R AND D JOURNAL, VOL. 18, NO.2, JULY 2OO2

Solar chimney porrl/er plarrt performancecharacteristics

D.G. Krogerl J.D. Buyrt(First received November 2001; Final version May 2002)

The per,forrn ance characteristics o.f o large solar chimneypower plant are eualuated. The reference plant studied has

a glass-couered collector and a chimney that is 1 500 rrlhigh with a diameter of 160 m. A turbo-generator is lo-cated at the base o.f the chimney. The draught and releuantenergy equations applicable to the plant are solued .fo, speci-

.fi,ed meteorological data at a particular site 'in South A.frica.It is shown that the output o.f the plant changes measurablyduring the doy and that power is also generated during thenight, due to the therm,al capacity of the ground under thesolar collector. By optimising the shape and hei,ght of thesolar collector, the annual power output can be increased.

Greek

a absorptanceA difierentiale emissivityq efficiencyo Boltzmann constant, W l^'Knp density, kg/*t or reflectance0 angler transmissivity

Subscripts

a ambient or air or absorptanceb beam

:"' ffi*:?'ionoo

:rt",:,p pressurer radial or roof or radiationD drag or Darcyd diffuse

f frictiong groundh convective heat transfers support or skyskA skyt turbine or transversalt:

l,Irlo'generator

IxrnoDUCTroN

A solar chimney power plant consists of a central chimtr€y,surrounded by a solar collector that consists of a transpar-ent canopy or roof supported a few metres above groundlevel, as shown in Fig. 1.

A turbine driving a generator is located at the base ofthe chimney. Solar radiation passing through the canopystrikes the ground below it from where heat is transferredto the adjacent air by means of convection. Due to buoy-ancy, the heated air flows towards the centre of the collectorand then up the chimney where it drives the turbine.

Tests conducted at an experirnental solar chimney powerplant located at Manzanares in Spain have shown thatthe concept is sound and that performance trends are inline with predicted values.l,2 Preliminary studies have indi-cated that large solar chimney power plants are potentiallyeconomically viable. 3'a

In this study, the performance characteristics of a large

b

CnCncp

de

fHhIKkmnPpPrq

RReT

Ttury

NoUpNcLATURE

exponentdrag coeffi.cientextinction coeffi.cientspecific heat, J/kg Kdiameter, msurface roughnessfriction factorheight, mheat transfer coeffi.cient, W fm2Ksolar radiation, W l^'Ioss coeffi.cientthermal conductivity, W/mKmass flow rate, kg/tnumberpitch, m or power, Wpressure, N/m2Prandtlheat transfer rate, W l^'gas constant, J fkg KReynolds numberradius, mtemperature, K or oC

thickness, m or time, s

velocity, m/sco-ordinate or depth, m

1. Departlltent of Mechanical Engineering, University of Stel-lerrbosch, Private B"g Xl, Matieland, 7602 South Africa( d gk@ uraties. su n.ac.za)

2. Department of Mechanical Engineering, University of Stellen-bosch

Fig. 1. Solar chimneY Power Plant

solar chimney reference power plant, having dimensions as

Iisted in Appendix A, were determined for meteorological

conditions as given in Tables 41 and A2. These latter con-

ditions are applicable at a site located near Sishen (27.67"

South, 23.00" East) in South Africa. It was shown thatthe performance of the reference plant can be improved by

modifying the collector geometry.

AXALYSIS

To find the power generated by a solar chimney power

plant, &s shown schematically in FiS. 1, the relevant

draught and energy equations have to be solved simultane-

ously.1. The power output of the plant can be expressed as

P_ - D pressure drop)

mlPu

(1)

where 4rn is the efficiency of the turbo-generator.

The piessure difference due to a column of cold air out-

side the chimney and a column of hot air inside the chimney

is the driving force or potential that causes the air to flow

through the plant. Blaine k Kr6gers evaluate the effect

of different ambient conditions on the'potential and show

that for the case where adiabatic lapse rates are assumed

outside and inside the chimneY

R AND D JOURNAL, VOL. 18, NO.2, JULY 2OO2

where Kl is the collector inlet loss coefficient.

Canopy supports are arranged radially with a radialpitch P, and a tangential pitch P1. Air flowing radiallyinwards in the solar collector experiences a pressure dropacross a circle of supports at a particular radius. If theheight of the canopy or roof is given by Hthis pressure drop is

dp" : C"Dm2d,r2(u-t)7 (8zr' pPrnSrSo) (4)

where C, o is the drag coeffi.cient of the particular supportand nr, is the radial air mass flow rate.6

The pressure drop due to all supports is obtained by the

following summation:

AP" -Crnm'd, n"ff"t (r, - frrPr)2(b-l) (5)

Wko p*

where nr1 is the total number of support circles.

As the air flows radially inwards it accelerates (if b < 1)

with the result that the pressure drops:6

LPo.":f3 13

IaP

tn" Or"rr.jre drop Lp tdue to frictional effects under the

collector are given by Kroger k BuysT and Beyers8 while

the pressure drop across the turbine inlet Lpt, can be ex-

pressed in terms of a specified turbine inlet loss coefficient

Ktt Similarly, the pressure drop Lp"o due to the drag

of appurtenances such as spokes or other reinforcements

inside the chimney can be expressed in terms of a loss co-

efficient K"D.For a chimney of constant cross-sectional area, the

change in pressure due to the change in momentum, be-

qorAeAr 9ro rAOAr Qr. rAOAr

IIp,. rAOArcOr,r Btt

t- (nraearHcpr)

m69cpT+h (m6gc1116,'

pn raearcon 3{nr--- J--I f -* f,n*h1-qf,ls)azl raear

i

rtenl

low

FA,y*ca,cc

potefl,

rr*\pr\P",

oe

PtAA

nglum()-Lp+1.+l

ivirvolr

LpT:A

(

bi

2

ur

tut

nrc

Po,-Ar-t

:th

L7;*Pcf

tial' rate

P'*LPt.-+A

'ra

Pt'A1

+

Lp- P,['- { \'-:f:3{i{/;;'lThe pressure drop between the essentially stagnant am-

bient air at 1 and at the inlet 2 to the collector is given

byLpn : (n - pz) - KrpzuZtz + pruzrl2 (3)

Turbo-generotor

collector

l.f=H zkz/r)o

L__ L9u'-''j'1- jurounol

-

Fig. 2. Control volumes in collector

R AND D JOURNAL, VOL. 18, NO . 2, JIJLY 2OO2

tween the inlet and the outlet of the chimney, can be ex-pressed as

Lp.o." : l+* I ("a?) ]' ( r I pa- 1 I pn)

wherewhere qo is the heat absorbed by the glass, i.e.

^ (1 - p) (1 - rba) Io , (1 - p) (1 - rd,a) Ia ,., r\Y.a- - \rDl

where the total radiation per unit area of horizontal surfaceis

In - Iu * Ia. (16)

According to Duffie k Beckmanll the beam reflectanceat the upper surface of the glass can be expressed as

where d is the zenith angle of incidence. For diffuse radia-tion the approximate reflectance is determined at 0 : 60oi.e. Pa :0.0934.

The beam transmittance through the glass roof due toabsorption is given by

-1- t,./ [cos{arcsin(sin 0 /I.526) }]Tbo - e ve

(7)

If it is assumed that the turbulent flow in the chimneyis fully developed, the frictional loss can be expressed ap-proximately as

Lp.r : f . (Ho - H5) l+*l ("a?)l' t (2pqd.) (8)

where according to Haalande

f":27778["r,,{t#) '* (*) "'}] ' (e)

where e" is the surface roughness of the concrete.2. The energy equation applicable to the elementary corr-

trol volume about the air stream in the collecter as shownin Fig. 2 is

#r^a.,cpr) A".&b,a: eghr L'0 A'r * qrn r L, 0 A,r

Since p - p I Rr and changes in cp and p are negli-gible, this equation together with the continuity relation0l0r (^a,t) A" - -a l& @ r a 0 Lr f/) can be simplifiedto give for fully developed flow

p cp ,# * (#)# :egh*q.n

:hg(Tn-T,)+h,(7,-T)

According to Gnielinski,l0 the heat transfer coefficientsunder the roof and on the ground for fully developed flowcan be expressed as

h - k (f o 116) (Re -1 000) P, I(12)

[" {r 07 + 1 2.7 (f o/8)o ' (pro Gr _1) }] '

For developing flow near the inlet of the collector

ocp rK* ffi)#:egh*q,r,(13)

:hg(Tn-To)+t,(7"-T")

Krdger k BuysT give values for h for developing flowunder the roof and on the ground.

3. Assume that the temperature difference between thetop and bottom surfaces of the glass roof is negligible andapply an energy balance to the elementary control volumeshown in Fig. 2:

The transmittance of diffuse radiation considering onlyabsorption, Td,a is the same as that of Tbo evaluated at0 - 60".

The net longwave radiation heat transfer rate betwseenthe ground and the roof is given by

es,: o (Tn4 -7,4) I (rlen + 1 lr, - L). (19)

The convective heat transfer rate from the glass roof tothe air stream under the roof for fully developed flow isgiven by

where theis

0 L,r H "oT.) (10)

( 11)

(14)

for developing flow at the inlet of the collector.The convective heat transfer rate from the roof to the

ambient air is given by

era : hro (7, - T") . (22)

Presently, no reliable equation exists for the convectiveheat transfer coefficient hro. The follou'ing relation will beemployed:11

h,o = b.T + B.8u_ (29)

where u- is the wind speed at the roof elevation.The net longwave radiation heat transfer rate between

the glass roof and the clear sky is expressed as

and

where thegiven by

Qrh - h, (7, - T)

Qrh - h, (7, - T")

Qr": ero (rrn -rlno)sky temperature according

T,ka - 0.05 52Tr'5

(20)

(21)

(24)

to Swinbankl2 is

( 18)

(25)Q" * Qg, - Qrh - Qra - Qrs : Prcortr}T, l0t

34

4. The energy equation applicable to the elementary con-trol volume in the ground (assuming thermophysical properties of ground are constant) as shown in FiS. 2 is givenby

R AND D JOURNAL. VOL. 18. NO.2, JULY 2OO2

NUMERICAL SIMULATION

The performance of the solar chimney power plant is de-termined by maximizing the power output:

uTo , 02ToPscno$: KsE

AP AP 7Ts nr_-_rr

0m ' ATr 0m(26)

(28)

(2e)

P^P-:egh*eg,-eg. (27)''g 0z

The net solar radiation per unit area absorbed by theground is13

(1 - p)2 rbo.eg Iu

(1 - p2ur?o) [1 - pa(l - on)]

To solve this equation the following conditions are appli-cable: At z -0

Equations (11), (14) , (26), and (27) are semi-discretizedby replacing spatial derivatives with finite difference ap-proximations. The resulting equations together with equa-tion (29) are a set of differential-algebraic equations whichcan be solved numerically using a standard computer codesuch as DASSL.14

RpsuLTs

The murimum electrical power output of the referenceplant on the 21st of each month is shown in Fig. 3.

There is a pronounced peak output shortly after middayand a significant difference in output during the summerand winter months. Due to the heat stored in the groundsome power is also generated at night.

Examples of the temperature distributions in the groundunder the collector at a radius of 200 m at different tirnesof the dry in December and in June are shown in FiS. 4and Fig. 5. The former shows conditions near the surfaceof the ground more clearly.

70Solar timp

OE:0O

0.2 0.4 0.6

Depth, m

Fig. 4. Temperature distribution in ground near surface

The output of the reference plant, which is 341 GWh/a,can be increased by changing the shape of the collector roofand its inlet height H2. As shown in FiS. 6 a mancimumpower output is attained when b - 1 and Hz :3.3 m. Forvalues of b

flow separation in the collector due to the fact that the flowarea increases.

By enlarging the collector area the annual power outputcan be increased. This is shown graphically in FiS. 7 forb - 1. At every collector diameter there is a correspondingoptimal inlet height.

Qg

+(1 - pa)' r d,ads Ia

(1 - p2ar2ao) [1 - pa(l - or)]

At z: @t }Tnl0, - 0.

120

lo0

20

0

r20

100

=80b60ao. 40

DOC

60

''^ toq)L.d)E40a')ocb30F

20l0 lsTime

>80b60=oo"40

20

0 5 l0 15

Time

Fig. 3. Maximum electrical output of reference plant

R AND D JOURNAL, VOL. 18, NO. 2, JVLY 2OO2

lt)

20

Fig.5.

Depth, m

Temperatttre distribution in ground

420

400

380

360

340

320

300 246H2'*

Fig. 6. Annual power output as function of b und H2

CoxcLUSroN

The performance characteristics of a large solar chimneypower plant are determined. It is shown that in such aplant there is a pronounced peak output shortly after solarnoon, whilst power is also generated at night due to theenergy storage capacity of the ground. The output of thereference plant considered can be increased by modifyittgthe shape and inlet height of the solar collector. A furtherincrease in power output can be attained by increasing thecollector diameter. Due to greater heating of the air underthe collector with increasing collector diameter, heat lossesto the environment will also increase. For the particularplant under investigation the nett increase in annual poweroutput is approximately linear over the range of collectordiameters shown in Fig . 7.

RprpnENCEs

[1] Haaf W, Friedrich KG k Schlaich J. Solar Chimnevs. Part 1:Principle and Construction of the Pilot Plant in Manzanares.

4000 s000 6000 7000 8000

Collector diameter d' m

Fig. 7. Annual power output as function of collector diameter (b - 1)

Int. J. Solar E'nergy, 1983, 2, pp.3-20.Haaf W. Solar Chimneys. Part 2: Preliminary Test Results fromthe Manzanares Plant . Int. J. Sola'r E'ne'rgy, 1983, 2, pp.141-161 .

Schlaich J & Schiel W. ^9ola'r Ch'irn'netJs, Encyclopedia of Physi,-cal Scie'nce a'nd Technolog,U,3rd edn, 2000.Schlaich J. Tension Structures for Solar Electricity Generation.E'ngi'nee'ri'ng Stru,cttt"res, 1999, 21, pp.658-668.Blaine DC & Krdger DG. Analysis of the Driving Potential of aSolar Chirnney Power Plant. R. €i D Jou'r'nal, 1999, 15, pp.85-94.Hedderwick RA. Performance Evaluation of a Solar ChimneyPower Plant. MSc(Eng) thesis, University of Stellenbosch, Stel-lenbosch, South Africa, 2001.

t7l Kroger DG & Buys JD. Radial Flow Boundarv Layer Develop-ment Analvsis. ^R €i D,Io,urnar, 1999, 15, pp.95-I02.

[8] Beyers M. Finite Volume Method for the Analysis of the Thernro-flow Field of a Solar Chirnney Collector. MSc(Eng) thesis, Uni-versity of Stellenbosch, South Africa, 2000.

l9l Haaland SE. Sirnple Explicit Formulas for the Friction Factorin'Turbulent Pipe Flow. Tra'ns. ASME, J. Flu,ids E'n,gi,'neeri,'ng,1983, 105, pp.89-90.

[10] Gnielinski V . Forsch. In,g. Wese,n, 1975, 4L.[11] Duffie JA & Beckman WA. Sola'r Engi'nee'ri'ng of Thermal P,ro-

cesses. Wiley Interscience, New York, 7974.[12] Swinbank WC. Long-wave Radiation from Clear Skies.'Qu,a'rt.

J.R. Meteorol. Soc., 1963, 89.[13] Modest MF. Radiati'ue Heat Tra'nsfer. McGraw Hill, New York,

I 993.

[14] Brenan KE, Campbell SL U Petzold LR. Nurnerical Solutionof Initial-value Problems in Differential-Algebraic Equations.514M,1996.

ApppNDrx A

For purposes of comparison a reference solar chimney plantand its operating environment is defined.

P ower plant speci,fr,cat'ions :

a. Chimney

Chimney heightChimney inside diameterChimney drag coefficient due toappurtances (based onchimney cross-sectional area) K.D: 0.1Chimney inside surface roughness €c : 2 x 10-3 rn

i r H r=z4

i i ,/,rt./!t r./ r

i /4Iz:3.5i*tt/l I

t,/rry-. Ini2 ;3.4i. Itl

:3.3 m i

H": t 500 md" :160 m

cl

Eo:,=g:)-JoL.a.)

'oo.ct-tr?.H

60

"'^ soG)t{=E400)aF30F

I 200

r 000

800

600

400r0

clrLa

B()h

l|

J

o.I

=oL.c)

'oo.(€-))l-.

l2l

[3]

[4]

[5]

16l

36

b. CollectorCollector outside diameterCollector inside diameterCollector inlet heightCollector roof shape

Collector inlet loss coefficient(based on inlet area)Collector roof roughnessCollector supports (diameter)Drag coefficient of supportsTangential pitch of supportsRadial pitch of supportsCollector roof material properties:(5 mm thick green of edge glass)DensitySpecific heatThermal conductivityThicknessExtinction coefficientEmissivityCollector upper convectiveheat transfer coeffi.cient

d2-2rz-4000mdt :2rs - 400 mH2 - 10 mH - Hz (rzlr)owhere b - 0.5

K; - 1

€, :0d" - 0.15 mC"n - 1

Pt - 10 mP, :10 m

p,:2700kg/-tcp, : 840 J lkg Kk, :0.78 W/mKt, : 0.005 mC.:321m€7 :0.87

ho :5.7 W l^' K

R AND D JOURNAL, VOL. 18, NO.2, JULY 2OO2

c. T\rrbineT\rrbo-generator efficiency Tts : 0.8Ttrrbine inlet loss coefficient basedon turbine cross-sectional area) Kti :0.25

d. GroundTypeDensitySpecific heatThermal conductivityGround roughnessEmissivityAbsorbance

e. Ambient conditionsAir pressureWind speed

granite

Pg:2640kg/-tcps :820 J lkg Kkg : I.73 W/mKe s :0'05 m€g : 0'9CIg : 0'9

pa :90 000 N/-'uto :0 m/s

Air temperatures are presented in Table A.1, whilst detailsof the solar radiation are given in Table A.2.

Table A.l Ambient air temperature

Solartimel23+5 t2Il0 2+232ll9IBt7r6l5t4l3

JunFeb

MarAp.Muy

JunJulAugS.POctNovDec

2s.52 2s.09 24.66 2+.33 23.8024.89 24.46 2+.03 23.60 230t722.s9 22.t6 2t.73 2 I .30 20.87

lB.l9 t7.76 t7.33 16.90 16.+7

15.96 15.53 15. l0 t+.67 t4.2413.16 t2.73 12.30 I l.B7 rt.++14.06 13.63 13.20 t2.77 12.34

t+.79 14.36 13.93 13.50 13.07

19.59 19.16 18,73 18.30 t7.8722.09 2 r.66 2t.23 20.80 20 37

22.52 22.09 21.66 21.23 20.802+ .92 2+.+9 2+.06 23 .63 23 .20

23.37 22.9+22.72 22.31

20.++ 20.0116.04 15.61

l3.B l 13.38

I l.0l 10.58

I l.9l I l.4Bt2.6+ t2.21t7 .+4 I 7.0 r

19.94 19.5 I

20.37 19.94

22.77 22.34

22.5t 24 t0 25.9

2l.BB 22.70 2+.5

lg.s8 20.70 22.815. r8 16.50 lB.B

12.95 12.52 l4.B10. l5 9.72 l l .31r.05 10.62 ll.4r l.7B l 1.35 t3.716.58 16. l5 l B.s

19.08 r9.40 21.520.00 22.20 2+.1

21.91 24.00 25.8

27.6 29 0 30.026.2 27.6 28.7

2+.5 2s.9 26.8

20.6 22.0 23.016.9 18.4 19.5

13.6 15.4 16.5

13.8 15.7 l 7.0

l s.9 t7 .7 19. l

20.6 22.2 23.5

23.3 24.8 2s.925.7 27.0 27.9

27.+ 28.6 29.7

30.s 30.7 30.529.+ 29.5 29.3

27.4 27.5 27.3

23.6 23.9 23.620.2 20.+ 20.3t7.3 t7 .7 t7.517.9 lB.3 lB.220.0 20.s 20.5

24.3 2+.7 2+.7

26 6 26.9 26.92B.s 28.6 28.4

30.1 30.4 30.3

30.1 29.30 28.l028 7 27 90 27.47

26.5 2s.60 25.t723.0 2t.20 20.7719.4 18.97 l8.5416.6 t6.17 t5.7417.5 t7 .07 r6.6419 9 l 7.80 t7 37

2+.t 22.60 22.t726.3 2s.20 2+.6727 .9 27 .00 25. l029.7 28.90 27.50

27.67 27.2+

27 04 26 6l24.7+ 24.3t20.3+ 19.91

rB.l I 17.68

15.3 I l4.BB

l6 2l 15.78

16.94 16.5 l

2t.74 21.31

2+'2+ 23.8I24.67 24.24

27.07 26.64

26 Bl 26 38 25.9526. rB 25.75 2s 3223.88 23.+5 23.0'219.48 19.0s 18.62t7.25 r6.82 16.39t4.45 t+.02 13.5915.35 t4.92 t+.+9r6.08 15.65 t5 22

20.88 20.45 20.02

23.38 22.95 22.s223.81 23 38 22.9s26.2t 25.78 25.35

Table A.2 Total and diffuse solar radiation on a horizontal surface W/m

I,tIhI,tIhI,tIhI,tIhI,tIhI,tIhI,tIhI,tIhI,tIhI,tIhI,tIhI,tIhI,IIt,

Jun l3B 52

Feb 68 46

Mar00Apr00Muy00Jun00Jrl00Aug00S.p00Oct 66 +5

Nov 135 62

Dec 157 58

l0B 762 126 909r09 691 t2+ 845102 604 l2l 76384 489 l 12 64+66 +07 85 562

63 368 BB sl766 +07 90 562

91 483 106 636109 578 t27 730l2l 673 l4l 822I 12 7+3 126 887103 773 l0B 91 7

136 1003 140

t+4 942 l5l130 865 l3B129 745 t34l0l 664 106

109 616 I 17

107 664 l 13

t27 735 125

139 827 r49156 9l 7 t65133 979 t37r 19 1009 12l

1035 135 1003 140 909976 ls6 942 160 B4s

900 t+4 865 l3B 763780 l4B 745 t42 644700 105 664 100 562650 lll 616 105 5t7700 l 12 664 106 562

770 t23 735 r25 636861 155 827 149 730950 l8l 9t7 lB3 822l0l0 l3l 979 t37 BB7

1040 I 14 t009 r3l 917

136 762 130 572161 691 145 496

l4s 604 133 406

129 489 l0B 299

96 +07 77 22093 368 70 190

96 407 77 220I 14 483 l0l 295146 578 l2l 388t73 673 155 +83

t+2 7+3 t3+ 558r28 773 t2+ 587

82 l3B +0

75 68 24540031 0 0ll 0 0600t2003200sB0090 66 2887 r35 +586 t57 +9

357

279lB0ll035t935

99lB2272

348375

572496406299

220190

2202953BB

483

558

587

357

279190

100

35l935

99l82272

348375

B9

B6

72

50

IB

l0l75078

95

90B3

l14l14r0278

4844

48

7l97135

lt7I l6