Chimney shape numerical study for solar chimney power …tsl.energy.hust.edu.cn/__local/D/78/9D/E738EB6A7532BE01... · 2017-10-16 · Chimney shape numerical study for solar chimney

Chimney shape numerical study for solar chimneypower generating systemsTingzhen Ming1,*,†, Renaud Kiesgen de Richter2, Fanlong Meng1, Yuan Pan3 and Wei Liu1

1School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan, China2Tour-Solaire.Fr, 8 Impasse des Papillons, F34090 Montpellier, France3College of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, China

SUMMARY

A large number of researchers have paid great attention to solar chimney (SC) power generating technology, but only a fewhave studied the chimney configuration. Taking a 10MW SC system as an example, the physical and mathematical modelsillustrating the fluid flow, heat transfer and output power features of the system are established. Based on constraints such asequal chimney bottom section area or equal chimney surface area, the impact of several sizes of three different chimneyconfigurations upon the chimney outlet air temperature and velocity, system output power and efficiency is analyzed andthe influence of the height-to-diameter ratio (H/D) of the cylindrical chimney on system performance is studied as well.After a comprehensive analysis of system output power and efficiency, it is proved by the numerical simulation that thecylindrical chimney would be the best choice among the three basic configurations, whose optimum H/D value ranges from6 to 8. Copyright © 2011 John Wiley & Sons, Ltd.

KEY WORDS

solar chimney; output power; efficiency; chimney; collector; turbine

Correspondence

*Tingzhen Ming, School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan, China.†E-mail: [email protected]

Received 12 April 2011; Revised 14 June 2011; Accepted 9 July 2011

1. INTRODUCTION

Issues of energy security and environmental protection havebeen featured prominently in China recently and if not effec-tively addressed, they will severely impede China’s eco-nomic development. During the 2009 Copenhagen ClimaticChange Conference, the Chinese government announcedthe goal of controlling greenhouse gas emission, by 2020,to reduce the carbon dioxide emission per unit of the grossdomestic product from 40% to 45% compared with 2005’sfigures [1]. It is, therefore, necessary for us to push forwardthe development of the renewable energy power generatingtechnologies, which are of great importance if China is tomeet the emissions reduction goal.

The solar chimney (SC) is an energy-saving and envi-ronmentally friendly renewable energy power generatingtechnology compared with existing coal-fired power sta-tions, featuring continuous power generating and low oper-ation costs in contrast with other current renewable energypower generating technologies [2,3]. For Weinrebe [4], in1999, the greenhouse gas emissions calculated in CO2

equivalents (g/KWh) form a 200MW SC, almost similaras for wind turbine or a dish Stirling, almost four times

lower than for photovoltaics, and more than 50 times lessthan for an Australian coal plant (respectively, 18, 16, 21,84 and 980g/KWh). Meanwhile, for Bernardes [5], theecological analysis results in approximately 170 and 70gCO2-equivalents/kWh, respectively, for 5MW SC and100MW SC. The consumption of exhausting energeticand mineral resources as well as specific CO2 decreaseswith larger plants. This also depends on the life expec-tancy taken for the SC which can be up to more than100years. Moreover, it wastes no water resources as itdoes not need any heat sink and could help improve thesurrounding environment as well as rebuild local ecosys-tems. Suitable to be adopted in arid and semi-arid areasas well as developing countries where solar insolation isabundant, it implies a wide field of applications with goodprospects [6].

Many researchers have carried out studies on SC forseveral decades. In the beginning, the main focus wason the influence on system power generating perfor-mance based on thermodynamic analysis [7–9]. Later,in order to conduct costs pre-estimation on large-scale SCsystem, the research group led by Prof. Sherif [10–12]established mathematical models and experimental devices

INTERNATIONAL JOURNAL OF ENERGY RESEARCHInt. J. Energy Res. 2013; 37:310–322

Published online 23 September 2011 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/er.1910

Copyright © 2011 John Wiley & Sons, Ltd.310

describing the fluid flow and heat transfer features of theexperimental systems while von Backström et al. [13,14]put emphasis on turbine performance of the SC sys-tem. Furthermore, steady state numerical simulationsof fluid flow and heat transfer based on a two-dimen-sional SC model were performed by Pastohr et al.[15]. Recently, Maia et al. [16] evaluated the influence ofsome parameters on the behaviour of the airflow in a solarchimney (SC) and showed that the height and diameter ofthe chimney are the most important physical variables.As well, Bonnelle et al. [17] optimized the height-to-diameter ratio (H/D) ratio from the trade-off between, onthe one hand, the cost which is a function, not necessarilyproportional, of the surface of the envelope, and on theother hand, of the fluid mechanics losses (turbulent lossesand loss of the dynamic pressure at the top of the stack),which are both roughly proportional to the kinetic energy.Their conclusions are that these losses are strongly deter-rent against too thin chimneys, but are quite negligiblefor large diameters.

Ming et al. [18] set up an analytical model of a systemdriving mechanism and carried out calculation to show theinfluence of system relative pressure and driving force onthe output power and efficiency, followed by a detailedstudy on power storage features of the SC system [19–21].The dependence of the work potential on the air flowinginto the air collector from the heat gained inside the collec-tor, air humidity and atmospheric pressure as a function ofelevation has been studied by Ninic [22]. As the air flux isvery important and as the chimneys are located in warmand dry deserts, humidity is low, the air is never saturatedat any height inside of the SC towers envisioned in thispaper and the temperature and pressure conditions insidethe chimney never reach the dew point. However, severalpublications have studied the cloud formation in theplumes of SC [23–25].

In fact, some researches also concentrated on shapesand configurations of the SC’s chimney, where researchershold contradictory opinions. In numerical calculation andtheoretical analysis, Schlaich et al. [6] chose the cylindricalchimney, with von Backström [13,14] and Pasumarthiet al. [10,11] using the divergent chimney and conicalchimney respectively.

In this paper, based on a 10MW SC, we developed themathematical models to describe the fluid flow, heat trans-fer and output power features of the SC system mainlyconsisting of energy storage layer, collector, turbine andchimney and put more emphasis on chimney configura-tion’s influence on SC system performance. However, theanalysis of the chimney strength and resistance to windload or to earthquakes, are not in the scope of this paper.The use of a double curvature surface is known for struc-ture strengthening, and quite often, the cooling towers havehyperbolical shells, and chimneys are usually reinforced bystiffening rings [26–28]. In addition, the outside cross windinfluence on the air discharge from the top of the chimney isa very important effect; related research work can be foundin reference [29,30].

2. PHYSICAL AND MATHEMATICALMODEL

2.1. Physical model

At first, we set up axisymmetric physical models of 10MW SCs (with basic parameters as shown in Table I)based on two-dimensional assumptions. Taking Case 1 inTable I as an example, the collector is 1000m in radius,and its height varies from 2.5m at its periphery to 10m inthe center. The chimney is 800m high, and its diameter is80m at its base. From its base to the top, the chimney di-ameters vary linearly, i.e. Dt=40m means chimney diam-eters decrease from 80m at the base to 40m at the top. Inthe physical model, the collector canopy is made of trans-parent glass, and the bottom porous soil bed serves as theenergy storage layer. In order to reduce the heat loss, thecollector and the chimney are smoothly connected. Besidesthis, a simplified turbine model based on two-dimensionalassumptions is placed at the chimney bottom. The energystorage layer is 5m thick.

2.2. Mathematical model

The system performance of a SC depends on the systemdimensions and the ambient conditions. The former mainlyincludes the chimney height and radius and collector radius,while the latter includes the solar radiation, ambient temper-ature and wind velocity. The analysis described in this paperis based on the following simplifying assumptions:

1. Axisymmetric flow of the air in the collector, i.e.non-uniform heating of the collector surface in termsof the sun’s altitude angle is neglected.

2. Air flow inside the collector and the chimney can beregarded as incompressible flow, and Boussinesq hy-pothesis is applicable in this system.

3. The collector is placed over a plain surface. There isa slope from the inlet to the center of the collectorcanopy, but it can be negligible considering its largecollector radius.

4. An average value for the optical properties of a cer-tain material is considered to estimate the global so-lar radiation incident on the absorber surface. In themeantime, for a certain global solar radiation, airflow and heat transfer of the system are regarded assteady state.

Table I. Parameters for basic dimensions of the 10MW SCs.

Case

Collector Chimney

Radius Height Height Diameter configuration

1 1000m 2.5–10m 800m Db=80m, Dt=40–120m2 1000m 2.5–10m 800m Db=100–60m, Dt=60–100m3 1500m 2.5–12m 600m Db=Dt=60–160m

Chimney shape for solar chimney T. Ming et al.

311Int. J. Energy Res. 2013; 37:310–322 © 2011 John Wiley & Sons, Ltd.DOI: 10.1002/er

The numerical simulation was processed by softwareFluent 6.3.26, adopting the finite volume method for thesolution of the differential equations, the standard k�eequation model as the turbulent flow model, standard wallfunction method in wall treatment SIMPLEC algorithm inpressure and velocity decoupling, the QUICK form in for-mulating momentum equations and energy equations.

The fluid within the collector and the chimney flowsvigorously and turbulently. The axisymmetric forms ofcorresponding continuous equation, Navier–Stokes equa-tion, energy equation and turbulent flow equation basedon two-dimensional assumptions are as follows:

@u

@xþ 1

r

@ rvð Þ@r

¼ 0 (1)

r@ uuð Þ@x

þ 1r

@ rvuð Þ@r

� �¼ � @p

@xþ @

@xmþ mtð Þ @u

@x

� �

þ 1r

@

@rmþ mtð Þr @u

@r

� � (2)

r@ uvð Þ@x

þ 1r

@ rvvð Þ@r

� �¼ @

@xmþ mtð Þ @v

@x

� �

þ 1r

@

@rmþ mtð Þr @v

@r

� � (3)

r@ uTð Þ@x

þ 1r

@ rvTð Þ@r

� �¼ @

@x

mPr

þ mtsT

� �@T

@x

� �

þ 1r

@

@rr

mPr

þ mtsT

� �@T

@r

� � (4)

r@ kuð Þ@x

þ 1r

@ rvkð Þ@r

� �¼ @

@xmþ mt

sk

� �@k@x

� �

þ 1r

@

@rmþ mt

sk

� �r@k@r

� �

þGk � re

(5)

r@ euð Þ@x

þ 1r

@ rveð Þ@r

� �¼ @

@xmþ mt

se

� �@e@x

� �

þ 1r

@

@rmþ mt

se

� �r@e@r

� �

þ ek

c1Gk � c2reð Þ

(6)

where, Gk is a production item of turbulent flow kinetic en-

ergy caused by average velocity grade and Gk ¼�r gu′iu′j @uj@xi

; Gb is a production item of turbulent flow ki-

netic energy caused by the uplift; sk and se are constantsin the k�e equation; bis the volume expansion coefficientand b�1/T.

Air flow within the energy storage layer, the collec-tor and the chimney are interrelated. Therefore, whenthe heat transfer and fluid flow features of the air insidethe energy storage layer are studied, air flow within theother two parts should be taken into consideration aswell. As the energy storage layer is made of materialssuch as soil, gravel sand, etc., which could be seen as

porous medium, the air normally flows slowly com-pared with that inside the chimney and the collector.The Brinkman–Forchheimer extended Darcy model isabout to be employed in numerical simulation [31].

@u

@xþ 1

r

@ rvð Þ@r

¼ 0 (7)

r’2

@ uuð Þ@x

þ 1r

@ rvuð Þ@r

� �¼ � @p

@xþ @

@xmm

@u

@x

� �

þ 1r

@

@rrmm

@u

@r

� �� mu

K

� rFffiffiffiffiK

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu2 þ v2

pu

þrgb T � Teð Þ

(8)

r’2

@ uvð Þ@x

þ 1r

@ rvvð Þ@r

� �¼ @

@xmm

@v

@x

� �

þ 1r

@

@rrmm

@v

@r

� �� mm

v

r2

� muK

� rFffiffiffiffiK

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu2 þ v2

pv

(9)

rmcp;m@ uTð Þ@x

þ 1r

@ rvTð Þ@r

� �

¼ @

@zlm

@T

@x

� �þ 1

r

@

@rrlm

@T

@r

� �(10)

where, ud、vd represent Darcy velocity within the energystorage layer; ’、mm、lm、ls and la are porosity, surfaceheat conduction coefficient and effective viscosity of theenergy storage layer and heat conduction coefficient ofsolid materials and the air, respectively; and lm=(1�’)ls+’la,mm=m/’; K, C, respectively, represent permeabilityand inertia coefficient of the energy storage layer.

K ¼ db2’3= 175 1� ’ð Þ2

� �(11)

C ¼ 1:75’�1:5=ffiffiffiffiffiffiffiffi175

p(12)

where db is the grain size of the porous medium.

2.3. Boundary conditions and solvingprocedures

The given boundary conditions are as follows: the heattransfer coefficient by convection between the collectorcanopy and the ambient is 10W/(m2�K), with the ambi-ent air temperature being 293K; the collector inlet servesas pressure entrance while the chimney outlet acts as pres-sure exit; the chimney wall is regarded as adiabatic; thegiven temperature of the energy storage layer bottom is288K [32], where the soil temperatures several meters un-der the ground surface can be considered as constant andlower than the ambient. In addition, the solar radiation go-ing all the way to the ground could be viewed as a heatsource placed on a 0.1mm in a deep thin layer. Then thesolar energy will be absorbed by this deep thin layer and

Chimney shape for solar chimneyT. Ming et al.

312 Int. J. Energy Res. 2013; 37:310–322 © 2011 John Wiley & Sons, Ltd.DOI: 10.1002/er

changes into thermal energy. One part of this thermal en-ergy will transfer to the airflow within the collector, theother part being stored within the energy storage layerand transferred to the deep ground. The gravitationalacceleration is 9.8m/s2. Moreover, taking into consider-ation both the pressure distributions inside and outsidethe system, we define both the collector inlet and the chim-ney outlet as pressure boundaries and assume the relativepressures as 0Pa, that is, the static pressures of sameheight inside and outside the collector inlet are thesame, and those of same height inside and outside thechimney outlet are also the same. The air, therefore,flows through the chimney outlet without changing itsvelocity and maintains a constant dynamic energy[19]. The SC pressure-based turbine, though with nearlythe same air velocity at its front and back, would not followthe Betz’ theory in terms of output power due to the signif-icantly changing pressures. Consequently, as to a giventurbine pressure drop, the turbine output power could beobtained by Equation (13):

Wshaft ¼ �shaft�Δp�V (13)

where, Wshaft is the turbine shaft output power; �shaft is theturbine energy transfer efficiency: �shaft=80%; Δp is the

turbine pressure drop; V is the volume rate of flow of theair at the chimney outlet.

For an SC system with an energy storage layer, solar ra-diation into the system can be divided to two parts: (i) en-ergy absorbed by air flow inside the collector; and (ii)energy stored by the energy storage layer during daytimewith solar radiation. The second part should not be in-cluded when we analyze the system efficiency. Thereby,the system efficiency can be obtained as follows:

�sys ¼Wshaft

Qair(14)

where, �sym is the system efficiency, and Qair is the energyabsorbed by the air flow inside the collector.

In the case of a three-dimensional numerical simulation,the whole configuration of the turbine can be given in de-tail without any assumptions like in this two-dimensionalnumerical simulation, and the turbine rotation speed canbe given or controlled in advance [33].

According to Equation (13), there are two strategies tocontrol the output power of the SCs: pressure drop acrossthe turbine or volume flow rate [34]. These two parametersare coupled together in SC systems, one being confirmed ifthe other is given. As the volume flow rate is almost impos-sible to be known beforehand, the pressure drop across theturbine will serve as boundary condition in this numericalsimulation. Detailed boundary conditions of different sec-tions are shown in Table II.

Table II. Boundary conditions.

Place Type Value

0.1mm top layer ofthe ground

Heat source 2�106–10�106W/m3

Bottom of the ground Temperature 288KSurface of the canopy Wall T=293K; a=10W/(m2�K)Surface of the chimneyWall qchim=0W/m2

Collector inlet Pressure inletPr,inlet=0Pa; T0=293KChimney outlet Pressure

outletPr,outlet=0Pa

Turbine Reverse fan Pressure drop: 0–1000Pa

Table III. Comparison between the simulation results and theexperimental data.

Solar radiation 1040W/m2 Experiment Simulation Error

Collector air ΔT (K) 25 25.26645 +1.066%Ground surface Tmax (K) 345 351.43248 +6.4KOutput power (kW) 41 40.196 �1.96%Chimney inlet velocity (m/s) 9 8.812802 �2.079%

Figure 1. Sketch of a 10MW solar chimney power generating system.



The mesh number of the SC system was nearly500,000. When numerical simulation procedure was ex-ecuted, further increase in the mesh was less than 2%variation in the output power value which was takenas a criterion for grid independence. All the numericalsimulations were carried out with the double precisionsolver. The iteration errors were 10�7 for continuity, mo-mentum and turbulent equations, while it was 10�11 for theenergy equation. The numerical simulation procedure wasexecuted by using A standard PC with Intel PentiumDual E2180 2.00GHz CPU and 4.00GB RAM, andthe time spent for each simulation result was about5–6 h. Cases of different chimney configuration had little ef-fect on the time consumption of numerical simulationprocedure.

3. VALIDITY

In order to verify the validity of the numerical simula-tion results in this paper, detailed comparison betweenthe numerical simulation results and the experimental

data collected was carried out. The computation parameterswere set according to the following experimental data[3], which served as the boundary conditions and ambientconditions of the numerical program: solar radiation was1040W/m2, ground absorptivity was 0.56–0.67, the trans-missivity of the PVC membrane was 0.8, ambient temper-ature was 303K, thermal conductivity of the soil from thesurface to the deep ground was: 0–1cm, 0.5W/(m�K);1–5cm, 0.7W/(m�K); 5–10cm, 1.2W/(m�K); 10–20cm,1.5W/(m�K); 20–150cm, 1.5W/(m�K). Other detailed ex-perimental data and the corresponding numerical simu-lation results are shown in Table III. As indicated inTable III, the simulation results are quite consistent withthe experimental data. Besides, its difference from the ex-perimental data is less than 2.5%. These errors may be as-cribed to the following parameters which were not reportedin literature [3]: ambient air velocity, cloud in the sky,ground absorptivity and the PVC transmissivity distribu-tions along the collector radius and the ambient air humid-ity. Hence, it can be concluded that the numericalsimulation method applied in this paper is effective andfeasible.

020

30

40

50

60

70

Chimney b, t diameters80 to 40m80 to 60m80 to 80m80 to 100m80 to 120mC

him

ney

outl

et a

ir t

empe

ratu

re /°

C

Turbine pressure drop /Pa1000800600400200

Figure 2. Comparison of chimney outlet air temperature.

0 200 400 600 800 10000

2

4

6

8

10

12

14

16

Chi

mne

y in

tlet

air

vel

ocit

y /(

m/s

)

Turbine pressure drop /Pa

Chimney b, t diameters 80 to 40m 80 to 60m 80 to 80m 80 to 100m 80 to 120m

Figure 3. The effect of chimney shape and turbine pressure drop on chimney inlet air velocity.



4. RESULTS AND ANALYSIS

When the solar radiation is absorbed by the energy storagelayer, the temperature of the energy storage layer will in-crease, with solar energy being stored as thermal energy.This stored thermal energy will be divided into three parts,one part is used to heat the air inside the collector, part ofwhich will ultimately transform to electricity; one part isstored for the system night-running, leaving the rest trans-ferring to the deep underground as heat loss. Detailed de-scription can also be seen in related references [3,6](Figure 1).

4.1. Comparison based on equal chimneybottom section area

As shown in Table I, Case 1 mainly focuses on how thechimney configuration affects system performanceparameters under the circumstances of equal chimneybottom section area. With the bottom diameter remaining80m, five cases, namely, the chimney top diameter being

40m, 60m, 80m, 100m and 120m respectively, are tobe analyzed. Among them, the first two are conicalchimneys, while the last two are divergent ones. Topdiameter being 40m or 120m, the field angle of an800m-high chimney is 2.86�, which is still within ourcapacity. With the solar radiation energy being 500W/m2

and the ambient temperature being 293K, the calculationsare carried out, whose results are shown in Figure 2 toFigure 5.

The driving force of a SC comes from the differencebetween air density of the outside air and the air insidethe chimney, which will be enlarged with the increaseof chimney height. For a certain SC being given collec-tor and chimney geometric parameters, the volume flowrate and air temperature increase can be obtained ifboundary conditions are given as shown in Table II.Maximum volume flow rate, minimum air temperature in-crease and buoyancy are obtained if the pressure dropacross the turbine is set at 0 Pa. An increase of turbinepressure drop will result in a higher air temperature, greaterbuoyancy and lower flow rate.

0 200 400 600 800 10000.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6


Chimney b, t diameters80 to 40m80 to 60m80 to 80m80 to 100m80 to 120m

Eff

icie

ncy

/

Figure 5. The effect of chimney shape and turbine pressure drop on system efficiency.

0 200 400 600 800 1000

0

2

4

6

8

10

12

14

Out

put

pow

er /M

W


Chimney b, t diameters 80 to 40m 80 to 60m 80 to 80m 80 to 100m 80 to 120m

Figure 4. The effect of chimney shape and turbine pressure drop on system output power.



It is clear that chimney configurations also have an ef-fect on the thermal performance of SCs. The impacts ofchimney configurations on its outlet air temperature and in-let air velocity are respectively illustrated in Figure 2 andFigure 3. It can be seen that with the growth of turbinepressure drop, the outlet air temperature climbs while theinlet air velocity slowly decreases, since growing pressuredrop lessens the air flow driving force and velocity, thus in-creasing the air temperature. Besides, based on a givenpressure drop, the outlet air temperature lowers and the in-let air velocity goes up as the top diameter of the chimneyincreases, but the variation becomes insignificant when thediameter is larger than 80m. Pressure drop being above800Pa, cylindrical and divergent chimneys are nearly thesame in outlet air temperature and inlet air velocity.

The influences of different chimney configurations onsystem output power and efficiency are demonstrated inFigure 4 and Figure 5. It could be seen from Figure 4 that,when the chimney top diameter remains unchanged, theoutput power first goes up before going down with an in-creasing turbine pressure drop, and it is positively

correlated with the diameter variation of the chimney topbased on a given pressure drop. When the diameter is lessthan 80m, its growth brings about obvious increment inoutput power which changes insignificantly as the diameteris larger than 80m. We may come to the conclusion that itis unwise to choose the conical chimney for its relativelysmaller output power. In addition, it is worth mentioningthat a larger diameter lessens the pressure drop neededfor driving the output power to hit its peak value. Whilean insignificant decrease in air flow velocity caused bythe increase of a relatively small turbine pressure dropraises the production of the volume rate of air flow andthe pressure drop, a bigger turbine pressure drop wouldgreatly influence the air velocity, thus lowering the outputpower.

Figure 5 shows that when the chimney top diameterremains a constant, the system efficiency rises with the in-creasing turbine pressure drop, and when the turbine pres-sure drop is given, it goes up with the increasing diameteras well. Just the same as the output power, as the diameteris larger than 80m, the efficiency varies insignificantly

0 200 400 600 800 100020

30

40

50

60

70

Chimney b, t diameters100 to 60m90 to 70m80 to 80m70 to 90m60 to 100mC

him

ney

outl

et a

ir t

empe

ratu

re /°

C


Figure 6. The effect of chimney shape and turbine pressure drop on chimney outlet air temperature.

0 200 400 600 800 10000

3

6

9

12

15

18

Chi

mne

y in

tlet

air

vel

ocit

y /(

m/s

)



Figure 7. The effect of chimney shape and turbine pressure drop on chimney inlet air velocity.



with the change of chimney top diameter. In terms of theSC system, the divergent chimney will lead to a significantincrease in costs with only a small increment in system out-put power and efficiency as shown in Figure 4 and Figure 5.Therefore, it is proved to be unnecessary.

4.2. Comparison based on equal chimneysurface area

As shown in Table I, Case 2 mainly analyzes, assumingequal chimney surface area, how different chimney config-urations influence system performance parameters. Thechimneys’ average diameter remains 80m. Choosing fivetypes of chimneys whose diameter variation spans frombottom to top are 100–60m, 90–70m, 80–80m, 70–90mand 60–100m; the calculations are conducted with the so-lar radiation energy being 500W/m2 and the ambient tem-perature being 293K, whose results are shown in Figure 6to Figure 9. The comparisons are made between chimneysof the same chimney surface area, as the costs of the

chimneys are in proportion to their chimney surface area[3,11]. It follows that the divergent chimney may costmore than the conical one, and it would be appropriate tochoose the former one if its output power and efficiencycould be improved.

The effects of the chimney top diameter and turbinepressure drop on the chimney outlet air temperature and in-let air velocity are shown in Figure 6 and Figure 7. Asmentioned before, as turbine pressure drop increases, theoutlet air temperature climbs while the inlet air velocitygradually falls. Besides this, for a given turbine pressuredrop, the outlet air temperature of the cylindrical chimneyis the lowest while the inlet air velocity decreases as thechimney bottom diameter becomes larger. Figure 8 andFigure 9 respectively describe the impact of chimney con-figuration and turbine pressure drop on system outputpower and efficiency. It could be seen that, in terms of sys-tem output power and efficiency, the cylindrical chimneywould be the best choice among all the three, as it hasthe smallest total flow resistance and the largest mass flow

0 200 400 600 800 10000.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6



Eff

icie

ncy

/

Figure 9. The effect of chimney shape and turbine pressure drop on system efficiency.

0 200 400 600 800 1000

0

2

4

6

8

10

12

14

Out

put

pow

er /M

W



Figure 8. The effect of chimney shape and turbine pressure drop on system output power.



rate, thus reaching the optimum value of output power andefficiency. To conclude, it would be best to use cylindricalchimney in the SC system.

4.3. The influence of the chimneyslenderness ratio, H/D

In order to determine the details of the chimney config-uration, the influence of H/D of the chimney is ana-lyzed in this part. As shown in Case 3 of Table I,comparisons were made between cylindrical chimneys ofdifferent H/Ds by changing their diameters (60m–160m).The calculations were carried out with the solar radiationenergy being 600W/ m2 and the ambient temperature be-ing 293K, and the results are shown in Figure 10 toFigure 13.

Figure 10 and Figure 11 illustrate how the chimney di-ameter and turbine pressure drop affect the chimney outletair temperature and chimney inlet air velocity, showing thechimney diameter remaining a constant. The chimney out-let air temperature continuously increases while the inlet

air velocity takes on a reverse changing trend as the turbinepressure drop grows. As for an invariable turbine pressuredrop, a longer chimney diameter (a smaller H/D) gives riseto a lower outlet air temperature and a smaller inlet air veloc-ity. However, the decreases of the temperature and velocitygradually slow down and become really unnoticeable untilthe diameter reaches 120m.

Figure 12 and Figure 13 describe how chimney diameterand turbine pressure drop affect the system output power andefficiency, illustrating that the chimney diameter’s growthwithin 100m brings about a noticeable increment in outputpower and efficiency while its rise only leads to tiny changein output power and efficiency when it is beyond 100m.Therefore, we can see from these two figures that it wouldbe best to use chimney with H/D within 6–8 in the SC sys-tem. The chimney would be 120–170m in diameter if it is1000m high, which is fully consistent with Schlaich’s design[6], and also with Petrorius findings [35] that the optimumslenderness ratio in terms of output power is around 5 or 6,smaller H/D increasing the risk for the plant to experiencecold air inflow.

0 200 400 600 800 100010

20

30

40

50

60

70

Chi

mne

y ou

tlet

air

tem

pera

ture

/°C

Turbine pressure drop (Pa)

Chimney slenderness ratioH/D=10H/D=7.5H/D=6.0H/D=5.0H/D=4.29H/D=3.75

Figure 10. The effect of chimney slenderness ratio on chimney outlet air temperature.

0 200 400 600 800 10000

2

4

6

8

10

12

14

16Chimney slenderness ratio

H/D=10 H/D=7.5 H/D=6.0 H/D=5.0 H/D=4.29 H/D=3.75

Chi

mne

y in

let

air

velo

city

/(m

/s)

Turbine pressure drop (Pa)

Figure 11. The effect of chimney slenderness ratio on chimney inlet air velocity.



It should be pointed out that, comparing Figure 12 withFigures 4 and 8, the variation of output power with turbinepressure drop is not in the same way. This is because thecombination of collector radius and chimney height can af-fect the total pressure potential of the system. Higher chim-ney can result in larger driving force, but less collector areawill not make the air temperature increase to a certainvalue with a given solar radiation, so the system outputpower decreases rapidly when the turbine pressure drop in-crease to some extent.

The following analysis will concentrate on the effect ofthe chimney slenderness ratio H/D and solar radiation onsystem performance. With the geometric parametersshown in Case 3 of Table I, we carried out a study on thecorresponding variation of performance parameters whenglobal solar radiation changes from 200W/m2 to 1000W/m2.The influence of chimney H/D and solar radiation on sys-tem output power and efficiency could be worked out (asshown in Figure 14 and Figure 15), with the turbine pres-sure drop remaining 400Pa. From these figures, it can be

seen that output power increases and system efficiencydecreases with increasing solar radiation, the reason ofwhich can be found in former research work [18,20]. Fur-thermore, the figures also show that, when the chimney di-ameter is within 100m (H/D>6), the output power andefficiency increase significantly as the diameter rises, butthey change insignificantly with a diameter beyond 100m. This further increase in diameter would only lead to ahigher cost. Therefore, on the premise of a comprehensiveconsideration of the chimney construction costs, an opti-mized chimney diameter for a certain chimney height canbe achieved according to the above results.

5. CONCLUSION

The chimney is a key part in providing driving forcefor the SC system, and an appropriate configurationdesign would in a way lower the total system con-struction costs. The steady state numerical simulation

0 200 400 600 800 10000.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6


Eff

cien

cy /


Figure 13. The effect of chimney slenderness ratio on system efficiency.

0 200 400 600 800 1000

0

2

4

6

8

10

12


Out

put

pow

er /M

W


Figure 12. Comparison of system output power.



based on two-dimensional assumptions is carried out in thispaper, with the intention of analyzing how chimney configu-ration influences the SC system characteristic parameterssuch as output power and efficiency, the steady state numer-ical simulation based on two-dimensional assumptions iscarried out in this paper. According to the numerical simula-tion results, both the divergent chimney and the conicalchimney are not recommended to be used in the system.The former one, though to some degree improves the systemefficiency and output power, also causes increases in con-struction costs as well, and for the conical one, both the effi-ciency and output power decrease greatly. Therefore, after anoverall analysis of the configuration’s influence on systemoutput power and efficiency, it would be best to use the cylin-drical chimney, whose optimum H/D value could be chosenfrom 6 to 8 in actual construction.

NOMENCLATURE

D = Chimney diameter (m)u = Average velocitymagnitude in the axial direction (m/s)r = Co-ordinate in radial direction (m)T = Temperature (K)T0 = Temperature of the environment (K)g = Gravity, g=9.807 (m/s2)Pr = Prandtl number (dimensionless),Pr ¼ cpm

kX = Co-ordinate in axial direction (m)Sf = Source item

Greek symbols

Δ = Difference or increasev = Kinematic viscosity (m2/s)mt = Turbulent dynamic viscosity coefficient

200 400 600 800 10003

6

9

12

15

18

21

Chimney slenderness ratio

H/D=10H/D=7.5H/D=6.0H/D=5.0H/D=4.29H/D=3.75

Out

put

pow

er /M

W

Solar radiation /(W/m2)

Figure 14. The effect of chimney slenderness ratio and solar radiation on system output power.

2000.8

0.9

1.0

1.1

1.2

1.3

1.4

Chimney slenderness ratio

H/D=10H/D=7.5H/D=6.0H/D=5.0H/D=4.29H/D=3.75

Eff

icie

ncy

/

Solar radiation / (W/m2)1000800600400

Figure 15. The effect of chimney slenderness ratio and solar radiation on system efficiency.



m = Dynamic viscosity (kg/(m�s))b = Coefficient of cubic expansionr = Density (kg/m3)k = Turbulent kinetic energy (J/kg)e = Dissipation (W/kg)se = Prandtl number of dissipationsT = Prandtl number of turbulencesk = Prandtl number of pulse kinetic energy 1.0Γf = Generalized diffusion coefficient

Subscript

b = Chimney bottome = Environmentt = Viscous dissipation effect caused by turbulent

characteristicse = Dissipationk = Kinetic energyf = Porosityt = Chimney topT = Turbulent flow

ACKNOWLEDGEMENT

This work was supported by the National Key R&DProgram of China (Grant No. G2007CB206903) andthe National Natural Science Foundation of China(Grant No. 51036003, 50721005).

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