, a user can also switch type of the facet's shape from spherical facets to parabolic facets or to flat plate mirrors.

Fig. 1 The user's menu of the sample realization of the VNASC program (the case of a solar furnace with a heliostat).

Fig. 2 The image of the solar disk in the concentrator with spherical facets. The viewpoint is at the focal point of the system.

The Distribution menu shows tables of the concentration ratio and the flux density distributions on the receiver surface.

The Sun image sub menu is the key section of the program main menu. It allows to observe transformed images of the solar disk. Let us consider two sample pictures that are shown on Fig. 2 and Fig. 3.

The first sample picture (Fig. 2), which parameters could be set by the Sun Image menu, shows the sun image how it is seen from the focal point of the concentrator. Parameters of errors mostly correspond to an ideal system. The only alignment average error of 1 mr seems to be realistic. Nevertheless this simplest example shows advantages of visual methods. It is seen very good that the right half of the facet array works more effectively than the left one. The solar image covers all the area of each facet.

One can see the image of the gap between two parts of the heliostat’s mirror. In fact, we are observing the image of the concentrator’s facet system, in which we can see the image of the heliostat, in which in a turn we can see the image of the sun. The transformed images of the heliostat’s support column and the landscape are seen through the heliostat mirror gap.

Fig. 3. The image of the solar disk in the concentrator with parabolic facets. The viewpoint is 25 cm from focal point.

Fig. 4 The sample C++ (OWL 2.5) realization of the VNASC program.

The second sample picture (Fig. 3) serves to explain the previous one. Facets of the concentrator of the Solar Furnace of DLR are spherical. Now we are considering an imaginary case of the same project as if facets had been precise parabolic fragments.

The viewpoint is shifted 25 cm towards the concentrator. Alignment errors are omitted. This precise concentrator reproduces the heliostat’s image on the landscape’s background in a very understandable manner. The increased solar disk image is very good seen in the middle of the picture.

The sun image increases, if the viewpoint is located nearer to the focal point. It will occupy the whole heliostat’s image if the viewpoint is just the focal pint. In fact, we would see only one central point of the solar disk from the focal point of a precise parabolic concentrator. Spherical facets of the Fig. 2 transform such an ideal regular image and split it in many separate images.

5. SAMPLE REALIZATION OF C++ VERSION

The C++ version of the VNASC basic source code was developed to improve user's interface and to construct more convenient and flexible menu structure of the program. All advantages of Windows visual programming were used together with advantages of the sun image visualization.

The simplest sample of the VNASC realization by means of Object Windows is shown on Fig. 4. This version is focused on an investigation of several separate elements of multi-facets concentrating systems.

User can change location and a curvature of a spherical facet to observe how the sun image fit in the aperture of facets of several dimensions. Some useful intermediate functions could be displayed by a simple mouse click.

The program also calculates the value of the concentration ratio as a function of the curvature's radius for five values of the facet's radius.

It is very useful to interpret results of this calculation with the help of solar images. For example, there are some cases when the optimal facet's curvature seems to be optimal at a value of the meridian curvature of the parabolic frame. The sun image visualization helps to avoid such a mistaken interpretation. It helps to understand that in this specific case only a small part of a large facet is occupied by the solar disk image. The numerical analysis should be based not only on the concentration ratio calculations but should also use the average brightness over the entire facet's aperture that is relatively low in such cases.

6. CONCLUSIONS

The scientific visualization methods (8) found their places in several areas of research and design. They are also applicable to several tasks of the solar concentrators' optics.

Visualization methods are corresponding to the solar concentrator's nature itself.

The general approach and the specific technique of solar image visualization, that are described in this paper, allow to work out very effective computer models of solar concentrating systems that improve the 3D imagination of designers and serve as very intuitive and convenient tool for the measurement and experimental result' interpretation.

The VNASC program, which sample realizations are described, allows to simulate all steps of a concentrating process in any particular solar concentrating system. It takes into account all geometrical factors and all types of errors that appear in solar installations, including Gauss errors of reflecting surfaces, alignment errors of facets, and sun-tracking errors of a heliostat control system.

The program allows to simulate both types of solar concentrators, solar furnaces with heliostats and solar power installation of a direct sun tracking.

REFERENCES

(1) Baum I. V. “The Theory of Solar Energy Concentrators” (in Russian). The Ph. D. dissertation, Krzhizhanovsky Power Engineering Institute, Moscow, 1975, 120 p.

(2) Baum I. V. ”Concentrateurs produisant un champ donne d'irrediation du recepteur”. Colloque International Electricite Solaire. Toulouse, 15 mars, 1976. France, Toulouse, 1976, pp. 947956.

(3) Baum I. V. “A mathematical simulation model of the solar power system optics” Colloques internationaux du CNRS. Systems Solaires Thermodynamiques. France, Marseille, 1980, pp. 339344.