Journal of Energy Technologies and Policy ISSN 2224-3232 (Paper) ISSN 2225-0573 (Online) Vol.3, No.6, 2013

www.iiste.org

Journal of Energy Technologies and Policy ISSN 2224-3232 (Paper) ISSN 2225-0573 (Online) Vol.3, No.6, 2013

www.iiste.org

10

Journal of Energy Technologies and Policy ISSN 2224-3232 (Paper) ISSN 2225-0573 (Online) Vol.3, No.6, 2013

www.iiste.org

Chimney

Transparent material

Turbine

air flow

air

flow

R

H

solar collector

Figure(1) Circular Collector Solar Chimney Theoretical Analysis The heat energy transferred from the patch is given by : =ℎ − …………………….(1) are the temperatures at surface converted by the selective material and any position H in the When and covered area A and h is the converted transfer coefficient is given by: h=h (Re, Pr, K, L) in a case of a turbine[12]: / . ℎ = 0.036 ……………………(2) Known for circle collector surround the square of side L . The area of the surface is given by : = =

!

+

i.e. = "/√2 So converted area is: =% & = " Substitute in Eq.(1) &

= " ℎ '− ………………….(3) On the other hand heat transferred from the patched area to air under the canopy is given by: = ()*+ , − ' ………………….(4) Where: is the temperature of mass of air inside the chimney. , () is mass flow rate (Kg/s) ,which given as: () = ρ- U + ………………………….(5) Where /0 is the ambient density of the air . 1 is the velocity with which the mass flows The cross section area of the opening around the circular patch of radius (L/√2) as: + = 2%L/√23 + = √2%"3 So the Eqs.(4) can be written as: 11

Journal of Energy Technologies and Policy ISSN 2224-3232 (Paper) ISSN 2225-0573 (Online) Vol.3, No.6, 2013

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4 = √2%"3/0 1*+ , − …………………….(6) For the circular chimney of radius R and velocity V which air impinges on the rotor blades of air turbine is given by : % 5 = √2%"31 ………………….(7a) 6!7

…………………..(7b) 1= √ Hence the heat transfer to the air under the chimney is (after Substituting Eq.(7b) in Eq.(6)): 5

4 = √2%"3/0 *+

, − √2"3 4 = %/0 *+ 5 , − …………..(8) Combination Eqs.(3) and (8) we get: & " ℎ '− = %/0 *+ 5 , − 89 :; 6 ! 7 <= ><?

ℎ=

! !B

5=

5= ∴

89 :; 6 ! .

=

5=

&^

&

C

<@ ><A <@ ><A <=><?

D& &

<@ ><A <=><? .

&

……………..…..(9)

E

C D

F

……………..(10) G G G

L

G 6! HIJ: G KJ 89 ;

<@ ><A

M

<= ><?

D

…………………….(11)

F

G G

G L G 6! HIJ: G KJ 89 ;

M

D

..……………..(12)

By using Eq. (7a) the instantaneous electric power Pi produced by a single turbine is readily derived as : C /, % 5 …….……………….(13) P = Q Where : C /0 is the density of the air at temperature , and factor is the ideal limit for extraction of power . Q From Eqs.(11) and (13) , the instantaneous electric power is : "D % > = 3.0 × 10 T U V P E 3 2 WG

= 1.1 × 10> T W! H …………………..(14) 6 Where T at 300K and 1 atmospheric pressure at dry air: P

T=

8= G

WG 0G : WG K L 89 ;

= 1.148 ∗× 10>

………….(15)

Eq.(14) shows that the instantaneous electric power depends mainly on the dimensions of the solar chimney for given temperature ratio τ . Substituting Eq.(15) into Eq.(14) yield: "D >E U V D P = 1.2628 × 10 E 3

12

Journal of Energy Technologies and Policy ISSN 2224-3232 (Paper) ISSN 2225-0573 (Online) Vol.3, No.6, 2013

www.iiste.org

Table(1) Solar Chimney Electric Power Generation of Square Collector [2] L=500m

L=400m

L=300m

L=200m

L=150m

τ

6E-10

2E-13

3E-13

0

0

0.5

0.009

0.00032

4.2E-06

1.3E-08

1.3E-10

1.5

19.38

0.68

0.009

0.000027

2.7E-07

2.5

3015.7

106.1

1.4

0.0043

0.000043

3.5

130784.3

4601.6

61.55

0.187

0.0018

4.5

2653433

93360.94

1248.8

3.8

0.038

5.5

32513832

1143998

15302.5

46.7

0.46

6.5

2.78E+08

9786871

130912.5

399.5

4

7.5

1.82E+09

63974780

855748.1

2611.8

26.2

8.5

9.64E+09

3.39E+08

4538540

13852.4

138.9

9.5

4.33E+10

1.82E+09

20365804

62159.9

623.67

10.5

1.69E+11

5.96E+09

79713097

243298.1

2441.1

11.5

Table(2) Solar Chimney Electric Power Generation of Circular Collector [present work] L=500m

L=400m

L=300m

L=200m

L=150m

τ

0.00058

6.3E-11

8E-13

0

0

0.5

0.02

0.0009

0.000011

0.000000027

3.5E-10

1.5

54.685

1.9

0.024

0.000058

0.00000074

2.5

8500.5

299.09

3.79

0.009

0.00011

3.5

368648.16

12970.8

164.7

0.39

0.005

4.5

7479364.7

263161.1

3341.7

8.03

0.1

5.5

115234734.6

3224645

40998.7

98.39

1.2

6.5

784049213.6

27586744

350315.1

841.8

10.6

7.5

5125169802

1.8E+08

2289938.4

5502.7

69.8

8.5

27181819989

9.56E+08

12144902

29184.2

370.6

9.5

1.21973E+11

4.29E+09

54497860

130958.6

1663.1

10.5

4.77411E+12

1.68E+10

213308188

768952

6509.6

11.5

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Journal of Energy Technologies and Policy ISSN 2224-3232 (Paper) ISSN 2225-0573 0573 (Online) Vol.3, No.6, 2013

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3,500

3,000

Power (Watts)

2,500

2,000

1,500

1,000

500

0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5

τ Fig.(2)) Curves showing simulated power output for circular collector solar chimneyes of different lengths when H=R=1.5m H=R= Results and Discussions ( in which we Figure(2)) shows the relationship between output power of circular collector as a function of (τ), can see that the output power increases exponentially with (τ). ( The curves show that the minimum threshold value of τ beyond which appreciable power (103 W) can be generated by a viable solar chimney power generating plant with a circular collector is approximately 2.65. Thereafter the power increases rapidly after each threshold value of τ for each specified dimension of the chimney. The dimensions of a reasonably sturdy stu solar chimney power plant that would generate energy of the t order of 103W, for example, is L = 150 m, H = 1.5 m and R = 1.5 m. This specific dimension requires that τ = 10.15. from our calculations in table(1) which were compared with that in table(2), we can see that the circular collector solar chimney gives more output power than square shape because it gives more heat transfer surface than the square. There are a number ber of reasons as to why a large area of land must be used as a solar collector. These reasons include the fact that the overall conversion efficiency from solar energy to electricity is 2–3%. 2 There is a temperature drop with altitude of about 10 C0 for a 1000 m chimney. Large quantities of warm air have to be lifted from the ground to chimney top which results in gravitational energy loss. The air that leaves the chimney is above ambient temperature at that altitude also resulting in thermal energy loss. Ass ambient air is drawn into the collector and warmed, expands with little increase in pressure and the majority of solar input is lost in the simple expansion of air before it reaches the turbine [13–17]. Conclusions From the present work we can deduce the following conclusions: 1-In Fig.(2) the he curves show that there exist threshold values of the temperature ratios, τ at which significant power (P=103W) can be produced by a solar chimney of specific dimensions. Above the threshold values, τ, the instantaneous electric power increases exponentially. 2-The The circular collector gives more output power by 1.5% than the square collector solar chimney. 3-The circular collector installation ation has higher stability and more heat transfer area than the square collector solar chimney.

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Journal of Energy Technologies and Policy ISSN 2224-3232 (Paper) ISSN 2225-0573 (Online) Vol.3, No.6, 2013

www.iiste.org

References [1] Stefanie Fiedermann, Jadranka Halilovic and Torsten Bogacz,2009," Solar potential of the Sahara Desert with an introduction to solar updraft power plants". [2] Frederick N. Onyango, Reccab M. Ochieng,2006," The potential of solar chimney for application in rural areas of developing countries", ELSEVIER, Fuel 85 , 2561–2566. [3] H.-J.Niemann, F.Lupi, R.Hoeffer, W.Hubert , C. Borri,2009, "The Solar Updraft Power Plant: Design and Optimization of the Tower for Wind Effects". [4] Reinhard Harte , Gideon P.A.G. Van Zijl,2007," Structural stability of concrete wind turbines and solar chimney towers exposed to dynamic wind action",ELSEVIER, Journal of Wind Engineering and Industrial Aerodynamics 95,1079–1096. [5] Jörg Schlaich, Rudolf Bergermann, Wolfgang Schiel, Gerhard Weinrebe,2004," Design of Commercial Solar Updraft Tower Systems – Utilization of Solar Induced Convective Flows for Power Generation", Schlaich Bergermann und Partner (sbp gmbh), Hohenzollernstr. 1, 70178 Stuttgart, Germany. [6] Egger, Daniel (2002): Moderne Solartechnologien und ihre zukünftigen Perspektiven. ETH Zürich. [7] Weinrebe G, Schiel W. Up-draught solar tower and down-draught energy tower – A comparison. In: Proceedings of the ISES solar world congress 2001, Adelaide. [8] Schlaich J. The solar chimney: electricity from the sun. Geislingen, Germany: C. Maurer; 1995. [9] Von Backstro¨m TW, Gannon AJ. Compressible flow through solar power plant chimneys. ASME J Sol Energy Eng 2000;122(3):138–145. [10] Padki MM, Serif SA. On a simple analytical model for solar chimneys. Intl J Energy Res 1999;23(4):345–9. March 25. [11] United Nations environmental programme (UNEP). Chemical pollution: a global overview. Geneva: UNEP; 1992. [12] Tiwari GN, Sangeeta S. Solar thermal engineering systems. NewDelhi: Narosa Publishing House; 1997. [13] Weinrebe G, Schiel W. Up-draught solar tower and down-draught energy tower – A comparison. In: Proceedings of the ISES solar world congress 2001, Adelaide. [14] Schlaich J. The solar chimney: electricity from the sun. Geislingen,Germany: C. Maurer; 1995. [15] Von Backstro¨m TW, Gannon AJ. Compressible flow through solar power plant chimneys. ASME J Sol Energy Eng 2000;122(3):138–145. [16] Padki MM, Serif SA. On a simple analytical model for solar chimneys. Intl J Energy Res 1999;23(4):345–9. March 25. [17] United Nations environmental programme (UNEP). Chemical pollution: a global overview. Geneva: UNEP; 1992.

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