Solar and Renewable Energies

Transcription

1 Physics 162: Solar and Renewable Energies February 2, 2010 Prof. Raghuveer Parthasarathy Winter 2010

2 Lecture 9: Announcements Reading: Wolfson 10.2, Chapter 4 Homework: Problem Set 4, due Thurs. Feb. 4. Homework: Microwave Exercise Part II, due Thurs. Feb. 4. Yes, we re finished grading the quiz. Comments later today... MidtermExam: Thursday Feb. 11

3 Hydropower (addendum) We finished discussing hydroelectric power (gravitational potential energy kinetic energy electrical energy (electromagnetic induction)) In our brief discussion of hydropower related environmental issues I noted that more than 1 million people were displaced recently for the Three Gorges Dam construction in China. I did not mean to imply that constructions in China are the only instance of displacements or that displacements haven t occurred in the U.S....

4 Hydropower (addendum)... in fact, a particularly profound and tragic example occurred nearby: the Dalles Dam construction in the 1950 s on the Columbia River at Celilo Falls, submerging Native American settlements and fishing areas that had existed for the past 15,000 years. A philosophical question: Can we supply 7billion people with many kw of power without tragedy?

5 Work and Energy Another illustration of work, energy, etc. Suppose I compress and release a spring to launch a ball of mass M upward. (Like a pinball machine.) It travels to a max. height of h. (The grav. potl. energy equation is E grav = Mgh.) How much work is done by the spring? A. Mgh B. We can t answer unless we know how fast the ball accelerates C. We can t answer unless we know the elastic potential energy of a compressed spring.

6 Work and Energy Principles: Energy & work are equivalent; energy is conserved The spring does some work; This gives some kinetic energy to the ball; At the highest point it s all converted to grav. potential energy. Therefore the work done must be equal to this energy: Mgh. M, g, and h are all we needed to know to determine the work done by the spring!

7 Work and Energy But I thought Work = force distance. Don t we need to know the force? We could figure out force a spring exerts, what distances are involved, etc. to determine work. This is fine, but (a) it s a more difficult route, since we don t know the force, and (b) it has to give the same answer: Mgh. The work done is the work done, however you calculate it. So think of an easy way to calculate it!

8 Work and Energy Another illustration. The elastic potential energy stored in a compressed spring is proportional to the square of the distance it s compressed. If you like equations: E spring = (½)kx 2, where k indicates the stiffness ( spring constant ) of the spring, and x is the compression distance. Suppose I compress my spring twice as much. How much higher will my ball go up? A. Same; B. 2 ; C. 4 ; D. 8

9 Work and Energy All the spring s energy kinetic energy grav. potl. energy. Doubling x, x 2 is 4 larger, so E spring is 4 larger, so... E grav = Mgh must be 4 larger, so h must be 4 larger. Think about this and realize that it doesn t follow from memorizing equations, but from the principle of conservation of energy.

10 Wind Power The essence of wind power is simply kinetic energy electrical energy. Wind turns windmill blades, running a generator, generating electricity. How much? What does this depend on? istockphoto.com

11 Wind Power Last time we figured out that the power carried by wind is proportional to the third power of the wind speed, i.e. P v 3. Why?(Think about this!) In brief: the kinetic energy in the wind v 2, and the time each piece takes to hit the blades 1/v, so power = energy / time P v 3. (i.e. v v v) So doubling v doesn t double P; it increases the power by 2 3 = 8! (i.e. 2v 2v 2v = 8 v 3 )

12 Wind Power Suppose the wind speed drops by a factor of 10. By how much does the power carried by the wind drop? A. 10x B. 30 C. 100 D. 300 E It drops by a factor of 10 3 = 1000.

13 Wind Power How does power depend on the size of the wind turbine (i.e. windmill)? For the next question, call the radius of the circle swept by the blades r. Imagine that the wind turbine captures all the kinetic energy incident on the circle the blades sweep out (blue). (The extent to which this is true depends on the blade thickness and the blade speed relative to the wind speed.) r

14 Wind Power Question 3 Suppose you can build (A) one wind turbine with a large radius, r, or (B) two wind turbines with radius r/2. These would be placed in the same area (i.e. v is the same.) Which do you build to maximize your power generation? (Think about this) A. One r windmill. B. Two r/2 windmills. r C. These are equivalent Discuss.

15 Wind Power Since more blocks of air hit a larger wind turbine, it generates more power. How much more? An amount proportional to the area of the turbine and hence r 2. How do I know this? You learned at some point A circle = πr 2. This is important, but the really important part is the r 2. Any area involves length length that s what area is. r

16 Wind Power Question 3 Suppose you can build (A) one wind turbine with a large radius, r, or (B) two wind turbines with radius r/2. These would be placed in the same area (i.e. v is the same.) Which do you build to maximize your power generation? A. One r windmill. B. Two r/2 windmills. r C. These are equivalent So the r turbine generates 4 the power of the r/2 turbine.

17 Wind Power Which brings us to the worst graph you ll ever see. (Unless you read USA Today.) from Energy for Sustainability, J. Randolph and G. M. Masters (Island Press, 2008)

18 Wind Power This plots turbine height vs... nothing. The x axis conveys no information. There are data on power, but you have to read the numbers from text! Let s use these numbers to make a decent graph: As expected, power r 2. A good line, despite different manufacturers, different engineering, etc. You can t avoid the Physics!

19 Wind Power Now we know: Power v 3, and A (area) (or r 2 ), which we can combine: Power Av 3. Can we figure out the missing pieces to turn into =? Sure, but I want to stress that figuring out the above scaling relations is the important part! Let s return to our imaginary blocks; let s say they are cubes of size s s s. How do we know what s is? Hang on... Each cube has KE = (½)Mv 2, where M is the mass of air in the cube and v is the velocity.

20 Wind Power Lets write M in terms of the density of the air (ρ, easy to measure) and the cube volume (s 3 ). Densityis mass / volume, so ρ=m/s 3, i.e. M = ρs 3. The KE of each cube is KE = (½)ρs 3 v 2. Each cube travels with velocity v. Velocity = distance / time, so the time it takes for each cube to cross the circle is t = s/v. (Think about this.) (Time = distance / velocity) s s s s

21 Wind Power The KE of each cube is KE = (½)ρs 3 v 2. t = s/v. r # cubes that fit in the circle is A/s 2. Therefore the Power = Energy / Time for all cubes = A v P= ρ s v The s s cancel! 2 s 2 s 1 3 A simple expression for wind power. P = ρ Av 2 (Agrees with our scaling relations) Think through this yourself that s better than watching me go through it.

22 Wind Power The KE of each cube is KE = (½)ρs 3 v 2. t = s/v. # cubes that fit in the circle is A/s 2. Therefore the Power = Energy / Time for all cubes = (# cubes) (kinetic energy per cube) / (time to hit ) r Note: Our P is all the power carried by the wind.

23 Elephants Why did we derive this? To show where it comes from and to illustrate how scientists analyze things... We made up s s s cubes, and the parameter we made up (s) disappeared from our answer. That s the beauty of Physics, which reminds me of a story about elephants...

24 Efficiency The power carried by wind hitting a turbine: P 1 = 2 ρ Av 3 How much can we convert into the kinetic energy of the blades (and then into electrical energy)? Recall for hydroelectric power we lost some energy to friction, but there was no fundamental limit on energy conversion efficiency if we reduce friction, we improve efficiency. In practice, efficiency > 80%

25 Wind Power: efficiency For wind power there is a fundamental limit on the fraction of the wind s kinetic energy that is transferred to the blades, and it depends on the turbine construction. Here s why: A windmill that intercepts all the wind velocity, so the velocity is zero downstream, presents a wall of stagnant air that diverts arriving wind around the windmill. So efficiency is low. A windmill that intercepts little wind will only reduce v (and KE) a small amount; only this small amount will drive the blades. So efficiency is low.

26 Wind Power: Efficiency A graph of efficiency (i.e. fraction of wind power harnessed) vs. the ratio of the airspeed down and up stream of the blades looks like: The maximum isn t efficiency =1 (100%), but rather 0.59 (59%). This follows from aerodynamics, and is known as the Betz Limit.

27 Wind Power: Efficiency This limit has nothing to do with friction it s a fundamental limit on the max. possible efficiency of energy transfer. Friction further lowers efficiency. How well do real turbines do? Not bad... ratio of blade speed at tip to wind speed.

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29 Wind Power: Calculation A little calculation (example). Being environmentally conscious, I decide to install small turbines under my nostrils, harnessing my exhaled breath to generate electricity. How much power is carried by my breath? P = ½ρAv 3. 1 cm A = nostril area 2 (0.01 m) 2 = m 2. ρ = air density = 1.2 kg/m 3 1 kg/m 3 v 0.1 m/s (about 10 s to go 1 meter, I m estimating) So: P = ½ (10 1 ) 3 Watts = 10 7 W.

30 Wind Power: Calculation How much power is carried by my breath? P = ½ (10 1 ) 3 Watts = 10 7 W. If my turbines operate at the max. possible efficiency, how much power do they generate? About W. Betz limit This does not seem worthwhile...

31 Wind Power That s the Physics of Wind Power. (Quiz results) (Start demo)

32 Quiz results Solutions are posted. In general not bad, except #2: (#2) Work = force distance; always true. Doesn t matter what color the sky is, what your breakfast was, or what time is involved. If you know force, and know distance, you know the work involved. w/o #2, mean is 23/31 = 74%

33 Wind Power That s the Physics of Wind Power. History: A very long history Thousands of years of using wind for propelling ships, grinding grain, pumping water, etc... The first wind turbine to generate electricity: 1891 (A Danish inventor, Poul la Cour) istockphoto.com

34 Wind Power History: A very long history US: 1930 s, 40 s: hundreds of thousands of (small) wind turbines across the Great Plains (before an extensive electrical grid) 1980 s, 1990 s: little interest in wind in the U.S.; Lots of technology development in Europe (esp. Denmark, Germany, Spain)

35 Wind Power Since then, a rapid rise in wind power. US ( ) 39% increase in capacity in 2009! New York Times, Jan. 26, 2010 The Economist, 4 Dec (You don t have to remember these numbers)

36 Wind Power: Abundance Wind power: Abundance? Hard to estimate; depends on things like how much land can be used Total wind power that could be harnessed in the U.S. (estimated by Pacific NW Natl. Lab): W, which is 5 kw per person (roughly) With strict land use regulations, about W, which is 1.5 kw per person, about the same as the per capita electricity consumption.

37 Wind Power: Abundance Practical concerns would limit us to getting 20% of this. Wind power is Unevenly distributed in time (variable) Unevenly distributed in space (often far from population centers) Issues of energy storage (due to variability in time, etc.), power grid design, etc. Future developments stay tuned! Still: 20% of our total electricity would be great! (2008: 1%). Some graphs...

38 Blue bars: % of electricity from wind power 2005 Lots of wind power research (80 s, 90 s, now) China (2008)

39 Blue bars: % of electricity from wind power (2008): 1% I ve plotted 2008 data just for the U.S. and China China (2008): 0.4%

40 Wind Power Another global comparison The Economist, 4 Dec. 2008

41 Wind Power: Environmental Impacts How green is wind power? Renewable Energy Source Clean, non polluting, no CO 2 emissions Fast energy payback it takes a few months for a wind turbine to generate (i.e. convert) as much energy as it took to manufacture it! (Not true, e.g., of solar cells.) Some noise (but not a lot)

42 Wind Power: Environmental Impacts How green is wind power? Renewable Energy Source Clean, non polluting, no CO 2 emissions Fast energy payback Some noise (but not a lot) Some people complain about killing birds...

43 Wind Power: Environmental Impacts Some people complain about killing birds... but this simply is not a real issue! from Energy for Sustainability, J. Randolph and G. M. Masters (Island Press, 2008)

44 Wind Power: Environmental Impacts How green is wind power? Renewable Energy Clean, non polluting, no CO 2 emissions Fast energy payback Some noise (but not a lot) They don t kill many birds Aesthetics & related complaints a big deal.

45 Wind Power: Environmental Impacts Aesthetics & related complaints a big deal. Many people really don t like wind turbines spoiling the view. This issue splits environmental groups. Which is better: wind turbines in sight, or coal plants out of sight? A major issue, severely limiting wind power implementation! (E.g...) What do you think?

46 Wind Power: Environmental Impacts How green is wind power? Renewable Energy Clean, non polluting, no CO 2 emissions Fast energy payback Some noise (but not a lot) They don t kill many birds Aesthetics.

47 Wind Power The future? Probably more wind power (projected) Lots of interest in offshore wind turbines Advantage: Stronger winds Disadvantage: high cost ( 40% more), aesthetics (near shore) Present: 1% of wind power is from offshore; about 20 offshore farms in Europe, & more planned; 0 in U.S. (1 planned) people That s wind power. The Economist, 4 Dec. 2008