Journal of Solar Energy

Volume 2015 (2015), Article ID 326536, 10 pages

http://dx.doi.org/10.1155/2015/326536

## Ray Tracing Study of Optical Characteristics of the Solar Image in the Receiver for a Thermal Solar Parabolic Dish Collector

Faculty of Mechanical Engineering, Department of Energetics and Process Technique, University of Niš, Niš, Serbia

Received 15 June 2015; Revised 2 September 2015; Accepted 27 September 2015

Academic Editor: Santanu Bandyopadhyay

Copyright © 2015 Saša R. Pavlovic and Velimir P. Stefanovic. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This study presents the geometric aspects of the focal image for a solar parabolic concentrator (SPC) using the ray tracing technique to establish parameters that allow the designation of the most suitable geometry for coupling the SPC to absorber-receiver. The efficient conversion of solar radiation into heat at these temperature levels requires a use of concentrating solar collectors. In this paper detailed optical design of the solar parabolic dish concentrator is presented. The system has diameter mm and focal distance mm. The parabolic dish of the solar system consists of 11 curvilinear trapezoidal reflective petals. For the construction of the solar collectors, mild steel-sheet and square pipe were used as the shell support for the reflecting surfaces. This paper presents optical simulations of the parabolic solar concentrator unit using the ray tracing software TracePro. The total flux on the receiver and the distribution of irradiance for absorbing flux on center and periphery receiver are given. The goal of this paper is to present the optical design of a low-tech solar concentrator that can be used as a potentially low cost tool for laboratory scale research on the medium-temperature thermal processes, cooling, industrial processes, polygeneration systems, and so forth.

#### 1. Introduction and Survey of Literature

This paper presents the numerical results of the optimization of the solar image in a receiver for a fixed absorber in a solar parabolic concentrator, which was a project supported by the Ministry of Education, Science and Technological Development of Republic of Serbia. The device which is used to transform solar energy to heat refers to a solar collector. Solar thermal collectors have been widely used to concentrate solar radiation and convert it into medium-high-temperature thermal processes. In addition, the list of possible alternative applications of this technology is growing, due to the problems of oil dependency and global warming. They can be designed as various devices including solar cooker [1], solar hydrogen production [2, 3], and Dish Stirling system of harvest electricity [4, 5]. The main types of concentrating collectors are parabolic dish, parabolic trough, power tower, a Fresnel collector with mirror or lens, and stationary concentrating collectors. The ideal optical configuration for the solar parabolic thermal concentrator is a parabolic mirror. The parabolic mirror is very expensive to fabricate and its cost escalates rapidly with increase of aperture area. The parabolic mirror can be designed with large number of elementary components known as reflecting petals or facets. Usually reflecting petals are made from glass and their thickness is from 0.7 to 1.0 mm. Traditionally, the optical analysis of radiation concentrators has been carried out by means of computer ray-trace programs. Recently, an interesting analytical solution for the optical performance of parabolic dish reflectors with flat receivers was presented by O’Neill and Hudson [6]. Their method for calculating the optical performance is fast and accurate but assumes that the radiation source is a uniform disk. Saleh Ali et al. [7] have presented a study that aims to develop a 3D static solar concentrator that can be used as a low cost and low energy substitute. Their goal was to design solar concentrator for the production of portable hot water in rural India. They used ray tracing software for evaluation of the optical performance of a static 3D Elliptical Hyperboloid Concentrator (EHC). Optimization of the concentrator profile and geometry is carried out to improve the overall performance of the system. Kaushika and Reddy [8] used satellite dish of 2.405 m in diameter with aluminium frame as a reflector to reduce the weight of the structure and the cost of the solar system. In their solar system the average temperature of water vapor was 300°C, when the absorber was placed at the focal point. The cost of their system was US$ 950. El Ouederni et al. [9] were testing parabolic concentrator of 2.2 m in diameter with reflecting coefficient 0.85. Average temperature in their system was 380°C. Rafeeu and Ab Kadir [10] have presented simple exercise in designing, building, and testing small laboratory scale parabolic concentrators. They made two dishes from acrylonitrile butadiene styrene and one from stainless steel. Three experimental models with various geometrical sizes and diameters were used to analyze the effect of geometry on a solar irradiation. Liu et al. [11] presented a procedure to design a facet concentrator for a laboratory scale research on medium-temperature thermal processes. The facet concentrator approximates a parabolic surface with a number of flat square facets supported by a parabolic frame and having two edges perpendicular to the concentrator axis. Authors [12] presented a physical and mathematical model of the new offset type parabolic concentrator and a numerical procedure for predicting its optical performances. Also the process of design and optical ray tracing analysis of a low cost solar concentrator for medium-temperature applications is presented. This study develops and applies a new mathematical model for estimating the intercept factor of the solar concentrator based on its geometry and optical behaviour. Pavlovic et al. [13] developed mathematical model of solar parabolic dish concentrator based on square flat facets applied to polygeneration system. The authors developed optimization algorithm for search of optimal geometric, optical, and cost parameters. They have applied Monte Carlo ray tracing methodology which is used for analysis of the optical performance of the concentrator and to identify the set of geometric concentrator parameters that allow for flux characteristics suitable for medium- and high-temperature applications in trigeneration and polygeneration systems. A 164-facet concentrator will deliver up to 8.15 kW of radiative power over 15 cm radius disk located in the focal plane. Their system had an average concentration ratio exceeding 100. Hasnat et al. [14] presented two prototype parabolic dishes. Dunn et al. [15] investigated experimental evaluation of ammonia receiver geometries with a 9 m^{2} dish concentrator. The 20 m^{2} dish is mirrored with around 2,000 flat mirror tile facets arranged in concentric rings on a parabolic fiber glass support structure. Size of mirror facets is from 5 cm to 10 cm. Johnston et al. [16] analyzed optical performance of spherical reflecting elements for use with parabolic dish concentrators. This concentrator consists of 54 triangular mirrors. The effective rim angle of the dish is 46°. The 54 units are composed of nine separate panel shapes, each of the shapes is duplicated six times. The focal length of system is 13.1 m.

The decision to make solar parabolic concentrator with 11 petals is based on large number of design concepts that are realized in the world. This concept already proved to be useful in solar techniques, especially in production of heat and electrical energy as well as in trigeneration and polygeneration systems.

The basic idea behind this research is to start with primary concept of solar parabolic concentrator which will generate from 10 to 25 kW in polygeneration systems. Only with employment of parabolic concentrating systems it is possible to obtain high temperatures in range from 200°C to 800°C and high optical and thermal efficiency of concentrating solar collectors.

#### 2. Geometrical Model of the Solar Parabolic Concentrator and Receiver

The design of the solar parabolic thermal concentrator and operation are presented. Optical design is based on parabolic dish with 11 curvilinear trapezoidal petals. Solar dish concentrators are generally concentrators that concentrate solar energy in a small area known as focal point. Dimensions of reflecting surfaces in solar dish concentrator are determined by desired power at maximum levels of insolation and efficiency of collector conversion.

The ray tracing technique is implemented in a software tool that allows the modelling of the propagation of light in objects of different media. This modelling requires the creation of solid models, either by the same software or by any computer aided design (CAD) software. Once in the optical modelling software, portions of the rays of the light source propagate in the flow of light, in accordance with the properties assigned to the relevant objects, which may be absorption, reflection, transmission, fluorescence, and diffusion. The sources and components of the light rays, adhering to various performance criteria involving the system parameters, result in simulation of the spatial and angular distribution, uniformity, intensity, and spectral characteristics of the system. Mathematical representation of parabolic concentrator is paraboloid that can be represented as a surface obtained by rotating parabola around axis. Mathematical equations for the parabolic dish solar concentrator in Cartesian and cylindrical coordinate systems are defined as where are and are coordinates in aperture plane and is distance from vertex measured along the line parallel with the paraboloid axis of symmetry; is focal length of paraboloid, that is, distance from the vertex to the focus along the paraboloid axis of symmetry. The relationship between the focal length and the diameter of parabolic dish is known as the relative aperture and it defines shape of the paraboloid and position of focal point. The shape of paraboloid can be also defined by rim angle . Usually paraboloids that are used in solar collectors have rim angles from 10 degrees up to 90 degrees. The relationship between the relative aperture and the rim angle is given byThe paraboloid with small rim angles has the focal point and receiver at large distance from the surface of concentrator. The paraboloid with rim angle smaller than 50° is used for cavity receivers while paraboloids with large rim angles are most appropriate for the external volumetric receivers (central receiver solar systems). = 0.59. = 0.59 is focus/diameter ratio—ratios of focal distance to diameter of aperture reflector. Increasing the ratio reduces the rim angle. Paraboloid, with marginal angle, is a little curved, and its focal point and the receiver must be far from the surface of the concentrator. Paraboloid with rim angle of less than 50° is used when reflective radiation passes into the cavity of the receiver, while the paraboloids with large edge angles are most suitable for external receivers.

The geometric concentration ratio can be defined as the area of the collector aperture divided by the surface area of the receiver and can be calculated by The designed solar parabolic concentrator has geometric concentration ratio = 100.

##### 2.1. Parameters Design of Solar Parabolic Concentrator

Mechanical design of the solar parabolic concentrator is done in 3D design software CATIA, Dassault Systemes, USA. Parabolic shape of solar concentrator is obtained by entering and coordinates for selected points. For calculation of necessary points that define parabola public domain software Parabola Calculator 2.0 [17] is used. The calculated coordinates ( and ) for designed parabola are shown in Table 1. The calculated values are performed for 22 points in the parabola curve. The equation for parabola is