5. THERMAL CONVERSION OF SOLAR RADIATION. Content

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1 5. Introuction 5. THEMAL CONVESION OF SOLA ADIATION Content 5. Introuction 5. Collectors without concentration 5.. Otical efficiency of the flat collector 5.. Thermal efficiency of the flat collector 5..3 The whole efficiency of the flat collector 5..4 The cylinrical collector 5.3 Solar raiation concentration 5.3. Collectors with motionless otical system 5.3. Collectors with mobile concentrator 5.4 Solar thermal ower lant The conversion of solar raiation into thermal energy haens in nature by absortion in the earth surface, lanetary ocean an vegetation. Solar collectors are utilize to control this absortion an irect the thermal energy to consumers. This energy is conveye from collectors to consumer by a liqui or gaseous heat carrier. The main arameter of this heat carrier is the temerature when leaving the collector, which eens on: - ower ensity of the incient raiation, - concentration coefficient of the raiation - sun osition tracking - otical efficiency of the collector, - thermal efficiency of the collector. Photovoltaic anels may be connecte in series to obtain a higher voltage or in arallel to obtain a higher current intensity. On the contrary, a higher temerature of the heat carrier cannot be obtaine by series connection of some collectors, because the greater is the number of connecte collectors, higher are the thermal losses. For this reason many ifferent tyes of collectors were built, each of them having a secific fiel of interest. A general classification of solar collectors can be mae by the concentration factor oint of view: S c C () S where S C reresents the entire area of the collector exose to the sun, an S is the heate area of the collector. In this resect, there are two categories: - collectors without concentration of the solar raiation, c = - collectors with concentration, c >. The first tye of collector is intene for heat carrier temerature u to 00 0 C, while the secon tye collectors can reach a temerature level u to C. 5. Collectors without concentration Because c =, S C = S or, with other wors, the exose surface an the heate surface are equal. This tye of collector resents some avantages: - both comonents of solar raiation, the irect an the iffuse ones are utilize; Master EMSE, engleză, 05 /6

2 - an accurate tracking of the sun ath is not comulsory; - simle structure, easy available materials; - small investment an maintenance exenses; - great number of consumers for heat at low temeratures; - goo efficiency by comarison with the hotovoltaic conversion. The simlest tye of collector without concentration is the flat collector (fig.). Its oeration is base on the so calle greenhouse effect which consists in selective behavior of transarent boies crosse by raiations with ifferent wave lengths. Thus, the solar raiation, having short wave length, crosses glass an air without imortant attenuation while the infrare raiation emitte by the receiving late, having much greater wave length, is strongly attenuate. After crossing the colorless glass, the solar raiation is absorbe in the receiving late, black ainte. The late warms u until an equilibrium is establishe between the entering solar energy an the heat losses. Circulation tubes Colourless glass eceiving late Thermal insulation 5.. Otical efficiency of the flat collector Fig. Solar collector flat tye The otical efficiency is efine as the ratio between the absorbe energy in the collector late an the solar raiating ower alie on the uer surface of the collector. The ifference between these quantities reresents the losses owe to the reflexion, refraction an absortion in the transarent layers an as well as to the artial absortion of the light in the receiving late. Taking into account only one transarent layer an neglecting, for the beginning, the absortion of the light in this layer, the transmission coefficient, D [.u.] owe to the reflexion an refraction rocesses can be etermine (fig. ). (-) 3 (-) 5 (-) (-) 3 (-) 5 (-) - (-) 4 (-) 6 (-) (-) (-) 4 (-) Fig. Solar rays roagation across the transarent layer Master EMSE, engleză, 05 /6

3 The transmitte energy through the transarent layer can be evaluate by aing the successive comonents in fig. D n n By aing the terms between brackets, results D n Because <, (n+) 0, so that D. (3) If there are s transarent layers, after a similar reasoning, the transmission coefficient becomes () D s (4) The reflexion coefficient can be evaluate by the Fresnel equation for the reflexion rocess of an un-olarize raiation which roagates from a meium characterize by a refraction inex n into another meium with refraction inex n : sin tg. (5) sin tg θ an θ are the angle of incience an resectively the angle of refraction, governe by the refraction law: thus n sin n sin. If the incient raiation is erenicular to the surface of the transarent layer, 0, n n. (6) n n The transmission coefficient D eens on the angle of incience θ accoring the grah in fig. 3. An imortant conclusion resulting from this figure is that the otical efficiency of the flat collector maintains unaffecte when the angle of incience changes with ± egrees from the irect orientation to the sun. The incient raiation is artially absorbe by the glass, so that the transmitte ower, D, eens on the ath length through glass,, uon the exonential law: D D k e. (7) k is the attenuation coefficient, which eens on the chemical comosition of the glass. For examle, a glass with very low content of Fe has k = 0,04 cm -, while a rerocesse glass can reach a value k = 0,3 cm -. Master EMSE, engleză, 05 3/6

4 s = 3 4 Fig. 3 Transmission coefficient D eenence of the incience angle Subtracting the transmitte ower D from D, the result is A which reresents the absorbe ower having as consequence a warming of the glass: k A e (8) Consiering a glass of 0,5 cm thick, the light attenuation reresents 7,5% for the best quality glass an 5% for the oorest quality one. Further, the transmitte raiation is artially absorbe by the receiving late, eening on the absortion coefficient A. A new reeate rocess of absortions an emissions takes lace, like that resente in fig. 5. The incient raiation on the receiving late will be consiere as irectional one, like it comes from the sun. The emitte raiation from the late is iffuse, because the late which must absorb the raiation as much as ossible has a lusterless surface. Glass D D(- D(-A ) D(-A ) D(-A ) D(- 3 eceiving late DA DA (-A ) DA (- Fig. 4 Taking over the solar raiation in the absorbing late A new reflexion coefficient is introuce to evaluate the iffuse raiation reflecte from the glass, whose value eens on the number of glass layers. For examle, = 0.6, 0.4, 0.9 if the number of glass layers, s, is, or 3 resectively. By aing the ower comonents entering the receiving late [u.r.], the result reresents the otical efficiency of the collector. ot DA ot DA DA n n A DA A... DA A... A A... A n n... Master EMSE, engleză, 05 4/6

5 ot DA A A n. (9) Because -A < an <, the secon term of the nominator can be neglecte, so that the otical efficiency becomes 5.. Thermal efficiency of the flat collector DA ot A. (0) The heat eveloe in the absorbing late can be ivie in three main comonents: - the heat transorte by the flui to the consumer, - the heat accumulate in the collector materials, which are warming u, - the heat losses from collector to ambient sace. If the ensity of the solar raiation an the heat carrier mass flow are constant, the absorbing late temerature is constant, too. As consequence, for this stationary oerating moe, the accumulate heat in the collector materials can be neglecte in the equation of energy balance. The heat losses take lace through all the outer surfaces of the collector. Because the collector structure iffers on the uer irection by comarison with the others sies, the basic heat transfer mechanisms have ifferent weight on these irections. On the uer sie revails the heat losses by raiation an convection. On the other sies of the collector, the conuction mechanism is ominant, because the temerature of the external surfaces is low enough to can neglect the raiation an convection losses. To calculate the whole heat losses, the next equation may be consiere: Q KtS t ta, () where K t is the whole heat transfer coefficient, S is the area of the uer surface of the collector, equal with the receiving late area t is the average temerature of the receiving late t a is the temerature of the surrouning air. Because the global heat transfer coefficient is ifficult to evaluate, an electrical similarity of the heat transfer can be suggeste. Consiering a otential ifference U U alie to a resistor, the current intensity, may be written U U I. Similarly, the heat transmitte, er unit of surface, between two arallel surfaces, having ifferent temeratures t > t an the transfer coefficient k, is t t q k t t. t U I U T t q Fig.5 The analogy between the electric current an the heat transfer T Master EMSE, engleză, 05 5/6

6 Thus, the thermal resistance is similar to the electric resistance, the temerature ifference is similar to the electric voltage an the heat flow is similar to the electric current. For examle, the iagram in fig. 6 reresents the equivalent electric circuit for the flat collector in fig., having two transarent layers of glass. t is the temerature of the receiving late, t a is the air temerature, t g, t g are the temeratures of the two glass layers an t c is the temerature on the sie an back surfaces of the collector. t a t3 t g t t g t t4 t c t5 t a t Fig.6 The equivalent of the heat losses in the flat collector The electric analogy allows exressing the global thermal resistance, t. On the uer sie of the collector, the three thermal resistances are connecte in series so that: u t t t3. On the others sies of the collector, the thermal resistances are connecte in series, too: b. t4 t5 The global thermal resistance t will be: ub t, u thus the global heat transfer coefficient, K t is Kt. t To calculate the heat resistances, the heat transfer rocesses must be analyze. From theoretical oint of view, the uer structure of the collector can be moele by arallel surfaces having infinite sizes an ifferent temeratures. Consiering a air of surfaces with the temeratures t an t, the heat transfer between them, by raiation an convection, obeys the next equation: 4 4 T T q C t t. () The first term in the right art of this equation reresents the transfer by convection, while secon term, by the raiation rocess. The significance of the symbols in the revious equation are: α C is the heat transfer coefficient by convection, σ is the Stefan-Boltzmann constant ( W/m 0 K 4 ), ε an ε are the emission coefficients by raiation from the two surfaces. By extracting the term (T T ) as a common factor in this equation, results: b Master EMSE, engleză, 05 6/6

7 q C T T C T T T T T T. (3) This way, two heat resistances in fig. can be written as: t, t. C For the heat resistance t3, the moel structure is ifferent, the atmoshere being one of the two surfaces. Thus, for the heat transfer by raiation to the atmoshere, the heat transfer coefficient is: 3 g T g T a T g T a. For the heat transfer by convection to the atmoshere, an emirical equation is recommene: c v t (4) where v t is the air see arallels with the uer surface of the collector. To aly this algorithm is necessary to know the temeratures of the arallel surfaces, that is ifficult to obtain. As consequence, simler methos are utilize for the collector esigning: - nomograhs base on the analytic equations, vali for secific collector structure or materials; - emirical equations, exerimentally rove as vali for secific structure an materials. A heat transfer by conuction rouces through the thermal insulation on the back an sie walls of the collector, accoring to the next equation: q is t t, (5) is is where δ is reresents the thermal insulation thickness, λ is is the coefficient of thermal conuction of the insulating material. Thus, is t 4. (6) The heat losses, by raiation an convection, from the sie an back surfaces of the collector, can be neglecte because the both temeratures are very close. As consequence, t5, resectively, k 5 = The whole efficiency of the flat collector In orer to calculate the collector efficiency, some energy quantities must be efine: - the incient energy on the uer surface of the collector W ESf, (7) where E is the ower ensity of the sun raiation, S is the area of uer surface of the collector an f is it s orientation factor; - the energy eveloe in the receiving late is a C Master EMSE, engleză, 05 7/6

8 - the energy losses in the otical system of the collector - the whole heat losses W ESfot ; (8) W3 ot ESf ; (9) W4 KtS t ta. (0) Two ossibilities to efine the collector efficiency are relevant: the whole efficiency W 3 W 4 g. W By relacing the above efine energy quantities, results so that η g < η t. Kt t ta g ot. () Ef the inner (thermal) efficiency W Kt t ta t 4. () W Ef These two efficiencies are linke by the equation g ot t ot, (3) The collector efficiency eens on more factors like sun ower ensity, collector orientation, the temerature of the receiving late, the air temerature etc. For a goo quality collector, in a normal regime of oeration, the energy losses have the average values: Tye of losses Loss weight otical losses by reflexion x 4%=8% by refraction x 3.5%= 7% thermal losses convection 7% raiation % conuction 3% energy losses, total 47% The global efficiency results to be 53%, much greater than that of the hotoelectric cells. However, the temerature ga between the receiving late an the air influences the whole efficiency, like fig. 7 shows. The nonlinear eenence is owe to the heat losses through raiation which een on the 4 th ower of the temerature. The highest temerature of the late is reache when the heat carrier oes not circulate, while the collector is exose to the sun. At this temerature all the energy losses from the collector equalize the receive sun ower. Is very imortant to know how great this temerature for an aequate esigning of the collector is so that it coul oerate in every regime without amages Master EMSE, engleză, 05 8/6

9 η ot.fig.7 The flat collector efficiency versus absorbing late temerature An examle of flat collector esign is shown in fig.8. Aluminium frame Glass eceiving late Coer tube Thermal insulation Fig. 8 The flat collector 5..4 The cylinrical collector A cylinrical collector consists in two tubes: the inner, metallic tube having a ark surface in orer to absorb the solar raiation, surroune by a transarent tube, fig. 9. Through the inner tube flows the heat carrier flui. Fig. 9 The cylinrical collector Master EMSE, engleză, 05 9/6

10 This structure of collector resents some avantages by comarison with the flat collector: the illuminate surface area of the inner cyliner remains unaffecte by the sun osition on the sky; if the sace between tubes is emty (avance vacuum) the convection an conuction heat losses are avoie, so that the whole efficiency can be much imrove. Fig. 0 Different structures of cylinrical collectors To increase the receive sun ower, the absorbing surface must increase too. However, this growth is limite because if the inner tube iameter grows, the volume of the flui grows too, as well as the thermal inertia of the collector. More cylinrical collectors can be connecte in arallel an arrange on a late surface like a flat collector. To utilize the solar raiation which asses between inner tubes, the surface of the outer tube can be covere with a mirror layer. Thus, the reflecte raiation reaches the absorbing surface (fig. 0, left). Another solution is to a an absorbing flat surface to the inner tube (fig. 0, right). In this manner, the entire solar raiation reaches the absorbing surface, but the ineenence of the sun osition on the sky will be artially lost. However, remains unaffecte the main avantage of heat losses iminution. Thermal insulation Collector Distribution ie Glass with low Fe content Absorbing surface Fig. Cylinrical collector esign Desite it is more exensive than the flat collector, the cylinrical one are nowaays much more aske because it s better efficiency. 5.3 Solar raiation concentration To obtain a concentration coefficient greater than, an otical system must be inserte between the sun an the absorbing surface (the receiver). This otical system is base either on the reflexion or refraction henomena of the solar irectional raiation. The iffuse raiation can not be concentrate. Master EMSE, engleză, 05 0/6

11 Deening on the mirror geometry, the concentration coefficient may vary between an 0 4 that mean a similar growth of the ower ensity on the absorbing surface. Some losses however, aear owing to the quality of the otical system. As the concentration coefficient greater is, an accurate solar osition tracking is necessary in orer to reserve an efficient oeration of the collector. This orientation must be ermanent an nees an ineenent energy source. The solar collectors with concentrating systems can be ivie in two categories: collectors with motionless otical system collectors with mobile otical system 5.3. Collectors with motionless otical system The flat collector associate with sie mirrors The simlest way to concentrate the solar raiation is to a one or two sie mirrors to a flat collector (fig.). The solar raiation arrives at the flat collector surface irectly an reflecte from the mirrors. Fig. Flat collector associate with mirrors The concentration coefficient is variable, eening on the sun osition on the sky. Sometimes, the entire ower reflecte from the mirrors reaches the flat collector surface. Other times, only a art of the reflecte raiation arrives at the collector surface, eening on the incience angle on the mirrors. Flat collector associate with arabolic mirrors Two segments of arabolic mirrors, P an P are arrange to lean on the sie ens of a flat collector; the axes of the arabolic surfaces are isose symmetrically against the flat collector axis, uner an angle θ. The both centers of the arabolic surfaces, oints B an D, are locate on the flat collector surface. The arabolic surfaces concentrate the incient rays towars the mirror center, if that rays are arallel with the mirror axe. Fig.3. The ouble-arabolic mirrors collector Master EMSE, engleză, 05 /6

12 If the angle between the collector axe of symmetry an the incient rays are smaller than θ, all the solar ower entering the collector arrives at the absorbing surface. If that angle is greater than θ the solar energy is artially or totally reflecte from a mirror towars another mirror an then back to the atmoshere. Deening on the size of angle θ, the collector can oerate 5-7 hours aily. The geometrical concentration coefficient is c. sin Actual values of this coefficient vary from to 0. The sherical concentrator with mobile receiver A sherical mirror reflects the irectional raiation towars a linear focus, arallel with the incient rays (fig.4). If the mirror is fixe, the receiver must erform a motion with two egree of freeom in orer to follow the sun ath on the sky. The receiver movement nees smaller ower consumtion than the mirror orientation. The concentration coefficient becomes highest if the mirror angle is 0 0. For a erfect mirror surface, this maximum is Collectors with mobile concentrator Fig.4 The sherical concentrator The arabolic mirror A arabolic mirror is obtaine by rotating a arabola aroun its axis. This mirror has the highest concentration coefficient among all other tyes. Fig. 5 shows the otical behavior of this mirror. The sun isc is seen from the sun-earth istance as the base of a circular cone having the to angle of 3. The two sie rays which arrive at the mirror to (oint A) reflect maintaining the same angle between them, so that in the focal lane aears a circular light sot with iameter f. The rays cone which arrives in oint B, reflects, too an, crossing the focal lane, an ellisoial light sot aears, having the main axis > f. Taking into account all the mirror oints situate at angular istance θ from the mirror axe, the image in the focal lan becomes a circle with iameter. If θ = 90 egrees, all the focal lane will be illuminate an if θ > 90 egrees, a concentrate light will aear on the surface exose to the sun. These two last situations are not interesting for sun collectors because, obviously, the ower receiver surface must be smaller than the mirror aerture in orer to not shaow its surface. Master EMSE, engleză, 05 /6

13 Since as greater is the angle θ, the focal sot iameter grows, the ower reflecte from the mirror surface sreas on a greater surface in the focal lane. Thus, the ower ensity on the focal lane surface iminishes from center to ege. Theoretically, the ower ensity changes as fig.6 shows; the curve has a flat zone corresoning to the circle of iameter f. Because of eviations of the actual mirror from the geometrical shae, the ower ensity changes as the curve shows. The iameter of the absorbing surface chooses accoring to the urose that is intene for the mirror. That urose can be: to obtain the higher ossible temerature on the receiver; to collect the entire raiation reflecte from the mirror surface. Fig.5 The arabolic mirror Fig.6 The ower ensity on the absorbing surface In the first case, the receiver iameter must be equal with f. The maximum concentration coefficient is reache for an aerture angle of 90 egrees an is equal to c max (4) tg 6' Fig. 7 Determining the concentration coefficient Master EMSE, engleză, 05 3/6

14 In the secon situation the receiver surface chooses of iameter. The concentration coefficient is efine as Since results Finally S D c D (5) S We note, in fig. 7, AD = f an BF =. Consiering the triangle BCF, results D = BC = sinθ. (6) From the triangles GFN an FHM: GH MN (7) cos GF = FH = tg6, tg6' (8) cos sin cos c tg6' sin tg6', (9) that means the concentration coefficient eens on the aerture angle θ. The function sinθ has the maximum value equal to, an that haens if θ = 90 egrees, or θ = 45 egrees. For θ = 45 egrees the concentration coefficient reaches the value c max 55. (30) 4 tg 6' In fact, the realize mirrors have eviations from the theoretical geometric shae so that the otimum aerture grows to 60 egrees. In this case the concentration coefficient can be only Even this value can not be obtaine; ractical values are 4-5 times smaller. The cylinrical arabolic mirror is obtaine by translating a arabola along a straight line. The sun image on the focal lane is now a rectangular one, which length is equal to the mirror length. The geometrical concentration coefficient is having the maximum value S D c D, (3) S c max 07. tg 6' Large arabolic mirrors are built from many small mirrors, so isose to follow a arabolic surface. The small mirrors may be flat or curve. Such a mirror will have a smaller concentration coefficient, of course, than a arabolic mirror. Two examles are shown in fig. 8 an fig Solar thermal ower lant Collecting the solar raiation with large mirror systems, a high steam temerature may be Master EMSE, engleză, 05 4/6

15 eceiver otation sinles Fig. 8 Cylinrical arabolic mirror (Fresnel concet) Suorts Flat or curve mirrors obtaine to generate electricity through the conventional thermoynamic cycle. Two main tyes of such lant are built. a) The lant with istribute collectors (fig. 9). Every collector has a mirror an a receiver where the heat carrier is warme u. A ie system collects the flows of heat carrier from all receivers an transorts it to the steam generator. The size of such a lant is limite, u to some hunres of kw, because the heat losses in the collecting ie system. Heat carrier eceiver Steam Steam turbine Parabolic mirror Steam generator Conenser Pum Pum Fig. 9 Solar lant with istribute collectors b) The lant with fiel of mirrors an central receiver (fig. 0). The receiver is lace on a tower to where the reflecte raiation arrives from a very large number of mirrors arrange aroun the tower. The energy losses are much smaller in this case because the absortion of the solar raiation is very small in air an the length of the high temerature ies are limite to the tower height. Some realize lants have installe ower u to tens of MW. Master EMSE, engleză, 05 5/6

16 eceiver Tower Steam Water Fig. 0 Parabolic system with a fiel of mirrors Master EMSE, engleză, 05 6/6