Review of Angrist bk Direct Energy Conversion (1976)

l Stanley Angrist, Direct Energy Conversion (Third Edition, 1976,AB) @ ccrtents: 1, Introduction. Resources, the Qunit and soon. 2,Energy Storage Batteries, mechnical storage, flywheels, etc. 3.Semiconductors Introduction to, alittle book onthe basics. h.Thermoelectric Generators Mainly npbar devices. Generate electricity from heat, also coolers. 5.Photovoltaic generators. Photons impinge onnpjunction devices, etc. 6.Thermionic generators. Roughly, vacuum tube diode devices convert heat toelectric current. 7.MHD generators. Use matter flow (charged plasma) instead ofusual wire motion inmagnetic field togenerate current via Maxwells equations. Might becompetitive and more efficient than regular method since fewer moving parts. e 8.FuelCells. 9.Other modes ofdirect energy conversion. Nernst effect generator, ferroelectrics, peizos, other ideas. Appendix Dt basic thermo review asrelevant tochapter 4. Direct Energy Conversion, byStanley Angrist_ (Mechnical Engineer, Carnegie Mellon) e ynacon, jenthen Chapter_1: General Introduction. 1.In1920, coal provided 78%ofUSenergy, oilwas1%, gaswasLf. In1973, coal provided 18% ofUSenergy, oilwas 46%, gas was31%. This shows arather dramatic shift Iwould say. 2.Thebasic Qnumbers: OneQ=10°aru, Total USenergy use inyear 1973 was: .08 Q World use ofenergy in1850 was .01Q/year.Worlduseofenergy in1977was.2hyear. Estimates ofreverves ofsay fossil fuels measured inQare very difficult to make. World petroleum reserves are between J,and 60Q. 3.Space has been strong motivation for direct conversion because ofweight and size requirements. Chapter 2:Energy Storage. fact: efficient auto engine isonly 15% gasoline tomotive power.fossilfuleplantgetsperhapsnoe/ peak-shaving, load-leveling, base load (that which isused 24hours/day). 1.Longdiscussion ofvarioustypesofbatteries. Iskimonly. e2.Thermal storage. England used concrete for electric heat leveling. Water is very good, waxes, salts athigher temperatures. Typical stroage is100BTU/Ibor10,000 BTU/eubicfoot. This isofcourse heat offusion. 3.Mechanical storge: (a)during off-peak, useexcess base power to_pump water to higher elevation, then bring itback during peak. Overall efficienty isperhaps70h.souse3off-peak kiltomakeanetwooh-poak KelleObviously highcapital costs, basic efficienty is90%. (b)Useoffpeak base energy tocompress air inmine caverns, then bring itback out again .Efficiency isnot mentioned for this. (c)Flywheels, see1973 Scientific America®. Youwant lightweight strong N compositve fibers togetvery high RPM. Vacuum wheel will gofor perhaps 6months. . Auto size systems have been built. Chapter 3:Introduction toSemiconductors. ,Avery long chapter with all the basic solid state stuff. Ithink Ican safely skip this, Iknow it. Chapter 4:Thermo-Electric Generators. History: Seebeckwas1821 Y,Peltierwas1834,awatchmaker aeLenz was 1838, able tofreeze and melt water using Pelteir effect yo Kelvinwas +gotrelation between effects, predicted Thomson effect. Appendix. D2 ; Convarsrer] (22pages) @ovisDueQraors4OsterttsyM6)basedovDimeropprandte. Gecst+"Mhaguas"Vor-Bubloruin TermeC162) atsPesos WBidvedoweASuven.Proceaarad™ ((968) (ODduet, Torre, Wears cokeeWak TeWe[OmefewerBow|.Oreiadonsogeprogpoardqencotgalin, fo“osea™+Rameydees T=AbyXy [vasQuovammodonical sadotinna) abecetahndinwemnteohopiesawrernsl. foes[Gators “elfen| Jase: rrsadl DraaCallow |mebod a om= ww .pCeBeteyesA;gebirFim(Sy\=tyre’ issaberag WeoberSat—R=WAcoeecotdupeYa VR. Yun g-oR aoeTe-LOR Mypeaerhpaceve. 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Bou: D=NoxVtwr-%. 0,ockuah pouot=~Tae#5Xu 14 t ee faRepenen . Qofer)=es TeKe reOe eG a) Jey (ane) Sogeeeeaye Dera Wh se+TEFOLK enae) OK, what isgoing onhere? Author isconsidering anenergy converter tobe asort ofmachine with certain characteristics: inour présent example, there are several ways you can “touch” this machine. Atthe start you cannot say that any ofthe channels isapriori input oroutput. For the picture heshows, there are four things you can do}. 1)you can supply and drain heat using the two heab reservoirs. This relates to the heat flux tern shown above. 2)you can affect the mass which flows through the device, perhaps changing its pressure orchecmical state somehow (fuel). Ithink youarenotsupposed tochange its termperature but maybe that isalso allowed. Your affecting this mass flowcouldxmbeaninputoroutput ofenergy fromthismachine. e 2 3)Finally, you can put inortake out work and electrical energy. Soall these things coule goonatonce. The above equation then tgells you how tocompute the rate atwhich entropy isdissipated bythis machine, However, weare usually only interested inthe simple case inwhich only two of the above flux/force terms arepresent.Call onethe input, the other the output, andwrite: weLoar D=4X;-IX, andefficiency =IX,/IsXy Onsager: Nelek+bO%) TWaLadki +Leo-%) _ doemt", e .—4 S (@)_(lielis(*)e YLog—boo)\Ko Alea,bot Anon aeMewotegunr's. Comoleowathom (2\grag)=X,v \ TI Keyoh[Veid Ae N w eooukpatneecover.beyAAncei‘auncleea!|. ) Near Abo . ~ a * tYody~k(& CD=GK *KN Xl \Cu“es J: ~ YueoySotearedbhnpfle [WohDeon"|.~~ a v @okmwwher NNGoes+RY; R= asasheamce : C= aamduste oe . 7) vaso) yeeconTeheRSargormbly henceD=o- rnsuer yeeoot gitT qonglid &,Caecoy) )aawst awl.D=0. Example: picture shows adam where water isrun through aturbine togenerate mechanical]| power. The two terms here are mass flow with associated potential energy difference (assume very slow flow rate sonokinetic), andtheshaft with angular velocity and torque. Inthis system, C=leakage conductance ofwater through turbine. Ie, @ havingC40hurtsbecause usesupmassflowbygenerates nowork.R=theshaft friction effect. The parameter alpha ismass displaced per revolution ofturbine and isthe interaction parameter. Poiht made: example ofR,Cuncoupled and even class (X's aredyandtorque) What you want istominimize the dissipation Dwhich isameasure ofyour lows! Ie,itmeasures P,(max) ~P,(actual). Howclose canyougettothetheoretical maximal powef! e Inthe weater driven turbine example, since Rand Cwere uncoupled, you could atleast inprinciple get them both very small and thus approach thetheoretical max efficiency (which Iguess is100% for such amachine). Example 2:Thermoelectric generator. Atemp gradient (driving force) produdes apotential gradient (output force), sothis iseven class machine. Thedésign shown however iscoupled: you want tominimize R(electrical resistance) by making area large onthe legts, but you want tominimize C(Fourier heatconduction 2oss)bymaking semeareagnali. Youcannot winonboth,sothis isacoupled device. Example 3: ADCelectric generatorf. Here the input flux iscurrent I,the output force is..STOP. The output force isvoltage out, the input flux isangukar rotation of shaft. This isodd class. R=internal resistance, C=shaft friction inverse. Again, uncoupled socan approach ideal efficiency, ie, can makd dissipation vanish. Example 4: Nernst generator. This thing generates avoltage output doe to crossed thermal and magnetic fields! AThermomagnetic deivce. Output is voltage (force), input isheat flus q,soodd class. Like the thermoelectric devices, Rand Care electrical resistance and heat conductance and are coupled, 80you cannot get ideal efficiency from aNernst. About efficiency: There isofcourse atheoretical efficiency that wecannot doanything about (eg, theCarnot efficiency). Butthesecond quation is: what isyour effmnitivmknex effectiveness towards achieving this theoretical max efficiency. Ie,evenwhenD=0youarenotgetting 100%efficiency because, eg,your low temp reservoir auld have tobeatabsolute zero. D#0 isameasure of how far away you are tothe theoretical mex. 80 eta=Yoko =effecitveness, =1whenDaQ. Ty Given your set ofthree constants forany system (like the eamples above) you can compute the effectiveness. You can find the output flux which maximizes this effectiveness, and thus get max effectiveness formulas. The result for eitherevenoroddclassmachinesisthis: ytu BNoung lpr~4 feaSp om m0 ‘Vapear aC >el. = orRC0)PC*>ffl= e Angrist Chapter_hi| Thermoelectric Generators. ry} lelHistory.Seebeckvoltage,Peltierheat,Thomsonheat,etc,verybrief. 4e2 The Thermo-electric Effects. Amaterial has acertain property called alpha(T), the thermoelectric power. Ifyou make ajunction oftwo materials, thedifference inthese alphas atsome Tiscalled the Peltier coefficient. Ifyou integrate this alpha difference from hot tocoled (or around aloop), you get the Seebeck voltage. This ishow afurnace thermocouple generates its few millivolts toactivate aswitch. Ifyourunacurrent through ajunction between twomaterials atT(or ifthejunction generates thecurrent somehow, does notmatter), youfind that the junction gives off orabsorbs heat, the Peltier heat. ThePletiercoefficient PIisjustTtimestheAlpha,soPI,=T(a,-a,)s andthePeltier heatgiven offatajunction isjustthisPItimes"the electric current. Thus, Pelteir isinteraction between anelectric current and amaterial gradient atconstant system temperature. Seebeck onthe other hand requires a temperature difference and amaterial difference, nocurrent involved. The Thomson effect involves heat transfer where thére is acurrent and atemp gradient, but nomaterial gradient. Again, the effect isproportional tocurrent and temp gradient. The coefficient is related tothe temperature derivative ofthe alpha coefficient. Beebeck: material andtemperature gradient (nopotential gradient, noI) Peltier: material andpotential gradient (no temp gradient) e Thomson? potential andtemperature gradient (nomaterialgradient)Thus you see that each ofthese “effects” involve two ofthe possible three gradients. Ageneral effect would involve all three. Ofcourse all are really facets ofthe same thermo process, soyou expect coefficients toberelated in avery simple way, which isinfact the case. 44o3 Solid State Description ofThermo effects. os Vig=Near -Astleree atboge. a : [34> IVs. Tra=Tea) =RM 4, IyaTen =Jeon /%vGAL.at Boyle pe (&&) S(paSauk—ateecataoe]Giamenl| at ~ThaTea=Gti (~lve) =E1E-&)+ 28 Cd Tn=0dea (wth/oe) = .? -2- Inthis section weseetheactual mechanism which causes these thermo effects. Basic object ofinterest isametal-semiconductro junction. Suppose electron goesfrommetalinton-typesemi.Assumecontactisohmicsoignorelittle eflare inhand diagram. Themetal ofcourse hasafermi level, which continues into thesemi. Butelectrons cannot exist atthefermi level inthesemi because itisinthemiddle ofthegap. Blectrons have tobesent uptothe conduction band inorder for them togetinto then-type bar. The junction itself must supply thermal energy togetthese entering electrons uptothe conduction band. Thus yougetPeltier cooling atajunction where electronsgofrommetal ton-type. ThePeltier coefficient isroughly dE/e where dEis fheenergy jump electrons must make. Actually, other factors obviously come into play, but this issimplest idea. Similarly, where holes enbr ap-type bar, yougetcooling because those holes take ajump down toflow inthe valence band. Where electrons enter a p-type bar, you get Pelteir heating. Soconsider anNPbype device. Where electrons enter the n-type you get cooling. Where electrons leave then-type yougetheating. Where hmksx electronsenter thep-type youalsogetheating, etc,. Thusbgsic design ofaheater/cooler lookslikethis: war het (= 4FI/allcontactsohmic. xl oot Thus youcanchain these things together. Notice that there arenoactual NP e Junctions. The Seebeck and other coefficients have opposite sign for Nand Ptype bars, mainly due tosign ofmajority carrieer. This isaway totell what type material you have. Even intrinsic has aSeebeck because holes and electrons have different mobilities. General result for Seebeck isgiven for any semi. ListAnalysis ofaThermoelectric Generator. Here anobvious NPgenerator isanalyzed. Wefind theT(x) temperature distribution inthe presence ofdrawn current I. There isJoule heating intheNandPbarsduetoshmrmatmmnduekinctiymatiodx. resistivity 3.Thereisalsoheatflowthrough thebarsduetothermal conductivity \.sPapiemodel assumes perfect contacts, soallloss isinthebars themselves. TheSeebeck coefficient alpha isjust a,+@,both positive numbers, ie,things areinseriessosospeak. Peltier isTtimes Ehissum,soitactually works. Efficiengy: Nowcomes thecrucial question. Define ny=P,/a, -Ie,foronewattofheatenergy inputatthehightemperature, howmany’‘rolemightyouget out inelectrical power? Note: Quick review ofheat engine efficiency. Defined byn=workout/heatin atTy.Noengine canbemore efficient tha theCarnot engine shoen=dT/Ty .That is, n=1-1,/Ty (seeZpage235). Thisisonlyachived onlyifengine operatesperfectly’reversibly andthere iszero entropy dissipation. Ifentropy isgenerated, (ie,ifthereissomeirreversibiliy inyourheatengine),thenyouractual e@efficiency will beless than this theoretical Carnot max. Soifyour thermal engine actsbetween 600°K and300°K, thetheoretical maxonefficiency is50%. BUT, thereal question is:howclose canapaticular oo 3. device come to the theoretical max?!! 0 Te @Rauie cudiad be, “=F (Dheo.max=IH=): Ba R=bardottrote (her 44) K=bardotel Tomek omduchait (enw 4d's). oc=dalle] —affechne Gelade« Qn, Ra=DeadAsoroteres + daBe=ae=ayAcmeck ioegeesheydomyeRK,hencewaxE,qe bd Znar=2-Cl) ae .(Send~S$yboo Queall iyemortophmige R(remm);aeft toe ae (Ben >ot=(1+2’Tar) ' aU relatCOFE anigoeMatt+Te/Ty Zta>a0 ke. emulti-stageeffictonoyealoulations eterTskipthatandgotorpage15ét08sous |DeanEames,(Ahommadschic aechicprecgear), = ° @+,=anne =60K T= Bo. Te= ante =300° MQcmakenak oeBram TaQed Bushy * 0, \Glells 1+230= urspv/?e. at -3 | Be 22610" Pc . ~ aophmigegeet, KEBOmW/*C KR Sade \ Mat=WATGemex, Vet=ADT (Buk Selh) =\28on. eat=14-2anmge. Pat=MYwakte44Ne= \h- 9=13wakkar Book goes,on toconsider power outoptimization andthen power density optimization.(power/em?). Youseethatatypical iemscaledevice candeliver 20ampsat1/10voltwithabout 10%efficiency at600-300 tempdifference, certainly quite respectible Iwould say. Materials seem relatively cheap? Maybe not. Idea: letyour tworeservoirs betheearth atdepth 1foot anddepth 10feet. Inwinter andsummer yourunyour heat engine inreverse directions, always generate electricity! Obviously you need some economics onthis. 4.5 Analysis and Design ofThermoelectr: er, Similar tolastsection forthermo generator. Thecoefficient ofperformance willbeBeta=96/?theheatremovedatlowtempdividedbymotororinputpower. Asbefore, youoptimize geometry. Thenyouoptimize oninputcurrent I.Questions of interest are: 1)what ismaxrate that heat canbepumped out? e 2)whatismaxdeltaTthatcanbemaintained, sayversusambient. - Ss QeoxprFaregle |Dwrmeshachic corde). ~~ . op 0 eTe=S2PK, cmleoot =3NK =ANC. Leggt bicdsambred o Yes aye =oc lah aia,¢\aarlt =dwatte . Ww Zw éNing,\Ie3 Une seme ance PHN relent. WY 29ane Ck=(=)=. Pa DareatmeadeR=135waledowokeNTwalleofactly« ee tetsusLAOhertbeer AheeWtbebere BRowhsYI, 4.6 The Figure ofMerit. Why are semiconductors best? Consider the continuum from insulator to metal conductor. Itturns out that the seebeck coefficient decreases asyou increase n,but the resistivity also decreases and that isgood. Generall it seemsthatmeritfigure Zmaxesoutintheygeion of.nthatissemiconductor.Generall the doping isroughly n=10° to10°) which ishigh compared tosayepitaxy of10/5. Typical Seebeck is250nV/degree. Rollie Ure and Heikes did @paxxexxtkx paper onthis subject, noits a 1961 book: Thermoelectricity. They figure that afactor of10imppovement in the figure ofmerit for these semiconductor materials would make thermal electric and cooling competitive with conventional methods inboth areas! Recall that this Angrist book is1976. Iwonder what improvements have been made sofar??? .7Actual Devices. Here the Air-Vac design isconsidered, along with various peripheral probelsm such asthermal expansion. ALittle Coleman jobbie that looks like a lantern can generate 9volts at200 mWfor 24hours. Teledyne company makes radio-isotope driventhermalgneratorsforVikingandsimilarmachines.Typical rdparameters are: 800°K =Ty, 160°K =To, input power 4000 watts (thermal),electric output power 400watts. Density of10watts/kg weight. Materials are selenides. Alittle cooling system isalso discussed, .End ofchapter. -6- Journals appearin ginthe references; e Journal ofApplied Physics Journal of Heat Transfer British Journal ofApplied Physics Intersociety Energy Conversion Engineering Conference Transactions ofthe Americal Society of H,R and ACEngineers 7 Chapter5:Photovoltaic Generators eThis isthe first material Ihave read onthis important and crucial form ofsolar energy. The basic ideas are quite simple: You know that inanpjunction there isaspace charge region ofstrong electric field. Ifaphoton "hits" inthis physical region, itcan create an electron-hole pair which isthen separated bythe field and isdriven out, so tospeak, where itappears asacurrent. Thecurrent caused byincident photons iscalled I,,ordensity J,.Essentially except forcertain loss factors this current density is “J,=eJp, where Jp, isthe flux ofphotons with energy greater than the gap. Typically’ this is 2/3 ofall the photons from the sun. what are the loss factors (see 5-30). The factor (1-r) isreflection loss atthe surface, which you usually get rid ofwith amatching layer. Then the factor (1-exp(-aL)) represents the fact that not all photons are absorbed where you want them tobeabsorbed, ieinthat junction. There are other semiconductor inside losses which are grouped into another factor. Generally speaking, however, the photo-current isreasonably close in value toetimes the useable photon flux. Now this photo current simply adds tothe normal junction current which is nonzero ifsome voltage isonthe junction, ie: N/K T=Is—To\ecy) =>\oe=WaBa)4Ve tHere J.isthe usual saturation current (density). Ifyour photojunction isopen circuifed (oc), then theabove tells youtheopen circuit voltage your diode will generate! Ifnolight, you get novoltage out. Itreally issimple. The next step istowrite P= JV (power density), and tofind the voltage and current that cause mex power. Then you can use this toget the max efficiency. Roughly speaking you get this: efficiency =VayJy/NonEay where Vmax power and Eaverage ofeach incoming photon. Finally you can roughly set J,=n, thenumber ofuseable photons. This suggests atheoreticalLimit §nsuffdevices: since E,,=1.2eVandsince V,=.l,volts youarealready down to33%. Then theuseable proton fraction isabout2/3 soyouaredown to about 22%. Devices have been made easily with 10%andupto15%. Themain problem ofcourse isthe costg ofsuch devices! Device Design: you ofcourse want alarge area ofjunction close tolight source. Use apsubstrate with athin nlayer onthe surface, only .1micron thick. This distance seems tooptimixe the number ofphotons absorbed inthe useful volume. Perhaps you could bias the thing with the battery charged toget the volume idealized. The substrate contact iseasy, the surface contact isusually agrid of metal layed onthe surfece and ofoptimal width and pattern, Apracticaldesignismentioned.Acrucialnumberisthis:theuseable ryphoton flux when multiplied byeis48mA/cem® forsilicon. Perhaps this isareasonable value andnotoptical. So50mA/em* iswhat youaregoing to getoutof1cm’, less inefficiency (which inexample reduces this toabout 13mA/cm2 ) aa "ae Themaxpower output voltage isabout .55volts, andthemaxpower current isabout 12mA. Thus wearegetting about 7nWW/em®. What doIthink ofthat!? Thisbecomes70watts/m® whichisinfactabout7%ofthe1000watts/m2. eTypical efficiency =10% Typical electric DCpower generated =100watts/n ofsilicon. Silicon ofrequired grade costs $100/1b. Fabrication ofsuchcellsisdiscussed, theCdScellalsomentioned as being cheaper. Present idealized costofcellsisabout$1500pernm?=@100watts. Thinkofthisas$15,000 forakilowatt. Obviously noonecanreally afford thisfortheirroof.Installed ncuelar plantisonly$1500/kw theysay,so that isthe problem. Massproduction methods however mightmakeasilicon farmfeasable. This issomething tolook into, articles are referenced: Cherry, JofEngineering for Power 94A2April 1972. Other details 1)evenif15%efficiency isreached, youstill haveproblem ofweather degradation ofthe cells and you have toalways bereplactng them. 2)amassmarket isneeded before massproduction willbegin onthese things.At presentthe$15000/kwinstallation figureisjusttoohighcomparedtothe e$1500/kw for even nuclear. 3)Perhaps some other material will have abetter band gapandbeable touse more ofthe solar photons. 4)water andclouds affect solar flux. Evenwithanideal gapat1.70eV,the maxtheoretical efficiency ofacell seems tobeabout 32%. This ispretty good though, inmyopinion. Thereal factor iscost, notefficiency aslongasinreasonable range. Thischapter wasagoodintroduction tothesubject. About50pages. Many references given, butbook isalittle outofdate, being 1976.