In nature it is solar power that creates wind power. Consider the example of the sea breeze. The sun heats both land and sea, but the land heats up more quickly and reaches a higher temperature than the sea. The air over the land becomes hotter than the air over the sea and the hot air rises, creating an area of lower air pressure(close to the surface).Air moves from the area of higher pressure over the sea to the area of lower pressure over the land. The cool sea air heats up as it moves over the land and so it rises, creating a cycle. The result of this cycle is a steady wind moving from the sea to the land .In this example from nature, the land is acting like a solar collector, changing sunlight into heat. The heated land heats the air and creates a wind. Wind turbines can harvest this wind energy.Wind from the Sun is a new technology for obtaining power from the sun and wind. This hybrid system turns the sun's light into heat, then uses that heat to create a wind within a horizontal large-diameter pipe. The wind inside the pipe is converted into electric power using a series of wind turbines A wind from the sun power plant would imitate this same type of system that occurs in nature, but with a greater degree of control and predictability. This will results in amore reliable wind with a higher average wind speed.
2. THE SOLAR COLLECTOR
2.1 Materials
A large area of land is covered with a material with low reflectivity (dark in color). This material collects the sun's energy in the form of heat, and is therefore called the collector. The area of land covered is circular.
More of the sun's light turns to heat when it strikes a dark material. If the material were a light color, such as white, then much of the sun's light would be reflected. Black is the best color to use for this purpose.
The collector should be black ceramic gravel. Tiles of black ceramic would work, but it might be time-consuming to layout all of the tiles. Gravel will allow water to pass through into the ground below whenever it rains. Perhaps the best material to use for the collector would be black ceramic gravel. This material should be easy to spread over the ground and will allow rain to pass through to the ground.
The solar collector converts the energy from sunlight into heat. The heat from the collector causes the air above the collector to also increase in temperature. The purpose of the solar collector is to heat the air so that it will rise, creating a wind. The energy in the wind is converted to electricity using wind turbines.
Any matter black color will absorb, rather than reflect, visible light. However, in order to convert as much of the sun’s energy to heat as possible, the solar collector must also absorb light well in the ultraviolet and infrared wavelengths. The energy from sunlight is approximately 5% ultraviolet light, 44% visible light and 51% infrared light. A carbon-based pigment (known commercially as “carbon black”) will absorb greater than 90% of the energy from light across the spectrum of ultraviolet, visible, and infrared wavelengths. Carbon black is a common pigment used in industrial paints.
Any one of a large number of different materials could be covered with carbon black pigment for use in the solar collector. The solar collector material does not need to have high thermal mass. Since the goal is to transfer the heat from the collector to the air, the collector does not need to retain the heat. Black ceramic gravel is heavy enough not to blow away in the wind, will allow rainfall to pass through to the ground beneath, and can be spread over a large area of land by machinery, requiring much less manual labor. It is also less expensive to manufacture than many other materials. Black ceramic gravel is one of the better materials for the solar collector. The black color would have to come from carbon black pigment, either painted on the ceramic after firing, or fired into the clay itself. A 100 Megawatt solar chimney power plant is projected to have an increase in air temperature of 35.7 degrees Centigrade . This comparison suggests that the small scale tests showed a high enough increase in temperature to drive a Wind From The Sun power plant. In other words, an area of ceramic heated by the sun gets hotter if it is surrounded by more hot ceramic. The surrounding hot ceramic keeps the ceramic within from losing much of its heat. A very large area of land covered with black ceramic gravel should theoretically increase in temperature to a much greater extent than a small area of land.
2.2 Size
The optimum size of the collector depends on a number of factors. Since a Wind from the Sun power plant has not yet been built, the optimum size can only be estimated at this point in time. A comparison with a similar technology, the Solar Chimney power plant, will give us a reasonable starting point for such an estimate.
The Solar Chimney power plant operates on similar principles to the Wind from the Sun power plant.
Both use a solar collector to heat air. Both generate wind from the rising of the heated air. According to Schlaich, a Solar Chimney power plant with a solar collector of 4000 meters in diameter and a 1500 meter tall chimney will produce 600 GWh/y. The area of such a collector would be approximately 12.566 million square meters (Лr2). A Solar Chimney power plant is planned for Mildura, Australia. That power plant will have a 4000 meter diameter collector and a chimney about 1000 meters high. The estimated power output is just under 500 GWh/year, due to the shorter chimney. A Wind from the Sun power plant would ideally be located in an area of the world with solar radiation of 2300 kWh/m2y or greater. The system’s energy input can be determined by multiplying the area of the solar collector (12.566 x 106 m2) by the amount of solar radiation (2300 kWh/m2y), giving us a value of 28,900 GWh/year. The energy input times the efficiency of the system gives us the power output. In the above examples of Solar Chimney power plants, the efficiency of the first power plant would be 2.07%; whereas, the efficiency of the second power plant will be about 1.7%.
The efficiency is calculated by dividing power output (600 and 500 GWh/y, respectively) by power input (28,900 GWh/y). For the Wind from the Sun power plant, the efficiency has not yet been determined.
But, even with a low overall efficiency, a sufficient amount of power might be obtained from such a system. Increasing the area of the solar
2.3 Temperature
The increase in temperature of the solar collector is what drives the entire system. The higher the temperature of the collector, the higher the temperature of the air, and the more wind power the system can generate.
How hot will the collector get? In small scale tests, an area of 36 square feet was covered with black ceramic. The ceramic in direct sunlight increased in temperature as much as 40 degrees Centigrade (72 degrees Farenheight) above ambient temperature (26 degrees Centigrade; 80 degrees Farenheight). The test took place at 42 degrees latitude in August. Estimated solar radiation for that place and time is 5 to 6 kWh/m2 per day. The amount of solar radiation would be significantly higher in the southwestern U.S., where daily solar radiation values reach 7 to 8 kWh/m2 per day. At such locations, the temperature of the black ceramic solar collector would also be significantly higher.
A 100 Megawatt solar chimney power plant is projected to have an increase in air temperature of 35.7 degrees Centigrade (The Solar Chimney, Jorg Schlaich, Edition Axel Menges, p. 37). This comparison suggests that the small scale tests showed a high enough increase in temperature to drive a Wind From The Sun power plant.
A large-scale collector should give an even greater increase in temperature than 40 degrees Centigrade. A small collector loses some heat to its surrounding perimeter. A large collector has less perimeter per unit area and so loses less heat. The collector will be hotter towards its center
The solar collector will tend to be hotter towards its center and cooler towards its perimeter. A smaller solar collector loses some heat to its perimeter. A larger collector has fewer perimeters per unit area and so loses less heat to its perimeter, making the center of the collector hotter than the perimeter. The center of a very large solar collector will reach a significantly higher temperature than the outer edges of the collector. However, the crucial temperature difference is in the air.
3.1 Air Movement
Hot Air Rises:
A number of factors make the rising column of air above the collector significantly narrower than the collector's diameter:
(1) Hot air rises. The hotter the air, relative to the temperature of the surrounding air mass, the faster the air rises. The collector is hotter in its center, making the air in the center also hotter. The air over the center of the collector rises faster, because it is hotter. The hotter air towards the center of the collector rises faster than the air over the perimeter, causing the air over the perimeter to curve inwards as well as upwards. This effect narrows the rising column of air over the collector.
(2) As the cooler air moves inward from the perimeter towards the center of the collector, it gradually increases in temperature as it spends more time over the hot collector. The hotter the air gets, the faster it rises. The cooler air, which moves mostly horizontally while at the perimeter, moves more and more vertically as it moves towards the center and increases in temperature. The result is that the path of the air curves upwards as it moves inwards (see diagram below), and so the rising column of air is much narrower than the collector itself.
Thus there are two factors which make the air hotter over the center of the collector, first, that the center of the collector itself is hotter and, second, that the air in the center has spent more time over the collector.
(3) The rising air in the center meets with less resistance as it rises, because it is surrounded by air that is also rising. This factor causes the air towards the center to raise faster, drawing in air from the perimeter, and again narrowing the rising column of air.
(4) As the hot air over the collector rises, new cooler air must move in from the sides around the collector to replace the rising air. The cooler air at the perimeter moves inward from 360 degrees around the collector. This results in a wind moving inwards towards the center of the collector. Air movement over the perimeter of the collector is more horizontal than vertical. This wind pushes the rising column of air inwards, again making the column of air narrower than the collector itself.
For the above reasons, most of the updraft over the collector occurs around the center of the collector. Therefore, the air pressure will also be lowest towards the center of the collector.
The air pressure over the solar collector is lower than the air pressure over the surrounding land. The reason is that the collector is heating the air above it, but the surrounding land remains at ambient temperature. The heated, rising air results in an area of lower air pressure. The low pressure over the collector is maintained as long as the collector is being heated by the sun.
Air moves from an area of high pressure to an area of low pressure. The rising hot air significantly lowers the air pressure over the collector relative to the surrounding land. The air from the land surrounding the collector moves in towards the center of the collector and also rises upwards. In this way, the solar collector creates wind. This wind moves from 360 degrees around the collector in towards its center and upwards. The updraft created should be quite strong, since it is the result of air moving in from 360 degrees.
The effect is such that the air over the center of the collector rises just as if it were confined within a chimney. A solar chimney-like result is achieved without the expense of a tall vertical structure. This virtual chimney effect depends upon the diameter of the collector and the difference in temperature from the center to the edges of the collector. The effect is greater with a larger collector and a larger increase in temperature towards the center. The hotter the air, the faster it rises; the faster it rises, the more the air from the perimeter is drawn in towards the center. The updraft created by this effect produces an area of low air pressure in the center of the collector.
3.3 Air Pressure
In a closed container, when we increase temperature, volume remains the same, so pressure must increase to balance the system. However, in the case of a solar collector in the open air, the collector increases the air temperature, causing air volume to increase and pressure to decrease. The decrease in air pressure is what drives the Wind from the Sun system. This same decrease in air pressure is seen in nature in the case of a sea breeze.
Calculating the change in pressure in a system open to the atmosphere is complex. The pressure is affected by the changing temperature of the solar collector, by changes in atmospheric pressure, surface winds, and humidity. In addition, the solar collector causes a strong updraft, which contributes to the decrease in pressure over the collector. Future experiments are needed to quantify the solar collector’s effect on the air pressure over the collector. What is clear, though, even at this point in time, is that the solar collector will decrease the air pressure over the collector.
4) Air Channel:
A very large diameter pipe or air channel connects the area of low air pressure over the solar collector to an area of higher air pressure away from the heat of the collector. Air moves from high pressure to low pressure, creating a wind within the pipe.
The amount of wind power generated by this system depends on the air pressure difference from the center of the collector to the surrounding land. An air pressure difference of about 400 Pascals should generate a wind speed of 15 meters per second (m/s). An air pressure difference of about 700 Pascals should generate a wind speed of 20 m/s.
More than one pipe can feed air into a large collector. The diagram below shows a 4-pipe power plant. The optimum number of pipes has not been determined and will depend on the size of the collector, the amount of heat generated by the collector, the length and diameter of the pipe, and the time of year. The sun is higher in the sky and gives more sunlight in the summer than in the winter. It may be that the plant will operate more pipes in summer and fewer in winter.
The diagram below shows 4 pipes, each of which is 2000 meters in length and 175 meters in diameter. The solar collector has a diameter of 4000 meters. The pipes extend 1500 meters into the collector because the inner portion of the collector has the lowest air pressure. The pipes extend only 500 meters away from the collector. Cool air is constantly moving in towards the collector, so perhaps the pipes could extend an even shorter distance away from the collector.
The pipes shown in the diagram above are circular in cross-section. However, they could be rectangular in cross-section .This shape may be less expensive and easier to build. It should also take better advantage of the heat from the collector, since it will be closer to ground level. To obtain the same cross-sectional area, these rectangular air channels (instead of pipes) would need to be about 60 meters high by 400 meters wide. Pipes of the same cross-sectional area would have a diameter of about 175 meters.
Air flows into the air channel (blue rectangles below) from the perimeter of the collector. Air flows out of the air channels near the center of the collector and rises upward. The air rises for two reasons. First, a strong updraft occurs in the center of the collector. The updraft results from the solar collector heating the large volume of air which does not travel through the air channels. Second, the air which does travel through the air channels is heated by the collector as it travels through the air channels and after it exits the air channels.
The figures above show an example of 4 pipes per collector and an example of 2 air channels per collector. However, the optimum number has not been determined yet. Perhaps such a power plant would only need one air channel to produce sufficient power. A test plant would have to be built and measurements taken in order to have sufficient data to make such a determination.
The hot air rising from the center of the collector creates and maintains a low pressure area in the center of the collector. The pipes have a constant difference in air pressure from one end to the other. The air pressure is higher away from the collector and lower towards its center. This difference in air pressure moves air through the pipes.
Each pipe has pressure-staged wind turbines which present a kind of obstacle to the air movement. The wind turbines remove mechanical energy from the wind in the pipes and convert it to electricity. Even so, air continues to move through the pipes because the rising hot air in the center of the collector maintains a significantly lower air pressure at one end of the pipe.
The wind speed can be controlled by increasing or decreasing the size of the collector. Such a change can even be made after the power plant has been built, by covering or uncovering part of the collector's surface with a white material. In summer, the collector will tend to reach a higher temperature and produce a higher wind speed. It is possible to reduce the wind speed by covering part of the collector, thus reducing the effective size of the collector. In winter, the collector will not reach as high a temperature and so the collector can be completely uncovered to obtain maximum wind power.
5 Wind Velocity
The wind velocity (V) through the air channel depends mainly on the total pressure difference (ΔPtot) from one end of the air channel to the other. Air density (D) is a much less significant factor. In Equation (5), velocity is multiplied by air density, so that a greater air density would seem to increase power. However, Equation (6) below shows that the square root of the air density affects the velocity. Since that velocity is cubed in Equation (5), overall, a greater air density provides less power. Higher air temperature generally results in lower air density, which, in this system, will provide higher air velocity and greater power.
Equation (6) can be solved for the total pressure difference (Ptot), giving us Equation (7) below
ΔPtot = V2*D*3/2…….. (7)
This equation assumes that the wind turbine extracts the theoretical maximum power by reducing pressure across the turbine (ΔPs) by 2/3rds of the total pressure difference (ΔPtot). Table (1) below compares total air pressure difference (ΔPtot) and air velocity (V) through the air channel, to power available in the wind per square meter (P1), to swept area of the wind turbines (A) and total power output (P2). Air density is assumed to be 1.165kg/m3 (The value for 300C and standard atmospheric pressure). Note that a 50% increase in velocity increases power output by 3.375 times. Total power output (P2) is simply the product of the power of the wind per square meter and the total swept area (A) of the turbines. Note that total power output is the theoretical maximum, actual power output will be less than is theoretically possible.
Air velocity will increase towards solar noon, when solar radiation is greatest, and decrease as sunset approaches. Maximum air velocity will also increase as summer approaches and decrease as winter approaches. Since power is based on the cube of air velocity, more power will be generated in the middle of the day and the middle of the year. However, locations closer to the Equator will have less of a difference in power production between summer and winter.
6 Wind Turbines:
A series of very large wind turbines within the pipe turn the wind into electricity with a high degree of efficiency. Each pipe can contain several turbines and each collector can support several pipes.
For a power plant with a collector diameter of 4000 meters, the interior diameter of the pipes would be 175 meters and the cross-sectional area would be about 24,050 square meters. A pipe of that size could support multiple wind turbines in a variety of configurations. One possible configuration is shown below. Seven large turbines, each with a diameter of about 55 meters, can fit within a pipe of this size.
Of course, the pipes do not have to be round in cross-section. They can certainly be rectangular, as shown below. Again, seven large turbines, of about 55 meters in diameter each, can fit within a rectagular pipe with the same cross-sectional area as the round pipe.
The swept area of a wind turbine with a diameter of 55 meters is about 2375 square meters. If a 175-meter pipe has 7 wind turbines, the swept area is 16625 square meters. But if the same 175-meter pipe had 1 large wind turbine with a diameter of 173 meters, the swept area would be 23500 square meters. This represents an increase in swept area of over 40%. Since swept area is roughly proportional to power output, the output would be increased by 40% by using one large wind turbine, instead of 7 smaller ones.
The air velocity (V) or wind in the air channel depends on the total pressure difference from one end of the air channel to the other (Ptot) and on the air density (D):
Ptot = V2 * D * 3/2
The power (P) available in the wind follows the formula:
P = 0.5 . D . V3
A 15 m/s wind will generate about 1965 Watts per square meter. So, if the total swept area of the wind turbines is 25,000 square meters, the power generated will be about 49 Megawatts. A 20 m/s wind will generate about 4660 Watts per square meter. So, if the total swept area of the wind turbines is 25,000 square meters, the power generated will be about 115 Megawatts.
The larger the solar collector, the greater the air pressure difference, the greater the power produced. A larger solar collector may also be able to support more than one air channel, providing a greater total swept area and more total power produced.
7. Alternate Design Possibilities
The above design for a Wind from the Sun power plant requires a large area of land to be covered with black ceramic gravel. What would be the effect on the environment of covering thousands of acres of land with gravel? And if the power plant one day had to be dismantled, what would be the cost to remove the gravel? The large solar collector required for a Wind from the Sun power plant is a significant concern within this type of solar power. An alternate design is possible, which either omits the solar collector, or uses a smaller collector. The collector’s purpose is to produce an area of lower air pressure relative to the surrounding land. Such pressure differences also occur naturally, as seen in the example of the sea breeze. If the location of the Wind from the Sun power plant were chosen astutely, the natural air pressure difference might be sufficient to produce enough power to operate the plant economically. Most sea breezes are between 0.3 and 1.0 kilometers in depth, yet the wind velocity can exceed 12 m/s. An air channel of less than one kilometer, connecting the air over a large body of water to the air over an adjacent land mass could find a sufficient natural air pressure difference to produce a significant amount of power. And the cost of building the power plant would be reduced significantly because the amount of land required would be lessened, and the expense of a large quantity of black ceramic gravel would be eliminated. Another possible location with a natural air pressure difference would be at the border between two different types of land topography. The cause of the differing air pressures would generally be the difference in reflectivity of the two areas and differences in how quickly each area is heated by the sun.
If the natural difference in air pressure is not sufficient, a solar collector (reduced in size from the power plant described in 1 – 5 above) could augment the natural pressure difference. To increase efficiency, place air channel so that one end is over a large body of water. The water will be much cooler than the collector and will increase the air pressure difference along the air channel.
8. Conclusions
At this point in time, two conclusions are clear. First, this type of system will produce some power. The sun will heat the collector, which will heat the air. The higher air temperature will expand the air, reducing air pressure. Air must move from high to low pressure, through the air channel and past the wind turbines, producing power. A sea breeze works much the same way and produces significant wind. Some power can certainly be produced in this way. Second, the system has not been built and tested to a large enough scale to determine how much power will be produced. Will the air pressure difference be large enough to produce significant air velocity through the air channel? Will the system produce enough power to be economical? What are the possible ecological effects of such a large solar collector? Further study is needed to answer these and other questions.
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