Subject: solar chimneys for thermal and electrical power

From: [email-masked] (Nick Pine)
Date: 10 Sep 1996 12:18:26 -0400

The 1996 World Renewable Energy Congress in Denver had several papers on solar
crop drying, written by people from Canada, France, Mexico, Scotland, Iran and
Australia. In "Modelling and Experimentation of the 'Shell' Dryer" (pp 682-685
of the proceedings), M. Fournier et al discuss the performance of a dryer that
looks like a portable circular charcoal grill, that has been used in Africa
since 1984, which has a dark-colored shallow upright cone with no glazing 
covering a shallow inverted lower cone. The food (eg mangos) is sliced thin
and placed on racks around the lower cone, which has holes in the bottom. It
is warmed only by radiation from the upper cone. They find an approximate
"drying constant" for mangos of Ks = 0.5/thi exp(-3000/Tf), where thi is the
slice thickness. They don't explain Ks and Tf (the fruit temp?) H. El Salman
might, in "Measure de la vitesse de sechage de quelques produits," DUR,
Universite de Perpignan (1989.)

How about a regional solar crop dryer that also makes electricity, along the
lines of the paper "Helio-aero-gravity electric power production at low cost,"
(Renewable Energy, V. 2, No. 2, pp 183-189, 1992) written by M. A. K. Lodhi
and M. Yusof Sulaiman of the physics departments of Texas Tech (Lubbock, TX
79409) and Univ. Pertanian Maylaysia (43400 UPM Serdfang, Selangor, Maylaysia.)
Dr. P. N. Sastry of Devipuram, India, would like to build these into low-cost
houses... His colleague Alok Baveja ([email-masked]) would be happy
to hear from people who could help with this.

Abstract: The power production from the helio-aero-gravity concept can be
demonstrated by selecting a flat patch of land in an isolated desert where
solar radiation is abundant. The land may be sprayed with black paint [or
covered with mushrooms on wire racks?] and canopied with some transparent
material. A chimney containing an air turbine is to be installed at the center
of the black patch [see appendage, for a cheap chimney.] At the periphery of
the patch, the canopy should be kept above the ground leaving sufficient
space for cold air to enter the region under the canopy. The black patch
is heated by direct sun's radiation entering through the transparent cover.
The cold air gets heated as it moves over the heated land surface under
the canopy. Due to the pressure difference, the hot air will rise into the
chimney and drive the turbine. The power thus generated could be about 50
megawatts per square kilometer of land at a low cost per energy unit. A
systematic theoretical study is carried out to investigate the scientific
and technical merits of this system for large scale power production, in
particular to investigate heat transfer processes in the system in a
quantitative manner.

Figure 1 of the paper shows an inverted funnel, with a large transparent
canopy over some blackened ground, and a convective chimney rising up out
of the middle, with a rotor about halfway up the chimney, and a hole at
the top of the chimney.

Some quotes:

  We describe the helio-aero-gravity device in an analogy. It may be best
  understood as an upside-down hydroelectric plant with storage reservoir,
  penstock and turbine or an 'inverted solar collector.'

  The idea of harnassing solar energy with the so-called 'chimney effect'
  has evolved in the recent past independently [1-7]... Only Schlaich and
  collaborators [2] have made a breakthrough by building a pilot project at
  Manzanares, Spain. Krisst [5] demonstrated in a 'backyard type' device in
  West Hartford, Connecticut, USA an output of 10 W with a 10 m tall chimney
  on a patch of circular area of radius 3 m. Kulunk, on a microscale basis
  produced an electric power of 0.14 W with a 2 m tall chimney of 3.5 cm radius
  on a patch of area 9 m^2 in Izmit, Turkey. He reported the rotor power as
  0.45 W, the efficiency of the generator as 31%, the temperature and pressure
  difference of air at the two ends of the chimney to be 4 K and 200 Pa...

  Some of the heat is transmitted to the ground. It starts moving back to the
  surface at night, thus forcing the air to continue running the turbine in
  the chimney, of course with reduced output. The output during the night time
  is about one third to one sixth of the output during peak hours while the
  sun remains shining [2.]

  For the purpose of calculating the power that the air turbine extracts from
  the rising air in the chimney we need an expression for the velocity of the
  air v striking the blades of the turbine. Assuming the area swept by the
  rotor be be approximately Ac, the instantaneous rotor power Pr available
  is given by [7]

     Pr = ETAr 1/2 RHOm V^3 Ac   (Ac = pi r^2),

  where ETAr (to be measured) is the power coefficient. The author in [8]
  uses the value of ETAr to be 16/27 based on the Betz limit [10,11] which
  was obtained for a single plane actuator in a free stream situation. Here
  we are solely concerned with the efficiency of the system in which
  mechanical energy can be extracted from the flow by means of propellors
  in the duct-enclosed type flow. Our goal here is to maximize power
  extraction from the system, not the flow. The objective is to load the flow
  enough to extract maximum power, but not enough to choke it off. The
  opimization, in principle, will yield much higher efficiency than Betz
  for an open stream situation. Recently, there have been attempts and claims
  [12] to have achieved an efficiency more than the Betz limit... 

  In order to compute the rotor power we borrow a set of values of the
  temperature measured at the Manzanares experimental station [2] on a
  certain day during its operation. The set of those values is given by:
  Ts = 348 K, Tm = 323 K, Tl = 313 K and Ta = 303 K. The rotor power,
  for the dimension of that system given in Table 1, is 67 kW...

  Table 1. Rotor power production Pr and peak efficiency ETA for a location
  where the insolation is 1 kW/m^2. The Carnot efficiency ETAc is 14.2%,
  except for entry one, which is 13.2%.

  No.    r(m)    R(m)   Hc(m)    Hp(m)  Pr(MW)  ETA(%)

  1      5       122    195      0.25   0.067   0.14
  ...
  9      50      800    1000     0.50   132.1   6.6

  where r is the rotor radius in meters,
        R is the radius of the canopy (collector) in meters,
	Hc is the chimney height in meters,
	Hp is the gap at the opening of the periphery in meters,
	Pr is the rotor power in megawatts, and
	ETA is the efficiency.

  The helio-aero-gravity plant operates on the basis of the difference
  between the temperature of the air at the bottom of the chimney and the
  ambient temperature. This differential essentially creates a draft strong
  enough to turn the turbine installed inside the chimney. The turbine may
  start with a wind speed as low as 3 m/s which may be obtained at a
  temperature differential of around 4-5 K. It is, however, desirable to
  operate the plant at a temperature differential of 20 K...
 
  Some references:

  [1] M. A. K. Lodhi, Solar Desert Chimney, Proc. Int. Sym. Workshop on
  Renewable Energy Sources (Edited by M. K. Bhatti et al) p. 219 (1893);
  Thermal collection and storage of solar energies, Proc. Int. Symp. Workshop
  on Silicon Technology Development (Edited by A. Mufti and T. N. Veziroglu),
  p J1 (1987); Hydrogen City. Intl. J. Hydrogen Energy 12, 783 (1987).

  [2] W. Haaf, K. Friedrich, G. Mayer and J. Schlaich, Solar Chimneys,
  Int. J. of Solar Energy 2, 141 (1984).

  [3] J. Schlaich, Solar Chimneys. Periodica 3, 45 (1983).

  [4] L. B. Mullet, The Solar Chimney, The Energy Group, Dept. of Engineering,
  Univ. of Reading Preprint, pp 1-14 (1983).

  [5] R. J. K. Krisst, Energy Transfer System, Althernative Sources of Energy
  63, 89 (1983).
  
  [6] E. W. Jacob and D. D. Lasier, SERI Preprint/TR-211-1950 (1984).
  
  [7] H. Kulunk, A prototype solar convection chimney operated under izmit
  conditions,. Prod. 76th MICAES (Editied by T. N. Veziroglu), p. 162 (1985).

  [8] F. Kreith. Principles of Heat Transfer. International Textbook Co.,
  pp 286 and 311 (1958).

  [10] A. Betz and Z. Gesamte, Das Maximum der Theroretisch Moglichen
  Ausnutzung des Wurdes durch Windmotorem. Turbine Wesen 17, 320 (1920).

  [11] D. R. Inglis, A windmill theoretical maximum extraction of
  power from the wind. Am. M. Phys. 47, 416 (1979).

  [12] D. R. Inglis, Wind power and other energy options. Univ. of
  Mich. Ann Arbor (1978).

Recall the giant inflatable Goodyear tires and Ronald McDonalds and Wendys? 
My neighbor sells pumpkins at Halloween, and he has a 5' inflatable lighted
pumpkin with a small blower... I wonder if we might make a vertical linear
version of that balloon collector, a three-chambered tubular animal that
looks like a bird from the top? Could it be almost self-supporting, with
some solar heat? Or more than self-supporting, with a hole at the top and
a windmill at the bottom? A 0.004" x 16' wide x 100' long roll of greenhouse
polyethylene film weighs 37 pounds and costs $82...

Hmmm. 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 with a few pinholes.   .    up   ..   up     .
Cool air would blow up from the bottom and          .   .     .   .
up through the ducts marked "up", and be warmed          south
as it filters through the black plastic and moves 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 (why do we have this strange urge to make electricity?)

The base might contain some 55 gallon drums full of water. The top might last
5 years or more, if deflated when the house were warm enough and at night and
in windy times and in summertime onto an 8' roller, or deflated into one place
using internal tethers, somehow. It might say "Eat at Joe's," or some other
custom inspirational message. We could have neighborhood contests, to see how
tall we could make these things. Perhaps we could buy them from Jade Mountain. 

Nick

---

From: [email-masked] (Catherine Woodgold)
Date: 10 Sep 1996 20:57:34 GMT

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.

In a desert where land and hot air are cheap, this may still
be a cost-effective way to make electricity;  I don't know.

There are engines that use smallish temperature differences
(tens of degrees I think) to drive them, perhaps converting
more of the heat into mechanical energy.  Baer's diving engine?
An engine that uses bimetallic parts that move when warmed
or cooled?  Or that uses memory metal:  that stuff I forget
the word for that assumes one shape at one temperature and
a different shape at a different temperature.

Anyway, for low-cost electricity where land is plentiful
and cheap materials must be used, the chimney sounds good.

Cathy

---

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

Catherine Woodgold <[email-masked]> wrote:
 
>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...

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