Solar Energy March 5, 2009

Solar Energy March 5, 2009 Solar Energy Larry Caretto Mechanical Engineering 496ALT Alternative Energy March 5, 2009 Homework assignment on nuclear power due tonight. Reading for tonight and next Tuesday – Chapter 13 on solar energy Reading for March 12 and 14 – Chapter 15 on wind energy (Note typographical error for this reading assignment in course outline.) ME 496ALT Alternative Energy 1 Solar Energy March 5, 2009 Outline • Solar radiation basics – Angular profiles – Optimum tilt angles – Radiation Intensity – Black body radiation – Solar air mass • Design of solar collectors – Heat transfer losses – Computing fluid temperatures 2 Tonight is the first of two lectures on solar energy. It will deal mainly with the basics of solar radiation and how those basics are used in the design of solar collectors. We will consider mainly solar thermal collectors tonight and will discuss solar generation of electricity next Tuesday. ME 496ALT Alternative Energy 2 Solar Energy March 5, 2009 3 http://www.geog.ucsb.edu/~joel/g110_w07/lecture_notes/sun_angle/agburt0 2_17b.jpg (accessed March 11, 2007) The earth has an elliptic orbit about the sun. The closest earth-sun distance, 147,500,000 km, which is called the perihelion, is reached on January 3. The furthest earth-sun distance, 152,500,000 km, called the aphelion, is reached on July 4. The difference in the earth sun distance between the aphelion and perihelion does not have a significant effect on climate. The difference in seasons is caused by the tilt of the earth. During the northern hemisphere summer the tilt gives more incoming solar radiation to the northern hemisphere and less to the southern. Thus, the southern hemisphere has a winter while the northern hemisphere has summer. At the northern hemisphere summer solstice the sun is pointing directly at the tropic of cancer. At the northern hemisphere winter solstice the sun is pointing directly at the tropic of capricorn. The usual analysis of solar energy takes an earth centered coordinate system which views the sun as in motion about the earth. Copernicus and Galileo may be turning over in their graves about this, but this is really a coordinate transformation to consider a different origin for the relative motion of the sun and the earth. When viewed from the earth, the angle of the sun relative to the earth changes from -23.5 to +23.5 during the year. This angle is known as the declination angle. ME 496ALT Alternative Energy 3 Solar Energy March 5, 2009 Declination Angle & Relative Earth-Sun Distance 30 Solar Declination Angle 1.03 20 1.02 s Declination angle c Relative distance 10 1.01 0 1.00 -10 0.99 Declination Angle (degree Relative Earth-sun Distan -20 0.98 -30 0.97 0 40 80 120 160 200 240 280 320 360 Julian Date 4 This chart was prepared using equations for the declination angle and the relative earth-sun distance accessed on March 11, 2007 at the web site: http://solardat.uoregon.edu/SolarRadiationBasics.html We see that the declination angle goes from -23.5 degrees in at the end of the year to +23.5 degrees in midyear. As noted previously, the earth-sun distance goes from 147,500,000 km on January 3 to 152,500,000 km on July 4. The relative distance between the earth and the sun plotted here is the actual distance divided by the average distance. Of course, the orbit of the earth around the sun actually takes 365.2422 days. The use of leap years makes the empirical formulas only approximate ones. Note that the Gregorian calendar used in the US and Europe today has 365.2425 days per year on average. ME 496ALT Alternative Energy 4 Solar Energy March 5, 2009 Solar Angles • Azimuth is daily variation • Declination is annual variation 5 Reference: http://www.homepower.com/files/pvangles.pdf (accessed March 11, 2007) The angles used in defining the location of a solar collector are confusing because they are a combination of two kinds of angles. The first relate to the three- dimensional earth-sun geometry; the second relate to the local planar geometry where a local plane is a tangent to the earth’s surface. The solar declination is the angle that the sun makes with a plane through the equator. In the picture in the lower right the sun will rotate about the North-South (horizontal) coordinate through the year. The solar angle (labeled as θ in this diagram) is more conventionally given the symbol δ, which is used in subsequent slides. The azimuth angle is the angle that the sun makes with the a coordinate system based at a given location. At local solar noon, the sun is due south and the azimuth angle is zero. The azimuth angle is based on the local horizontal plane (horizon). The azimuth angle, z, is different from the hour angle, h, defined on the next slide. The azimuth angle, z, is based on the local horizon, which is a horizontal plane, tangent to the earth’s surface. The hour angle, h, is based on the rotation of the spherical earth. ME 496ALT Alternative Energy 5 Solar Energy March 5, 2009 Solar Angles II 6 http://www.srrb.noaa.gov/highlights/sunrise/azelzen.gif accessed March 9, 2007 Here is another view of the azimuth angle. Although this chart shows it being measured clockwise from north, it is generally considered to be zero when the sun is due south. Note that the angles considered here are in a plane at a given location. This plane is tangent to the surface of the earth. These angles are different from angles considered in a spherical coordinate system. This chart also shows the zenith angle, z, and the elevation angle, h, which is later designated as α in these notes and other references. Both these angles are measured with respect to a horizontal plane that is tangent to the surface of the earth at a given location. Note that the elevation angle, h, goes from 0 at sunrise to 0 at sunset. ME 496ALT Alternative Energy 6 Solar Energy March 5, 2009 Solar Angles III from the sun center 7 Reference: Jui Sheng Hsieh, Solar Energy Engineering, Prentice-Hall, 1986. The equatorial plane is a plane that passes through the earth’s equator. A line from the center of the sun to the center of the earth makes an angle, δ, with this plane. This angle is called the declination angle. It varies from 23.47o to –23.47o depending on the time of the year. The declination angle can be approximately computed by the following equation where n is the day of the year (January 1 = 1; December 31 = 365); this is sometimes called the Julian date. ⎡360 π ⎤ δ = ()23.45o sin ()284 + n ()δ in degrees ⎣⎢365 180⎦⎥ The latitude, L, at a particular location, P, is the angle with one side on the equatorial plane, its center at the center of the earth, and the other side passing through the location P. The hour angle, h, is a measure of the time of day. It is zero at the local solar noon and advances 150 per hour as the day progresses. With this definition, the hour angle is negative before the local solar noon and is positive after it. ME 496ALT Alternative Energy 7 Solar Energy March 5, 2009 Angles for Tilted Collector 8 Reference: Jui Sheng Hsieh, Solar Energy Engineering, Prentice-Hall, 1986. Here the large horizontal plane is tangent to the surface of the earth at a given point. The smaller collector surface is tilted at an angle s from the horizontal plane and an angle ψ from the south (westward direction positive and eastward direction negative.) i is the angle between the normal to the tilted surface and the line of the direct sun rays. This chart also shows the zenith angle, z, and its complement, the altitude angle, α. (α + z = π/2.) These are two ways of measuring the same thing. The zenith angle is the angle between a line from the sun to the position on the earth and a vertical line, normal to the earth at that point. The elevation angle is the angle between a line from the sun to the position on the earth and a plane parallel to the earth at that point. Angle relationships are complex results of solid analytical geometry and trigonometry. The azimuth or altitude angle is given as follows. cos z = sin α = sin L sin δ + cos L cos δ cos h The angle i for a tilted collector is found from the following equation cos i = sin L sin δ cos s – cos L sin δ sin s cos ψ + cos L cos δ cosh coss + sin L cos δ cos h sin s cos ψ + cos δ sin h sin s sin y Simplifications are possible for a southward facing collector where ψ = 0. Sunrise and sunset occur when the elevation angle, α = 0. ME 496ALT Alternative Energy 8 Solar Energy March 5, 2009 Equation of Time 9 Reference for chart: http://freepages.pavilion.net/users/aghelyar/aghpage2.htm The solar time used in the calculation of the hour angle must account for the differences between local time and standard time and certain differences due to the earth and its orbit. The later include the effects of the variable speed of the earth in its elliptic orbit about the sun and the tilt of the earth in its orbit. These two effects are summarized in the equation of time plotted above.

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