The links below provide an outline of the material for this lesson. Be sure to carefully read through the entire lesson befor returning to Canvas to submit your assignments.
We’re trying to figure out how big the problem is and what we can do to minimize bird mortalities.
— Eric Davis, Feb 2014. (Assistant regional director for migratory birds at the US Fish & Wildlife Service’s Sacramento office, commenting on bird deaths at the Ivanpah concentrating solar power plant.)
Solar concentration is the most cost effective way to achieve sufficiently high temperatures for generating steam for useful work. Concentration of solar radiation is acheieved by using an optical device between the source and absorber, and that allows to decrease the effective area of the absorber and associated radiative energy losses. As such, concentrating collectors are advantageous when high temperatures are needed. The one remaining caveat is that concentrating technologies typically rely on the direct normal irradiance component of the solar resources. Hence, locations with regularly clear skies and high levels of direct radiation (such as the southwest US and southern Spain) are best suited for concentrating solar power.
This lesson will take us one week to complete. The list of assignments for this lesson is provided in the table below. More detailed instructions are given on respective pages of this lesson and in Canvas modules.
Tasks | Assignment Details | Access/Directions |
---|---|---|
Readings |
Required:
Supplementary:
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Registered students can use the following link to access the online textbook [1] through the University Library. |
Assignment | Problem set from D&B - calculation of concentrating collector characteristics | Specific directions for this Assignment are provided on the respective page of this lesson. |
Quiz | 10 multiple choice questions based on lesson readings. | Registered students can access the quiz in the Lesson 4 Module in Canvas. |
Discussion | New ideas for developing cost-effective concentrating collectors (Sunvapor case) | Please read directions and post your reflection in Lesson 4 Discussion in Canvas. |
If you have any questions, please post them to our Questions and Answers discussion forum in Canvas. I will check that discussion forum daily to respond. While you are there, feel free to post your own responses if you, too, are able to help out a classmate.
There are many different types of configurations of solar concentrators, ranging from cylindrical that focus on a line (tube) to circular that focus on a point (power tower). As was already mentioned, the main purpose of these configurations is to increase the radiation flux on the receiver, and that effect is achieved through reflection of light from multiple anlged or curved mirror surfaces. Figure below provides schematics of several common types of concentrating collectors.
The light concentration process is typically characterized by the concentration ratio (C). By physical meaning, the concentration ratio is the factor by which the incident energy flux (Io) is optically enhanced on the receiving surface (Ir) - as shown in the Figure below. So, by confining the available energy coming through a chosen aperture to a smaller area on the receiver, we should be able to increase the flux.
The ratio of area of the receiver to the area of the aperture, Cgeo = Ar/Aa is called the area concentration ratio (in some sources also called geometric concentration ratio). It is easy to use, as the areas of the devices are known, although it is adequate only when the radiation flux is uniform over the aperture and over the receiver. Also, please note that for some imaging concentrators, the area of the available receiver surface can be different from the area of the image produced by the concentrator on the receiver. So, if the image does not cover the entire surface of the receiver, we need to use the image area to estimate the concentration ratio.
The concentration ratio can be also represented by the energy flux ratio at the aperture and at the receiver. In this case, it is termed flux concentration ratio Copt (in some sources - optical concentration ratio) and can be directly applied to thermal calculations.
In case the ambient energy flux over the aperture (insolation) and over the receiver (irradiance) is uniform, the geometric and optical concentration ratios are equal (Cgeo = Copt).
The concentration ratios are important metrics used to characterize and rank optical concentrators. There is a theoretical limit to solar concentration. For circular concentrators - 45,000, and for linear concentrators - 212, based on the geometrical considerations; however, these limits may be unreachable by real systems because of non-idealities and losses. In general sunlight, concentration systems are roughly classified into: low concentration range (C<10), medium concentration range (10<C<100), and high concentration range (C>100). However, only some of the systems provide uniform concentrated light flux (e.g., V-troughs or pyramidal plane reflectors) and can be characterized by a single concentration ratio. Many systems with curved reflecting surfaces (e.g., conical, parabolic, spherical) create a distribution of flux density over the receiver and would rather be characterized by a variable C over the receiver width. In that case, a local concentration ratio (Cl) is the main parameter to characterize the performance of the ideal concentrator:<100),>
where I(y) is determined for any local position y from the center of the produced image, and Iap is the intensity of the incident radiation at the aperture.
In many typical cases of imaging concentrators, the reflectance of the surface (ρ), i.e., the fraction of light radiation reflected from the surface compared to the total incident radiation, is also taken into account. Then the local intensity of the concentrated light, I(y), can be described as follows:
Next we are going to refer to the following text to learn more about the optical and thermal performance of concentration collectors.
Book chapter: Duffie, J.A. Beckman, W., Solar Engineering of Thermal Processes, Chapter 7: Sections 7.1-7.4.
Nonimaging concentrators are called "non-imaging" because they do not produce any optical image of the source, as opposed to imaging concentrators, which produce an image of the sun by reflecting it on the receiver. The non-imaging concentrators are able to reflect to the receiver all of the incident radiation, either beam or diffused, intercepted over a wide range of incidence angles. These systems are not precise, but they are more flexible. For example, if the right hand side of the sun is reflected to the left hand side of the receiver, the image of the sun is not preserved while the total energy incident on the aperture of the concentrator is additive. The most commonly used technology that leverages nonimaging optics is the compound parabolic concentrator (CPC).
The typical concentration ratios of CPCs are in the single digits. Despite the low concentration ratios of nonimaging systems, nonimaging systems can be very useful for increasing the performance of systems are relatively low costs, particularly in regions where the solar resource is less than ideal for concentrating systems to begin with (such as most of Europe and the northeast of the US).
The following reading describes in detail the optical principles and energy paths in the CPC collectors.
Book chapter: Duffie, J.A. Beckman, W., Solar Engineering of Thermal Processes, Chapter 7: Sections 7.6-7.8.
Imaging concentrators are used to achieve the highest temperatures that are currently achievable with a solar thermal system. Imaging concentrators enable a very large aperture area with a small absorber area, effectively reducing thermal losses at high temperatures. Ray tracing is used to evaluate such concentrating collectors during the design process. By (often digitally) drawing careful geometric reflections within a concentrating collector system, the distribution and angles of incidence of radiation on the absorber can be determined. This is a useful tool for both imaging and nonimaging concentrators, and can be used to show how active tracking systems on imaging concentrators (where the incident radiation is always perpendicular to the aperture) enable a much wider aperture with reduced reflectors compared with nonimaging systems. The typical concentration ratios of the currently existing large-scale systems that are using imaging concentrator technology (Ivanpah, SEGS, etc.) range from in the tens to as high as the low to mid hundreds.
Parabolic imaging concentrators are probably the most studied, both analytically and experimentally. To understand how these collectors are designed, it is necessary to understand the geometric properties of a parabola.
When light is reflected from the parabolic mirror onto a receiver to produce the optical image, the main parameters considered in the energy analysis are image size (width) and intensity of radiation within that image. Various models and examples of estimating those parameters are provided in the following reading.
Book chapter: Duffie, J.A. Beckman, W., Solar Engineering of Thermal Processes, Chapter 7: Sections 7.9 - 7.10.
After you complete all assigned reading in this lesson, please take the reading quiz in Canvas (Lesson 4 module)
This homework assignment consists of two quantitative problems that are closely tied with the readings. Please study examples in Chapter 7 (D&B book) as they can be especially helpful in developing the solutions.
Problems: 7.2 and 7.6 from the D&B textbook (see Appendix A)
As was requested in previous lessons, please complete these problems by hand, clearly showing your work step by step. While you should feel free to use any calculation software or spreadsheets behind scenes, I will only read and grade your hand-written solutions. The recommended format for hand-written problems should include underlined statements of:
A sample hand-written problem is given in the Lesson 2 Module in Canvas.
Please create electronic images of your hand-written solutions (via scan or camera) and save them in a single PDF document. If you have series of images of your pages, you can first insert them into a MS Word document in proper order, and then save the file as PDF.
The assignment is due by 11:59 p.m. (your local time) on Wednesday. Please see the Calendar in Canvas for specific due dates.
Concentrating solar power is a very useful tool that enables reaching high temperatures in solar energy conversion systems. Without concentration, the generation of electricity by conventional steam turbines using energy directly from the sun would not be cost effective. Optical concentration proves to be very advantageous since it reduces thermal losses and increases the useful energy gain.
Please double-check the to-do list on the Lesson 4 Introduction page [2] to make sure you have completed all of the activities listed there before you begin Lesson 5.