Ammonia Absorption Downdraft Tropical Calc 1

8/19/2019 Ammonia Absorption Downdraft Tropical Calc 1

1/14

Calculationsfor an

Implementation of the Absorption Cooled Energy TowerRobert J. Rohatensky

January 24, 2007

Jupiter Beach FLA, !A

Tropical Climate, "igh "umidity, #$ months of % &$'C temperatures

Document Version 1.0

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2/14

Overview

This location with warm temperatures, hih solar isolation an! humi!ity woul! best be suite! by asystem that continually "unctions in a !own !ra"t mo!e with a!!e! air compression to e#tract as muchwater as possible "rom the air at the top o" the tower. $ compression turbine an! restriction throuh thecoolin heat e#chaner woul! increase the air pressure an! temperature throuh the coolin coils toimpro%e thermal trans"er. The air woul! !ecompress below the coolin coils with most o" the water %apore#tracte! an! the cool !ry air woul! ha%e a hih neati%e buoyancy.

The "act that water %apor is lihter than air is counter&intuiti%e "or many people. The !ensity o" !ry airat sea le%el is 1.2'( )* an! water %apor is 0.+04 )*. #tractin the water %apor "rom the air an! coolinit causes the air to be much more !ense than the ambient air outsi!e the tower.

The %ery hih absolute humi!ity in this location creates a lare amount o" con!ense! water capture.This water is substantial an! besi!es bein potable or usable "or hy!roen electrolysis can be use! "ora!!itional power eneration.

High Humidity Tropical System

This pae, imaes an! other !ocumentation on this website are copyriht Robert J. Rohatensky, January 2007

an! are publishe! un!er the Desin -cience *icense.

mailto:[email protected]:[email protected]


3/14

Night Operation

This system woul! continually operate in !own&!ra"t mo!e coolin the air. This woul! reuiresubstantial anhy!rous an! aueous ammonia storae an! lare thermal solar collectors to reco%er all o" theammonia use! !urin sunliht perio!s.

Climate

/$-$ -ur"ace meteoroloy an! -olar nery

$t *atitu!e 0 an! *onitu!e &104$%erae ele%ation +4 meters

(onthly A)eraged Insolation Incident *n A "ori+ontal !urface -.h/m$/day0*at 2.'(*on &+0.17

Jan 3eb ar $pr ay Jun Jul $u -ep 5ct /o% Dec$nnual$%erae

10&year $%erae (.2+ 4.11 4.+7 .++ .'' .4+ .(2 .1+ 4.( 4.21 (.44 (.0 4.2

(onthly A)eraged Air Temperature At #' m Abo)e The !urface *f The Earth 1 C0*at 2.'(*on &+0.17

Jan 3eb ar $pr ay Jun Jul $u -ep 5ct /o% Dec$nnual$%erae

10&year $%erae 1'.' 20 21.1 22.4 24.' 2.+ 27.( 27. 2.+ 2 2( 20. 2(.+

(onthly A)eraged 2elati)e "umidity 30

*at 2.'(*on &+0.17

Jan 3eb ar $pr ay Jun Jul $u -ep 5ct /o% Dec

10&year $%erae 71.4 '.2 +.4 .7 '.( 71.' 71 71.1 7(.( 72. 7(. 72.1

Tower Design

The power output o" the win! turbine in the tower is base! on the air %elocity an! the !iameter o" thetower. The air %elocity is base! on the buoyancy o" the air e#ternal to the tower, the !ra loss across the

heat e#chaner an! tower walls an! the e#it loss. 6n this location the annual hih humi!ity an! temperaturelen!s itsel" to a "ocus on lowerin both the temperature an! the water %apor percentae insi!e the tower.These two "actors a""ect the neati%e buoyancy o" the air in the tower. ecause there is no enerye#pen!e! in e#pan!in the pressuri8e! ammonia in the coolin coils, the power output o" the system is base! on the heiht an! !iameter o" the tower, the sur"ace area o" the heat e#chaner an! the ambient airtemperature an! humi!ity.



http://eosweb.larc.nasa.gov/cgi-bin/sse/grid.cgimailto:[email protected]://eosweb.larc.nasa.gov/cgi-bin/sse/grid.cgimailto:[email protected]


4/14

$ssumin a me!ium scale system with a tower heiht o" 100m an! a !iametero" 20m narrowin to 1m in the lower section. The tower will "unction in acontinual !own&!ra"t mo!e.

$ compressor turbine is a!!e! to the top o" the tower to increase the air pressure abo%e the heat e#chaner. This increase in air pressure increases thetemperature o" the air an! allows "or a larer temperature !i""erence between the

intake air an! the heat e#chaner plates an! also increases the contact "actor.

The col! plateso" the heat

e#chaner are at &((9 an! as the air is"orce! throuh un!er pressure, almost all o"the moisture in the air will con!ense on theheat e#chaner.

$s the air lea%es the restriction o" the heate#chaner, it will !rop in pressure :there"oretemperature; an! ha%e a %ery low moisture content. These"actors will cause the internal air in the tower to ha%e a %ery lareneati%e buoyancy "actor.

The hih humi!ity means that a %ery lare amount o" water will con!ense on the heat e#chaner an!this !istille! water by&pro!uct may be utili8e! !omestically, "or irriation or "or hy!roen electrolysis.

Wind Turbine Power Calculation (Summer Months)

This chart "rom patent


5/14

Target Air 4elocity5 $'m/s

To achie%e the !esire! 20 m)s air %elocity (000 cubic meters o" air per secon! nee! to be mo%in throuhthe turbine. The top an! bottom o" the tower are wi!er so althouh the same %olume o" air is mo%in intothe top o" the tower the air %elocity is lower throuh the larer area. The e#it loss where the output airmeets the e#ternal air is re!uce! by ha%in a larer area an! lower %elocity.

This assumes a heat e#chaner hori8ontal sur"ace areao" > 11 m2.

The oal is to remo%e the reuire! amount o" heat an!water "rom the air at the top o" the tower to cause theneati%e buoyancy to achie%e the reuire! air %elocityacross the tower heiht. 6n this mo!el the con!ense!air is allowe! to !rip o"" the coolin coils an! isinore! in the power calculation.

The "ormula "or air !ensity is

The speci"ic as constant ??R?? "or !ry air is

The taret is to lower the 24@9 a%erae ambient air to [email protected] !ry air the !ensity at 101.00 k=a at 24@9

3or 24@9 air at 70A relati%e humi!ity, the air is appro#imately 2.1A water %apor with a !ensity o" 0.+04k)m(. This o""sets the !ensity by 0.+04B.021



Area of turbine: A= r 2

A=7.52×3.14159

176.71m2−hub area=150m

2

R dry ,air =287.05 J

kg ×K

Area of top inlet: A= r 2

A=3.14159×102

314.59m2−heat exchanger area=200m

2

V a=U × A

3000m

3

/s÷200m

2

=15 m /s

Air volue through turbine: V a=U × A

20m /s×150m2=3000m

3/s

= p

R ×T

10100 /2+7.0

2'7.1=1.1+4kg /m

(



6/14

3or !ry air the !ensity at 101.00 k =a at 0@9

$lthouh the relati%e humi!ity o" the air in the tower a"ter coolin is 100A :below outsi!e air !ew point;the 0@9 temperature means that the absolute humi!ity is at appro#imately 0. A.

E6ternal Internal

E6ternal Air Temperature 24@9 :2'7.1@C; 0@9 :27(.1@C;

2elati)e "umidity 70A 100A

Air 7ressure

:+m 100m abo%e sea le%el;

101.00 k =a 101.00 k =a

Air 8ensity 9 1.2+ k)m( 1.17 k)m(

The %olume o" the air insi!e the tower is 2 truncate! cones

V =R 2rR r

2h/3R

2rR r

2h/3

V =×10210×7.57.5

2×75×10

210×7.57.5

2×25

V =72649.33m3

The a%ailable potential enery is the neati%e buoyancy o" the !enser !ry col! air insi!e the tower relati%eto the air outsi!e the tower.

F =V × i −o×9.8

F =72649.33×1.285−72649.33×1.176×9.8F =77603.01N

The a%erae %elocity o" the air mo%in !own the tower without !ra



10100/287.05273.15

=1.288kg /m3

1.288×0.9940.804×0.006

=1.285kg /m3

1.184×0.9790.804∗0.021=1.176 kg /m

3

http://en.wikipedia.org/wiki/Pascal_(unit)http://en.wikipedia.org/wiki/Pascal_(unit)mailto:[email protected]://en.wikipedia.org/wiki/Pascal_(unit)http://en.wikipedia.org/wiki/Pascal_(unit)mailto:[email protected]


7/14

The peak %elocity o" the air a"ter it "alls 100m :e#clu!in e#it loss;

The assumption is that with exit loss the air moving through the turbine would be near the average velocity. The exit loss is substantial and is caused by the downdraft air having to push the static air at the bottom. With exit loss, the real velocity of theair will be much less than the peak velocity.

The design of this particular system includes a compression turbine. The compression turbine and it’s affect on the airvelocity is not taken into account in the power calculation, but it’s power input will be subtracted. The increase in velocity dueto the compression turbine shouldn’t affect the average or peak velocity down the 100m tower substantially.

The ross power usin a hy!ro "ormula is the "low rate in k)s :o" buoyancy; times '.+ times heiht.

W =flow rate⋅g ⋅hW =1.285 –1.176×3000×9.8×100W =199920=320kW gross power

(0kE consistently 24 hours

per !ay.

Alternate Flow Calculations Using the Stack Effect Formula

$nother metho! o" calculatin the air "low throuh the tower is by usin the -tack ""ect "ormula



a= 2g!

2

V a=

2×9.8 m /s2×100m2

V a=22.14m/s

a= 2g!

V a= 2×9.8 m/s2×100 m

V a=44.27 m /s



8/14

!=" A 2 ghT h−T #

T h

F G stack e""ect "low rate, mH)s$ G "low area, mI9 G !ischare coe""icient :usually taken to be "rom 0. to 0.70; G ra%itational acceleration, '.+ m)sIh G heiht, mTh G warm temperature, C Tc G col! temperature, C

This will i%e the "low rate in m()s, but !oesnt take into account !i""erences in absolute humi!ity.

0.65∗314∗ 2∗9.8∗100∗297.15−273.15

297.15 =2567

3/s

The 27m()s usin the -tack ""ect calculation plus the a!!itional "low attribute! to the !ensity!i""erence in the !ryer air is a reasonable crosscheck o" the buoyancy calculation which was (000m()s.

The exact calculation of the power output of the wind turbine is complicated and there are a lot of fluiddynamics involved. The econd !aw of Thermodynamics "#arnot $fficiency% limits the amount of power

out of the wind turbine to the amount of power put into the heat pump minus efficiency loss. &n estimateof ' (0) of the solar energy input of the heat pump should be reasonable for the electrical power outputof the wind turbine.

The compression turbine is estimate! to take (0A o" the ross power. This is only a intuiti%e estimate an!is base! on some o" the enery put into the compression bein recapture! by the power turbine. *orework needs to be done evaluating the performance improvement of compressing the air as it is movingthrough the heat exchanger and the effects on heat transfer, overall system efficiency and air temperatureas it decompresses leaving the heat exchanger.

stimate! lectrical power output o" win! turbine

+400 kEh)!ay Kross L compression turbine G


9/14


10/14


11/14

Pressurized Anhydrous Ammonia Requirements

The heat capacity o" ammonia %apor is (.0 J)mol C with molar mass o" 17.0(04.

The latent heat o" ammonia is 1(' J) C with a boilin point at atmospheric pressure o" &((@9.

To remo%e 1+( E o" heat with liui! ammonia chanin state an! bein warme! to &1(@9, the latentheat is appro#imately 00# the speci"ic heat.

To raise ammonia %apor 20@C it takes 2.0' J M 20 ) G 41.1+ Joules per ram.

To remo%e 4 E o" heat "rom the air#;$ -g/s o" liui! ammonia must be e%aporate! an! heate! 20@C :to &1(@9;

*iui! ammonia !ensity is +1.'1 )l.The pressuri8e! liui! ammonia input is 1(2,0)s at +1.'1 )*

#?@< litres/s of liuid ammonia to transfer #=D(. of heat from ;'''m$/s of air

5peratin 24 hours per !ay is a total consumption o" 1'4. # 24 # 0 # 0 G 1 million litres per !ay o"liui! ammonia.

Ammonia Recovery System

The solar collectors woul! nee! to boil enouh aueous ammonia to meet the 1'4 *)s constant intake!urin sunliht hours.

$mmonia !issol%es in water at +'.' )100 ml at 09.

To absorb the ammonia %apor at the 1(2 k)s rate is 1(2,0 ) +'' G 147. *)s o" col! water.

The absorption o" ammonia in water is e#othermic :i%es o"" heat;, as the ammonia %apor is !issol%e!the aueous ammonia solution increases in temperature an! absorbs all o" the heat enery in the ammonia%apor. The temperature o" the water increases an! the aueous ammonia remains at its %apor point. 6"there is no increase in pressure, any increase in aueous ammonia temperature will cause the ammonia to boil.



35.06

17.0304=2.059J /g K

g /s×spe#ifi# heat ×K g /s∗late)t heat 187$000$000=!×20×2.059!×1369187$000$000

! =41.21369

187$000$000

! =1410.2!=132$605g /s

14000/681.91=194.5* /s



12/14

The aueous ammonia is pumpe! to appro#imately 200 psi pressure prior to enterin the heatin stae.The pump uses enery but substantially less than a compressor !ue to the smaller %olume. The amount o"heat to e#tract the ammonia is the latent heat o" the output ammonia which is 1 million litres or 11million k per !ay plus the heat reuire! to raise the water the same temperature. The aueous ammoniasolution is at appro#imately 0A an! shoul! be at the %apor point at all times.

The heat to boil o"" the ammonia is

=132$605g /s×1360J /g K =180$J /s,$W 12h×2=4.4+Wht /day

The solar input is o%er 12h, but it has to reco%er the ammonia "or the 24h perio!.

*ocal -olar ra!iation a%erae kEh)m2.


13/14

30003/s×0.015=45kg /s

45 */s of distilledwater

The system will pro!uce ?< L/s of distilled water or almost 4 million litres per !ay at a heiht o" 100m.

6" the water !ri%es a water turbine at the base o" the 100m tower, the ross power isW =flow rate⋅g ⋅h

W =45×9.8×100W =44.1kW gross power

Eith the e""iciency o" a water turbine at 0A the net power "rom the con!ense! waterW =44.1kW ∗0.5W =22kW Net le#tri#al

The con!ense! water capture?


14/14

Electrical Output

Ein! turbine output G

Documents

Ammonia Absorption Downdraft Tropical Calc 1