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re: nuclear cooling tower windmill
20 jan 2001
craig wrote:

> ...what we need to do is come up with a (efficent) way of turning heat
> energy into electrical energy... (without needing a temprature difference).

here's a naive efficiency estimate for these "helio-aero-gravity" towers,
huge chimneys with wind turbines at the top surrounded by acres and acres
of greenhouses in deserts to make a "solar wind" up the chimney...

suppose we start with our old friend the empirical chimney formula,

cfm = 16.6 av sqrt(hdt), where av is the vent area at the top and bottom, 
                         h is the height difference in feet, and
			 dt is the (f) temperature difference. 

the airstream's heat power in btu/h is roughly cfmdt = 16.6h^0.5dt^1.5
for a 1 ft^2 chimney. with a constant power heat source (the acres and
acres of greenhouses), this equation naively implies that the taller
the chimney, the smaller the temperature difference and the larger the
air velocity. smaller temperature differences are better, representing
less waste heat. we might think of chimneys as transformers that increase
the air velocity of a heat source and reduce the temperature difference.

for a 1 ft^2 chimney, the power density is 16.6h^0.5dt^1.5 btu/h-ft^2,
and the air velocity v = 0.1886h^0.5dt^0.5 mph.

paul gipe's wind power book says wind power density is 0.05472v^3 w/m^2,
where v is in mph. he says the best rotors achieve 40% efficiency (vs the
60% betz limit, which may not apply for a chimney)... 90% efficiencies
for the transmission, generator, and power conversion make the wind power
density 0.01596v^3 w/m^2 or 0.00506v^3 btu/h-ft^2. 

so the heat-to-electrical power conversion efficiency of the chimney
is e = 100x0.00506(0.1886h^0.5dt^1.5)^3/(16.6h^0.5dt^0.5) = 0.0002h %,
where h is the chimney height in feet. e = 0.002% for a 10' chimney, 
0.02% for 100', 0.2% for 1000', and 2% for 10,000'.

this doesn't account for the heat loss through the greenhouse glazing or
chimney walls, or air friction in the chimney, nor the fact that the 
weight and cost of a tower increase a lot faster than the height...


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