combustoremitter design tool for a thermophotovoltaic energy converter lindler

7/28/2019 Combustoremitter Design Tool for a Thermophotovoltaic Energy Converter Lindler

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~ Pergamon Energy Convers, Mgmt Vol. 39, No. 5/6, pp. 391-398, 1998Published by Elsevier Science LtdPrinted in Great BritainPIhS0 19 6- 89 04(9 7) 0001 8- 6 0196-8904/98 $19.00 + 0.00

C O M B U S T O R / E M I T T E R D E S I G N T O O L F O R AT H E R M O P H O T O V O L T A I C E N E R G Y C O N V E R T E R

K E I T H W . L I N D L E R a nd M A R K J . H A R P E RUnited States Naval Academy, Naval Architecture, Ocean and Marine Department,590 Hollow ay Road, Anna polis, Mar yland 21402-5042, U.S.A.

(Received 5 July 1996)

Abstract--Recently, there has been a renewed interest in thermophotovoltaic (TPV) energy conversion.A TPV device converts radiant energy from a high temperature incandescent emitter directly intoelectricity by photovoltaic cells. The current research at the U.S Naval Academy involves the design,construction and demonstration of a prototype TPV converter that uses a hydrocarbon fuel (such asnatural gas) as the energy source. Since the photovoltaic cells are designed to convert radiant energyefficiently at a prescr ibed wavelength, it is imp orta nt that the tempe ratur e of the emitter be nearlyconstant over its entire surface. The U.S Naval Academy is developing a small emitter (with a highemissivity) that can be maintain ed near 1478 K (2200F). This paper describes the comput er spreadshe etmodel that was written as a tool to be used for the design of the high temperature emitter. Published byElsevier Science Ltd.Thermopho tovoltaic Spreadsheet Energy conversion Combust ion Thermal emitter

N O ME N CL A T U RE,4 = AreaD = Pipe (or hole) diameter

DIV = Parameter used to control convergencef = Fluid friction factorF~ 2 = Radiat ion shape factorg = Gravitational constanth = Convection heat transfer coefficientHE = Head loss for fluid flowkr = Fluid resistance coefficientk = Thermal conductivityL = Pipe lengthLHV = Fuel lower heating valuem = MassP = Pressureq = Rate of heat transferRe = Reynolds numberT = TemperatureV = Fluid veloci ty% = Percentage of fuel combustedAx = Segment length

Greeks =E = Emissiv ityr/= EfficiencyY = Specific weig htp = Densitycr = Stefan-Boltzmann constant/~ = Viscosity

INTRODUCTIONA l t h o u g h t h e p h o t o v o l t a i c e ff e c t h a s b e e n k n o w n f o r o v e r a c e n t u r y , i t d i d n o t b e c o m e u s e fu lu n t i l 1 95 4. A t t h a t t i m e , r e s e a r c h w i t h s in g l e c r y s t a l s il i c o n d e v i c e s w a s s u c c e s s f u l a t i n c r e a s i n ge f fi c ie n c y f r o m 1 t o 6 % [ 1 ]. E f f ic i en c ie s r e m a i n e d b e l o w 2 5 % u n t il 1 98 9 w h e n t h e G a A s / G a S bt a n d e m c e l l d e m o n s t r a t e d e f f ic i e n ci e s i n e x c e s s o f 3 5 % [ 2 ] . W h i l e c e ll e n e r g y c o n v e r s i o n e f f i c ie n c yc a n n o t b e n e g l e c te d , p o w e r d e n s i t y is m o r e i m p o r t a n t a s f a r a s c el l e c o n o m i c s is c o n c e r n e d . S o l a r

391


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392 LINDLER and HAR PER: COMBUSTOR/EMITTERDESIGN TOOLpho tovo l t a i c s a re l im i t ed by inhe ren t p rob lems wi th t he sou rce . F i r s t , t he sun i s app rox imate ly 93mi l l i on mi l e s away caus ing the ene rgy dens i ty reach ing the ea r th t o be ve ry smal l . A l so , t he sunon ly sh ines du r ing the day , and expens ive ba t t e ry s to rage i s requ i red fo r ex t ens ive pe r iods o f c loudcover . S ince the ene rgy sou rce fo r T PV energy convers ion i s ma n-ma de , no such expens ive s to rageis requi red .

T h e r m o p h o t o v o l t a i c s h a s m a n y a d v a n t a g e s o v e r c o n v e n t i o n a l p o w e r s y s t em s . S o m e o f t h e seadvan tag es a re mo du la r i t y , po r t ab i l i t y , w ide cho ice o f fuel s , s i len t ope ra t i on , reduced a i r po l lu ti on ,rap id s t a r tup and h igh ene rgy dens i ty . TPV migh t be used fo r po r t ab l e e l ec t r i c power , s t andbyelect r ic power, s tand a lone e lect r ic generat ion , resident ia l cogenerat ion and c lean e lect r ic vehic les .

Severa l g roup s a re cu r ren t ly i nvo lved in the dem ons t ra t i on o f TPV t echno logy . JX Crys t a l s Inc .bu i l t the w or ld ' s f i r st TPV genera to r t ha t success fu lly i n t eg ra t ed in f ra red sens it ive GaS bpho tovo l t a i c cel ls w i th a na tu ra l gas f ired emi t t e r [3 ] . The T ecogen D iv i s ion o f Th erm o Pow erCorpora t ion i s a t t empt ing to ach i eve a 300-500 wa t t TPV se l f -powered gas fu rnace , enab l ingopera t ion in t he even t o f el ec tr i c g rid ou t ages [4 ] . Sweden i s in t e res t ed i n u s ing T PV t echno log yfo r cogene ra t ion o f hea t an d e l ec t r ic i t y u s ing woo d as t he fue l [5 ]. N AS A Lewis Resea rch C en te ra n d M c D o n n e l l D o u g l a s A e r o s p a c e a r e i n v o lv e d in a T P V p r o j e c t w h ic h e m p l o y s c o n c e n t r a t e dso l a r ene rgy as t he hea t sou rce [6 ] .

E M I T T E R D E S I G NA cy l ind r i ca l des ign fo r t he TPV emi t t e r was chosen fo r i t s s imp l i c i t y and i t s ab i l i t y t o reduce

the rmal l o sses t o t he su r round ings . Ga seo us fue l f rom a p ressu r i zed t ank f l ows in s ide a sma l ld i amete r " f l ame tube" a s shown in F ig . 1 . A l a rge r d i amete r t ube a round the f l ame tube con ta insthe ox idan t f l ow and se rves a s t he emi t t e r su r face . Pho tovo l t a i c ce l l s a re p l aced in a cy l ind r i ca lpa t t e rn a ro und the emi t te r . N um ero us ho l es i n the f lame tube a l l ow the fue l t o f l ow th rough tothe ox idan t . T he f ue l -o x idan t mix tu re i s i n it i al ly i gn i ted by a spa rk . Once ign i t ion has been s t a r t ed ,

E x h a u s t

H e a t E x c h a n g e r

/E m i t t e r tube

.c, ITPV cells

F l o w m e t e r " - - - ~ 1 ~ ~ Valve

~ A i r ~

I g n i t e r

~ml

- - F lo w m et e rValve

F u e l

Fig. 1. Schematic of the TPV co mb ustor system.


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LINDLER and HARPER: COMBUSTOR/EMITTER DESIGN TOOL 393

H E A T F L O W L I N E SPV Cell P~ ~ Cell

F l a m e T u b e I mfuel LHV F l a m e Tubec T k ffi conduction

/

m c p d e l T ~ ~ 1 ~ F u e l c = c ~ e ~ i o nt r - - ~ i m i o n

Fig. 2. Flowchart showing the heat transfer mechanisms for a single combustor node.

combustion is maintained as long as fuel and oxidant are supplied. Fuel flow is contro lled by thenumber and size of the holes in the flame tube and by a pressure reducing valve located on thefuel tank. Oxidant flow is controlled by a pressure reducing valve on the oxidant tank. In orderto improve system efficiency and to maintain the emitter at cons tant temperature, the hot exhaustgas leaving the combustor can be used to preheat the oxidant.

A computer spreadsheet model of the entire TPV combustor system was written by the authorsin order to design a constant temperature emitter. The computer model solves for the temperaturesand mass flow rates at all points in the system. In order to solve the necessary energy and massbalances, the flame tube and emitter are numerically broken into 20 segments. The inputs to theprogram include all dimensions and materials describing the system, fuel and oxidant type, fuelpressure, air/fuel ratio and heat exchanger effectiveness. The program solves for the pressure,temperature, density, viscosity and mass flow rate at each point in the system by simultaneouslysolving the mass and energy balances for each of the 20 segments. Heat transfer by convection,conduction and radiation are included in the model. Figure 2 shows the mechanisms of heattransfer for each o f the 20 fuel, flame tube, combustion gas, emitter and photovoltaic cell segments.

SPREADSHEET DESCRIPTIONThe thermophotovoltaic combustor design program was developed using the "Quattro Pro 5.0for Windows" spreadsheet. Spreadsheets, such as this one, are organized as a notebook with"pages". Each page consists of a matrix of "cells" arranged in rows and columns. The user can

input text, a numerical value or a formula in the cells. The formula in one cell can refer to thevalues stored in other cells on the same page or another page of the spreadsheet. This gives theuser the ability to model extremely complex engineering problems involving equations that are"circula r". The combustor design is said to be circular because, for example, temperature affects


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394 LINDLER and HA RPER : COMBU STOR/EMITTERDESIGN TOOL

P r e s s u r e

F u e lP r o p e r t i e s

Ox i dan tP r o p e r t i e s

Ve l oc i t y H e a d L o s s

C o e f f i c i e n t

R e y n o l d sN u m b e r

Dens i t y

Vi s cos i t yP r e s su r e ~ ~ r M a s s F I

Dro ps / k , . R a t e

N e t E n e r gyT r a n s f e r

M a t e r i a lP r o p e r t i e s

Fig. 3. Flowchart showing the circular nature of the com bustor design problem.

d e n s i t y w h i c h a f f e c t s m a s s f l o w r a t e s w h i c h a f f e c t th e n e t e n e r g y t r a n s f e r w h i c h , i n t u r n , a f f e c t st e m p e r a t u r e . T h e c i r c u l a r n a t u r e o f t h e p r o b l e m a t h a n d is a c t u a l l y m u c h m o r e i n v o l v ed . F i g u r e 3is a fl o w c h a r t r e p r e s e n t a t i o n o f t h e c ir c u l a r n a t u r e o f th e c o m b u s t o r d e s i gn p r o b l e m . T h e a r r o w si n F i g . 3 i n d i c a t e w h i c h p r o p e r t i e s a r e r e q u i r e d t o c a l c u l a t e e a c h n e w p r o p e r t y .

E a c h e l l i p s e i n F i g . 3 r e p r e s e n t s a s i n g l e p a g e o n t h e s p r e a d s h e e t . T h e r e a r e s e v e r a l a d d i t i o n a lp a g e s f o r d a t a i n p u t , g r a p h i c a l o u t p u t , h e l p s c r e e n s a n d a c o v e r p a g e w h i c h a c t s a s a t a b l e o fc o n t e n t s . T h e t a b le o f c o n t e n t s , s h o w n i n F ig . 4 , a ll o w s th e u s e r t o j u m p t o a n y o t h e r p a g e o nt h e s p r e a d s h e e t t h r o u g h t h e u s e o f " m o u s e b u t t o n s . " I n g e n e r a l, a fi rs t t i m e u s e r w o u l d " c l i c k "t h e m o u s e b u t t o n l a b e l e d H E L P a n d w o u l d b e l e d t o s e v e r a l p a g e s t h a t d e s c r i b e d h o w t o u s e t h ep r o g r a m . A f t e r r e t u r n i n g t o t h e t a b l e o f c o n t e n t s , th e u s e r w o u l d c h o o s e " D a t a I n p u t . " A s a m p l ed a t a i n p u t p a g e a p p e a r s a s F i g . 5 .

T h e n u m e r i c a l v a l u e s t h a t a r e s h a d e d i n F ig . 5 in d i c a t e t h e v a l u e s t h a t t h e u s e r c a n s p e c i f y . A l lo t h e r v a l u e s a r e " l o o k e d u p " o r c a l c u l a t e d b y th e s p r e a d s h e e t . F o r e x a m p l e , i f t h e u s e r c h a n g e dt h e e m i t t e r m a t e r i a l f r o m s t ee l to g l a s s, t h e v a l u e s f o r d e n s i t y , s p ec i fi c h e a t , t h e r m a l c o n d u c t i v i t y ,e m i s si v it y a n d t h e r m a l c o e f f ic i e nt o f l in e a r e x p a n s i o n w o u l d b e " l o o k e d u p " b y t h e p r o g r a m , a n dv a l u e s t h a t h a d b e e n p r e v i o u s l y s u p p l i e d o n t h e " M a t e r i a l P r o p e r t i e s " p a g e w o u l d a p p e a r o n t h e" D a t a I n p u t " p a g e . A l s o , t h e m a s s o f t h e e m i t t e r s eg m e n t w o u l d a u t o m a t i c a l l y b e re c a l c u la t e d .I n o r d e r t o s e e t h e e ff e c t o f t h is m a t e r i a l c h a n g e , t h e u s e r w o u l d p r e s s t h e F 9 f u n c t i o n k e y t o c a u s et h e p r o g r a m t o r e c a l c u la t e . I n g e n e ra l , th e F 9 k e y m u s t b e p r e s s e d m a n y t i m e s d u e t o t h e c i rc u l a rn a t u r e o f t h e p r o b l e m . A f t e r t h o u s a n d s o f i te r a t i o n s ( e a c h r e q u i ri n g h u n d r e d s o f c a lc u l a ti o n s ), t h es p r e a d s h e e t s l o w ly c o n v e r g e s t o t h e ne w s o l u t i o n . T h e u s e r c a n c h a n g e t h e n u m b e r a n d d i a m e t e ro f t h e h o l e s d r i l le d i n e a c h o f th e 2 0 s e g m e n t s o f t h e f l a m e t u b e , t h e t y p e o f f u e l a n d o x i d a n t , t h ef u e l p r e s s u r e a n d t h e a i r / f u e l r a t i o i n o r d e r t o d e s i g n a c o m b u s t o r t h a t a c h i e v e s a n e a r c o n s t a n te m i t t e r t e m p e r a t u r e .


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LINDLER and HARPER: COMBUSTOR/EMI TTER DESIGN TOOL 395

D ~ a I n p u t 1P r e s s u r e s iV e lo c i t i e s ~ iR e y n o ld s N u m b e r s i iH e a d L o s s ~ iT e m p e r ~ u r e s l i iD e ns i m lV i s c o s i t i e s l i iM a s s F l o w R a t es iC o n v e c t i o n C o e f . i

C o n v . H e a t T r a n s f e rR a d . H e a t T r a n s f e rC o n d . H e a t T r a n s f e rP r e s s u r e D r o p sN e t E n e r g y T r a n s f e r

M a t e r i a l P r o p e r t i e sF u e l P r o p e r t i e sO x i d a n t P r o p e r t i e sG r a p h s

Fig. 4. The table of contents that appears in the TPV combustor design program.

M A T H E M A T I C A L M O D E LWhile all the engineering equations used by the TPV spreadsheet are too numerous to list, some

of the major equations are given below. In order to calculate the mass flow rate through the holesin the flame tube, the head loss equation is solved for the holes in the flame tube in terms of fuelvelocity and the pressure drop between the fuel and the oxidant.

HL = + Ekf -- 7 (1)

I F lame TubeM=e,e, I I P [ 4e7 pick I 0.031, . D . ~ i n I c I " 3 1 A r ~ " i 11"76808sO . D . i / i In I k I 251A r=e 1"8849~Len~h l i l i i i i n I ' I 0 " ~ lA~e x 6 .0 .3 7Len/se~ I 0.6 in I ~ I 7"2E'061m ess I 0"015 958

D a t a I n p u tinin=in=in=Ib m

E m i t t e rMatedal ~ p 487 th ick 0 .0625 inI.D . ~ l n c 0 .1 13 A re a i 6 .1 26 10 6 in=O.D. in k 25 Are ao 6.361725 in=Length 12 in 0 .35 Area x 0 .650408 inzLen/se~ 0.6 in c 7 .2E-06 m as s 0.109982 Ibm

I ConnecUng P ipes I. = e , e l ~ I p l ~ g F h i = I 0.031 nI o ~ i n I c I 9 15 1~ " i 12593699n '~o .D . ~ l n I k I 2 2 3 p ~a o128.27433 n '~ ILengt, I =an I ' I O0 23p~e x10.070023n',~ I/ I " I 9'lE'OSlmess 10.271825 ~ l

Fuel f l ow ra te (ca lcu la ted) 2 .2070 Ib~ r I ]Fuel f l ow (expedmen~ l ) ~ Ib~ rA i r /Fuel Rat io ( Ib~b) = ~ 0 ,06 excess oxygen ( Ibmole/hr) Fuel Cp

Fig. 5. Data input page that appears in the TPV combustor design program.

H XPipe1

E f f e t ~ e n e s s = %kcold =k h ~

PV Cel l Temperature = 72 F

Com bustor Eft . ==

Fuel LHV 21504 B tu/ IbFuel R 96.32 f l - lbf / IbmRFuel k 1 .299 1.299Oxidan t R 53.56 f l - lbf / IbmR

0 . 538 B t u / I bm R


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396 LINDLE R and HARPER: COMBUSTOR/EMITTER DESIGN TOOL

This equation is then solved for velocity.V= f 2gAP_ (2)

The values of the fluid resistance coefficient (kf) for the entrance and exit to the hole are given as0.34 and 1.00, respectively [7]. For laminar flow, the friction factor (f) is calculated by the wellknown equation:

64f = Re (3)where Reynolds number ( R e ) is determined by:

R e - p V D (4)The above equations again show the circular nature of the problem at hand, as the velocity of

the fuel indirectly depends on the velocity of the fuel. Once the velocity of the fuel through eachof the holes is found, the mass flow rate of the fuel is calculated by:

i n = p A V (5)The mass flow rate of the fuel as it flows axially in the flame tube is calculated by conservationof mass. The mass flow through any section of the flame tube is simply equal to the sum of the

flow rates through all of the holes ahead of the section. Similarly, the flow rate of combustion gasesbetween the flame tube and the emitter is calculated by adding the mass flow rate of fuel as it joinsthe oxidant flow. The spreadsheet also performs a chemical balance in order to keep separate trackof the moles of oxygen, nitrogen, carbon dioxide and water vapor flowing between the two tubes.Equation (1) is also used to calculate the axial pressure drop for the fuel and combustion gasesflowing in the combustor and in the pipes leading to and from the combustor.

Once the velocities are known, the values of the convection heat transfer coefficient are foundby equations given by Ref. [8] for forced convection inside the flame and emitter tube. Similarly,the convection coefficient for free convection outside the emitter tube is calculated using equationsfound in Ref. [9]. Radiation shape factors between the flame tube segments and the emittersegments and between the emitter segments with the photovoltaic cells are found by an extremelycomplex equation for shape factors between concentric cylinders found in Ref. [10].

Once the convection heat transfer coefficients and radiation shape factors are known, theconvection and radiation heat transfer (qoo,v and qraa) rates can be calculated. The spreadsheet alsocalculates the heat conducted (qond) from any flame tube segment or emitter segment to the adjacentsegments.

q ... = h A ( T w a l , - T g a s ) (6)qrad = F , _ 2 E a A ( ~ - ~ ) (7)

- k A A T (8)q c o n d = AXThe heat of combustion of the fuel flowing through the holes of any given segment are assumedto be added to that segment and to the next three segments in the percentages given by the user.These percentages are shown as 30, 40, 15 and 15% in the "Data Input" page, Fig. 5.

qcombustion = ~ o m b u s to r % p ~ l fu , lL H V (9)Next, the spreadsheet calculates the net heat into or out of each segment of the combustor.

q,et = ]~q . . . " [ - ~ ' ~ q r a d -~- Zqo,d + qcombustion (10)


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L I N D L E R a n d H A R P E R : 3 97

I000

C O M B U S T O R / E M I T T E R D E S I G N T O O LE m i t t e r Temperature

so o

6 0 0

4 0 0[- -

2 0O

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .

, .

j . - . . . . . . . . . . . . . . . . . . . . : . . . : : : : : : : . . . . . . . . . . . . . . . . . . . . . . . . .6

I I I ' I ' I a I '0 2 4 6 8 10 12

Locat ionF i g . 6. E x p e r i m e n t a l a n d c a l c u l a t e d e m i t t e r t e m p e r a t u r e v s l o c a t i o n f o r t h e g l a s s e m i t t e r .

U n d e r s t e a d y - s t a te c o n d i t i o n s , t h e n e t h e a t t r a n s f e r s h o u l d b e z e r o . I f t h e s p r e a d s h e e t d e t e r m i n e st h a t t h e n e t h e a t t r a n s f e r i n t o a n o d e is p o s i ti v e , t h e n t h e a c t u a l n o d e t e m p e r a t u r e m u s t b e h i g h e rt h a n t h e p r e v i o u s l y c a l c u l a t e d v a lu e . T h e n e w t e m p e r a t u r e f o r t h e n e x t i t e r a ti o n i s th e n c a l c u l a te db y :

qnet ( l l )T,,o~ = To~d+ DI----VI n t h e a b o v e e q u a t i o n , D I V is a u se r s p e ci fi e d p a r a m e t e r . T h e f i n al s o lu t i o n d o e s n o t d e p e n d o nt h e v a l u e o f D I V , b u t a l a r g e v a l u e w i ll l e a d t o s l o w c o n v e r g e n c e a n d a s m a l l v a l u e c a n l e a d t om a t h e m a t i c a l i n s ta b i li ty .

S P R E A D S H E E T V A L I D A T I O NB e f o r e t h e s p r e a d s h e e t c o u l d b e c o n s i d e r e d a s a d e s ig n t o o l , i t w a s n e c e s s a r y t o v a l i d a t e t h a t

i t p r o v i d e s r e a s o n a b l e r e s u l t s . T h e s p r e a d s h e e t w a s u s e d t o d e s i g n a l o w t e m p e r a t u r e( a p p r o x i m a t e l y 7 0 0 K = 8 0 0 F ) g l a s s e m i t t e r . G l a s s w a s c h o s e n s o t h a t t h e f l a m e c h a r a c t e r i s t i c sc o u l d b e o b s e r v e d . T h e s p r e a d s h e e t h a s t h e c a p a b i l i ty o f p l o t ti n g p r e d i c t e d a n d a c t u a l e x p e r i m e n t a lt e m p e r a t u r e s o n t h e s a m e g r a p h . T h e r e s u l t s f o r t h e g l a s s e m i t t e r a r e s h o w n i n F i g . 6 . T h es p r e a d s h e e t p r o v i d e s f a i rl y g o o d r e s ul ts , s l ig h t ly o v e r p r e d i c t i n g t h e t e m p e r a t u r e o n t h e s e c o n d h a l fo f th e e m i t t e r. T h e l o w t e m p e r a t u r e s p r e d i c t e d a n d m e a s u r e d a t t h e b e g in n i n g o f t h e e m i t t e r a r ed u e t o t h e f a c t t h a t a r e c u p e r a t o r w a s n o t u s e d f o r h e a t r e c o v e r y , a n d t h u s, c o l d a i r w a s u s e d f o rc o m b u s t i o n .

T h e g l a s s e m i t t e r w a s r e p l a c e d w i t h a s t e e l t u b e a n d t h e r e s u l t i n g c o m b u s t o r w a s o p e r a t e d a ta s li g h tl y h i g h e r t e m p e r a t u r e . T h e m e a s u r e d a n d c a l c u l a te d t e m p e r a t u r e s a r e s h o w n i n F i g. 7 .A g a i n , t h e s p r e a d s h e e t d o e s a r e a s o n a b l e j o b a t p r e d i c t in g e m i t t e r t e m p e r a t u r e s . T h i s ti m e , t h es p r e a d s h e e t s l ig h t l y u n d e r p r e d i c t s t h e t e m p e r a t u r e s o n t h e f i rs t h a l f o f t h e e m i t t e r a n d s l ig h t l y o v e rp r e d i c t s t h e t e m p e r a t u r e o n t h e s e c o n d h a l f .

C O N C L U S I O N SC o m p u t e r s p r e a d s h e e t s a r e v e r y u s e f u l f o r s o l v i n g c o m p l e x c i r c u l a r e n g i n e e r i n g p r o b l e m s .

A d v a n t a g e s i n c lu d e t h e a b i l it y t o o r g a n i z e l a rg e n u m b e r o f i n te r r e l a t e d e q u a t i o n s e a s i ly a n d t op r e s e n t r e s u l t s g r a p h i c a l l y . T h e m a j o r d i s a d v a n t a g e i s t h e t i m e r e q u i r e d t o c o n v e r g e t o a n e w


8/8

398 L I N D L E R an d H A R P E R : C O M B U S T O R / E M I T T E R D E S I G N T O O LE m i t t e r T e m p e r a t u r e

1 2 0 0

, - , I 00 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6 0 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 00 I I I I I I J I I I I0 2 4 6 8 1 0 1 2

L o c a t i o n

Fig. 7. Experimental and calculated emitter temperature vs location for the steel emitter .

s o l u t i o n o n c e c h a n g e s t o t h e d a t a a r e m a d e . T h e s p r e a d s h e e t d e v e l o p e d f o r th e d e s i g n o f at h e r m o p h o t o v o l t a i c c o m b u s t o r / e m i t t e r h a s b e e n v a l i d a t e d u s in g t w o d i f fe r e nt e m i t t e r s a t m o d e r a t et e m p e r a t u r e s . T h e s p r e a d s h e e t w i ll b e u s e d t o d e s i g n a h i g h t e m p e r a t u r e e m i t t e r ( 1 47 8 K = 2 2 0 0 F )t h a t w i l l m a i n t a i n a n e a r c o n s t a n t t e m p e r a t u r e p r o f i l e . I t i s e x p e c t e d t h a t t h e t e m p e r a t u r e p r o f i lew i ll b e f l a t te r t h a n a c h i e v e d i n t h e v a l i d a t i o n t e s t s, a s h o t e x h a u s t g a s e s w il l b e u s e d t o p r e h e a tt h e a i r e n te r i n g t h e c o m b u s t o r .Ackn o wled g emen t s - -M id sh ip ma n Rob er t S . McHenry, U SN conducted the comb ustor experiments.

R E F E R E N C E S1. Chapin, D. M ., Fuller , C. J. and Pearson, G. L., Journal of Applied Physics, 1954, 25, 676.2. Frass, L. M., Gee, J. M. and Emergy, K. A., 21st IEEE Photovoltaic Specialist Conference, 1990, p. 190.3. Fraa s, L. , Ballantyne, R., Samaras, J. and Seal, M., Proceedings of the First NR E L Conference on ThermophotovoltaicGeneration o f Electricity, 1994, pp. 44-53.4. Krist, K., Proceedings of the First NR E L Conference on Thermophotovoltaic Generation of Electricity, 1994, pp. 54-63.5. Broman, Lars and Marks, Jorgen, Proceedings of the First NREL Conference on Thermophotovoltaic Generation ofElectricity, 1994, pp. 133-138.6. Stone, K. W., Leingang, E. F. , Drubka, R. E., Chebb, D. L., Good, B. S. and Wilt, D.M., Proceedings of the 30thlntersociety Eng ineering Conferenc e, 1995, pp. 713-718.7 . A SH RA E, AS H RA E Gu id e a n d Da ta Bo o k- -Eq u ip men t Vo lu me . American So ciety of Heating, Refrigerating an d A irConditioning Engineers, 1969.8. Chapman, A. J. , Fundamentals of Heat Transfer. Macm illan, New Y ork, 1987, pp. 326-327.9. Kreith, F. and Bohn, M. S. , Principles of Hea t Transfer. West Publishing Com pany, St Paul, M N, 1993, pp. 327-328.I0. S iegel , R. an d Howell, J. R ., Thermal Radiation Heat Transfer. Mc Graw Hil l, New Y ork, 1972, p. 789.

combustoremitter design tool for a thermophotovoltaic energy converter lindler

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