Hi, myxlplix !
With the help of my resident steam buff and "Kempe's Engineers
Yearbook Vol 2" Morgan Bros. Publishers, London, 1958, Chapter "Air
Compression, Pneumatic Equipment, etc." by J. R. Quertier, an
appropriate formula would be:
1) In an isothermal change of conditions (either compression or
expansion) temperature remains constant ("iso" = equal , "thermal" =
temperature). Theoretical horsepower (hp) to compress and deliver gas
isothermally is:
hp = (( 144 * P1 * FAD) / 33000 ) * log e (P2 / P1)
where FAD is volume of gas @ initial conditions of P1 and T1 expressed
in cubic feet per minute with P expressed in pounds per square inch
(psi) absolute;
for
P = absolute pressure
p = gauge pressure
v = volume of gas at pressure P ( volume in cubic feet).
B = barometric pressure
T = absolute temperature
144 comes from the number of square inches in a square foot
33000 foot-pounds force per second is one horsepower
14.7 psi is one unit of barometric pressure at sea level ( or 1000
millibars).
log e is the natural or Napierian logarithm of the mathematical
expression that follows it.
P1 and P2 indicate initial and final pressures; T1 and T2 indicate
initial and final temperatures.
P = p + B = p + 14.7 psi
Note: T is assumed to be in Temperature Fahrenheit.
The above equation can be used to determine the "gas" horsepower for
water-cooled compressors of two or more stages with intercoolers
between stages.
This is fine where the gas is air; for exhaust steam, heat given to
the steam in each stage would need to be removed in the next
intercooler and many stages and intercoolers would be required to keep
the process even approximately isothermal.
However, at fairly typical steam turbine exhaust conditions the
equation for the horsepower (hp) to recompress this exhaust steam
(instead of putting it to a condenser) might read using the formula
given above :
hp = (( 144 * 1.0 * 16.6 ) / 33000 ) * log e ( P2 / 1 )
where P2 is the absolute pressure in the boiler to which the exhaust
steam is to be returned (without a condenser in between).
Boiler pressures can vary considerably between individual units, but
for - say - 600 psi (not terribly high for some modern power
stations) we can expect that the horsepower calculated above will come
to about 54% of the output power of the turbine. Taking into account
various losses there is obviously little advantage in using this
method as opposed to condensing.
2) In an adiabatic compression no heat is added to the gas and no
losses (due to friction and eddies) occur. ("Adiabatic" = without
transference of heat. Chambers.) It conforms to the equation:
P (v raised to power gamma) = constant, where gamma is the ratio of
specific heats at constant pressure and volume.
Hence:
P1 / P2 = ( v2 / v1) raised to power gamma - ( T1 / T2) raised to
power (gamma / (gamma-1))
Theoretical horsepower for single stage adiabatic compression is
given by:
hp = (( 144 * P1 * FAD) / 33000 ) (gamma / (gamma-1)) ((P2/P1) raised
to power (( gamma-1) / gamma -1 ))
In practice, heat is given out during compression and hence:
P (v raised to the power n) = constant where n < gamma.
For air
n = 1.2 to 1.25 for slow speed water jacketed compressors, or
n = 1.3 to 1.35 for high speed air cooled compressors.
For air gamma is usually given as 1.4 and for superheated steam
gamma = 1.387 ; from:
"Steam Engine Theory and Practice" by William Ripper, Longman's, 1908
:
but note that turbine exhaust steam is not likely to be superheated.
The conclusion generally is that it takes as much or more energy to
recompress ("pump") exhaust steam and feed it back to the boiler as it
does to condense it and simply pump it back in as water . In addition
a lot more mechanical complication is required.
As for web resources, Subrata Bhattacharjee
has a selection of java applets for performing various tests at:
http://thermal.sdsu.edu/testcenter/javaapplets/
"You can solve just about any thermodynamic problem (at the
undergraduate level) and perform parametric studies without a single
line of programming with these applets.
The range of topics includes basic concepts, evaluation of
thermodynamic states, first law of thermodynamics for closed and open
systems, second law of thermodynamics, entropy and availability
analysis, power and refrigeration cycles, generalized charts, gas
mixtures, air conditioning, combustion, and gas dynamics."
They can be run on-line, or you can purchase the programme - free to
educators. Details and a slideshow tutorial are at:
http://thermal.sdsu.edu/testcenter
A professional software supplier is Archon Engineering who supply
Steam Tables software at US$40.00 - download a free trial - at:
http://www.archoneng.com
"Steam Tables - (Metric and US units) This program provides the
thermodynamic properties of water using IFC formulation for industrial
use. Knowing any two properties, the user is able to completely define
the properties of water/steam. Unlike most steam table programs, this
program also provides the user with the point's location on the T-S
diagram. Multiple points can be connected by a line, defining the
user's process system. It even gives you the steam quality."
A book with the same information is "Steam Tables: Thermodynamic
Properties of Water Including Vapor, Liquid, and Solid Phases" by
Joseph H. Keenan, Frederick G. Keyes, Philip G. Hill, Joan G. Moore
January 1969
ISBN: 0-471-46501-1 which is available for £139.00 from:
http://www.wileyeurope.com
A very clear abstract of a paper on "Direct Solar Steam Generation" by
W.D.Steinmann and W. Eck of the German Aerospace Centre's Institute of
Technical Thermodynamics can be found at:
http://www.meike.com/solarpaces.au/symposium/papers/Stei2.pdf
Contact details for Wolf Steinmann are at the head of the article.
Of other possible interest:
The pressure vessels and piping division of the fluid-structure
interaction committee of ASME International held a symposium at which
a paper on "PRELIMINARY RELAP5 SIMULATIONS OF MULTIPLE STEAM GENERATOR
TUBE RUPTURE EVENTS IN KOREA NEXT GENERATION REACTOR" was scheduled to
be given by J. H. Jeong, Cheonan College of Foreign Studies; K. S.
Chang, Sunmoon University, S. J. Kim, Korea Advanced Institute of
Science and Technology; & J. H. Lee, Korea Institute of Nuclear
Safety, KOREA
http://www.cfdcanada.com/ptrans.html
If that is of interest a transcript might be available through CFD
Canada whose site
has a wealth of articles, scientific papers, "Stories of the month"
and simulations promoting their CFD modelling software FLUENT at:
http://www.cfdcanada.com
Keep scrolling down the very long page, and be warned the font they
have used is very, very tiny. Not all links work. But generally
articles are clear and easy to follow, and may help your general
research.
Also of general interest is the account of a steam-powered house in
Victoria, Australia at:
http://www.ata.org.au/45steam.htm
Search terms: "steam powered generator"
"thermal dynamics steam" |
