Solar EnetAn indicative figure of a solar chimney Power Plant with a circular solar collector and aFloating Solar Chimney inclined due to externalt figure( 1)Solaswarm airIrradiationWindSolarAir turbinesBecause of its patented construction the FSC is a freter than airan tilt when external winds appear Low cost Floating Solar Chimneys up to 1000 m withBy this innovating Floating Solar Chimney Technology of heights of the FSCs up to100Omp to 1
2 of the arhorizontal solar radiation on the solar collector surfacrted to electricitey power plants, due to their similarity to hydro-electric owerTheir similarity is due to the following facts:The hydro-electric Pps oo falling water gravity, while the solar aero-electricdue to the up-draftingThe electricity generation units of hydro-electric PPs are water turbines engaged toerators while the generation units of solaThe energy produced by the hydro-electric PPs is proportional to the falling wateright while the energy produced by the solar aero-eleproportional todrafting height of warm air, which is equal to the heightThat is why Prof J Sclaigh in his book named the solar chimney technology potplants as the hydro-electric power plants of deserts
Floating Solar Chimney Technologyof air ately equal to 1005Dexaverage air speed at the top exit of the solar chimney uHAm of the previous eqbeen simplified (see Papageorgiou, 2004), leadingT4+W2 T4T+。=0Where the coefficients wnd ws are given by the relations=C2(1k),2=C2(2kn+C2T)2=(1-k)C2C3+127C=Cr·(1) ws=-nr T CIThe proper root of the previous polynomial equation is the temperature tg the previous relations to calculate Taste by the formuTost=T,+C?TThus the overall electricgiven by theP=rm-C
(T -Tne)=m- c, (T o-T , -C, T:-)final resultthat thedefine, through the previcrocedure,based on the thermodynamic cycle analysis, the electrical porosed thermodanalysis, though it looks more complicated than the analysisDG, it is an equivalent thermodynamic analysis that takes into consideration all necessarynd non negligible effects and parameters of the process in the SAElPPro>for Tos calculation is given by Shlaigh in his relative bookThetion relating the average exit solar collector air temperaturenput air temperature Tthe point of optimal operation of the SAEP can beta Ga= i Cp(Toe- T02)+B Ac(Ta-Ta)approximate thermal power losses coefficient of the Solar Collector (to thebient and ground) per m of its surface area0g-To2) An average value of B for double glazing solar collectors
Solar Enhe annual average horizontal irradiance on the surface of the solar collectoThe annual average solar horizontal irradiance Gay is given by the formulaWy/8760hours, where Wy is the annual horizontal irradiation of theof the SAEPP, (in KWh/m2)icient for solar irradiation) An average value of thcoefficient ta for a double glazing roof is,70d ac is the solar Collectors surfaceUsing in the equation an approximation for the function Toa(ri ) it gives(A+li Cp/Ac)]-TozWhere To2 isto ground thermal storage around the SolarThe inlet ambient air teas passing above it is increasing entering toThe proper value of B,olar collector thermal lohas been calculatedtransfer analysis of the solar collector An introductihis analysis isthe next paragraph The heat transfer analysis uses time Fourier series in order to taketo account the ground thermal storage phenomena during a daily cycle of operationThe instantaneous efficiency of the SAEP is given by the formulawhere acG is theer arriving on the horizontal solar collector surfacearea Ac and Pis the maximum generated electric power This efficiency is for a given valtof horizontal solar irradiance G
However we can prove that for an almost constant mahorizontal irradiance G are almost proportional, thus the previous formula is giving also theannual efficiency of the SAEP defined as thehe annual horizontal irradiation arriving on top of the roof of the greenhouse of thele let us consider that a saep has the follodimensions and constantsAc =10%m2(DD=1H=800m,d=40m,k=049,ae average(Gav 240W/m2) In following figure the effect of the G on the power output as function offlow of this saeIf the maximum(daily average during summer operation) Ga is 500 W/m2 the maximumpower output of this SAEP, achieved for im =-10000 Kg/sec is 5 MW Thus its efficiency isapproximately 1% Let us assume that the rated power output PR of a SAEP is the maximumpower output for the maximum average solar irradiance Asm power output point of operation(nim)is approximately the same fe
Floating Solar Chimney Technologyd-40m, Wy-200DKwNY sqm/yearThus if weontrol the operation of the SaEP to operate with the proflow, close to mm, we should achieve almost the possimum electric power outputby the SAEP for any horizontal solar irradiance This is referred to as an optimal operationrule of thumb we can state that my for optimal operation of the SAEPbecalculated approximately by the formula tit"po(n-d2/4), where air speed is o it isestimated to 7-8 m/sec, the air density is given by p=po/(287307 15)and d is the internalctric power output per annual average horizontal solar irradiahis can be done using the thermodynamic cycle analysis for variable mass flow i and gavGav"21000008760-240w/m2, of the previously defined SAEP, is 094 %(i
e 6% lower thanthe calculated efficiency of 1% for thverage horizontalof 500w/m2)42 Maximum exit warm air speed without air turbinesd of the solarselector plus the FSC alone (ie without the air turbines)can be calculatIn the previous set of equations we shouldthat n=O Thus
Solar EnetToa"Toe and To4"To If we consider that the kinetic losses are approximately equal tothe frictinand taking intothat the eqtderivedWhere AT=To3-To (we can approximatelyder that ToRTThus theop air speed in a free passage solar chimney(without air turbines)given by the formula2gH5he fsc of h=800m heordinary values for coefficients a=1 1058 and k=0 49 and ambient air temperature To=296
2K(23 C)as function of AT is given in the next figureE5品agaC due to the greenhouFig 10 Free air speed as a functioerature increaseapproximate formula AT ta Gli p/Ac) where ta07, Pa4, cp"1005, andm=p D(nd2/4)where p-117Kg/dd=40m Thus The approximate double glazingsolar collector area, generating the free up-drafting air speed u can be defined by AT, u andG by the equation A it p/(ta G)/AT-PI
Floating Solar Chimney TechnologyThe approximate solar collector area Ae as a function of the temperature increase AT foralues of equivalent horizontal solar irradiance G=250, 300, 350, 400 and 450 w/m2,shown in the following figureIH-800m, d-40m), up-drafting air temperaturetemperatureue to the greenhouseFig 11 The solar collector area as a function of its generating temperature increaseExample: for a solar collector of surface area Ac=400Ha (ie
400000m2), with a diameterDa715m feequivalent horizontal solar irradiation G of 250W/m?, the createdemperature difference AT is-1450C and the free up-drafting air speed D inside the FSC ofH=800m height and d=40m internal diameter will be -21m/sec, while for G=450W/m2, AT2250C and uFor one dimensional analysis al and if the friction losses are negligible, i, e k-D, we ha(17)ng warm air top speedd free friction FSCdue to its buoyancy, is similar to free falling water speed due to/2-g43 The thernthe previous thermodynamic cycle analysis of the SAEP we should calculateair temperature Toa at the entrance of the air turbine or at the exit of the solcollector The calculation of this average temperature can be done by using the previouslyproposed approximate analysis However the temperaturearying auringIn order for the dabe calculated and consequently the electric power dailyiation using the previously proposed thermodynamic cycle analysis, we should make
Solar Enetof daily horizontal irradiance profile and ambient temperature daily profileThe SAEP heat transfer model with a circular collector is shown in the indicative diagram offigThe circular solar collector of this saep is divided into a series of m circular sectors ofwidth Ar as shown in the next figurethis figure the cut ofr sector of the solar collector of the saep is shown with thesfer coefficients of the process (radiatieground (Ts), moving air (T), inner curtain (Tc), outer glazing(Tw), ambient air (To) andIsk) Thed absorbs a part of the transmitted irradiation power due to the horolar irradiance(ta GThe wind is moving with a speed Dw and on the ground it is a thin sheet of water inside adark plastic film The ground is characterized by its density pgr, its specific heat capacity cgrand its thermal conductivityHorizontal solar irradiancyh,CoVerTT-J+TheHeeta GhWatertheight dh)Fig
12 The cut of a circular sector of a double glazing circular solar collectorcollector diameter and Din"Final internal diameter of the solar collectorThese consecutive circular sectorflcspecialtubesly parallel flat surfaces and therefore they have equivalent average diameterstowards the entrance of the first circulumed thatto Totdr due to the ground heat transfer convearound the solar collector As an approximation dT is estimated to 05K
Floating Solar Chimney TechnologyThe exit temperature of the first sector is the inlet temperature for the second etc and finallythe exit temperature of the final Mth sector is the Tos, i e the inlet stagnation temperature toThe solar chimney heat transfer analysis during a daily 24 hours cycleomplicated to be presented analytically in this text howeverthis analysis in order to have a clear picture of the operational characteristics of theSAEPs Using the code of the heat transfer analysis for movingvariation of the exit temperature Tos can be calculated Usincalculated dvalues of the Tas and by the thermodynamic cycle analysis fornim the daily power profile of the electricity generation can bewith this procedure the 24 hour electricity generation power profile of a SAEP with a solarand a FSC of H 800m height and d 40m internalwith annual horizontal solar irradiation Wy=1700 KWh/fithree electric pprofilesthout artifigeSAEP Df H-B0Om, d-40m Ac-10 sqkM, Wy-2000Kwn/sqrGround only25% coveredFig
13 The average daily SAEPs electricityermalWhile the smoother profiles are achieved when theis partlyd(-10%or-25%ofk tubes of 35cmdiameter filled with water, ie there is also additional thermal storage of an equivalewater sheet of 35-n/4=275 cm on a small pa
loating Solar Chimney TechnologyThe minimum electricd when the sun is just starting rising while theachieved about 2 hours after theground The power generation profile can become smoother if we increase the solar collectorhermal capacity This can be done by putting on its groundosed tubes filled withwater(as happens already in conventional greenhouses2 Historyearly in the first decade of the 20th centuryIn 1926 Prof Engineer Bernard Dubos proposed to the French Academy of Scieconstruction of a Solar Aero-Electric Power Plant in North Africa with its solar chimney onhe slope of a sufficient heigtain His proposhown in the following figure( 2)und in a book of 1954("Engineer's Dream"willy Ley, Viking Press 1954)TURBINE HOUSEONCREIE-APRONGLASS ROOg
2( from the book: "Engineers Dream"By: Willy Ley, Viking Press 1954)Lately Schaich, Bergerman and Partners, under the direction of Prof Dr Ing Jorg Schlaighthe german governmentThis solar chimney power plant, shown in next figure (3)was of rating power 50 KwItsof 4600 m and its solar chimneymade out of steel tubesof 10 m diameter and had a height of 195 m
Solar EnergyThis demo SAEP was operating successfully for approximately 6 years During its operation,The collected operational datain accordance with the theoretical results of theientific team of Prof Jorg SchlaiFig 3 A view of the Manzanares Solar Chimney Power Planttechnology
He proposed in his book the huge reinforced concrete solar chimneys of heightsof500m-1000mThe proposed concrete solar chihuge andnsive, Therefoivestment cost per produced KWh on the solar chimney technology with concretehe same cost range with the competitive solar thermal technologies Thertant benefitwith the major renenologies(Wind, SCP, PV)That is its abits solar collectors, with thermal storage facilities of365days/yearlast decaderal business plans and a series of scientific research papers have focusedhe solar chimney technology, whereby the author with a series of patents and papershas introduced and scientifically supported the floating solar technology (Papageorgiou004,2009)
loating Solar Chimney Technology3 Principles of operation of the solar chimney technology and its annuaefficiency Infor31 Short description andA large solar collector, usually circular, which is made of a transparent roof supported afew meters above the ground(the greenhouse) The transparent roof can be madeglass or crystal clear plastic A second cover made of thin crystal clear plasticse its thermalefficiency The periphery of the solar collector is open in order that the ambient air caa tall fabric free standing lighter than air cylinder(the floating solar chimney) placed innhouse which is up drafting theA set of air turbines geared to appropriate electric generators (the turbo generators)laced with a horizontalin a circular path around the base of the fscvertical axis inside the entrance of the solar chimney The air turbines are caged and caa rotor with several blades or a two stage machine(ie with a set of inlet guidingnes and a rotor of several blades)
The gear boxes are adjusting the rotation frequencytric generator rotatioand the electricThe horf of the solar collectorheating the ground beneath it TIeath the solar collector is becoming warm throughe greenhouse effect of the transparent roofThe buoyar to escape through the solar chimney As thep draftinhe chimney, fresh ambient air is entering from the open periphery of the greenhfresh air becomes gradually warm, while moving towards the bottom of the solarthe atmosphere This circulatingofferingenerators also to rotate Thus the rotational mechanical power of the air turbinestransformed to electrical power An indicative diagram of the SAEP operation is shown inThus the first two parts of the SAEPs form a huge thermodynamic device up drafting theosphere layers and the third part of the SAEP is thetricity generatingradiation in KWh/m2, at thelace of installation of the SAEP and is given by the meteorological data nearly everywhereThe average annual horizontal solar irradiance is given by Gav=W /AThe horizontal solar irradiatioflow m of the ambient air, cp1005 and To2 is equal to the averageK, in order that it is taken into account the outer air streamcreased inlet temperature due to its proximity to the ground on its entrance inside theolar collector
Solar EnSolar horizontal irradiationNLET VANESDFig 4 Schematic diagram of the SAEP in operation32 Annual average efficiency of SAEPsector ns is defined as thepower PTh absorbed by the air mass flow to the horizontal solargreenhouse roof GavAc, where Gay is the average horizontal irradiance and A theThe annual average double glazing solar collector efficiency nsc is theoretically estimated-50%, while the annual efficiency for the single glazing solar collector is estimated to 2/3Thus the averageGx
A where TthenIpower thermal losses PL(to the air turbineses and electric generators), plus waair kinetic power at the top exit of the solarThe maximum efficiency of the solar chimney is the Carnot efficiency defined as the ratio ofhe temperature difference betweerafting air divided by the ambient aireratureThis maximum efficiency has been proven(Gannon Backstrom 2000)to be equal to
Floating Solar Chimney TechnologyDue to friction and kinetic losses in the solar chimney the actual solar chimney efficiencyximately 90%um Carnot effie(close to the optimum point of operation of the SAEPThe combined efficiency nr of the air turbines, geathe product of the average efficiencies of itsthree major components ie the solar collector, the floating solar chimney and the turbo-ge efficiency of a SAEP of proper design, with a double glazing solarcollector should be approximatnx=(1
2H/1000%While for the SAEP with a single cover collector it is approximately:nay=(079H/1000%that if the annual horizontal irradiation arriving on the place of installation ofSAEP is 2000 KWh/m, the solar collector surface Km) and thelar chimney height is 750 m the SAEP can generate approximately 18 million Kwh Theme SAEP with a single glazing roof will generate apptely only 12 million KWhbe installed in a place of annual horizontal solar irradiation Wy in KWh/m2 the diagramshowing the relation between the annual efficiency of the SAEP and its FSC height H can beAc=10m2,d=40m700 KWh/m2(Cyprus, South Spain)The calculated efficiencyis practically independent of the annual horizontal solardepends on the FSC internal diameter d The reason is thaimaller diameter will increase the warm air speed at the top exit of the FSC andhe kinetic powerefficiencyry the solar collector diameter of the SAEP its FSC internal diameterspeed at the top exit ofthe FSC and consequently the annual efficiency of the SAEPd notice thatrder to receive the efficiency diagram as shown in thelowing figure(5)figure the kinetic and friction losses of the Floating Solar Chimneyternal diameter of the fsc ispriate in order to keep theeed in thef7+8 m/sec, and the FSC internal surface has a low frictionThe following figure(6) shows the variation of the annual efficiency of a SAEP of a FSCJar irradiation 1700KWh/mthe internal dialcalculated as a product of theThus taking into consideration that the annual efficiency is proportional to the
Solar EnGHa AHorzontal iradiation 1700 KW0
8Fig 5 Annual efficiency of a SAEP as function of its FSC heity by the SAEps is also proportional to the Floaar Chimney height H, is as follows:yThe constant c is mainly depending on the FSCs internal diameter d06505545FSC, height of FSC H-500AEP with internal fsc diameter
Floating Solar Chimney TechnologyTheoretical analysis of the Floating Solar Chimney technologyThe ground thermal storage effect and the daily electricity generation profile, have beendied by several authors(Bernades et al 2003, Pretorius Kroger 2006, Pretoauthor has used an equivalent approach on the daily power profile study oflar chimney SAEPs using the thermodynamic model see( backstrom gannFourier series analysis on the time varying temperatures and varying solarluring the 24 hoursor analof theparameters has been made leading to useful results for the initial engineering dimensioningnd design of the SAEPsThe imf these studies are that the solar chimney power plant annual powerthe outer glazing andout power production can be affected by the ground roughness and ground soli mennoaynamic cycle analysis proposed in ref (Gannon Backstrom 2000)is an excellentrmodynamic cycle of the solar chimney operation power plant using thethe study of ref(Backstrom Gannon 2000) is shown in the following figureTurbinedHcpKinetic lossthermodynamic diagram of the SAEPratures(marked with )are shown in the indicative diagram on the previous figureThe main thermodynamic cycle temperatdefined in the following tabl
Solar EnergyIsendropic temperature of ambient air in height HchimneyAmbient temperature in the ground around the solar collectorTo Inlet temperature in the air turbinesTose Exit air temperature from the turbo generatorture at thef the solar collectorT4 Exit temperature of the air mixed with the ambient air at the top of the exit layersTable 1 Thermodynamic cycle temperaturesTog to Toal is asroximately isobaric Thisinto consideration that the heat and expansion of moving air is takingThe processes Ta to To, Taste to T03tel and To to Tol are definitely isobaric by natureBy the analysis on the relations between the temperatures the following relationships can bet+C
T2T - +8Hand T-T工Whereby the parameters participating in the relations are defined as followsAch"nd2/ 4, is the solar chimney internf a usual value of 1, 05 8 calculated in (White 1999k-friction loss coefficient inside the solar chimneykin+ 4 Cd H/d where, for the operationholds numbernimney, the drag friction factor Cd is approximaWhite 1999)andfor no available data kinit is estimated to 0 15T-turbo generators overall efficiency, if not availablebientpressure on ground level at the place of installation of the SAEP, ifnot available data it is assumed as equal to 101300 Paambient atmospheric pressure on top exit at height H, estimated by the formulaPa-Pg gravity