Subject: Re: solar chimneys for thermal and electrical power

From: [email-masked] (Nick Pine)
Date: 18 Sep 1996 09:43:05 -0400

Catherine Woodgold <[email-masked]> wrote:
 
>Since the air is still hot when it exits the chimney, I guess that
>most of the energy is not converted to electricity but remains in the hot air.

Looks that way...

Page 185 of M A K Madhi's (b5mak2ttacs.ttu.edu) "Helio-aero-gravity electric
power production at low cost" paper (pp 183-189 in Renewable Energy, Vol 2,
No. 2, 1992) says a chimney of height Hc having air at the top and bottom at
temperatures and densities Tt, Tb, Rhot and Rohb would have a pressure
difference dP = 1/2 Rhob v^2, (equation 10) where v = sqrt(2/Rohb dP) and
dP =(Rhot-Rhob)gHc (12) and Rhot Tt = Rhob Tb (14) so v^2 = 2(Tb-Ta)/Ta gHc
or, rewritten, v = sqrt(2gHc(Tb-Ta)/Ta), reminiscent of the empirical chimney
formula cfm = 16.6 Av sqrt(hdT), in English units.

Does this mean that if we could somehow heat ambient 25 C (77 F) air to 55 C
(131 F) in, say a 6 m (20') chimney, we would have an air velocity in the
chimney of sqrt(2 9.8 6 30/(25+273)) = 3.44 m/s or 8.3 mph, with a power
density of 25 watts/m^2, using Paul Gipe's formula P/A = 0.6125 S^3,
where S is in m/s?

A 50' chimney heating 30 F air to 130 F might make sqrt(2 9.8 15.24 56/272)
= 7.82 m/s with a power density of 292 W/m^2...

A +/- 45 deg fixed Winston concentrator?                north
The south side could be transparent,                      ..
the north side could be reflective on both sides,   .   .    .   .
and the sides adjacent to the letters "dn"        .      .dn.       .
might be black poly film or shadecloth with     .    up   ..   up     .
pinholes. Cool air might come up from the bottom    .   .     .   .
through the ducts marked "up", and be warmed as          south
it filters through the black plastic and moves out the top,
or it might move back down to the ground, to enter and warm a building...

It might be 8' wide and 4' thick and 50' tall, using 1200 ft^2 of standard
greenhouse white and black and clear polyethylene film, heat-sealed at the
edges, costing 5 cents/ft^2, ie $60 for the whole thing, five stories tall,
and it might collect the heat equivalent of 4-6 gallons of oil per day, or
make some electricity.

How much solar aperture is required to heat 3.44 m^3/s of air 30 C? I'm not
used to metric units. Hmmm. Air weighs about 1 kg/m^3, with a specific heat
of about 1 kJ/kgC, so that's about 3.44 kJ/s or 3400 watts or 3 m^2, to make
25 watts, with an efficiency of about 0.7%, or 0.4% if the Betz limit applies.
The 50' version would need at least 8 m^2 or 80 ft^2 of solar aperture.
Seems reasonable. Could the windmill be at the bottom?

Nick