How wind kills coal

How wind kills coal. Underlying graphics from a report by the NREL.

Imagine you are a coal plant (gray area) that needs to run continuously to earn the ROI the investors were promised. Yikes, indeed!

Today Germany, tomorrow the world.

Maximum temperatures in glass-melt solar storage

Temperature field in a glass-making furnace in °K. (1820 °K = 1550 °C.)  Image quoted from L. Pilon et al.

As calculated in a previous post, the minimum (i.e., empty) temperature of a glass-melt storage is about 1340 °C (1610 °K) because of the need to supply high radiant flux (about 250 suns) to the steam tubes in order to achieve rated output. The maximum temperature depends on the high temperature materials available for the tank, the furnace roof, and the shading elements that modulate the radiant flux on the stem tubes.

Properties of ultra-high-temperature ceramic insulation. Image quoted from Rath USA.

Being optimistic, I'll say 1800 °C is an acceptable maximum glass-melt temperature—that's 250 °C hotter than a glass making furnace.

The storage temperature range is 1800 °C - 1340 °C = 460 °K, and the mean temperature is 1470 °C.  From Pilon et al., the specific heat, c, of molten glass between 1000 °C and 2000 °C is about 1231 J/kgK, so a 460 °K storage range stores 460 * 1231 = 566,000 J/kg. The density of molten glass in this temperature range is about 2300 kg/m3, so the volumetric energy storage is 1.3 E9 Jthermal/m3.

From the previous post, we need 5.3 E6 Jthermal/m2-land to store 15 hours of heat for rated output, so, spread over the land area of the heliostat field, the storage glass would form a layer 5.3 E6 / 1.3 E9 = 4 mm thick. That is less glass than would be needed for the mirrors!

Again from the previous post, the total land area for 3.2 GWe Gemasolar plant is 71 E6 m2, so the total storage volume is 71 E 6 * .004 = 284,000 m3, equivalent to a hemisphere with radius, r:

pi * 2/3 * r^3 = 284,000

r = 51 m, a pool with a perimeter of 2*pi*r = 320 m

At a thermal efficiency of 0.46, the rated thermal power is 3.2 E9 / 0.46 = 7.0 E9 Wthermal.

At 250 suns, the furnace wall area is 7.0 E9 / 250,000 = 28,000 m2.

With furnace wall area arrayed around the 320 m perimeter of the pool, the furnace wall is 28,000 / 320 = 87 m high, that is close to the height of the actual furnace walls at Plant Bowen, which appear to be about 75 m tall in photos. But I think 87 m is too tall in relation to the pool diameter (102 m) to comport with the earlier assumption of a 0.7 view factor, so this calculation is going to need more iterations.

Capacity factor and hours of solar storage

The Gemasolar plant in Andalucia, Spain operates at an annual capacity factor of 75% using just 15 hours of thermal storage.

The 17 MWe Gemasolar power tower in Fuentes de Andalucía, Spain is designed to operate at an annual capacity factor of 75%, and has run continuously for as long as 36 consecutive days. This remarkable accomplishment is achieved with just 15 hours of thermal storage. Clearly 15 hours of thermal storage is about the right amount for a solar plant!

Here are some statistics for Gemasolar gleaned from the National Renewable Energy Laboratory's site.

Projected annual output: 110,000 MWhr/yr = 12.6 MWe  annual average.
Rated output  (calculated from the 75% capacity factor): 16.7 MWe rated. 

Output per mirror area (304,750 m2) :
       41 We/m2 annual average,
       55 We/m2 rated.  

Land yield (1,950,000 m2; mirror/land ratio = 0.156):
        6.4 We/m2-land annual average,
        8.6 We/m2-land rated

The 15 hours of storage based on 40% thermal efficiency is:

15 hrs * 3600 s/hr * 8.6 We/m2-land * 1/0.40 = 1.2 E6 Jthermal/m2-land

A plant with telescopic heliostats and glass-melt storage would have some advantages over Gemasolar. Telescopic heliostats can be packed much more closely, increasing the mirror/land ratio to around 0.70, increasing land yield about 4.5 times that of Gemasolar. Also, because the glass melt transfers its heat to hotter steam (608°C vs. 565°C) the steam cycle efficiency can be greater, about 46% thermal efficiency as compared with 40%, a factor of 1.15 .

Now, the same Gemasolar statistics if rebuilt on the same land with telescopic heliostats and glass-melt storage:

Projected annual output: 110,000 MWhr/yr  * 4.5 * 1.15 = 65 MWe  annual average.
Rated output  (calculated from the 75% capacity factor): 87 MWe rated. 

Output per mirror area (304,750 m2 * 4.5 = 1,370,000 m2) :
       41 We/m2 * 1.15 = 47 We/m2 annual average,
       55 We/m2 * 1.15 = 63 We/m2 rated. 

Land yield (1,950,000 m2; mirror/land ratio = 0.156):
        6.4 We/m2 * 4.5 * 1.15 = 33 We/m2-land annual average,
        8.6 We/m2 * 4.5 * 1.15 = 45 We/m2-land rated.

The 15 hours of storage for the rebuilt plant becomes:

15 hrs * 3600 s/hr * 45 We/m2-land * 1/0.46 = 5.3 E6 Jthermal/m2-land

Plant Bowen in Euharlee, Georgia, is the largest coal-fired plant in the USA. It has four 800 MWe units, giving an aggregate rating of about 3.2 GWe. A telescopic heliostat / glass-melt power plant in Andalucia with 15 hours of thermal storage, having the same rated output of Plant Bowen, would occupy:

3.2 GWe-rated / 45 We/m2-land rated = 71 E6 m2,

or a circle 4.8 km in radius. The height of the central optics will be about 1/14 the field radius, or 340 m. This is about 11% higher than Plant Bowen's two 305 m smokestacks.

Plant Bowen, 3.2 GWe,

Direct absorption and storage of solar energy in glass melts

In a glass-making solar furnace, solar energy is directly absorbed in the semi-transparent melt.

Contrary to popular belief, renewable power does not "need" energy storage. When a GW of wind or solar power is brought online, the electric utility's least fuel-efficient 1 GW of conventional generating capacity is forced into semi-retirement. That is, those particular generating plants no longer have a job when the wind is blowing or the sun is shining. Since we have about 4 TW of conventional generating capacity to semi-retire in this way, renewable power will not be hurting for energy storage anytime soon. 

That said, in a thermal power plant some energy storage comes free—or at least at no additional cost—in the form of thermal inertia. The larger the plant, the more running time is extended by thermal inertia—and the cheaper it is to deliberately increase. Any process served by a solar furnace may benefit from this inexpensive form of energy storage. Since an all-glass, glass-making solar furnace will be first and foremost occupied in making its own glass parts, it is reasonable to look at the thermal inertia in the glass melt itself. 

A 2002 paper by L. Pilon, G. Zhao, and R. Viskanta looked at the thermophysical properties of glass melts. A melt of soda-lime glass is substantially transparent to both sunlight and high-temperature thermal radiation, so molten glass effectively has high thermal conductivity when it absorbs solar radiation directly or cools radiatively from high temperatures. For example, at 1400 °C (1700 °K,) a soda-lime glass melt has an effective thermal conductivity (phonic conduction + radiation) of 58 W/m-°K—that's more than the thermal conductivity of steel at room temperature.

Pilon et al. also give some representative numbers for industrial glass-making. They considered a glass melting tank approximately 16 m long, 7 m wide, and 1 m deep heated from above with a total heat input of 8.3 MW which averages to 72 suns (i.e., kw/m2) over the free surface of the melt. They estimate a maximum heat flux of 134 suns near the center. At melt surface temperatures around 1500 °C (1800 °K) they associate the maximum flux with vertical temperature gradients of about 1200 °C/m. At about 8 MWth, such an industrial glass-making furnace is only a small-scale model of a GW-scale solar glass-making furnace.

A coal-fired furnace for a 800 MWe generating unit might be 20 m x 20 m x 100 m high, corresponding to an average thermal flux per unit wall area of about 250 suns.

T-s diagram for a supercritical power plant. According to L & T Power, typical temperatures at points E and G for current technology are 565°C and 593°C, respectively; efficiency = 42%.

Heat balance for an advanced 800 MW power plant. Image quoted from Song Wu et al., "Technology options for clean coal power generation with CO2 capture." Mean temperature in the first heat (596 + 293)/2 = 445°C; second heat (608 + 342)/2 = 475°C; efficiency = 46%.

The steam tubes absorb heat over a range of temperatures, but 460°C may be taken as representative for the advanced supercritical cycle in the diagram above. At 460°C, a blackbody radiator emits about 16 suns (20 kw/m2.) The molten glass will need to be significantly hotter at its "empty" temperature in order to transfer a flux 250 suns to the furnace's steam tubes (in order to drive operation at rated power.) If the product of the emissivities and the view factor is about 0.7, the glass melt must be at a temperature where a blackbody emits about 380 suns, that is, around 1340°C. Using the thermophysical properties of soda lime glass melts quoted in Pilon et al., and the modified Rayleigh number, Ra*, defined in Bolshov et al., 1340°C is well within the range of turbulent convection for soda-lime glass. If we assume the pool of molten glass is a hemisphere 100 m in diameter, and that the average volumetric heating rate is 30 kw/m3, we have Ra* = 3E13 when the glass melt is at 1340°C.

Thermophysical properties of molten glass as calculated from the relations in Pilon et al.

Convection flow patterns and isotherms in a hemispherical pool with isothermal walls and top. Image quoted from Bolshov et al. The modified Rayleigh number, Ra* = 1E8 above, and Ra* = 1E9 below—much lower than the Ra* = 3E13 estimated for a GW-scale energy store.

Observed turbulent convection at Ra = 6.8 E8. Image quoted from X. D. Shang, X. L. Qiu, P. Tong, and K.-Q. Xia, Phys. Rev. Lett. 90, 074501 (2003).

What does an adaptive primary do?

An adaptive primary is a concentrating mirror that redirects sunlight to a fixed focus—no matter where the sun appears in the sky. A mirror that accomplishes this task must adapt its curvature as the sun rises higher or sets lower in the sky. To a first approximation, the curvature of the mirror is toric, that is, the mirror is always approximately shaped like a small patch on the surface of a torus. The adaptation required is slight, the changes in curvature will be scarcely visible to a viewer looking sideways at the mirror.

In the animation above—rendered in POV-Ray using Mega POV—the zenith distance of the sun varies from 15°  to 75°, while the adaptive primary acquires a toric curvature by the thin-shell bending of an initially spherical mirror. The POV-Ray scene description file for the animation is here.

In addition to changing its curvature, an adaptive primary needs to follow the sun in two angular dimensions: turning to face the sun's azimuth while also tilting its normal to one half the sun's zenith distance. (At the most an adaptive primary only needs to be tilted 45° away from horizontal.)

How to upload a Processing animation to Vine

Vines may be the most efficient way ever invented to convey a technical idea, but getting animations you make in Processing up on Vine can be vexing. The procedure below has worked for me using a MacBook (OS X 7.0.4) and an iPhone (iOS 7.0.4.) In addition to Processing and Vine, the freeware and apps you will need are GraphicConverter for Mac, Dropbox for Mac and iPhone, and Vinyet for iPhone. To add sound you will need QuickTime 7 Pro.

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In Processing, generate sequential 480 x 480 frame images numbering less than 144 (i.e., < 6 seconds @ 24 fps) using a zero-padded file numbering such as frame000.tif through frame139.tif.

GraphicConverter: File: Convert & Modify
Function : Convert
Destination format: MooV - QuickTime Movie
Options: Normal compression, 480 x 480, 24 fps
Select the range of .tif images to be used, and the destination folder for the .mov file.
Hit "Go."

Drag the resulting .mov file to your Dropbox folder.

Find the .mov file in the Dropbox app on your iPhone.
Click the up-arrow icon located on the bottom left of the screen.
Click "Save Video"—this saves the .mov file to your camera roll.

Open the Vinyet app.
Click on the photos icon at the bottom of the screen.
Click on the desired .mov file.
After your video displays, click on "Save" in the upper right.

Vinyet now wants to append more video, but the green bar at the top of the screen should show that you are just shy of Vine's six second limit: so click on the checkmark in the upper right.
Click on the curly V in the bottom right.
Add your Vine caption (noting the character count) and click "Dismiss" when you are done.
Select your Vine channel.
Click "Share Video."

After Vinyet declares your "successful"upload, you may want to verify on Vine that it really did upload successfully.

Note that you must have an email-associated Vine account for Vinyet to upload successfully to Vine.

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To embed your darling new Vine post in a blog or web page:

Find your vine on the Vine app.
Click on the three gray dots in the lower right.
"Share this post."
"Embed."
Fill in the address for the link to be emailed to, and click "Send."
Find the email in your inbox; click on the link.
If you want just the bare, looping video to display, choose "Simple"; if you want the surrounding info that you normally see on Vine, choose "Postcard."
Choose pixel dimensions. Note that 600px is more resolution that you uploaded. 320px transfers fast.
If there is an audio channel in your video, choose whether you want it to start playing automatically, or only at the viewer's request.
Copy the link displayed and paste it into the html of your blog post.
Surround the link with <center> …</center> if you want your vine to display centered in the column of text.

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If you want to add a soundtrack to your Processing-generated vine (without using iMovie,) this can be done with Quicktime 7 Pro, which is an older version of the QT player that comes with the modern OSX. Quicktime 7 can still be downloaded directly from Apple, and, from my experience, it still accepts Pro registration numbers that may have been purchased many years back.

Create an audio track timed to exactly match the length your .mov file.
Export it as AIF 48kHZ 16-bit.
Open both the .mov and .aif files using QuickTime 7 Pro.
Select the aif sound file.
Edit > Select All.
Edit > Copy.
Now select the .mov video file. Make sure the playhead is at the start of the video file.
Edit > Add to Movie.
Select the video file.
Window > Show Movie Properties.
You should see your new soundtrack in the list of properties.
File > "Save as." Save it as a Self-Contained file. You must use "Save as," because "Save" fails to generate a new .mov containing the soundtrack.

QuickTime 7 Pro can also be used in place of GraphicConverter in the .mov making procedure above by using  File > Open Image Sequence, and then clicking on the first frame in the numbered sequence of frames; however, the exported .mov will be about 100 MB, which is much larger than necessary for 6 seconds of streamed video. Nonetheless, "Open Image Sequence" is a very handy tool for monitoring a work in progress. For example, render every 12th frame of your animation and then use "Open Image Sequence" at 2 frames per second with View > Loop checkmarked to see a quick rough draft of your vine.

Phi plus an integer (φ + n) heliostat arrangements

Since the center of the heliostat field will be occupied by the central optics anyway, it may be advantageous to arrange the heliostats in a higher frequency phyllotaxis spiral, i.e., φ + n dots per turn rather than φ dots per turn.

 The problem presented by a low frequency (for example, frequency = φ = 1.61803398… dots per turn) is that the genetic spiral—the spiral that connects each dot to the next in order of radial distance—becomes so tightly wrapped upon itself that it will be useless as a structural element or indexing principle. Since we don't need to pack primaries closely in the center field, we may be better off with higher frequency spiral.

Again, these packings still work if the the dots are radially oriented ellipses.


Such ellipses explore possible mutual blocking between secondaries. The video shows that secondaries of telescopic heliostats can be centered directly over primaries that arranged along a phyllotaxis spiral, and still reasonably fill the field of view from the central optics with little overlap (which would indicate one secondary blocking the beam of another.)

Processing sketch here.