Physics, computer simulation and optimization of thermo-fluidmechanical processes of solar updraft power plants

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Solar Energy 98 (2013) 2–11 www.elsevier.com/locate/solener

Physics, computer simulation and optimization of thermo-fluidmechanical processes of solar updraft power plants Wilfried B. Kra¨tzig ⇑ Kra¨tzig & Partner Consultants, Buscheyplatz 9-13, D-44801 Bochum, Germany Available online 2 April 2013 Communicated by: Associate Editor Yogi Goswami

Abstract Solar updraft power plants (SUPPs) form a very modern and rather efficient solar power technology. SUPPs consist of the glass-covered collector area (CA), in its centre the solar chimney (SC), and around the SC’s perimeter the power conversion unit (PCU). To evaluate the power/energy harvest of such plants, computer simulations comprise all physical processes in the mentioned plant components. For this purpose the thermo-fluiddynamics is described and formulated. An important aspect is the modeling of the transformation of the solar irradiation into heat-flux of the collector airflow, requiring the combination of different physical fields, such as thermodynamics, fluidmechanics and radiation-physics. All this leads to a highly nonlinear process description for the SUPPs’ power harvests, for which solution fast computer algorithms are developed. In the course of the treatment, typical process variables of SUPPs are explained, and computed results for investigated plants demonstrate the capability of the derived software and the efficiency of SUPPs. The suitability of solar updraft power technology for arid zones in the world is finally detailed by example of two especially optimized SUPP-families. Ó 2013 Published by Elsevier Ltd. Keywords: Solar updraft power generation; Multi-physics simulation; Thermo-fluiddynamics; Low-concentrated solar thermal power; Solar power plant optimization

1. Introduction Solar updraft power plants (SUPPs) like in Fig. 1 are modern and rather efficient generation techniques for electricity from solar irradiation. To receive high power/energy harvests, they require large areas of unused desert, high solar chimneys, and highest possible solar irradiation. The latter is available in many inner-continental countries of the globe between the two tropics. The general working principle of a SUPP like in Fig. 1 will be elucidated as follows: Such plant, schematically shown in Fig. 2, essentially consists of the collector area (CA), the turbo-generators as power conversion units (PCUs), and the solar chimney (SC). In the CA, a large glass-covered area like a greenhouse, solar irradiation heats the ground absorber. From there, emitted convective heat ⇑ Tel.: +49 234 7099444; fax: +49 234 7099419.

E-mail address: [email protected] 0038-092X/$ - see front matter Ó 2013 Published by Elsevier Ltd. http://dx.doi.org/10.1016/j.solener.2013.02.017

warms up the air inside the collector, which expands, and streams towards the elevated centre of the CA. There in the PCUs, parts of the kinetic energy of the warm airflow are transformed into electric power. Source of this kinetic energy is the buoyancy of the warm air in the SC, the plant’s engine, creating a pressure sink at the PCUs’ outlets. This updraft-process draws permanently fresh air into the collector from the CA’s rim, creating a continuous flow of air through the power plant. Obviously, SUPPs are wind power generators (Backstro¨m et al., 2008) which produce their required wind flow themselves by use of thermal conversion of solar irradiation (Schlaich et al., 2005; Schlaich, 1995). Such artificial wind flow is available at least as long as the sun shines. Thus the purpose of the glass roof over the CA is to allow a maximum of solar irradiation passing through the glass, heating up the absorber – in the simplest case the ground – to highest possible temperatures. From the heated absorber, the internal airflow then is warmed up. Thus a second

W.B. Kra¨tzig / Solar Energy 98 (2013) 2–11

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Nomenclature solar irradiance (W/m2) air velocities in collector, chimney and turbine (m/s) p air pressures in collector, chimney and turbine (N/m2) q_ i , Q_ i total specific heat flux in collector element i (W) Dq_ i , DQ_ i heat flux increase in collector element i (W) DTi temperature increase of the airflow in element i (K) cp specific heat capacity of the air (J/kg K) T0 environmental temperature (K) G u

Fig. 1. Computer vision of SUPPs with 1000 m high solar chimneys.

purpose of the collector glass roof is to prevent convective and (IR) radiation losses of the heat flux of the internal airflow, escaping into the outer ambience. From these few words the reader may be convinced that any optimization of such solar collector requires modern high-tech glass technology. SUPPs are designed for best efficiencies in locations with annual solar irradiation above 2.00 MW h/m2 a, occurring

m_ mass flow rate of air through SUPP (kg/s) efficiency of collector ring-element DAcoll. ai qo ðhÞ, qi ðhÞ mass density of the air outside and inside SUPP (kg/m3) g gravitational acceleration (m/s2) R general gas constant for air (J/kg K) Ti absolute temperature (K) qc, qr heat transfers due to convection/radiation (W/ m 2) r = 5.6697  108 Stefan–Boltzmann constant (W/ m 2 K 4)

between the two tropics of the globe. But also European countries around the north rim of the Mediterranean Sea with annual irradiation of 1.95 MW h/m2 a offer fair locations. Slightly simplified, the efficiency of a SUPP depends on the solar irradiation, the size of the CA (air temperature) and on the height of the SC (air buoyancy). For example, a SUPP like in Fig. 1 with CA diameter of 6000 m and SC height of 1000 m in a Mena-location is simulated to deliver a maximum electric power of 250 MWp, on midsummer noon, and an annual energy output of 650 GW h/a. The present paper will translate the complicated physics of the above described, highly nonlinear processes into a fast computer algorithm for plant designs. Therefore it will begin with a mathematical modeling of the thermo-fluiddynamics of the entire plant, supplemented by the physics of the radiation/heat convection transfer processes. It further will present some typical computer simulated SUPP properties. Finally it offers evaluated estimates for the harvested electric energy and their generation costs. In anticipation of these results, Fig. 3 demonstrates for a solar updraft power plant typical power curves over solar days. One clearly can observe there the influence of the

Fig. 2. General working principle of a SUPP.

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W.B. Kra¨tzig / Solar Energy 98 (2013) 2–11 Power generation Pel [MW] 80 70 July

60 50 40 October

30 20 December

10 00:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 24:00

Solar time over day Fig. 3. Generated power Pel for typical months July–December, 750/3500-plant.

sunshine duration. But it also becomes clear that solar updraft power plants possess a natural storage component, by which electricity can be produced during night times. 2. Thermo-fluidmechanical processes of the plant 2.1. Pre-requisites of the plant model The following SUPP computer-model is based on onedimensional flow-tube theory. Thereby we prosecute a mass of air on its way through the collector, the turbines, and up the chimney. In this model, Eulerian description is applied with following assumptions:  The collector bottom is horizontal with equal ambient air pressure everywhere.  All thermo-fluiddynamics is modeled as onedimensional.  Air is assumed as an ideal gas due to Eq. (2.6).  The model is approximated as stationary, and the final computer program is applied in intervals of 1 h equivalent to the usual solar irradiation input data.  The collector glass roof may consist of single or of double glass panels.  The absorber can consist of black-colored soil or of water-filled heat reservoirs.

Fig. 4. Discretized collector ring element i.

from the chimney axis, and hi, hi+1 stand for the respective collector heights (Bottenbruch and Kra¨tzig, 2010). The thermo-fluidmechanical processes in the collector are then described by the following basic conditions: Conservation of mass m_ ¼ const:; Conservation of momentum _ i  mu _ iþ1 þ pi Acoll:i  piþ1 Acoll:iþ1 mu þ supporting actions ¼ 0;

In Fig. 4 we consider a one-dimensional collector ringelement with a characteristic finite volume of air at a certain time instant. Its length consists of a collector ring with ground/top surfaces DAcoll:i ¼ pðr2iþ1  r2i Þ. The nodal points i, i + 1 describe cross-sections Ai = 2prihi, Ai+1 = 2pri+1hi+1 of the airflow, in which ri, ri+1 denote distances

ð2:2Þ

Conservation of energy _ p DT i : Q_ i ¼ mc

2.2. Collector model

ð2:1Þ

ð2:3Þ

In these conditions, m_ abbreviates the mass flow rate of air (kg/s) through the plant, u the air velocity (m/s), p the pressure in the airflow (N/m2), Q_ i the total specific heat flux (W), and DT i the temperature increase of the airflow (K). cp abbreviates the specific heat capacity of the air (J/kg K). The solar irradiation G (W/m2) is coupled with the total amount of heat power Q_ i in the collector by the following relations:

W.B. Kra¨tzig / Solar Energy 98 (2013) 2–11

DQ_ i ¼ ai GDAcoll:i ; ) Q_ i ¼ Ri DQ_ i

ð2:4Þ

in which ai denotes the efficiency of the collector ring DAcoll.i in transforming solar irradiance G into heat increase of the collector airflow. This parameter ai will in the final computer program serve as interface between the problem of solar heating of the collector air flux in the CA elements and the description of the airflow through the entire plant. It will be determined successively and iteratively for each DAcoll.i, as described in Section 3. Bernoulli’s equation for two different locations i, i + 1 pi þ 0:5qi u2i ¼ piþ1 þ 0:5qiþ1 u2iþ1

ð2:5Þ

is applied to connect the ambient pressure and velocity of the plant outside the collector rim with its interior values. Assuming air as an ideal gas, we have with the gas law qi ¼ pi =RT i ;

ð2:6Þ

R as general gas constant (J/kg K) and Ti as absolute temperature (K), a relation which couples the fluidmechanical equations (Eqs. (2.1), (2.2), and (2.5)) with the thermodynamic conditions (Eqs. (2.3) and (2.4)).

gas Eq. (2.6), and DT approximated as constant over h, we solve Eq. (2.8) over tower height H analytically and gain: Dpmax ¼ gq0 H DT =ðT 0 þ DT Þ:

All previous conditions (Eq. (2.1)) till (Eq. (2.6)) formulate a nonlinear initial value problem, for its solution they have to be integrated numerically over the collector distance r starting at the collector rim. At the turbines’ outlets the air velocity uturb (or pressure pturb) has to be coupled to that one in the chimney foot. These quantities in general are evaluated from an initial value problem of the solar chimney. But because we are interested in computing speed, we apply for coupling an analytical solution of the chimney flow (Schindelin, 2002). So as in Section 2.2 we collect all necessary conditions for the chimney model: Conservation of mass m_ ¼ const:;

ð2:7Þ

Conservation of momentum: The SC transforms the _ gathered in the collector by heat of the air mass flow m, the solar irradiation, with its final temperature increase DTturb and pressure pturb into kinetic energy, using the difference in air density, the buoyancy, as driving force: Z H Dp ¼ g fqo ðhÞ  qi ðhÞgdh: ð2:8Þ 0

Herein qo ðhÞ and qi ðhÞ (kg/m3) stand for the heightdepending mass density of the air outside (index: o) and inside (index: i) the chimney, g for the gravitational acceleration (m/s2). Obviously, both density-profiles qo ðhÞ, qi ðhÞ influence the chimney’s buoyancy. With the barometric pressure dependence on height, a so-called standard atmosphere in meteorology, air again assumed as an ideal

ð2:9Þ

The 0-indexed quantities herein hold for the plant’s ambience at chimney foot. Bernoulli’s equation then delivers from Eq. (2.9) the important formula for the maximum air velocity at the chimney’s entrance: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi umax ¼ 2gH DT =ðT 0 þ DT Þ ð2:10Þ Conservation of energy: In a SUPP, (thermal) energy is only used to heat the airflow, e.g. to generate the buoyancy in the chimney. Since the airflow is not harvested energetically, we relinquish this sub-topic in the following. 2.4. Turbine model For our thermo-fluidmechanical SUPP model, the essential global physical process equations in the turbines are described as follows: Conservation of mass m_ ¼ const:;

2.3. Chimney model

5

ð2:11Þ

Conservation of momentum: This condition will be substituted by Bernoulli’s equation, applied to the airflow in the turbine: 1 Dpturb þ qu2turb ¼ Dptot : 2

ð2:12Þ

Turbine-engineers evaluate from here, and from details of the turbine’s design, with the pressure withdrawal factor j and by use of the maximum airflow velocity umax from Eq. (2.10), the following relation: pffiffiffiffiffiffiffiffiffiffiffi Dpturb ¼ jDptot : uturb ¼ 1  jumax : ð2:13Þ Herein Dpturb and uturb stand for average values of the pressure jump and the air velocity in the turbine, respectively. We stress, that Dpturb is not restricted by the Betz power limit, since SUPP turbines are ducted and not subject to open flows. Due to (Gannon and Backstro¨m, 2003) they can achieve turbo-generator efficiencies gturb of over 80%. Finally, from the total power of the maximum possible air flow Ptot = m_ u2max =2 of the SUPP, the harvested effective electric power Pel eff is found by multiplying Ptot with gturb and j: _ 2max =2: _ P el eff ¼ gturb Dpturb m=q ¼ gturb jmu

ð2:14Þ

2.5. Flow losses in the collector and in the chimney To offer the reader a clear overview over the applied concept, all conditions here have been derived without consideration of losses due to flow resistances in the collector and in the chimney, and due to bends of the air flow, which reduce the flow pressures, the flow velocities, and so the total efficiency of the SUPP. They all are considered by

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W.B. Kra¨tzig / Solar Energy 98 (2013) 2–11

identical concepts as applied in the design of industrial piping systems, see e.g. (Ka¨mmer, 2005), and the caused pressure differences are subtracted during the course of the analysis from the loss-free quantities.

exist manifold exchanges of convective/radiation heat power, which all have to be considered in the heat power balance conditions of such a plant simulation (Duffie and Beckman, 2006). Bases of all this are the convective heat power transfers (qc)

2.6. Simulation of the nonlinear thermal-fluidal plant behavior

qci ¼ hci T i

ð3:1Þ

with the heat transfer coefficients hci from one collector element i of absolute temperature Ti to another, and the radiation heat transfers (qr) due to Planck’s radiation law. These radiation transfers e.g. read between two parallel plates (Duffie and Beckman, 2006)

If we overlook Section 2, we find in Sections 2.2, 2.3 and 2.4 the fluid-thermodynamic governing equations of all plant elements, namely collector, chimney and turbogenerators. From them a nonlinear initial value problem NLIVP in the mass flow of air m_ through the complete SUPP is formulated, nonlinear, because of the nonlinear gas law Eq. (2.6), and because of the nonlinear coupling with Eqs. (2.9) and (2.10). Its solution requires the element-wise knowledge of the still unknown collector efficiencies ai introduced by Eq. (2.4). Obviously, up to now the above initial value problem does not contain explicit details of the collector/roof/absorber-construction. But clearly the thermal-radiation-transfers of the solar irradiation G into heat flux Q_ of the collector airflow will be decisively influenced by all those construction details of the collector.

qr1 ¼ qr2 ¼

Qr rðT 42  T 41 Þ ¼ 1=e1 þ 1=e2  1 A

or between one plate and the sky qr1 ¼ erðT 41  T 4sky Þ

ð3:3Þ

Herein; the e-values abbreviate optical emittances of opaque bodies, T always absolute temperatures and r the Stefan–Boltzmann constant equal to 5.6697  108 (W/ m2 K4). Values for emittances e can be found again in (Duffie and Beckman, 2006), convective heat transfer coefficients hc in the standard literature. To introduce the reader into the formulation of the heat power balance conditions of a collector ring-element we select due to Fig. 5 the simplest collector construction, consisting of one panel of glass (Temperature: T1), the heated air-flow (T2) and the soil absorber (T3). For this model the following thermal transfers q, all depending on their respective temperatures, have to be distinguished (Bottenbruch and Kra¨tzig, 2010):

3. Convective/radiation heat power transfers in the collector 3.1. Power balance conditions of the collector This collector construction is the most important component of a SUPP because of the convective/radiation heat power transfers from the solar irradiation into the heat flux of the airflow, here expressed by the efficiencies ai. In order to determine these ai, the physical transformation process of solar irradiation G into heat increase DT of the air flux m_ has to be modeled. At this point the collector design comes into play, because in its components – single or double glass panels, airflow, water heat storage, soil absorber –

 qrou gl thermal transfer by radiation (qr) from outer air (ou) into glass sheet (gl),  qrgl ou thermal transfer by radiation from glass sheet into outer air,

sisu gl qrgl ou

qrou gl

qcou gl

qcgl ou

Glass T1 qrgl so

qrso gl

qcgl in

qcin gl

qcin so

qcso in

εgl sisu gl Air T2 εgl αso sisu gl qrgl so

qrso gl

ð3:2Þ

Soil T3 qcso so Fig. 5. Scheme of the heat transfers of a glass/air/soil collector.

W.B. Kra¨tzig / Solar Energy 98 (2013) 2–11

 qrgl so thermal transfer by radiation from glass sheet into soil,  qrso gl thermal transfer by radiation from soil into glass sheet,  qcou gl thermal transfer by convection (qc) from outer air (oa) into glass (gl),  qcgl ou thermal transfer by convection from glass sheet into outer air,  qcgl in thermal transfer by convection from glass sheet into inner air,  qcin gl thermal transfer by convection from inner air into glass sheet,  qcin so thermal transfer by convection from inner air into soil absorber,  qcso in thermal transfer by convection from soil absorber into inner air,  qcso so thermal transfer by convection from absorber surface into inner soil,  sisu gl solar irradiation from the sun into glass sheet (=G). Assuming a stationary process, the total heat transfers into the glass, the inner air flow, and the soil absorber have to vanish. The convective heat transfers into the inner air flow, related to the total solar irradiation G, determine the desired efficiencies ai: Glass: qrou gl  qrgl ou  qrgl so þ qrso gl þ qcou gl  qcgl ou  qcgl in þ qcin gl þ ð1  egl Þsisu gl ¼ 0; Air: qcgl in  qcin gl þ qcso in  qcin so ¼ ai sisu gl ;

ð3:4Þ

Soil: qrgl so  qrso gl þ qcin so  qcso in  qcso so þ egl aso sisu gl ¼ 0: Herein aso denotes the broadband absorptance of the soil absorber (Pretorius, 2007). In this most simple collector construction we get with the first and last equations (Eq. (3.4)) two coupled algebraic conditions, depending on 4th (qr) and 1st (qc) powers of temperatures T1, T2 and T3. The third coupled algebraic equation of (Eq. (3.4)) contains only convective terms, and thus depends only on 1st powers of temperatures. It is written in such a way, that the heat flux increase Dq_ i ¼ ai sisu gl

ð3:5Þ

into the air of the ith collector ring element is expressed directly by the efficiency ai. The strongly nonlinear heat power balance conditions (Eq. (3.4)) have to be solved for all collector ring elements DAcoll.i, simultaneously with the analysis of the NLIVP for the entire SUPP: a considerable computing effort. For more complicated collector constructions (double glazing, water-filled heat reservoirs, double air compartments), the number of heat power balance conditions increases

7

strongly leading to an enormous computing effort (Backstro¨m et al., 2008; Bernardes, 2004; Pastohr, 2004). 3.2. Simulation of the entire plant behavior The derived equations require – because of their multiple nonlinearities – incremental-iterative solution strategies, which should work fast and lead to stable results. For this we start with the mentioned fluid-thermodynamic NLIVP of the Eqs. (2.1)–(2.14) for the mass flow _ see Section 2.6. Given G and T0 we select a starrate m, ter set of collector efficiencies ai > 0, one value for each ring-element i, and evaluate the solution of the NLIVP. This solution leads to a first approximation of temperatures of the inner airflow in each collector element DAcoll.i, for the above example T2i. Transfer of these collector air temperatures into the nonlinear algebraic heat power balance conditions (Eq. (3.4)) of the respective collector elements results into a new approximation of the collector efficiencies ai. With this thus improved set of ai the solution of the NLIVP is repeated for a new set of air temperatures T2i. This iteration is repeated until the difference of two consecutive values of Pel eff remains below a given bound. The whole solution process is imbedded into Excel and based on the modulus Excel-Solver. This Excel-add-in was originally developed for the treatment of optimization problems, and works on an incremental concept. Because it contains Newton–Raphson-procedures and gradient-methods, it is excellently suited for highly nonlinear simulation. This described procedure led to an extremely fast algorithm for the entire SUPP simulation, basis of the following numerical studies (Harte et al., 2012; Kra¨tzig et al., 2009). One should add here, that for simulations over 24 h per day a similar simulation concept for the night-service of the SUPP has to be supplemented, which applies the same basic equations, and will not detailed here. 4. The heat exchange process in the collector The SC is the power source of a SUPP. In order to achieve a maximum of buoyancy therein, it has to be fed from the collector with airflow of highest possible temperature increase DT at the turbines’ exits. Thus from a designer’s point of view, the most decisive plant component is the collector as heater of the inner airflow. For this purpose there exist different construction concepts to optimize this rather complicated heat exchange processes, described in Section 3 only for the simplest collector design. Some of such more complicated concepts shall now be elucidated by computed examples. Fig. 6 demonstrates this by virtue of a small SUPP with chimney height of 500 m, chimney diameter of 55.00 m in the throat, and collector diameter of 1500 m. The collector height starts with initial 5.00 m at the outer rim and increases to 12.00 m at the turbine house. The collector roof consists of double sheets of specially coated white

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W.B. Kra¨tzig / Solar Energy 98 (2013) 2–11

Temperature in °C

Position of turbo-generators

100.0 Surface of black soil absorber

80.0

60.0

Inner glass panel

Internal air flow

40.0 Outer glass panel

750 704 654

600

540

473

395

300

200

59

Distance from plant centre in m Fig. 6. Temperatures of glass panels, internal air and collector absorber.

glass, and the soil absorber is darkened by sprayed black concrete color. G = 1000 W/m2 of solar irradiation is assumed, and the ambient temperature is 25 °C. As one observes from Fig. 6, the outer glass panels increase their temperatures from 25 °C to 40 °C at the turbine house entrances. The inner glass panels are designed with 20 mm of insulating air layer, such that they get warmer, from 25 °C to 65 °C at the turbines. The hottest collector element clearly is the soil absorber which is directly heated from G up to 106 °C at the turbine house entry, a consequence of the assumed (nano-pigmented) blackening. Obviously, the collector is designed such that the internal air, the SUPP’s working medium, is heated from both sides: Mainly from below by the hot absorber, but also from above by the warmer inner glass sheets.

Temperature in °C

The main collector purpose, namely to transfer a maximum of solar heat onto the internal air flow, can be attained by different construction alternatives, e.g.:  Coated single glass panels with darkened soil absorber (Case 1).  Coated single glass panels with 20 cm of hermetically sealed heated water reservoirs located on black absorber (Case 2).  Most favorably coated double glass panels with darkened soil absorber (Case 3).  Most favorably coated double glass again with 20 cm heated water reservoirs over black absorber bottom (Case 4).

Position of turbo-generators

100.0 Case 3 Case 4

90.0

Case 2 Case 1

80.0

70.0

750 704 654

600

540

473

395

300

200

59

Distance from plant centre

Fig. 7. Temperature distributions of the absorber surface for different variants.

W.B. Kra¨tzig / Solar Energy 98 (2013) 2–11 Degree of efficiency

9

Position of turbo-generators

1.00 0.90 0.80 Case 4

0.70 Case 3

0.60 Case 2

0.50 Case 1

0.40 750

704

654

600

540

473

395

300

200

59

Distance from plant centre in m

Fig. 8. Degree of efficiency ai of transformation of solar irradiation into air flow heat.

The results of this optimization study are exemplarily given in Figs. 7 and 8. First from Fig. 7 we observe the different temperature distributions in the plant absorber, which can obviously reach or exceed temperatures of above 100 °C. Fig. 8 then plots the spatial distribution of the collector efficiencies ai of transforming solar irradiation G into heat flux of internal air, again for these four alternatives. As explained in Section 3, ai is the most important parameter for an efficient design of SUPPs: This function starts in all simulations with certain values at the collector rim, but decreases then because of the raising air temperature over collector distance r towards turbine’s entrances: Clearly, the warmer the internal airflow becomes, the lesser is the additional heat transfer. Obviously, double glazing seems more favorably than single panels, and closed water heat reservoirs increase the efficiency compared to simple soil absorbers (Schlaich, 1995). But before drawing premature economic conclusions, one should remember, that additional components require additional costs. Which solution finally turns out to be the best design requires detailed investigations of the complete SUPPs, evaluating the annual energy harvest and the required investments as well as maintenance/insurance costs. 5. Power generation, energy harvest, capital investment and LECs In the last decade, series of computer simulated optimizations for SUPPs have been carried out under the author’s guidance at Kra¨tzig & Partner Consultants, to optimize this power generation concept in many respects: chimney dimensions, collector sizes, glass properties of the collector roof, attributes of the soil absorber, investment conditions. All these simulations confirmed that the leveled electricity costs LECs (due to IEA-guidelines) of the harvested energy for SUPPs are considerable lower then for competitive renewable energy concepts, as will be sketched out in the following.

Reporting in detail on these optimization studies would take by far too many pages of this manuscript. Instead we will show here results for two smaller SUPP-families of 500 m and of 750 m of chimney height. A similar study for 1000 m chimney-SUPPs has recently been published in (Bergermann and Weinrebe, 2010), leading to similar results as ours. Both above mentioned investigated plant families have the following dimensions and properties: The chimney heights of the first plant family are all 500 m, their shell diameters/shell thicknesses range from 50 m/0.25 cm (top) over 45 m/25 cm (throat) to 90 m/40 cm (bottom). All chimney shells are stiffened by three external stiffening rings and an upper edge member. The outer collector diameters in the study vary from 1500 m to 2500 m; the collector heights start from 4.00 m at the outer rim increasing to 12.00 m at the power house entries. 16 turbo-generators of 9.00 m of diameter transform the kinetic power of the airflow into electricity. All chimney heights of the second plant family are 750 m, their shell diameters/shell thicknesses range from 75 m/0.28 cm (top) over 67.5 m/28 cm (throat) to 135 m/ 50 cm (bottom). Here the shells are stiffened by five external rings and an upper edge member. The outer collector diameters vary from 2500 m to 4000 m; the collector heights also start from 4.00 m at the outer rim increasing to 15.00 m. 16 turbo-generators of 14.00 m of diameter each deliver electric power. All collector roofs are covered with panels of double sheets of pure white glass from standard industrial production lines, 6 mm thick and mounted with 20 mm distance of airtight space. The light-transmittances are optimized such that sg out = 0.93 and sg int = 0.95. The outer faces of the external glass sheets resp. the inner faces of the internal glass sheets will be coated to prevent reflection of solar irradiance resp. to reflect IR-radiation. The soil absorber is again assumed to be artificially blackened by sprayed concrete color to achieve a broadband absorptance of asoil = 0.93.

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W.B. Kra¨tzig / Solar Energy 98 (2013) 2–11 Table 1 Optimization study for two SUPP families (G = 2.20 MW h/m2 a).

Fig. 9. Computer visualization of the 750 m solar chimney from the SUPP of Table 1.

The optimization study is carried out for annual solar irradiation of 2.20 GW h/m2 a, considering beam + diffuse radiation. For the cost estimates it is assumed that the (desert) collector areas are provided free of charges by the client. The plant site is assumed to be rather plane, such that it requires only insignificant leveling works. Table 1 summarizes the results of the studies by comparing those two plant configurations with the minimum LECs. For smaller or larger collectors the named LECs of 0.131 €/kW h resp. 0.099 €/kW h increase marginally. As expected, these production costs decrease with the size of the plant; they will further reduce for still larger plants, as has been confirmed by (Bergermann and Weinrebe, 2010). The previous Fig. 3 shows the electric power generated in the 750/3500-plant for (statistically) typical days of the last two quarters of a year, and Fig. 9 gives a computer artist’s impression of the SC. In meteorology, G generally is recorded in hourly intervals, so the computer simulation is also performed in hourly intervals, and the resulting values of Pel eff in Fig. 3 are connected linearly. This Figure clearly demonstrates the property of the SUPP-technology, namely to store solar energy in the absorber, and so to deliver electricity also during sun-free hours. This property can be extended, e.g. by (controlled) water storage devices due to (Haaf et al., 1983; Schlaich et al., 2005) or by a double-compartment collector as studied by (Pretorius, 2007; Pretorius and Kro¨ger, 2006). Both proposals act excellently in computer simulations, but require additional investments, and so may lead to higher LECs. 6. Summary and outlook Since Schlaich’s 1982 prototype SUPP in Manzanares there has been performed immense progress in many related technologies (Tingzhen et al., 2005; Zhou et al., 2007), like mathematical modeling, computer simulations, nonlinear coupled physical processes, wind engineering of tall structures and glass technology. This led to efficiency

500/ 2000

750/ 3500

Chimney height (m) Throat diameter of chimney (m) Top diameter of chimney (m) Outer collector diameter (m) Total annual energy harvest (GW h/a) Maximum electric power Pel max (MW)

500.00 45.00 50.00 2000.00 54.9 18.7

750.00 67.50 75.00 3500.00 219.4 75.0

Investments Chimney (M€) Double glazed collector (22.25 €/m2) (M€) Turbo-generators (0.65 M€/MW of Pel max) (M€) Additionals + Engineering + Tests (M€) Total investments (M€) Annuity including annual insurance (M€) Levelled electricity costs LECs (33 years) (€/kW h)

23.9 69.5 12.2 5.4 111.0 7.4 0.131

60.5 213.3 48.8 15.0 337.6 22.8 0.099

jumps for this type of power generation and to decrease of predicted production costs LECs, such that SUPPs presently represent that solar power technology with lowest estimated costs. What will bring the future for this concept? Presently electricity generating costs for concentrating solar power CSP lie close to 0.20 €/kW h (without heat storage tanks), and for large photovoltaic plants at 0.18 €/kW h, both in sun-spoilt areas. But even if further cost advantages of PV can be activated, solar updraft power generation seems to be far in advance. Anticipating scaling effects of plant sizes, electricity generating cost of around 0.08 €/kW h seem possible (Bergermann and Weinrebe, 2010), which will be identical to estimated classical fossil or nuclear source LECs in 2020. It is emphasized that the LECs in Table 1 are evaluated only for the first plant’s depreciation period of 33 years. After this period until termination of service life (>120 years), LECs will decrease to less than 0.02 €/kW h (few repairs, some substitutions and maintenance). Beyond that, a great advantage of SUPPs is the non-necessity of water for power production, neither for steam generation nor for steam re-condensation. However, some disadvantage of this low-concentrated solar thermal power technology is – like for all mirror technologies – the required cleaning of the collector glass after dust pollutions. Since glass areas are 4–6 times larger than for mirror plants, SUPP-technology will be especially suited for arid zones with scarce dust storms. References Backstro¨m, T.W.von, Harte, R., Ho¨ffer, R., Kra¨tzig, W.B., Kro¨ger, D.G., Niemann, H.-J., van Zijl, G.P., 2008. State and recent advances of solar chimney power plant technology. PowerTech 88–7, 64–71. Bergermann, R., Weinrebe, G., 2010. Realization and costs of solar updraft towers. In: Proceedings of the SCPT 2010 – Intern. Conf. Solar Chimney Power Technology. Ruhr-University, Bochum, pp. 63–68. Bernardes, M.A. dos Santos, 2004. Technische, o¨konomische und o¨kologische Analyse von Aufwindkraftwerken (Technical, economical

W.B. Kra¨tzig / Solar Energy 98 (2013) 2–11 and ecological analysis of solar updraft power plants). Dr.-Ing.-Thesis. Institut fu¨r Energiewirtschaft und Rationelle Energieanwendung, Univ. of Stuttgart. Bottenbruch H., Kra¨tzig W.B., 2010. Optimum design concepts for solar power plants. In: Proceedings of the SCPT 2010 – Intern. Conf. Solar Chimney Power Technology, Ruhr-University, Bochum, pp. 35– 42. Duffie, J.A., Beckman, W.A., 2006. Solar Engineering of Thermal Processes, third ed. John Wiley & Sons Inc., Hoboken, New Jersey. Gannon, A.J., Backstro¨m, T.W.von, 2003. Solar chimney turbine performance. ASME J. Solar Energy Eng. 125, 101–106. Haaf, W., Friedrich, K., Mayer, G., Schlaich, J., 1983. Solar chimneys. Int. J. Solar Energy, pp. 3–20. (and 1984, 141–161). Harte, R., Ho¨ffer, R., Kra¨tzig, W.B., Mark, P., Niemann, H.-J., 2012. Solare Aufwindkraftwerke: Ein Beitrag zur nachhaltigen und wirtschaftlichen Energieerzeugung (SUPPs: A structural engineering contribution for sustainable and economic power generation). Bautechnik, 89, pp. 173–181. Ka¨mmer, K., 2005. Calculation of cross sections of flues. In: CICIND Chimney Book, CICIND, Zu¨rich and Ratingen, pp. 57–77. Kra¨tzig, W.B., Harte, R., Montag, U., Woermann, R., 2009. From large natural draft cooling tower shells to chimneys of solar upwind power plants. In: Domingo, A., Lazaro, C., (Eds.), IASS Symposium on

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Evolutions and Trends in Design, Analysis and Construction of Shells. CD-Rom publication, Univ. of Valencia. Pastohr, H., 2004. Thermodynamische Modellierung eines Aufwindkraftwerks (Thermo-dynamic modeling of an updraft power plant). Dr.Ing.-Thesis. Bauhaus Univ. Weimar. Pretorius, J.P., 2007. Optimization and Control of a Large-Scale Solar Chimney Power Plant. PhD-thesis. Univ. of Stellenbosch. Pretorius, J.P., Kro¨ger, D.G., 2006. Solar chimney power plant performance. ASME J. Solar Energy Eng. 128, 302–311. Schindelin, H.W., 2002. Entwurf eines 1500 m hohen Turms eines SolarAufwindkraftwerks (Design of a 1500 m high tower of a SUPP). Diplom-Thesis. Univ. of Wuppertal. Schlaich, J., 1995. The Solar Chimney. In: Menges, A., (Ed.), Electricity from the Sun. Stuttgart. Schlaich, J., Bergermann, R., Schiel, W., Weinrebe, G., 2005. Design of commercial solar updraft tower systems. ASME J. Solar Energy Eng. 127, 117–124. Tingzhen, M., Wei, L., Guoliang, X., 2005. Analytical and numerical investigation of the solar chimney power plant. Int. J. Energy Res. 30, 861–873. Zhou, X.P., Yang, J.K., Xiao, B., Hou, G., 2007. Simulation of a pilot solar chimney thermal power generating equipment. Renew. Energy 32, 1637–1644.