the following content is provided under a Creative Commons license your support will help MIT open courseware continue to offer highquality educational resources for free to make a donation or to view additional materials from hundreds of MIT courses visit MIT opencourseware at ocw.mit.edu today there are more lectur and we uh um um I uh guest lectures uh one will be on the reliability of the materials at high temperature this last lecture also have to J Around schedule everybody so instead of what uh I will do is the next Friday uh we'll be talking about the reliability of the materials um this is Professor Christoper in the mat research in this long time I could get and uh uh then uh on on the week after next week uh we will have Dr Avan sonov talk about selective surface it's being working on several phot and uh so working the spectral control area help you again better talk than me and then say the final lecture uh we will be um um uh talking come back a little bit to talk about how we combine selected surface with and with uh also phot so we have learned thcs we have learned uh phot also uh so that's a solar solid state solar thermal energy conversion and uh today uh what I want to cover is the mechanical uh energy conversion solar uh to Electric solar mechanic is uh so let's uh uh recall what I was talking uh in the last previous lecture we talked about black body rision we mentioned a little bit on the the Earth motion and uh how we usually test uh solar Spectrum uh am01 m1.5 Etc and then um we Define r property those definition many different definitions as I said uh I don't expect they you remember all those details the the point is for spectral control it's very important to understand the wence dependence of the properties and then with that we discuss the uh maximum efficiency of solar thermal engines and maximum achievable temperature and uh again say emphasiz the selective surface but and we don't know you don't know how to do it yet but it's important so uh in today's uh uh lecture as I said I want to cover uh really the solar theral mechanical part and what will start with is the hot water system solar hot water and uh then we'll talk about the to bring up to a higher temperature we'll talk about the uh solar concentration and uh we talk about the maximum how much you can concentrate this solar radiation and then uh we look at how you could in Practical uh uh to do different ways of concentration and to do concentration you'll need to track the sun that's one of the problem Challenge and so I'll talk a little bit tracking long tracking and then I'll go to sort mechan if I have enough time I'll start a little bit I give you a preview of what control the surface properties uhne W um so s how water right uh it's very M but I I really appreciate this as probably mentioned before when I was a kid uh I grew up in China didn't have chance to take a half shower and now when I go back to my parents this in China and and they use solar power uh uh concept of course is very simple uh solar collector you absorb the solar radiation and you heat up the water um very simple concept right and also uh I want to give you a very simple uh backup Im so if you're mechanical engineer this will be pretty easy but uh I did this for the preparation of the class also out of my own curiosity uh first year from materal this probably a little bit more more uh say not not very familiar with you but uh it's a simple energy balance so what I want to ask is how much if I want to put in my uh own house uh how what's the area I live right solar H water and uh typical household uh water tank is about 80 gallon it's pretty it's a larger house if you have smaller so ring from 40 to 100 gon I guess and uh if I take a St temperature of water at 15° and I want to keep the water tank at 60° C so during a day right let's suppose I deplete all the hot water during the night and uh I want to store 80 during day I want to heat up the water from 15° to uh to 60° and uh it's a it's a so so you you you want to say how much what's this solar surface area how water surface area you want and it's simple energy balance right during the day how much solar radiation reset and then of course you consider efficiency of the absorber and then that balance the to heat up this much water how much energy you need so you do that energy balance the the area that what I want the solar radiation uh insulation uh and uh time of the day efficiency and equals the uh heat capacity that's stored in the hot water so I put in those lbers typically when people calculate uh you can see it's a little bit optimistic if you live in Boston you don't get a s wat okay and uh I took a a standard calculation sou one 5.5 hour so that's a average say uh uh the whole day average typical that's what people take when they test the solar cell s when they calculate solar cell output and efficiency of SAR thermal hot water system uh ranging from I'll tell you how to estimate efficiency but I take a typical L 60% okay so I need a 5 m here and uh uh in China I know it's very cheap and typically people install somewhere 1.5 2 meters so it's a lot very big tank most people live in apartment and they use less water okay uh in terms solar hot water there different form form uh format uh one uh of the format is a flat panel right so here we have what we have is the absorber that's uh uh typically is a frequency selected meaning they absorb solar radiation but do not or you want Reit a very small amount of theral emission when it hits up and so you can say the back side is insulation and this is absorber tube could be on top or on the bottom and typically they do not so in between is the air okay and uh uh uh the tank could be on the top of theber itself so in that case uh you don't put a tank uh in the basement and uh you can use the gravity of the water uh to drive the water flow to drive the hot water down let say the problem is your water flu rate is lot depends on how high you put the tank so if you live a low low buildings uh your uh your pressure is no uh and uh this is the example clearly war tank is not on the roof it's in the basement and in that case you use a pump to pump the water so it's a pressurized system so they're pressurized and this one is uh uh not force force system just natural and the one that's uh uh uh what I thought really uh interesting is this uh vacuum system and uh uh this is a this is a prominant used in China and uh uh it's a glass so it's a double layer glass inside uh is a black Co what looks black is actually inside outside is another glass clear glass so it's a circular and the inside glass is First Co with Selective surface and then you see all you evacuate it you see on the other side so it's a it's a it's a H jacket and uh in on this side because the vacuum so it has a g um the G what what does g do is say the evaporation is actually collected by this metal reactive is whatever evaporates and uh uh uh so you you would imagine so putting vacuum under s how long last and I actually with the Su of this I say uh the the Father the father of this technology in China and he said that he put this stuff early in the 90s in in chinua he from chinua University and uh and still working so after 20 years and that's uh considerable considerable because if you think about in my house I bought a TV I remember I first uh my first T is still working about more than 20 years and that's a CR it's a vacuum technology right see the screen of the TV uh say the uh tax R inside is actually Ultra hyd so uh the vacuum is pretty high and you can uh uh do a calculation find why if the vacuum is too low the air conduction Mak too much here and so this is a Evacuate the tube uh that glass this glass is really cheap I with the say the manufacturing s and uh uh the whole tube is about this Tye uh the diameter is a 50 mm and the manufacturer the double glass tube is about $1.5 per tube so really
cheap uh this one is a little more expensive uh it's not a glass glass and what it has is a metal absorber uh so it's a uh it could be a copper or aluminum again this is a cost right this is really the see the cost is a Cru here and uh this is selective absorptive codent again and uh so what it does is this is a heat pipe so the heat absorb conducts to the heat heat pipe so heat pipe is diameter is not this big that's too much copper right it's a small diameter pipe and so the heat is evaporate the liquid inside the pipe heat pipe and on this side you have Force water heat exchanger Force water take the heat away so this is a uh the uh one of the chip form unpressurized um uh so what it has is the Double Glass layer you fill the glass in inside glass with water I go back here inside right this is empty so you fill with water and when it heats up natural convention so the hot water goes up here and the cold water flows down so there's no it's a passive system no no pump at all and you put on the roof and uh then you can take a shower uh so that's a a typical family uh in China probably isuse about 15 to uh and this one is a force pressure right you put a separate tank you put a pump on through and force at the end okay so that's the uh uh how the what the system looks like again out of my own curiosity I say okay I'm going to estimate what's the efficiency uh of the system flat panel and the vacuum systems so this is a vacum a model for vacum system where I have a cylinder in inside is a cylinder inner cylinder so this cylinder uh there is one uh so actually this is a self tracking right no matter what Sun direction is the there's always side wall uh is is facing the perpendicular to this side so this is a have this does have some Advantage there in fact there's a uh startup company called cindra and they are putting solar cells like this so Circle along the circle of the cylinder and uh uh it's vacuum in between so uh incoming solar radiation uh is just the cross-section area uh that's I come the outer diameter and say the uh the um uh insulation solar insulation so absorbed how much is absorbed uh in terms of absorption the first thing you have to go through is the outer glass layer so that's a transmissivity p and then uh inside uh the surface is absorb Alpha is the absorptivity so that's absorptivity to solar radiation now this is a disadvantage here the radiation lws right uh radiation loss because the whole inner tube is absor uh is heated up so the surface area is actually the pi times the inner diameter is not just the cross-section flat compared to Flat is only uh uh the the flat area now is the whole surface area and then that's theity and uh I do a BL body uh simple BL body calculation the uh surface so what I did not consider is multiple reflection this surface emission I just say okay everything goes to the environment and in reality the some of this cannot go in fact the glass we TR some of the radiation back reflection and also uh the uh glasses non transparent in certain W range so with that I can say this is the absorbed radiation min the that differen is what I actually get into the hard time and then divided by what comes in so have my efficiency so this is a simple again backup envelope okay for fun yes question so the tube is pretty large I think the only half the total surface that's that's 100 right this cross-section area but the emission is pi D so that's a disadvantage okay and so that's that that's analy I'll show you the curve later on now I'm going to look at the hot water flat panel type so our flat panel type in between the air I was actually curious whether people use double glaze uh windows on here or not and what I found since they do not use it so it's just a uh uh one layer of glass so this is the air and uh selective surface uh and of course what you think about heat transfer this absorb solar radiation and then will conduct through the air conduct through glass and outside is electrial convetion so you have the uh uh resistance in series conduction air conduction resistance glass resistance convetion resistance so that's one part of the heat uh through conduction and conention and back side the thermal insulation can still leak he so back side I have a conduction and then I have re radiation goes through directly so I have three parts for the heat transfer and this is a my simple circuit the solar radiation come to this electon surface the energy now one part is go directly through radiation and the other part goes through the air glass uh conention outside and then the backside the insulation okay and they I put a resistance because I this is a something if you're not the mechanic or engineer didn't take heat transfer before this is probably n famar but this is similar like a circuit okay thermal resistance uh you you do the resistance calculation for air the thickness divide by thermal conductivity so the Gap thickness divide by conductivity divide by area and they say if you do that why don't you use th thicker and the problem is once you two th there start circulation convection start to happen so you look at the Double pan window in the typical window that thickness is not not it's a few millimet thickness so you don't use to th here so here I took a 10 10 mm and then say glass uh glass is a a few weeks ago there was a talk somebody is going to install a flat panel system in one of the MIT building MIT I don't know uhuh Ash okay I was surprised that uh the cost per was just a surprise for me because that's like a 13 15 year return uh uh I don't not understand why but I say it looks like they use a very uh very tough glass this is a steel uh what's the glass L you you you you harden the glass you can walk on it so uh but anyway but glass resistance very small really air resistance contion resistance those are the resistance that cost the toor that's this side the resistant and then the insulation resistance the back side so I put all this L together and did the energy uh loss again considering all the radiation so I have radiation loss I have the conduction loss the conduction conversion loss and with this loss I can again go calculate how much energy comes in absorb Mon's loss divide by what comes in and that's what I have okay uh those numbers I assume for example uh in the next graph I assume 95% absorption 5% emission this is what the industry can do so we have a researching a group on selective surface always I say how we can do better industry can do that at the meters per second okay select the surface 95% absorption 5% emission um and this hot water is of course the typical operational temperature is about 70 uh 80° so they do not operate at very high temperatures and when you go to higher temperature if you can go 500 Degrees still keep this uh you will be the best in the world it's very hard to do that okay that's that's the uh uh curve I have that's the vacuum system and this is the flat panel system and efficiency uh depends of course the temperature of the water essentially the temperature of the selective surface there and uh I went to a web and I found this depends on who you which website they looking people have different curves but I found the one that uh I thought closer to what I have um so uh this is this is a one company see that's a vacuum system that compared to flat panel flat panel goes to almost zero I don't believe that that's probably too small okay so uh but uh solar thermal is a efficiency compare of course the photo voltage is many times better and uh uh so in terms of if you look at what has been use is uh this is a chart I got from this uh uh publication it's uh and here is this side is solar thermal that's it's compare all the Renewables solar thermal here is a wind here's geothermal photo voltak solar thermal power plant ocean tile power power and uh uh you you find out that uh uh total capacity and the red is actually produced energy so so you can see the solar thermal is actually a pretty large part of how people are currently using renewable energy okay just heating up heating uh heating up the hot hot water meaning and this is a this is in terms of Technology uh uh vactive tube uh is dominant because China really China use it and uh uh flat panel 32% uh unaz The Collector uh and air collector so this is this is the where it's being used you can see the channel is off the chart here it has about 100 million square meter inall I don't understand way why we don't use the here and but I did say I I think I say Hawaii now has legislation if you have uh new house being built a new house built you have to put in hot water system can your from right you can go back check uh so um I was once talking to every time I have a chance I was asking people why and also price gets very high that's uh uh probably um uh because in China you can Ty household $300 they put that for system okay so that's solar thermal now we want to go to higher temperature right solar thermal is 80° 100° and uh you want now go to uh higher temperature and to have to get the higher temperature uh you need a concentration and now uh we need to look at the uh the concentration let me remind you I showed this before uh the uh the Earth itself uh see on the uh see the orbital is not just a perpendicular of this plant there's a 23.5 CH of the Earth right so on this side this is til on this side the same til that til is fix that's why we have summer and uh up uh the r direction we have a summer and uh uh winter okay and the uh degree suspended of the Sun by say if you view from Earth the degree is 35 32 uh second so that's uh um um that's about the0 five I forgot point about 4.5 degree okay and now uh the question I want to ask first is if you do concentration how much you can get what's the maximum concentration right uh so we can look at the theoretically um what's the limit the maximum seric limit is I cannot heat up object harder than this s right and now so that that you all agree but if I ask you can I concentrate radiation even with intensity harder than the Sun not not harder the intensity higher than the sun is that crazy or not huh okay you'll see it later okay so first we let's look at the first just energy balance if I think about the spherical uh radius from the sunand right and the area of the sphere times the energy flux and uh uh area of the uh see uh is a constant the once the energy leave the surface the larger you draw Circle the less is your intensity so the intensity of the this Earth think of circle here that is a capital r 4 pi r squ times whatever insulation outside the Earth's atmosphere right so this is the insulation outside the earth atmosphere this is the uh intensity on the surface of the S radius of the sand so that's energy balance conserve always of course you see oh there's something in between scatter a little bit light consuming uh uh the space is pretty much all empty right so now let me concentrate if I concentrate this concentration ratio and this intensity on the earth uh surface the Earth of the the Earth in solution and uh this is the energy I put in onto object that receive this concentr light right so energy balance will tell me in this case again uh this the object should be black body actually because you want to absorb every drop of solar [Music] radiation and because you you absorb the solar radiation you also rate so you want to absorb maximum you also rate Max maximum so it's black body so actually I put a say the energy absorb the balance the energy radiated I do perfect insulation so this is per unit area based this is per unit area based so that's the energy balance for the object that receive the concentrated light and of course as I said my condition is that this object cannot be harder than the seven right so so this is the uh concentration and uh from here I get my maximum concentration happens when this equal and that's the solar flux intensity divid by whatever in in Earth so that's R over small R based on my energy balance and if you look at R small R and this Thea here is a half angle sustain to Earth so that's a sin Theta Square so that's my maximum concentration and uh if you plug in the lumber I said 2 Theta this is 32 second so plug in lber that's about 46 100 thousand times it's the maximum you can get it's not the maximum people actually have achieved higher than this one okay this is a because the emission inside the object is is uh proportional I have one mistake here should be proportional to n Square not proportional to n okay so the mission inside object proportional n Square so so if I have a a medium like a water or glass right the inst intensity inside could be higher than the vacuum black body intensity and square and glass is uh two uh 1.5 so square is
2.25 and uh uh if you use silicon the N is about 3.5 the square is about 10 right so um if you do that again your limit is the temperature limit is not the intensity limit your temperature of the concentrated surface cannot be higher than the temperature of the Sun you do that you can your maximum is n² sin Theta squ okay so that's higher than the previous one and indeed this was achieved in the lab uh this is Roland uh Winston uh they have talk about this more detail this is a compound with the focus and non focus and they have shied 56 okay so that's the um from the second low perspective your absolute upper limit and now let's see how we can get there okay and uh you think I'm going to use a lens and this lens if I think about the lens okay so uh all all all parabolic 12 right we know that you have parel comes in it Focus one point so that's the the question is what's the concentration limit if you those are the image formation right using a lens using a uh uh using a lens or using a uh parabolic 12 you have a focal point that's a focal point this is the image so image forming of and remember the sign sustain angle that's the K right even though we say solar radiation is a parel light but when you want to do Focus you want to uh uh that that angle becomes important because previously you already say so what I want to say uh think about is if I have either l or parabolic control uh uh say the uh opening here is D and the uh forus uh uh here is a small d one is Big D the other is small D and I want to find the ratio okay let's look at it so if I do 2D uh this one is a flat right flat panel is if you do a tube you you have a different result but the here I'm a flat panel and this is the half of it and uh uh now I look at the uh this is a this is a vertical perpendicular line here so R * sin Theta here is 2 Theta so this is really if you think about parall line comes in this way and that's my reflection here and this one is my uh this line reflection so that's the uh uh edge of the uh solar cor there and so R * sin Theta gives me this one right perpendicular line and d/2 so that's here times this is a five and here is a five so here is also five so D over 2 * cosine 5 is all G me this SE segment so I have a equation geometry here geometrical relation and then I have this R and this R is about the same so R * sin Theta gives me d/2 right the open in there and then I have from here I can get my relation how much Focus I get capital D over small D I have sin 25 / 2 sin Theta so this is the uh maximum you will get uh this is the concentration you get and you will see the maximum happens is sin 25 = 1 right so 45° so when 5 = 45° here I have the maximum and that maximum is 2 sin Theta that's 107 my calculation maybe you can go back to check and if you use 3D X symmetric you square that and that's 4 sin th for the problem is now you can say this is a factor of four smaller than the limit right thermodynamic is 1/ Sina here if you form an image your limit is a factor of force more and how you can reach that maximum limit okay so image Optics it's a little bit too constraint you ideally you want everything goes to one point right and you want to form an image so this is a uh here there's another slides that I just copied from Winston's book and uh uh if you have if you want to focus on the cylinder that's one or Pi smaller uh than the previous slide now uh there's another way to do it that's a long image method this is a uh Rand winance baby and uh uh if you read uh his rational is starting from this one over four how you can get to the maximum sum damic limit and here is one way there's no simple mathematic in terms of the shape of the concentrator but this is how uh he would explain so this is where the area you want to Flat this is a flat plate example you want to focus on a flat plate B Prime to D okay and uh uh this is the angle of incidence right so that's the maximum angle uh let's suppose uh this is the maximum angle that you accept the radiation coming in right if you have another angle higher than this it will uh not get in you will be blocked so uh if you this is the maximum angle so you take a string here at this point you take a strand uh this is the opening uh num a so you draw you keep this string fix lens fixed and you draw the curve down so this one will slide so the angle of incidence equals reflection that's what what is following this surface gives the surface such that the angle of incidence equals angle reflection of course is a specular surface that's being assumed and at the limit this one when is here the refle angle to the goes to D Prime okay so that's the image surface this is the image method it developed and now we can check where this one gets to maximum or not so this again simple geometry I have AC this section plus a b Prime that's the Str length right and the other limit so this is The Edge you look at the edge only a prime to B plus b b Prime right so this is the Str length this is the Str l and the same string so it's actually very convenient simple way to do uh the uh the geometry Al the surface is harder to express analytically and uh you know uh see the symmetry A B prime a prime B from symmetry they equal so you get rid of two variable in the above equation and your a uh is uh your AC is this one time Sina so a a prime time sin Theta and your concentration then is 1/ Sina remember before is say sin 25 over 2 Sina now you got rid of that factor of two in the two dimensional geometry and you go to 3D you actually reach 1 sin Theta squ so if you put your Theta angle of acceptance right if you just say I only accepted the solar com Theta s when when that that's your maximum you have to accept the all solar within that 20 uh 32 R right second so that's a maximum there but this is a conent because say If you think about uh Your Design you don't need that high concentration but you want a large angle acceptance particularly when you have also street light right you if you think about you don't always have parallel light you also have the scatter light and then uh typically people take a 820 depends on where you live and so scalar light is a actually approximate isotropic in all directions so tracking if you track only the solar part right maximum concentration anything that beyond that angle you can't C capture it so that's 80 that 20% is gone and so with this this is the other examples and if you read the paper it's interesting uh uh uh this is when you concentrate to a cylinder using the same string rule you can you can draw this and in fact those curves shows different acceptance angle Theta uh and the concentration ratio and also the height of the height versus aperture so uh the uh this High aperture right and if you look at it if you want three times concentration that's about 21° and height aperature is about 2 to 1 and also what's important is you can never make a perfect surface reflector so every time the lights light bounce once you lost a fraction of light right so this surface is lever perfectly reflecting 100% reflecting so you want to minimize that number of BNS because every time BNS it's absorb a fraction of it and when say aluminum is you can get about 97% reflection but that's 3% if you have 10 bounces 97 10 to power you'll get small L right so you want to minimize so he this this is the the average L of bums is he calculated uh for for this geometries okay so that's the this is the concentration right now you concentrate it particular when you go to higher concentration you have to track it because the the only certain angle is accepted right so you have to go track it so let's think about how we uh with the uh TI uh how you should do track right again think about the Earth has this 23.5 degree til and in fact I haven't figur out all this a little bit detail in the earth's motion yet that tell 23.5 is the average L which it turns out the Earth is actually wble a little bit so it's wble that wobble happens between 22 to 24.5 okay and this will be important when you do the uh High concentration ratios and the acceptance angle so uh if you think about so that's what I I listed uh think in the summer right Northern Hemisphere and in the winter I come from uh so winter thousand hamere get there share of the sunlight and now let's think about the why of course it's easy to think why you need the tracking so I Lear say your radiation come in perpendicularly and when you come at the angle the mod energy you get is time Sina so you don't get all the energy you could get if you if you make this plate perpendicular to the re direction right but the uh uh the insulation not only just a s theeta change you also if you think about the the Pence through the atmosphere right different angle of incidence the Pence going through the atmosphere changes called 1/ cosine Theta sickness cosine Theta Direction relation so uh so you uh your insulation also changes and if you combine all this together uh uh those are some of the places people measure per square meter how much energy comes in and uh uh so this is like low than netive 45° uh anybody remember Boston mag I was I thought I was going to check but I forgot okay so we're close on this L you can say this a not very good solution so my calculation was too optimistic I need about 78 square me for my hos okay so how which direction is should track right if you have a solar power water or solar panel should oriented the South loss East West right so uh of course this is a this is the East West uh this is the rotation the angle rotation is uh East West Direction so of course if you do Only One X tracking you want the maximum the amount of energy received the your solar Cale area or your aperture then you want to do the uh AIS in the south north Direction and then your rotation is the uh uh so that it's a East West direction right and then say in the other direction you remember the the Earth is say uh the the Tilt right during the summer and the winter that degree will go from go back here right so this angle F fits the uh your solar cell here this on the summer and then when you go to the uh winter side this side right your anle change so the uh uh so ideally you want to track both directions okay there is one uh case people have done before uh that uh uh I think it's interesting where you do not me tracking or you do seasonal adjustment and this is just when you have a low concentration and they people use the v v sh so uh this are the uh you put a solar cell here those surfaces are reflecting surfaces is a wave group okay and uh now if you orent those way in the uh East West direction if you think about East West Direction those groups in the east west so I you you you you will use this one means you can the light here you don't need to put the solar cell so you can actually increase the flux here by a factor of two you use a less two times less of area so uh uh the the typically for this geometry uh this Grove geometry uh uh you have you can get that say concentration ratio is uh 2.5 to
three times so you can operate in that range low concentration R range and then if you do will do a little bit what you need here is a seasonal change because the acceptance angle in the uh South North Direction uh will change so uh um but there are also people now developing this Mo I was check and there people actually do tracking littleit tracking so there are even people doing South North Direction tracking but in the in theory so for those low concentration looks like you put it in Direction you still don't capture that s Theta right the sort of insulation that that's still will change because your angle coming at an angle your your projected area you're not tracking uh perpendicular there but you you use less in this case you if you do this concentration you use two or three times less solar shell so you cut a cost okay so this is the uh uh what we uh talked about is the uh concentration and tracking and uh uh I uh in terms of PV people do s concentrated P there are there's effort uh there are some uh uh company startup company I'm not sure how successful they they have been in deploying uh this is particularly when when you think about the high efficient solar cells like gum asite the maximum here you can get about 40% right that's very expensive so what you want is use a high concentration ratio to reduce the cost uh per unit area say s of incoming cost and uh uh but say the um I'm not sure how successful they are commercially and uh I know one of the problem is actually the ke transfer is a problem and the other is it's very I I think it's very important to keep the light the uniform so uh if the higher the concentration you have the if your tracking is lot accurate your light goes off the your then uh uh so you're screwed so that's the the tracking accuracy becomes very important uh now I'm going to shift next to the uh solar uh the uh uh energy conversion system and uh uh the sort of mechanical uh energy conversion and one uh the most popular in use is the 12 so uh the absorber is a tube and you concentrate the light and uh uh or so this concentration could be either by parabolic mirrors uh all the frale uh arrays in this FR now so you can see the the mirror is individually adjusted so this is not part one uh say parabolic but the angle of each mirror is adjusted so that the light Focus to the pipe there it's called the FR but I think the FR is I my understand FR is real object that's a defraction side but anyway um and this is a u a dish where you concentrate uh to uh you track 2D uh here you could the uh just do 1D da packing or uh I'm not sure people do a season adjustment or not and here you do uh you need a 2d tracking is a dish structure or you do Tower you have was a uh station of the mirror reflecting uh and and uh uh uh to the Tower and 12 is the most uh uh commonly use look at the more Char structure where you have a parabolic mirror and you have the uh pipe inside in the focal plant and this is a a typ uh pipe the solar collector pipe again it's a vacuum so the vacuum is a pretty uh High vacuum here 10us 3 m right and uh uh the uh you can imagine the challenge because the pipe itself is a steel pipe uh steel pipe and then outside is coated with Selective resolver so um this is a um typically you can you can see the absorptance is larger than 95 emittance is less than 14% at 400° in and the outer clear glass is also coated and say uh so that so it's enter reflection coding so the transmission Tiber glass Transmissions about 93% now get to 96% and uh um the um what's if you look at this what's important how you make the Cale here right high temperature Cale is really say you have a tube 100 met long and thermal expansion and seale that's those are really critical Technologies so uh temp 12 plan got the collectors you have the uh steam turbine and you also uh have very often you have to have the gas fire so you have to code generation what what what do you what do you do in the light or what happens if you have clouds coming that's actually big heit there particular for p SAR theral actually slight better because theral inertia thermal ke capacity damping that that's that's one of the that solar Thal has and uh uh you could also do uh uh some uh storage I'm not sure here has storage uh but you could you could do uh storage and the solar stal plant here the fluid itself you can see is a close loop the fluid through the pipe is close well steam generation steam turbine typic is the water based steam turbine so that's the this is the other loop the steam Lo here and in fact the in the pipe they use oil and the oil is one problem you can't go to too high temperature you go to too high temperature you decompos and uh uh so the uh oil has a stability this this is a steel area where people doing research stability problem and how you can develop higher temperature oils you can you can get to higher temperature but the your oil will not okay and this is another just a picture here uh the TP uh they if you look at the install uh uh the uh typical installed and typical size of the plant is around 100 m 100 megawatt is small uh in terms of if you compare with coire right kire plant typically one steam turbine there is one gwatt okay and uh this is too small uh you can read uh your hand out but so those are examples and what I want to point out here are the concentration here it's typically uh those concentration is between 60 to 80 uh that's um the concentration ratio and you look at the cost of the solar theral this are the uh one case where different generation 30 megawatt uh this is a US dollar megawatt hour so if you do kilowatt hour you divide it by thousand so that's about 90 Cent 19 cents per kilowatt hour cold fire is about 5 cents power power PL so here is 16 cents and there's some projecting you scale up that will go down to 10 cents the efficiency again I'm not expecting to read it I'm just let me just quoted uh uh the view efficiency lambers uh uh the collector efficiency here is uh 50% receiver efficiency 82% and the cycle that's steam turine cycle efficiency here uh 45% right uh see right now is 38% so at the end if you combine all this efficiency here this is about uh between 13 to 17% the collection efficiency is not good collector efficiency here is only about 50% you lost a lot of light in the collection so there you want to minimize the Lum of reflection the other problem is your streight light right if you design High concentration if it's not parallel you don't fall into the focal point uh interesting to look at the cost uh the cost here uh the uh uh uh if you look at here we have 58 that's the collection system 58 and structure this is a uh this is this one uh the um does not include the uh the engine so you have the Storage seral storage is here and uh uh we have 14% is the power block I do not know what exactly is that okay and uh now here is the um so this is the parabolic and uh uh again this is a break down different materials the cost structure and uh so that's the uh I thought I was trying to find out I thought I saw it before where is the uh cycle huh oh okay yeah okay so that's that's where it is yeah so cycle the cycle itself is not the uh yeah this is yeah this is so the the first one is the the overall the bottom one is the uh field component so the uh uh cycle itself is not big top the uh collector look at I think was interesting look at this here metal support structure 29% right this is a big big stuff there the steel is use a lot of Steel and uh receiver 20% mural 9% Mass support is the big one so if you can cut that cost that's good the engine the engine is here 14 that's L compared to the the solar side okay so uh if you were in Jacob Car Talk a few weeks ago he give much he does a lot of the K St so you have mirors uh uh trag sign each one and reflect to the power the center there so it's like a big two big array of MIRS reflecting the light so the how the uh solar tower and uh uh what's interesting is this is what I learned from Jacob party is that the uh the fber size and he he put a question mark but I think the fber size is actually smaller than 12 the tower you don't want to build too big okay and uh L because but the temperature is much higher so the color efficiency should be higher and uh the problem is focer focus and he showed some very interesting pictures you don't always hit your target you have a lot of missing light like so if you look at around the uh the focal point you see lot of white light that's miss the scatter and so this is the absorber uh to uh different absorber uh ways to absorb the radiation and uh what uh in this Cas is so uh I showed I think in the last lecture once you get to higher concentration your absorption absorptivity is more important the emissivity is less important okay so uh this uh I think those are pretty uh it's not uh really spectral controlled surfaces uh there really not I think they only one or two span probably has but in us there The crimer Junction mostly is 12 but it does have a uh Power System uh and uh uh so here it gives you some uh in terms of the cost uh the field itself 40% power is uh uh 14% people storage 11 and the engine is 32 and uh so uh the uh this is the uh here is a structure reflector structure t% reflector 36% uh Drive is drive for the packing is 30% and the foundation so that's the packing system itself okay the uh car efficiency uh the this from the buper here is not much better uh than the uh uh no this one is not power I think sorry for that this one is not power this is still power I so I was going to this one okay uh the uh other form of the generator is a dish so this you you make smaller this one is say 2D say track and uh uh the problem is the generator here so you have the how you can make a small power G and here uh there a stering mechanical system so stering engine and if your mechanic engineer student here the second year they always build the a sterning engine it's a burner Benz is the sterning engine uh but so uh it's so the stting engine is very different from internal combust engine that's used in the car you can heat up uh one side of this turning engine and uh uh from external so external heating uh and then you generate the mechanical motion uh to drive uh to den power the cost is much higher I learned uh so uh I do not know anybody has is using this it's not mature the most mature is the 12 okay and uh so this uh we have an efficiency number here right here is the efficiency this efficiency is the uh I look this I don't it's a pretty high efficiency that's see uh but I I can't believe this number is 29 30% 39 and so this is the stting and uh that's that's all I have in terms of the Thal mechanical systems any questions if not I will go back so this is a big stuff and I'll go back to uh it's a it's a it's simp question I think the the last two uh well at least it's stting I don't think this mature enough to about dollar per wat and some I don't have exact L ask the people around this is 10 times more expensive than uh but uh the hel St uh I have not looked at how many deployment let's say there was there was one running together with the I think the primier junction the the 12 system so uh what I want to do in the rest of the time now it's coming back to we have too many simple hand we stuff now now I want to come back to a little bit more uh math and the math the reason we want to do Le is what what are you going to say is a selective surface and it's important to have the in the case of concentrating parabolic miror it's important to have less reflection each reflection you lose very small amount of energy so you want a high reflectivity you want the high transmissivity going through glass and once you get onto the surface you absorb solar radiation you want to spectr absorb the solar radiation but do not radiate so now we this is in terms of Technology some of the key Technologies and for those technology now you have to come back to the basics how you can develop further understand what what people have and develop further so the basic is Max and uh I'm not going to spend much time on the max equation if you want to really learn you you should take a course right but you all heard about Max equations it's so set of four equations for electric field for magnetic field Edge and displacement and magnetic induction right so uh I give you the definitions of those symol electric field magnetic field displacement and J is the current and they conceal relation related placement to electric field magnetic induction to magnetic field and those constants are the material properties electri permitivity magnetic perity okay Max and uh it's a wave equation to describe electromagnetic waves so if you go to solve those waves and uh because that's important what's important I say when you do the particularly selective surface very often in terms of the base on controlling the face of those waves okay so if you look at a a simple solution a way has a directional propagation V vector and it's electromagnetic field so electric field magnetic field turns out the solution tells you they are perpendicular to each other and in fact they form a right hand rule so you go from electric field to magnetic field some point to the point pointing uh the propagation Direction and uh uh to describe a wave uh wave we have wav length and pure in time pure the inverse is frequency angular frequency is 2 pi * per uh say uh uh uh 2 pi times frequency wave Vector has Direction but also has the it's the inverse of wavelength so wave L is one over Lambda 2 pi over wave Lambda give you the magnitude of the wave vector and the direction of the wave Vector is the UN Vector here and then if you uh solve the equation uh turn turns out at the end Theon and mu combined give you the uh fractal index of the material this is a property you can look at the different materials many times people have measured it's a sometimes it's called uh the uh object constant but it's not a constant it's a frequency dependent body okay so you have the real part and imagine part and uh uh since it's a wave So the plan wave simplest solution of this wave is electric field is a function of location time this is the direction it's a vector direction of the field right and uh uh the V Vector uh frequency complex ref index so that's your solution for electric field similarly for magnetic field and this two e and H perpendicular to each other and so that's your plan with solution this one you can subtitute back into max equation you find this satisfi Max equation okay and then so this is the field what's the energy energy is the product of e and H and particular this time a average this is time dependent but to do time average you can simply calculate the E cross H complex conjugated if you do complex con you see this I Omega T can there's no time there okay so that's poting and if I do that I will get for a propagation in homogeneous medium the pointing Vector is the real part of the refractive index mu c0 exponential decay function so this exponential decay that's the problem silicon we said right silicon fot will takes that Alpha is a problem is too small okay we have to use a very thick one to absorb and this Alpha is the absorption coefficient we we mentioned before and that's relate to the me part of the complex refractive index Extinction okay so this is a this is the uh uh uh see plan inside one medium now what I can control is really you with the interface to control so you got the interfaces when you have a light comes in reflection refraction right High School you will learn that and uh uh it because the light can actually have two uh uh say you decompose into two directions it's a transverse way two directions one is your electric field is in the plan of incident so direction of coming Norm from the plan of incidence right so if your electric field is withing the plan uh all your uh electric field is in the other direction so we have the uh uh electric field if it's in the plan of incidence the magnetic field is perpendicular right it's always perpendicular to electric field so will be in the perpendicular plan so that's the uh in this case we have transverse magnetic wave or parallel if that's for electric field different LS I always I can't remember this I always just say TM then I say transverse magnetic that's more intuitive okay H field okay that's the if we if the magnetic field is a PL incidence then electric field is perpendicular that's T it's perpendicular and S so you have Expressions when you have look at the calculate the interface you have to calculate for both solar radiation is a typical combination of 5050 we see we calculate we say oh you say there a 50 te 50 TM okay now what happens first thing is reflection if you have a smooth surface right angle of incidence equal angle reflection so that's a reflection Rule and then reflection is the angle change depends based on the refractive index and then you can actually calculate the magnitude of the field reflected and refractive and again this I I'm giving you the solution the point that I want to tell you those could be calculated okay and if you want to uh learn how to calculate you got you need to take a course or pick up the book read it yourself but it depends on what it depends on is the refractive index of the material on both sides and so you need to know the property very often although you think people should list it you go when you need it you don't find it that's one and even people list it you do solar seral you want high temperature you don't find it okay so there are lot of things you can do find them that's a when we when we do the uh we want to design the first Serv let's design let's deposit a film and try to measure properties right so those are they just the feel the reflection and the energy that's reflectivity transm it so you do reflection coefficient Square you get reflectivity transmissivity you have to plug in the uh some factors in the front but again those are all depends on the complex refractive index so the final one just one example where uh it's a calculation given the refractor index is between vacuum or air which is one and say dialectric took constant gold I also took a constant but remember it's not a constant it's a wence dependent so each wav length this can change but here is calculating only the angle dependence so if it's Dil so and CA is is say zero and uh here is for the T wave transverse electric and here is for the uh TM transe magnetic and then what's interesting is this Bristal angle and they're certain so that's how people make the polarized uh glas codings uh and uh you you can choose the polarization there certain angle you can get as a no reflection at a g go is a very good reflector you you look at that right reflectivity is almost close to one so when people do selective surface varable they start with aluminum metal it's good reflection in the infrared the problem is reflect up to about 2 micr or5 micr or4 m but you don't want to uh you do you do not want to uh reflect the solar radiation you want to absorb it so you try to put materials on the surface to absorb to make them absorb between the solar radiation up to 2 Micron and then you still keep the old say infr is very reflecting which is good because that means emissivity is small so people have developed like I said let's say the different coding even for the solar theral uh uh solar hot water I said very cheap right $1.5 per two you will you go through the factory you will see their vacuum deol I saw one vacuum deposition is it's about 100 m n continuously uh dep deposit in different layers and do it at that low cost it's amazing okay okay so I'll stop here
2024-07-04