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Thermal and technical analyses of solar chimneys

M.A. dos S. Bernardesa,*, A. Voßa, G. Weinrebeb

aInstitut f€ u ur Energiewirtschaft und Rationelle Energieanwendungen, Universit€ a at Stuttgart,

Heßbr€ u uhlstraße 49a, D-70565 Stuttgart, Germany

bSchlaich Bergermann und Partner, Hohenzollernstr. 1, D-70178 Stuttgart, Germany

Received 18 September 2002; received in revised form 15 August 2003; accepted 15 August 2003

Abstract

An analysis for the solar chimneys has been developed, aimed particularly at a comprehensive analytical and nu-

merical model, which describes the performance of solar chimneys. This model was developed to estimate power output

of solar chimneys as well as to examine the effect of various ambient conditions and structural dimensions on the power

output. Results from the mathematical model were compared with experimental results and the model was further used

to predict the performance characteristics of large-scale commercial solar chimneys. The results show that the height of

chimney, the factor of pressure drop at the turbine, the diameter and the optical properties of the collector are im-

portant parameters for the design of solar chimneys.

? 2003 Elsevier Ltd. All rights reserved.

1. Introduction

A solar chimney is a solar power generating facility,

which uses solar radiation to increase the internal energy

of air flowing through the system, thereby converting

solar energy into kinetic energy. The kinetic energy from

the air is then transformed in electricity by use of a

suitable turbine. A solar chimney consists of three main

components: (1) the solar collector or the greenhouse,

(2) the chimney, and (3) the turbine (Fig. 1). The col-

lector, supported a few meters above the ground, is

covered by a transparent glazing. Its main objective is

collecting solar radiation to heat up the air mass inside

it. Buoyancy drives the warmer air into the chimney,

which is located at the centre of the collector. A turbine

is set in the path of the airflow to convert the kinetic

energy of the flowing air into electricity. The collector

can be equipped with a water-storage system (4) to in-

crease the power production during the night.

The solar chimney was originally proposed by Pro-

fessor J. Schlaich of Stuttgart in 1968. In 1981 began the

construction on a pilot plant in Manzanares, Spain. A

50 kW experimental plant was built which produced

electricity for eight years, thus proving the feasibility

and reliability of this novel technology. The chimney

tower was 194.6 m high and the collector had a radius of

122 m. It produced an upwind velocity of 15 m/s under

no load conditions. Operating costs of this chimney were

minimal. Fundamental investigations for the Spanish

system were reported by Haaf et al. (1983) in which a

brief discussion of the energy balance, design criteria,

and cost analysis was presented. In a later study, Haaf

(1984) reported preliminary test results of the plant built

in Spain. Castillo (1984) presented a new chimney design

with a new structure of the chimney building supported

by a hot-air balloon. Mullet (1987) presented an analysis

to derive the overall efficiency of the solar chimney.

Padki and Sherif conducted an investigation of the vi-

ability of solar chimneys for medium-to-large scale

power production, 1989a and power generation in rural

areas, 1989b. Schlaich et al. (1990) studied the trans-

ferability from the experimental data of the prototype in

*Corresponding author. Address: Centro Federal de Educa-

cao Tecnologia de Minas Gerais, Departamento de Engenharia

Mecanica, Av. Amazonas 7675 Nova Gameleira, 30510-000

Belo Horizonte, Minas Gerias, Brazil. Tel.: +55-31-3319-5208;

fax: +55-31-3319-5248.

E-mail address: marcobernardes@des.cefetmg.br (M.A. dos

S. Bernardes).

0038-092X/$ - see front matter ? 2003 Elsevier Ltd. All rights reserved.

doi:10.1016/j.solener.2003.09.012

Solar Energy 75 (2003) 511–524

www.elsevier.com/locate/solener

Page 2

Manzanares to large power plants (5, 30 and 100 MW)

Yan et al. (1991) reported on a more comprehensive

analytical model in which practical correlations were

used to derive equations for the airflow rate, air velocity,

power output and the thermo-fluid efficiency. The pre-

sented model considers the turbine of a solar chimney as

a free wind turbine that, in reality, will deflect the wind,

even before the wind reaches the rotor plane. The pre-

sented maximum theoretical efficiency of 16/27 (or 59%,

Betz’ law) does not apply for the turbines of solar

chimneys. Padki and Sherif (1992) discussed in brief the

effects of the geometrical and operating parameters on

the chimney performance. Sampayo (1986) suggested

the use of a multi-cone diffuser on the top of the chimney

to allow the operation as a high-speed chimney and of

acting as a draft tube for any natural wind blowing.

Pasumarthi and Sherif (1997) conducted a study to

demonstrate that solar chimney technology is a viable

alternative energy technology suitable and adaptable to

hot climate areas such as those of Florida. A mathe-

matical model was developed to estimate the tempera-

ture and power output of solar chimneys as well as to

examine the effect of various ambient conditions and

structural dimensions on the power output. Tests were

conducted on a demonstration model, which was design

for that purpose. Two types of collectors were tested: (1)

extending the collector base and (2) introducing an in-

termediate absorber. The experimental temperatures

reported are higher than the theoretically predicted

temperatures. The authors explain that one of the rea-

sons for this behavior is the fact that the experimental

temperatures reported are the maximum temperatures

Nomenclature

Latin symbols

A

b

area [m2]

thermal

[Ws1=2K?1m?2]

specific heat [Jkg?1K?1]

friction factor [–]

Fanning friction factor [–]

gravitational acceleration, 9.80665 [ms?2]

incident solar radiation [Wm?2]

heattransferconvection

[Wm?2K?1]

chimney height [Wm?2]

radiationheat

[Wm?2K?1]

sky radiationheat

[Wm?2K?1]

wind convection heat transfer [Wm?2K?1]

thermal conductivity [Wm?1K?1]

height of roughness [m]

length of collector, thickness of the water-

storage system [m]

mass flow rate of air stream [kgs?1], mass

[kg]

Nusselt number [–]

p, p1, pt pressure, ambient air pressure, air pressure

inside the chimney [Pa]

P

power [W]

Pr

Prandtl number [–]

q

heat transferred to air stream [Wm?2]

r

radius [m]

Ra

Rayleigh number [–]

Re

Reynolds number [–]

Rl

ideal gas constant, 287.05 Jkg?1K?1

S

absorbed solar radiation [Wm?2]

penetrationcoefficient

cp

cw

f

G

H

h

coefficient

Hk

hr

transfer coefficient

hrs

transfer coefficient

hw

k

kr

L, Lw

_ m m, m

Nu

t

T

T1, TdpTs ambient, dew point temperature, sky tem-

perature [K]

Tf;i, Tf;o inlet, outlet temperature [K]

Tt

air temperature inside the chimney [K]

U

heat transfer coefficient [Wm?2K?1]

w

velocity [ms?1]

x

factor of pressure drop at the turbine

[–]

time [s]

temperatures [K]

Greek symbols

a

a1, a2, a3, a4 first cover absorptivity, second cover

absorptivity, transparent plastic film ab-

sorptivity, absorber absorptivity [–]

Dpfriction friction loss [Pa]

Dptot

total pressure difference in the chimney [Pa]

Dpturb

pressure drop across the turbine [Pa]

e

emissivity [–]

C

parameter [Wm?2K?1]

gt

mechanical efficiency [–]

j

specific heat ratio [–]

q, q0, qtair density, ambient air density, air density

inside the chimney [kgm?3]

r

Stefan–Boltzmann

[Wm?2K?4]

s

shear stress [Pa]

s1, s2, s3 first, second cover and transparent plastic

film transmissivity [–]

sa

transmittance considering only absorption

losses [–]

sr

transmittance of initially unpolarized radi-

ation [–]

thermal diffusivity [m2s?1]

constant,5.67·10?8

512

M.A. dos S. Bernardes et al. / Solar Energy 75 (2003) 511–524

Page 3

attained inside the chimney, whereas the theoretical

model predicts the bulk air temperature. Kreetz (1997)

presented a numerical model for the use of water storage

in the collector. His calculations showed the possibility

of a continuous day and night operation of the solar

chimney. Bernardes et al. (1999) presented a theoretical

analysis of a solar chimney, operating on natural lami-

nar convection in steady state. In order to predict

thermo-hydrodynamic behaviour of air, temperature

conditions were imposed on entrance, so as to guarantee

steady laminar flow along the device. The mathematical

model was analyzed by the method of Finite Volumes in

Generalized Coordinates.

(2000) presented a one-dimensional compressible flow

approach for the calculation of all the thermo-dynamic

variables as dependence on chimney height, wall fric-

tion, additional losses, internal drag and area exchange.

Gannon and Backstr€ o om (2000) developed an analysis of

the solar chimney including chimney friction, system

turbine, exit kinetic losses and a simple model of the

solar collector. The use of solar chimneys in areas as

crop drying and ventilation is considered beyond the

scope of the present work.

Backstr€ o om and Gannon

2. Analysis

The power output of a solar chimney depends on

parameters such as the ambient conditions (insolation,

ambient temperature, and wind velocity) and dimen-

sions of the chimney and collector. The analysis de-

scribed in this paper is based on the following

simplifying assumptions:

• axisymmetric flow of the air in the collector, i.e.,

nonuniform heating of the collector surface in terms

of the sun’s altitude angle is neglected;

• the collector is placed over a plain surface;

• the flow in the collector is considered as a flow be-

tween two parallel plates;

• the heat losses through the wall of the chimney are

neglected;

• the flowing humid air is considered as a mixture of

two ideal gases.

2.1. Collector

In this part of the analysis the temperature rise in the

collector section is determined. This is accomplished by

assuming an initial mass flow rate, while computing the

final value by employing iterative techniques. The col-

lector is considered as a cavity between two parallel

plates.

2.2. Thermal network

The collector of a solar chimney is a solar air heater,

which consists of an array of interconnected short solar

heat collectors. Applying the momentum equation

across a differential section of the collector yields

oðmuÞ

ot

¼ ? _ m mu2þ _ m mu1þ p1A1? p2A2? 2prrcs

ð1Þ

where s is the shear stress acting on the air in contact

with the collector surface (Fig. 2).

Two types of solar collectors can be used in a solar

chimney:

I(I) Single channel with air flow between top glass and

bottom absorber.

(II) Double channel design with single air flow between

absorber and bottom covers.

Both types can be provided with the water storage

system in channel where the air flows on the ground

(Fig. 3). For type (II), the following heat balance

equations are obtained from the thermal network at the

points considering the thermal contact resistance

Tf1: S1þ hr21ðT2? T1Þ þ h1ðTf1? T1Þ

¼ hwðT1? T1Þ þ hrsðT1? TsÞð2Þ

Tf1: h1ðT1? Tf1Þ ¼ h2ðTf1? T2Þð3Þ

T2: S2þ h2ðTf1? T2Þ

¼ h3ðT2? Tf2Þ þ hr32ðT2? T3Þ þ hr21ðT2? T1Þð4Þ

Tf2: h3ðT2? Tf2Þ ¼ h4ðTf2? T3Þ þ q

ð5Þ

T3: S3¼ h4ðT3? Tf2Þ þ hr32ðT3? T2Þ þ h5ðT3? Tf3Þ

þ hr43ðT4? T3Þð6Þ

Tf3: h5ðT3? Tf3Þ ¼ h6ðTf3? T4Þð7Þ

Fig. 1. Schematic drawing of a solar chimney.

M.A. dos S. Bernardes et al. / Solar Energy 75 (2003) 511–524

513

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T4: S4¼ h6ðT4? Tf3Þ þ hr43ðT4? T3Þ þ h7ðT4? Tf4Þ

þ UwðT4? T4;0Þð8Þ

Tf4: h7ðT7? Tf4Þ ¼ h8ðTf4? T5Þð9Þ

T5: h8ðTf4? T5Þ ¼ UbðT5? T5;0Þ

where h1, h2, h3, h4, h5, h6, h7and h8are the heat transfer

convection coefficients of the second cover, first cover,

first cover to air stream, transparent plastic film to air

stream, transparent plastic film to water, absorber to

water, absorber to air, ground surface to air respectively.

hr21, hr32and hr43are the radiation heat transfer coeffi-

ð10Þ

cients between the 2nd and the 1st covers, between the

first cover and the transparent plastic film and between

the transparent plastic film and absorber respectively. T1,

T2, T3, T4, T5, Tbrepresent the temperatures at the second

cover, first cover, transparent plastic film, absorber,

ground surface and ground temperatures, respectively.

Tf1, Tf2, Tf3, Tf4 represent the air temperature between

second and first cover, mean air temperature, water

temperature and the air temperature between absorber

and ground surface respectively. Ub, Ut, and Uwrepre-

sent the heat transfer coefficient at the ground, the top

loss heat coefficient and the heat transfer coefficient in

the water storage system respectively.

By assuming that the air temperature varies linearly

along each collector section, the mean temperature is

then equal to the arithmetic mean

Tf¼ðTf;i? Tf;oÞ

2

ð11Þ

The useful heat transferred to the moving air stream

can be written in terms of the mean fluid and inlet

temperature as

q ¼ CðTf? Tf;iÞð12Þ

where

C ¼ _ m mcp=prL

ð13Þ

By substituting Eq. (12) into Eq. (4) and rearranging

we obtain:

Fig. 2. Sketch of the flow in a solar chimney.

Fig. 3. Thermal network for the collector of solar chimneys.

514

M.A. dos S. Bernardes et al. / Solar Energy 75 (2003) 511–524

Page 5

• a 9·9 matrix (Eq. (14)) for the type (II) collector

with water storage,

• a 7·7 matrix (Eq. (15)) for the type (I) with water

storage,

• a 7·7 matrix (Eq. (16)) for the type (II) without

water storage and

• a 5·5 matrix (Eq. (17)) for the type (I) without water

storage.

h1

þhr21

þUt

h1

0

@

B

1

A

C

?h1

?hr21

000000

?

h1

þh2

??

h2

000000

?hr21

?h2

h2

þh3

þhr21

þhr32

0

B

B

B

@

1

C

C

C

A

?h3

?hr32

0000

00

h3

?

h3

þh4

þC

0

@

B

1

A

C

h4

0000

00

?hr32

?h4

h4

þhr32

þhr43

þh5

h5

0

B

B

B

@

1

C

C

C

A

?h5

?hr43

00

0000

?

h5

þh6

??

h6

00

0000

?hr43

?h6

h6

þhr43

þh7

þUw

h7

0

B

B

B

@

1

C

C

C

A

?h7

0

000000

?

h7

þh8

?h8

??

h8

0000000

h8

þUb

??

2

66666666666666666666666666666666666666666666666666666666664

3

77777777777777777777777777777777777777777777777777777777775

T1

Tf1

T2

Tf2

T3

Tf3

T4

Tf4

T5

2

66666666666666666666666666666666666666666666666666666666664

3

77777777777777777777777777777777777777777777777777777777775

¼

S1þ hwT1þ hrsTs

0

S2

?CTf2;i

S3

0

S4þ UwT4;0

0

UbT5;0

2

66666666666666666666666666666666666666666666666666666666664

3

77777777777777777777777777777777777777777777777777777777775

ð14Þ

h3

þhr21

þUt

0

@

1

A

?h3

0

?hr32

0000

h3

?

h3

þh4

þC

@

1

A

h4

0000

?hr32

?h4

h4

þhr32

þhr43

þh5

h5

0

B

B

@

1

C

C

A

?h5

?hr43

00

00

?

h5

þh6

??

h6

00

00

?hr43

?h6

h6

þhr43

þh7

þUw

h7

0

B

B

@

1

C

C

A

?h7

0

0000

?

h7

þh8

?h8

??

h8

0000

h8

þUb

??

2

666666666666666666666666666666666664

3

777777777777777777777777777777777775

T2

Tf2

T3

Tf3

T4

Tf4

T5

2

666666666666666666666666666666666664

3

777777777777777777777777777777777775

¼

S2þ hwT1þ hrsTs

?CTf2;i

S3

0

S4þ UwT4;0

0

UbT5;0

2

666666666666666666666666666666666664

3

777777777777777777777777777777777775

ð15Þ

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515