17.Thermo Photo Voltaic Cell

8/9/2019 17.Thermo Photo Voltaic Cell

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Electronics and Power-System Models: Thermo-Photo-Voltaic Cell

Thermo-Photo-Voltaic Cell

Introduction

The following example illustrates an application that maximizes surface-to-surface radiative fluxes and

minimizes conductive heat fluxes.

A thermo-photo-voltaic (TPV) cell generates electricit from the com!ustion of fuel and through

radiation ("ef. #). $igure %-&&depicts the general operating principle. The fuel !urns inside an

emitting device that radiates intensel. Photo-voltaic (PV) cells'almost lie solar cells'capture the

radiation and convert it to electricit. The efficienc of a TPV device ranges from # to %*. +n some

cases, TPVs are used in heat generators to co-generate electricit, and the efficienc is not so critical.

+n other cases TPVs are used as electric power sources, for example in automo!iles ("ef. %). +n those

cases efficienc is a maor concern.

Figure 2-55: Operating principle of a TPV device (Ref. 3) and an i!age of a protot"pe #"#te! (Ref. $).

TPV sstems, unlie tpical electronic sstems, must maximize radiation heat transfer to improve

efficienc. owever, inherent radiation losses'radiation not converted to electric power'contri!utes

to the PV cells/ increased temperature. $urther, heat transfer through conduction results in increased
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cell temperature. PV cells have a limited operating temperature range that depends on the tpe of

material used. 0olar cells are limited to temperatures !elow 80C, whereas high-efficienc

semiconductor materials can withstand as much as 1000C. Photovoltaic efficienc is often a function

of temperature with a maximum at some temperature a!ove am!ient.

To improve sstem efficienc, engineers prefer to use high-efficienc PV cells, which however can !e1uite expensive. To reduce sstem costs, engineers wor with smaller-area PV cells and then use

mirrors to focus the radiation on them. owever, there is a limit for how much ou can focus the

!eams2 if the radiation intensit !ecomes too high, the cells can overheat. Thus engineers must

optimize sstem geometr and operating conditions to achieve maximum performance at minimum

material costs.

The following model, which uses the 3eneral eat Transfer application mode, investigates the

influence of operating conditions (flame temperature) on sstem efficienc and the temperature of

components in a tpical TPV sstem. The model can also assess the influence of geometr changes.

%odel &efinition

Figure 2-5': eo!etr" and di!en#ion# of te !odeled TPV #"#te!.

$igure %-&4depicts the geometr and dimensions of the sstem under stud. To reduce the

temperature, the PV cells are water cooled on their !ac side (at the interface with the insulation).

The following e1uation descri!es the heat fluxes, radiative flux, and conductive flux2 after it comes the

!oundar condition e1uation
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where is the densit, kdenotes the thermal conductivit (56(m78)), Qrepresents the volume heatsource (56m9), n is the surface normal vector, his the convective heat transfer film coefficient (56

(m%78)), Tinfe1uals the temperature of the convection coolant, e1uals the surface emissivit, J0is the

surface radiosit expression (56m%, further descri!ed in the Heat Transfer Module Users Guide), and

e1uals the 0tefan-:oltzmann constant.

Conduction is alwas present on the different !oundaries. The model simulates the emitter with a

specific temperature, Theater, on the inner !oundar. At the outer emitter !oundar, it taes radiation

(surface-to-surface) into account in the !oundar condition. +t simulates the mirrors ! taing

radiation into account on all !oundaries and appling a low emissivit. The inner !oundaries of the PV

cells and of the insulation also mae use of radiation !oundar conditions. owever, the PV cells have

a high emissivit and the insulation a low emissivit. $urther, the PV cells convert a fraction of the

irradiation to electricit instead of heat. eat sins on their inner !oundaries simulate this effect

according to

where Gis the irradiation flux (56m%) and pvis the PV cell/s voltaic efficienc. The latter depends on

the local temperature, with a maximum of 0.2at 8008;

$igure %-&


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Figure 2-5*: PV cell voltaic efficienc" ver#u# te!perature.

At the outer !oundar of the PV cells, the model applies convective water cooling ! setting hto 5056

(m%78), and Tambto 2738. $inall, at the outer !oundar of the insulation it applies convective cooling

with hset to 556(m%78) and Tambto 2938.

Ta!le %-?* *.*

#

PV cell =9 %*** >?* *.=

=

insulation *.*& depicts the stationar distri!ution at operating conditions with an
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emitter temperature of 20008.

Figure 2-5+: Te!perature di#tri,ution in te TPV #"#te! en te e!itter te!perature i# 2 /.

As the upper plot in$igure %-&=shows, the PV cells reach a temperature of approximatel 18008. This

is significantl higher than their maximum operating temperature of 16008, a!ove which their

photovoltaic efficienc is zero (see $igure %-&< on page #?>).

+t is interesting to investigate what the optimal operating temperature is. The lower plot in $igure %-&=

investigates at what temperature the sstem achieves the maximum electric power output. The

optimal emitter temperature for this configuration seems to !e !etween 16008 and 17008, where the
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electric power (irradiation multiplied ! voltaic efficienc) is maximum.

Figure 2-50: PV cell te!perature (top) and electric output poer (,otto!) ver#u# operating te!perature.


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The next step is to loo at the temperature distri!ution at the optimal operating conditions ($igure %-

4*).

Figure 2-': Te!perature di#tri,ution and #urface irradiation flu1 in te #"#te! at an operating e!itter te!perature of' /.

5hen the emitter is at 16008, the PV cells reach a temperature of approximatel 12008, which the

can withstand without an pro!lems. @ote that the insulation reaches a temperature of approximatel

8008 on the outside, suggesting that the sstem transfers a significant amount of heat to the

surrounding air.

The plot also depicts the irradiative flux, which varies significantl along the circumference of the PV

cell and insulation acet. To further investigate this effect, $igure %-4#plots the irradiative flux along

a 1uarter of the circumference separatel at this operating condition. Clearl the variation it shows is

related to the positions of the mirrors and is an effect of shadowing.
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Figure 2-': Irradiation flu1 along te PV cell and in#ulation inner #urface for one uarter of te device circu!ference.

This plot can help optimize the mirror geometr as well as help decide how large the PV cells should

!e and where the should !e placed.

A general conclusion is that this tpe of modeling can shortcut the prototpe development time and

optimize the operating conditions for the finalized TPV device.

Reference#

#. http;66lmn.we!.psi.ch6shine6$lerTPVB.pdf.

%. http;66vri.etec.wwu.edu6viing%=paper.htm.

9. Courtes of B. $ontes, Catella 3enerics A:, 0weden.

?. Courtes of r. . 5ilhelm, Paul 0herrer +nstitute, 0witzerland.

Model Library pa!"

Heat_Transfer_Module/Electronics_and_Power_Systems/TPV_cell

%odeling 4#ing te rapical 4#er Interface

MODEL NAVIGATOR

1

Dpen the Model Na#igaor. $rom the $pa%e dime&'io&list, select .

2

+n the list of application modes, select *ea Tra&'+er Mod,le-.e&eral *ea Tra&'+er.


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3

ClicOK.

OPTIONS AND SETTINGS

1

$rom the Opio&'menu open the 0e'/.rid $ei&g'dialog !ox. 3o to the 0i'page. +n !oth the

0 mi&and y mi&edit fields, tpe -0.05, and in !oth the0 ma0and y ma0edit fields, tpe 0.05.

2

Dn the .rid page, clear the ,ochec !ox. +n !oth the 0 'pa%i&g and y 'pa%i&gedit fields tpe

0.002. Clic OK.

3

$rom the Opio&'menu, select Co&'a&'. +n the dialog !ox that opens, enter the

following names, expressions, and (optionall) descriptions2 when done, clic OK.

NME E1P2E$$3ON E$C23PT3ON

T_heater 000!"# Tem$erature% emitter inner'oundary

($_air 00!)/*+,"# S$ecific heat ca$acity% air

h_air 5!/*m2"# Heat transfer coefficient% air

T_air 21!"# Tem$erature% air

+_ins 0.05!/*m"# Thermal conducti3ity% insulation

rho_ins 400!+,/m# ensity% insulation

($_ins 00!)/*+,"# S$ecific heat ca$acity%insulation

e_ins 0. Surface emissi3ity% insulation

+_m 0!/*m"# Thermal conducti3ity% mirror

rho_m 5000!+,/m# ensity% mirror

($_m 670!)/*+,"# S$ecific heat ca$acity% mirror

e_m 0.0 Surface emissi3ity% mirror


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+_emit 0!/*m"# Thermal conducti3ity% emitter

rho_emit 2000!+,/m# ensity% emitter

($_emit 100!)/*+,"# S$ecific heat ca$acity% emitter

e_emit 0.11 Surface emissi3ity% emitter

+_$3 1!/*m"# Thermal conducti3ity% PV-cell

rho_$3 2000!+,/m# ensity% PV-cell

($_$3 670!)/*+,"# S$ecific heat ca$acity% PV-cell

e_$3 0.11 Surface emissi3ity% PV-cell

h_cool 50!/*m2"# Heat transfer coefficient%coolin, water

T_cool 24!"# Tem$erature% coolin, water

4Choose Opio&'-E0pre''io&'-$%alar E0pre''io&', then define the followingexpressions;

NME E1P2E$$3ON

rho_air .0e5!Pa#26.6e-!+,/mol#/*6.!)/*mol"#T

+_air 0*-.4280.695lo,0*a's*T!/"#!/*m"#

eta_$3 0.2*-*T/600!"#-2*T:900!"#

5

Dptionall, enter the descriptions ensity% air2 Thermal conducti3ity% air2 and

Voltaic efficiency% PV cell.

6

Clic OK.

GEOMETRY MODELING


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1

Create two circles. To do so, choose ra4-$pe%i+y Ob5e%'-Cir%le. $or the first circle, tpe 0.05

in the 2adi,'edit field, and for the second, tpe 0.04.

2

Clic the Creae Compo'ie Ob5e%!utton on the raw tool!ar. +n the $e +orm,la edit field, tpe

(2-(, then clic OK.

3

0pecif a rectangle ! pressing 0hift and clicing the 2e%a&gle!utton on the raw tool!ar. +n !oth

the Wid!and *eig!edit fields, tpe 0.05, and in the 06ba'eedit field, tpe -0.05. Clic OK.

4

0elect all the o!ects and clic the 3&er'e%io&!utton on the raw tool!ar. This creates the

composite o!ect CD%, which is a 1uarter of an annulus.

5

To create the first mirror, create two rectangles; $or each rectangle, press 0hift then clic the

2e%a&gle!utton on the raw tool!ar, enter settings from the ta!le !elow, and then clic

OK.

O7JECT W3T* *E3.*T

7$E 167$E 867$E

"# 0.0 0.002 Center -0.07 0.05

"% 0.002 0.009 Center -0.07 0.04

6

0elect !oth rectangles, then clic the Creae Compo'ie Ob5e%!utton on the raw tool!ar. Clear

the Keep i&erior bo,&darie'chec !ox, then clic OKto create the union.

7

$rom the ra4menu open the 9ille/C!am+erdialog !ox.

8

+n the :ere0 'ele%io&list clic the CO;folder, then select Vertices #, %, &, and >E#*. +n the

2adi,' edit field, tpe 0.5e-, then clic OK. This step creates the composite o!ect CD9.

9

Cop and paste CD9 ! pressing CtrlFC and then CtrlFV. 5hen pasting, specif the i'pla%eme&

for 0as 0.07and for y as 0.009. Clic OK.

1

0

0elect CD9. Clic the 2oae!utton on the raw tool!ar. +n the 2oaio& a&gleedit field tpe 75.

3o to the Ce&er poi&area2 in the 0edit field tpe -0.07, and in the yedit field tpe 0.07.

Clic OK.

1

1

Clic the Li&e!utton on the raw tool!ar. raw a line ! left-clicing at (*, *)'ou can read the

position in the lower-left corner of the user interface'and at (*.*?4, *.*#%). $inalize the line !

right-clicing in the drawing area.

1

2

"epeat the procedure in the previous step to draw three additional lines !etween the coordinates (*,

*) and (*.*%?, *.*?*), !etween (*, *) and (*.*#%, *.*?4), as well as !etween (*, *) and

(*.*?, *.*%?).1

3

0elect the circle o!ect CD% and the first line, :#. Clic the Coer%e o $olid!utton on the raw

tool!ar.

1

4

Gsing the mouse, select the annulus o!ect (now named CD?) and the second line. Clic Coer%e o

$olid.

1

5 0elect the annulus o!ect (now named CD%) and the third line, :9. Clic Coer%e o $olid.


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1

6 0elect all o!ects (press CtrlFA) and clic Coer%e o $olid.

1

7

Press CtrlFC to cop the new composite o!ect. Press CtrlFV, then clic OKto paste it with zero

displacement.

1

8 Clic 2oae. $or the 2oaio& a&glespecif 10, then clic OK.

1

9

"epeat the paste-and-rotate procedure for 60and 240degrees to complete the circular o!ect.

Press CtrlF to clear the selection !efore selecting the original composite o!ect to mae a cop and

then rotate it.

2

0

raw two circles using the menu item ra4-$pe%i+y Ob5e%'-Cir%le. $or the first one, tpe

0.07in the 2adi,'edit field, and for the second one, tpe 0.04.

2

1 Clic the


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PHYSICS SETTINGS

u,do!ain etting#1

$rom the P!y'i%'menu, select $,bdomai& $ei&g'.

2

+n the 3&i page, select all the su!domains. +n the T(0)edit field enter T_air.

3 3o to the .e&eralpage and specif the following settings2 when done, clic OK.

$ETT3N.$ $=7OM3N ;

$=7OM3N$> ?>@> A> ;> ;?>;A> ;B

$=7OM3N$> B>D> ;> ;;> ;F>;> ;@

$=7OM3N ;D

$=7OM3N$F>

k +_ins +_$3 +_m +_emit +_air

rho_ins rho_$3 rho_m rho_emit rho_air

Cp ($_ins ($_$3 ($_m ($_emit ($_air

Dpacit Dpa1ue Dpa1ue Dpa1ue Dpa1ue Transparent

6oundar" 7ondition#

1

$rom the P!y'i%'menu, open the 7o,&dary $ei&g' dialog !ox.

2

0elect the 3&erior bo,&darie'chec !ox to ena!le the specification of interior !oundaries.

3

0elect all the !oundaries of the mirror o!ects ! using the mouse to draw a !ox around each mirror.

Press and hold the Ctrl e on the e!oard to add selections.


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4

Clic the 7o,&dary Co&diio&ta!. +n the 7o,&dary %o&diio&list, select *ea 'o,r%e/'i&k. +n

the 2adiaio& ypelist, select $,r+a%e6o6',r+a%e. +n the edit field for $,r+a%e emi''i#iy, tpe

e_m.

5

+n the 7o,&dary 'ele%io&list, choose =, #?#, and #?> (the outer !oundaries of the

insulation). +n the 7o,&dary %o&diio&list, select *ea +l,0. +n the !edit field for the *ea

ra&'+er %oe++i%ie&, tpe h_air, and in the Tinfedit field for E0er&al empera,re, tpe T_air.

+n the 2adiaio& ypelist, select $,r+a%e6o6ambie&. +n the edit field, tpe e_ins, and in the

Tambedit field for mbie& empera,re, tpe T_air.

6

+n the 7o,&dary 'ele%io&list, choose #*#, #*%, #*&, #*4, #99, #9?, #?%, #?9, and

#>? (the inner !oundaries of the insulation). +n the 7o,&dary %o&diio&list, select *ea

'o,r%e/'i&k. +n the 2adiaio& ypelist, select $,r+a%e6o6',r+a%e. +n the edit field, tpe

e_ins.

7

+n the 7o,&dary 'ele%io&list, choose ==, #**, ##=, #%*, #&, #>#, and #>% from the list (the

outer !oundaries of the cells). +n the 7o,&dary %o&diio&list, select *ea 'o,r%e/'i&k. +n the !

edit field, tpe h_cool, and in the Tinfedit field tpe T_cool.

8

+n the 7o,&dary 'ele%io&list, choose #*9, #*?, ##&, ##4, #&&, #&4, #* (the inner

!oundaries of the cells). +n the 7o,&dary %o&diio&list, select *ea 'o,r%e/'i&k. +n the

2adiaio& ypelist select $,r+a%e6o6',r+a%e. +n the G0edit field for *ea 'o,r%e/'i&k, tpe

-;_ht,heta_$3, and in the edit field tpe e_$3.

9

+n the 7o,&dary 'ele%io&list, choose #%, #?9, and #?4 (the outer !oundaries of the

emitter). +n the 7o,&dary %o&diio&list, select *ea 'o,r%e/'i&k. +n the 2adiaio& ypelist,

select $,r+a%e6o6',r+a%e. +n the edit field, tpe e_emit.

1

0

$inall, in the 7o,&dary 'ele%io&list, choose #9#, #9%, #??, and #?& (the inner !oundaries of the

emitter). +n the 7o,&dary %o&diio&list, select Tempera,re. +n the T0edit field for

Tempera,re, tpe T_heater.

11 Clic OK.

MESH

1

$rom the Me'!menu open the 9ree Me'! Parameer'dialog !ox.

2

+n the Prede+i&ed me'! 'iHe'list select Coar'er.

3

3o to the 7o,&dary page. Gsing the mouse, select all !oundaries of the mirrors and of the emitter/s

outer !oundar. +n the Ma0im,m eleme& 'iHeedit field tpe e-.

4

0elect all inner !oundaries of the insulation and the PV cells (#*#, #*%, #*9, #*?, #*&, #*4, ##=,

#%*, #99, #9?, #?%, #?9, and #>?). +n the Ma0im,m eleme&'iHeedit field tpe 2e-. Clic 2eme'!, then clic OK.

COMPUTING THE SOLUTION

1

$rom the $ol#emenu open the $ol#er Parameer' dialog !ox.

2

Dn the .e&eralpage, find the $ol#erlist and select Parameri%. +n the Li&ear 'y'em 'ol#erlist

select ire% (=M9PCK). +n the Parameer &ame'edit field tpe T_heater, and in the


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Parameer #al,e'edit field tpe ran,e*000%00%2000.

3

Dn the Parameri%page, select the Ma&,al ,&i&g o+ parameer 'ep 'iHechec !ox. +n the

3&iial 'ep 'iHeedit field tpe 00. 0pecif a Mi&im,m 'ep 'iHeof 25and a Ma0im,m 'ep

'iHeof 00.

4

Clic the $aio&aryta!. +n the Ma0im,m &,mber o+ ieraio&'edit field tpe 50.

5

Clic OK.

6

Clic the $ol#e!utton on the Hain tool!ar.

POSTPROCESSING AND VISUALIZATION

$igure %-&>is the default postprocessing plot. To reproduce the plots in $igure %-&=, follow these

steps;

1

$rom the Po'pro%e''i&gmenu open the omai& Plo Parameer'dialog !ox.

2

Dn the .e&eralpage, clear the chec !ox next to the la!el Eleme& re+i&eme& (doing so disa!les

automatic refinement), then in the corresponding edit field tpe .

3

3o to the Poi&page. +n the Poi& 'ele%io&list, choose Point 4.

4

+n the E0pre''io&edit field, tpe ;_ht,heta_$3, then clic pplyto generate the upper plot.

5

Clic the .e&eralta!. $rom the Plo i&list, select Ne4 +ig,re.

6

"eturn to the Poi& page. +n the E0pre''io&edit field, tpe T.7

Clic OKto close the dialog !ox and generate the lower plot.

To generate $igure %-4*, follow these steps;

1

$rom the Po'pro%e''i&gmenu, open the Plo Parameer'dialog !ox.

2

Dn the .e&eralpage, find theParameer #al,elist and select ;@.

3

Dn the 7o,&darypage, select the 7o,&dary plochec !ox.

4

Dn the 7o,&dary aapage, select $,r+a%e irradiaio&from the Prede+i&ed G,a&iie'list.

5

Dn the *eig! aapage, select the *eig! daachec !ox.

6

$rom the Prede+i&ed G,a&iie'list, select $,r+a%e irradiaio&.

7+n the 7o,&dary %olorarea, select Cy%li%from the Color ablelist.
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8

Clic OKto close the dialog !ox and generate the plot.

9

To mae the axes and the grid disappear, dou!le-clic the 13$and .23!uttons on the status !ar

at the !ottom of the user interface.

To reproduce $igure %-4#, follow these steps;

1

$rom the Po'pro%e''i&gmenu, open the omai& Plo Parameer'dialog !ox.

2

Dn the .e&eralpage, find the$ol,io&' o ,'elist and select ;@. $rom the Plo i&list, select

Ne4 +ig,re.

3

Clic the Li&e/E0r,'io&ta!, and in the Prede+i&ed G,a&iie'list select $,r+a%e irradiaio&.

4

+n the 7o,&dary 'ele%io&list, choose #*%, #*?, #*4, ##4, and #9? (a 1uarter of the sstem/s

inner wall). Clic OK.

"elated

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Documents

17.Thermo Photo Voltaic Cell