h a l f b a k e r y"Not baked goods, Professor; baked bads!" -- The Tick
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Prompted by the linked idea, which suggests using a small
wind-turbine to generate electricity (and thence heat)
from a chilling arctic wind.
There is a better way.
Imagine a large funnel, consisting of a large hoop with a
plastic windsocky thing attached to it. The small end of
the funnel
is connected to a pipe. The pipe is closed at the
other end, apart from a small hole.
When facing into the wind, this arrangement will compress
the air in the pipe; the stronger the wind, the greater the
compression.
The (absolute) temperature of a gas rises as its
compressed. If the funnel raises the pressure of air going
through the pipe from 15psi to 18psi, then the temperature
of the air in that pipe will increase by a factor of 18/15.
Thus, air at -20°C (253°K) will be heated to +30°C
(303°K).
This must surely be the simplest way of extracting heat
Just run the hot pipe through your tent (or even through
your sleeping bag) and you're toasty warm even in the
arcticest of winds.
Suggested by:
Bask_20in_20the_20Antarctic_20breeze
[MaxwellBuchanan, Nov 03 2012]
Wind Powered Fridge (no moving parts)
Wind_20Powered_20Fr...o_20moving_20parts)
Could also serve as a heater [csea, Nov 04 2012]
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Annotation:
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And what precisely would be the proposed dimensions of
such an unlikely contraption? |
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math for windspeed for +3psi from a funnel ? |
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//what precisely would be the proposed
dimensions// |
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Mouth: 2m diameter. Funnel length: 4m. Funnel
exit diameter, and pipe internal diameter: 2cm. Exit
hole from pipe: 4.5mm. |
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See, I told you not to put your hand on the pipe. |
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//what precisely would be the proposed dimensions//
OK, seems reasonable. |
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//math for windspeed for +3psi from a funnel ?//
Yes, please, what windspeed? |
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I think we went through this with a cooling intent (though not in a tent!) using a Hilsch Vortex device. [link] |
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OK, I admit that the maths is a little outside my
scope. |
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However, a windspeed of 20mph is stated to give a
wind *pressure* of around 100 Newtons per square
metre, or about 0.02psi. |
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We are aiming for a pressure rise of 3psi, or 150
times greater than the wind pressure. At first
glance, this suggests that a 150-fold reduction in
area would achieve this. A 2m funnel feeding into
a 4.5mm exit hole would give an area reduction of
over 200,000 - much much more than 150-fold. |
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But of course it's not nearly that simple, and the
200,000 fold is a red goose. |
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So the question is, how do you determine the
pressure at the exit point of a funnel, given the
dimensions of the funnel and the speed of the
impinging wind? |
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There must be *some* pressure increase at the
exit of the funnel, even though it will not be
proportional to the area reduction. |
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As a final argument, bear in mind that there is at
least as much energy available from the wind as
we could extract using a wind turbine. Since a 2m
wind turbine in a strong wind will generate a
useful amount of power, it follows that this idea is
not energetically forbidden. |
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Bother. I can't tell whether you're just trolling now, but I'll trip trap over that bridge when I come to it. |
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Anyway, 20mph at 293K gives a stagnation pressure of about 48 Newtons per square metre (above the static air pressure). Someone forgot to divide by 2. And that's the absolute maximum pressure attainable - the narrower the constriction, the closer you get to that value. |
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Any simple tube/funnel/Nutrimatic cup facing into the wind at steady state produces pressure at most œ density * v² above the static pressure. Allowing any flow (which is necessary to harvest energy) reduces the pressure. |
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Of course it's possible to produce greater pressures, but you need a mechanical advantage - you need to pressurise a small flow of air by harvesting power from a large flow of air, for example by linking a compressor to a turbine. A steady-state funnel can't do that, as the two flows are the same. |
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It is also theoretically possible to use resonance, as a hydraulic ram pump does. But however you do it, there will be a high-volume, large area, low pressure waste flow as well as a low-volume, high pressure flow. There is no way around that. |
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If you were to use the wind to compress the air by some mechanical means, such as a belt-driven piston-type compressor, you'd get heat off the outside of the cylinder, or just the outlet pipe. You could use that heat, as in the original idea, then you'd have a nice tank of compressed air for blowing dust off your keyboard. |
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Good point, [bacon]. Plus, if you extracted the heat
from the compressed air and then allowed it to re-
expand, you could have a freezer for your wodka. |
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My wod is already pretty chilly at this time of year, ka. |
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//Any simple tube/funnel/Nutrimatic cup facing
into the wind at steady state produces pressure at
most œ density * v² above the static pressure.// |
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I've come back to this because the above equation
is pertinent to some other problems I'm thinking
about. So, if I have a wind speed of 5m/s, and if
air density is roughly 1kg/m3, I can get a pressure
of œ * 1 * 5² = 12 N/m² above ambient? Or have I
got a unit wrong
somewhere? |
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And since the shape of the 'funnel'
doesn't enter into the equation, doesn't that
mean that the pressure at the bottom of a 1m²
funnel is the same as the pressure on the face of a
flat board? |
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AFAIK the *average* pressure on the board will be closeish to the tube/funnel pressure. But assuming no work is done, the pressure near the edge of the board would be lower, since the air is moving faster. |
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OK, on further reading, is seems that the pressure at the centre of the plate is equal to the stagnation pressure, but the average pressure is somewhat less (because the pressure decreases towards the edges, as stated above). |
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Note that this applies to isentropic (no work is done), incompressible flow - which is closely approximated for static objects and flows well below the speed of sound. |
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And yes, your calculation appears to be correct. |
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