SUMMER . MEETING - LOS ANGELES, CALIFORNIA u JUNE 17-20,1963

. b

A LOOK AT THE THERMODYNAMIC CHARACTERISTICS OF BRAYTON CYCLES FOR SPACE POWER

by

ARTHUR J. GLASSMAN and WARNER I. STEWART National Aeranautics and Space Administration Cleveland, Ohio

A KKJK AT THE THERHODYRAMlC CE4RAlTERISTICS

OF BRAYTON CYCLBS FOR SPACE FCWER

By Arthur J. G l a s s m a n and Uarner L. Stevart

Fluid Systems Cnmponents Division lewis Research Center

Hational Aeronautics and Spmce Administration Cleveland, Ohio

I l ? r R O r n I O N

b3.Ar4

For a w i e t y of space missions, both manned and unmanned, there exists

a need for system capable of generating power for many thousands of hours

of continuous operation.

auxi l iary use in near space missions up t o many m e g a v a t t s f o r m e d missions

u t i l i z ing e l ec t r i c propulsion t o reach the other planets of our solar system.

Powerplant spec i f ic weight (powerplant weight per kilowatt pover output) f o r

t he bigb power level systems must be kept low because of (1) t h e large in-

herent s i ze of t hese systems andfor (2) t he strong dependence of e lec t r i c

rocket performance upon the powerplant weight.

Power requirements range irm a few ki loua t t s for

The most p rmis ing p e r generation system for near future application

t o missions requir ing power leve ls of several kilowatts o r more i s the indirect

conversion closed loop system where heat i s generated i n a nuclear or solar

Source and re jected by a radiator, with power being obtained frm a turbine

located i n the working f lu id loop. The rad ia tor has been shovn t o be the

largest cmponent and a major weight contributor t o t h e powerplant and m y

easily const i tute half o r more of t h e t o t a l weight, especial ly at t he high

power levels. Much a t ten t ion has been given t o the vapor-liquid (Fankine)

sys tm using a metal working f l u i d since t h i s system has a much be t te r themo-

dynamic potent ia l t han e gas (Brayton) system f o r obtaining t h e low radiator

I

specif ic areas and weights required for large power output applications.

cmpamble turbine inlet temperatures, a Brayton cycle radiator may require

mare than ten times the specific area (square feet per k i lova t t ) required fo r

a -ne cycle radiator ( refs . 1 and 2). Hovever, for non-propulsive power

systems of several h e e d kilowatts or less , where l o w specFPic w e i g h t is

not so c r i t i c a l a requirement, the -on cycle m e r i t s consideration because

its use eliminates (1) the problems assmiated with two phase f low in a zero

gravi ty environment, (2) t h e presence of a severely corrosive vorking f luid,

and (3) the poss ib i l i ty of erosion deanage t o t h e rotat ing cmponents. Much

of t he required equipnent and technology for t h e Wayton cycle is presently

available, and this aystem has a gocd potent-1 f o r multiple starts as vell

8 s f o r achieving t h e required low time r e l i ab i l i t y .

For

The thermodynamic character is t ics of Brayton cycle space power systems

bave been discussed t o a l imited extent by a nunher of invest igators (e.&,

refs . 1 t o 4). Eech of these studies, however, vas made f o r cer ta in idealized

or specif ic conditions and none of then considered a l l t h e pertinent system

parameters. In view of these considerations, an d y t i c a l investigation vas

conducted in order to supplement t he previous studies and obtain a be t t e r

understanding of t h e thermcd-c character is t ics of €uayton cycles f o r space

application.

I I

This paper presents t h e result8 of the iwes t iga t ion . I

I Sa(B0Is

Ai radiator internal heat t ransfer area

+ rad ia t ingarea s f z

e specific heat, Btu/(lb)(%) - P E recuperator effectiveness

I

c

h i

hR

Ah

P

P

r

T

Y

r E

'I

a

radiator gaa film heat transfer coefficient based on internal heat t rans-

f e r area, Btu/(br)(sq rt)CW

Btu/(hr)(sp it)(%)

radiator gas f i lm heat t ransfer coefficient bsaed on radiating area,

enthalpy cbmge, S+&b

sbattpover, In

pressure, psi.

pressure ratio [greater than unity)

temperature, OR

weight flow, lb/hr

specific beat ratio

emissivity

efficiency

Stefan-mltmann constant, 0.173~10~ Btu/(b)(aq it)(%') \

Subscripts:

C

CY

id

8

T

W

1

2

3

4

c q r e s s o r

cycle

ideal

S i &

turbine

w e l l

heat Source ex i t o r turbine inlet

turbine exit or recuperator inlet

recuperator ex i t o r radiator inlet

radiator exi t or canpressor inlet

5 cmpressor exit or recuperator inlet

6 recuperator exi t or heat source inlet

CYCLE AmALysIs

d sch-tic d i m oi a h y t o n cycle configuration is shown in fig-

ure l(a) and the corresponding temperature-entropy diagram in figure l (b ) .

The circled numbers correspond t o the s t a t e point designations used i n t h e

analysis. The beat swrce exit gas at point 1 ex€eads thmugh t h e turbine

t o point 2, thereby proauCing t h e mechanical work necessary t o dr ive the

canpressor and alternator. Frau the turbine, the gas enters t h e m u p e r a t o r

where it is cooled t o point 3 ( ~ 8 it transfers heat t o the gas fran t h e can-

pressor. F i ~ l cooling of the gaa t o point Z takes place in t h e radiator,

where the excess heat is rejected t o space. The gas leaving the radiator

is then canpressed t o point 5, heated in the recupcrator t o point 6, and

-her heated ba& t o point 1 i n the heat source.

can include a l iquid heating loop andfor a l iquid cooling loop.

t h e gas loop r e i n s the same as described above except that heat ex-

changers replace the heat s w c e and/or radiator.

Alternate coniigurations

However,

he purpose oi the cycle a n a l y ~ ~ s n s twoiold: (1) t o detemine cycle

performance, denoted by cycle efficleney, for any chosen set of cycle con-

dit ions, and (2) t o select a set of cycle teaperatures that is sanehov

adnurtegeous t o t h e system.

sme cr i te r ion had t o be chosen t o serve as a guide for t h e select ion of

desirable cycle temperatures. The most logical c r i te r ion seemed t o be mini-:

mum mea s i ze and/or weight; however, such a minimization procedure wvdd f f4

require an effort well bepnd t h e scope of a preliminary study.

Therefore, before t h e cycle analysis was started,

$

Experience

has shorn tha t t h e rad ia tor is (1) t h e largest componsnt, by far, i n a

nwlear-powered system, (2) one of the two largest components i n a solar-

powered system, and (3) a major contributor t o powerplant weight i n both

nuclear and solar systems. In addition, the s i ze and weight of t h e radiator

are greatly a f fec ted by cycle temperature selection. In a nuclear system,

t h e weight of t h e reactor, t h e other major weight contributor, is affected

t o a mxh smaller extent than is t h e radiator by the selected cycle temper-

atures because t h e s i z e of t h e reactor is determined primarily by nucleonics

considerations. In a solar systen, however, t h e s ize and weight of t h e col-

lector, t h e other l a r g e c q o n t n t , u e affected t o Lvge extent by cycle

temperature se l ek ion , but not t o t h e same extent as t h a t of t h e radiator.

Cons

te r ion fo; cycle temperature selection.

t h e size and weight of a f i n and tube radiator a r e minimized at approximately

t h e same cycle temperatures as are required t o minimize t h e radiating surface

O f D prime area rad ia tor . A prime area radiator, for t h e purposes of this

study, can be defined as e i ther a tubular radiator without f i n s or a tube

end f i n radiator with a 100 percent f i n efficiency.

area is an indicator of both s i ze and WeigM of t h e radiator, it was chosen

as the c r i te r ion for cycle temperature selection.

selected i n t h i s manner w i l l be very new t h e o p t h Ones for nuclear system

and vill deviate only s l i gh t ly frcm t h e optimum ones f o r solar system.

Lently, m e aspect of rad ia tor s i ze appeared t o he a logica l eri- gn Experience bas further shown that

Since prime radiating

The cycle temperatures

Cycle Efficiency

The cycle ana lys i s was made using mechanical s m power t o t h e alternator

as the basis.

assumptions.

Ccsnputation of cycle efficiency was performed using t h e following

[lj m e working f lu id is an ideal gas; con5equently, specific heat is

a ccnstant independent of temperature.

1 2 ) No heat losses f r w t h e system.

Cycle efficiency is defined as

N e t s m power = Heat supplied - heat rejected ‘W Heat supplied Heat supplied

Symbolically, t h i s def in i t ion is

n: (T - T ) - vc (Ts - T4) =T1 - !Is - T3 + T4 ( i j 1 6 ’CY = wCp(T1 - T6j T1 - T6

For a closed cycle using M ideal gas as wrkinp fluid, recuperator effective-

ness is expressed as

T2 - T3 T2 - Ts

T6 - T5 E=--- T2 - Ts

From equstion (Z), t h e folloving two relationships are obtained:

T6 = Tz - T3 T T5 (2a)

and

T~ = T~ - E ( T ~ - T ~ ) i 2b)

Substitution of equations (28) and (ab) irrto equation (1) yields

4 - T5 T - T 2 + T

1 - 1

T ‘CY - ET2 - (1 - E)T5 (3)

Division of both t h e numerator and t h e denminator by T1 and expression Of

T5iTl as (T5/T4)(TdJT1) fields

,

Esuation (4) shows cycle efficiency t o be a function of recuperator effective-

ness and t h e folloviag t a p e r a t u r e ratios:

exit t o inlet, and canpressor inlet t o turbine inlet.

turbine exi t t o inlet, ccmpressor

Rnpressor temperature ra t io (TdT4) UUI be expressed M a function of

turbine temperature rat io , turbine efficiency, ccmpressor efficiency, and

the pressure losses ia the heat t ransfer ccmponmts. The enthalpy change

of the fluid in t h e ccmprrssor is

cancellation of ycs and rearrangeme& equation (5) yiem

The canpressor pressure r a t io can be expressed as

( 5 )

AB seen fran equation ( 6 ) , t h e factor

inlet t o exit pressure divided by t h e r a t i o of cmpressor exit t o inlet pres-

sure and is also equal t o the product of t h e ra t ios of exit t o inlet pressure

fo r all t h e heat t ransfer ccmponents.

f ract ion of canpressor pressure ratio that can be recovered t o do vork in t h e

turbine and is an indicator c4 the heat tnrnsfer canponent pressure drops.

For t b e purpose of brevity, rT/rC w i l l be subsequently referred t o as the

loss pressure ra t io .

rT/rc is equal t o the ratio of turbine

Consequently, rT/rc represents the

The isentropic state equation is

(7)

and subst i tut ion of equatioule ( 6 ) ad (7) into equation (Sa) yields

The eutlmlpy chansc of the fluid in t h e turbine is

vhich upon simplification ad rearrangement yields

Substi tution of equation (Sa) into the isentropic state equation

* h = l - L (10) T1 %!

and subst i tut ion of equation (10) into equation ( 8 ) yields

Esnation (ll) is nnr substi tuted into equation (4) with a slight r m e -

m e n t to give t h e desired expression for cycle efficiency

Fluid spec i f ic capacity rate, vcdP, which is another indicator of cycle

performance, i s required for t h e cmputation of spec i f ic rad ia tor area and is

herein derived. The required flmr r a t e for t h e working f lu id can be expressed as

N e t shaft power Met work per pound of f l u i d

w =

which symbollcdly is

Substitution of equation (11) in to equation (13) and rearrangement yields t h e

desired expression fo r spec i f ic capacity rate.

?he working f lu id was a~sumed t o be a monatmic gas with a specific heat ratio,

r, of 1.67

Radiator Area

The rad ia tor i s considered t o be a tube or aer ies of tubes e i ther with-

out f i n s or wi th f i n s of 100 percent effectiveness (no res i s tance t o heat

t ransfer ) . Consequently, a n radiating area i s prime area. The f o l l m n g

assmptions are made for this caputa t ion :

(1) Sink temperature is constant for any given radiator. The sink tem-

perature can be defined as t h e equilibrium temperature that a body i n space

w i l l a t t a i n if t h e r e are no thermal influences other than t h e radiant heat

absorbed from and emitted t o space. Sink temperature, consequently, depends

on such controllable factors as t h e absorptivity-emissivity charac te r i s t ics

of t h e radiating surface and t h e orientation of t h e radiator with respect t o

t h e space radiant energy sources.

(2) The gas f i lm heat transfer coefficient is constant throughout t h e

radiator.

(3) The temperature drap through t h e tube w a l l is negligible.

(4) Heat conduction along t h e tube axis is neglected.

For an element of tube length, t h e heat transferred frm t h e fluid t o

t h e tube nrll must e q d the heat radiated.

(15) hi(T - Tw)dAi = 4 4 - Te)d$

A gas film heat transfer coefficient r e l a t ed t o radiating area can be defined

88

Substituting equation (16) i n to equation (15) and solving for T yields

'Z = T + - a€ (Tu 4 - Ts) 4 hR

(17 j

For t h e element of tube length under consideration, t h e decrease i n f lu id

sensible heat must also eqwl the heat radiated.

(18) -m d!T = oe(Tw 4 - T:)% P

Differentiation Of equation (17) and subs t i tu t ion of t h e d i f fe ren t ia ted ex-

pression in to equation (18) yields ?

E (19).;

i

Rearrangement of equation (13) in order t o separate t h e variables r e su l t s i n

DiTiding bath s ides of equation (20) by P

of 0 t o AR and Tv,3 t o T yields

and integrating between t h e limits

w, 4

where Tw is r e l a t ed t o T by equation (17) and wcp/P is obtained frm

quat ior . (14).

RESLTLTS OF ANALYSIS

The developed equations showed that cycle efficiency and Specific prime

radiator a rea a r e functions of several system design factors and two inde-

pendent temperature variables, turbine ex i t t o i n l e t temperature r a t i o and

compressor i n l e t t o turbine in l e t temperature ratio. Cycle efficiency, as

seen from equation ( le) , depends on Such design fac tors as turbine and com-

pressor efficiencies, loss pressure ratio, and recuperator effectiveness.

Specific prime rad ia tor area, equation (21), a l so depends on t h e above

mentioned design fac tors as well as t h e additional factors of tu rb ine in l e t

temperature, sink temperature, radiating surface emissivity, and gas heat

t ransfer coefficient.

The r e su l t s of t h e analysis are discussed first with respect t o t h e

e f fec ts of t h e cycle temperature variables and design fac tors on cycle e f f i -

ciency and then with respect t o t h e e f fec ts of these -e fac tors on spec i f ic

radiator area. mcept where athervise indicated, t h e following s e t of design

fac tors were used t o compute t h e cycle efficiencies and prime rad ia tor areas.

Turbine in l e t teaperatare, OR . . . . . . . . . . . . . . . . . . . . . 2160

Sinktemperat:ure, OR . . . . . . . . . . . . . . . . . . . . . . . . . 400

Twbine efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . 0.85

Cmpressor efficiency . . . . . . . . . . . . . . . . . . . . . . . . . 0.80

Iass pressure rat.io . . . . . . . . . . . . . . . . . . . . . . . . . . 0.30

Recuperator effectiveness . . . . . . . . . . . . . . . . . . . . . . . 0.80

Radiator surface emissivity . . . . . . . . . . . . . . . . . . . . . . 0.86

G a s heat t r ans fe r coefficient, Btu/(hr)(sq ft rad. area) (%) . . . . . 5

Cycle Efficiency

AS mentioned previously, cycle efficiency is a function of several

system design fac tors and two temperature variables.

system design factors, cycle efficiency is shown i n f igure 2 plotted against

compressor in le t t o turbine in le t temperature ratio, T4/T1, for several values

of turbine exit t o . i n l e t temperature ratio, T2/TP

note from f i w r e 2 a r e t h e rapid decrease i n cycle efficiency as

increases, and t h e f ac t t ha t a t each value of t he re is one particL- "

lar value of TZ/T1 t h a t maximizes cycle efficiency. As Tq/T1 increases f

frm 0.20 t o 0.55, maximum a t ta inable cycle efficiency decreases by more than

a factor of two.

For a given se t of

The important things t o

T4/T1

Tq/Tl @

o_

For a given se t of cycle temperature variables, t h e change i n cycle

efficiency with turbomachinery efficiency, loss pressure ratio, and recupera-

t a r effect.iveness a re presented i n figures 3(a), 3(b), and 3 ( c ! , respec-

1.ively. It i s seen from fign-es 3(a) and 3(b) t ha t cycle efficiency rapidly

deteriorates as t h e turbine and compressor e f f ic ienc ies or t h e loss pressure

r a t i o decrease. Reductions i n the turbine and compressor efficiencies f rm

0.90 t o 3.80 and 0.80 t o 0.70 result i n cycle efficiency decreasing by 30

and 65 percent, respectively, while sk i la r reductions i n loss pressure

ra1io cafise cycle efficiency t o decrease by 20 and 30 percent, respectively.

The need fo r high tilrbomachinery efficiency and 10% pressure drops i n a

Bra>t.on cycle sower system i s c l e a r l i e-”-ident.

cycle efficiency can be s igni f icant ly increased by increasing rec-cpperator

effectiveness and, for t h e typ ica l case presented, an effectiveness of 3,86

r e sa l t s i n a c r c l e efficiency double t h a t o’ctainable without a recuperator

( E = 0 ) .

occurs because as mme heat i s supplied t o the gas i n Che recuperator, less

heat must be supplied by the beat source. Recuperator weight, of course,

i s increasing with effectiveness and approaches i n f i n i t y as effectiveness

approac:ies one.

extent on t o t a l system weight and more w i l l be said about t h i s i n the

radiator a rea discussion.

Figure 3 ( c ) shows that.

The increase i n cycle efficiency with increasing effectiveness

The choice o f a design effectiveness depends t o a great

Radiator Area

Radiator area, too, is a function of several system design factors and

tire tempe?ature variables. Cs mentioned peviously, t h e conputted radiator

areas a re prime areas which CM be used t o (1) serve as a guide f o r t h e

selection of a desirable set O f cycle temperature variables, and ( 2 ) show

%x t.he design fac tors a f fec t both radiator area and t h e choice of tempera-

>lire variables. * .

Radiator area is plotted against T4/Tl i n f igure 4 for several values

of Y 2 / ? i , Examination of f igure 4 shows t h a t : (1) f o r each value of Tz/T,

there results a c u m e which has a rninimwn radiator area at some value of

T4/T1, (2 ) f o r each valne of T4/Tl there i s one valbe of that

yie;ds a minimum radiator area, and (3) an ervelope curve ( the dashed cwve

i n f ig. 4) drawn aromd t h e family of c w e s a l s o s:?ows a minimum radiator

area.

opposing factors which a f fec t radiator area. Radiative heat f lux i s pro-

port.ional t.a t h e fourth power of temperature; consequently, an increase i n

radiator temperature level w i l l act t o reduce radiator area.

seen from f&ze 2, cycle efficiency decreases with an increase i n radiator

temperatwe level; consequently, there i s an i i c rease i n radiator heat load

which w i l l act t o increase radiator area. 3. i s t h e i z t c a c t i o n of t h s e

t w o effects which cause t h e minimum observed i n f i g w e 4. As Seen from

figure 4, the choice of cycle temperature variables must be r e s t r i c t ed t o

those combinations y i e l d i w radiator areas i n the v ic in i ty of t.he minimum

i f the inherently la rge radiator is not to become even larger.

The shape of these curve6 i s readi ly explainable. There a re two

Rowever, as

The discussion t o follow w i l l show how t h e design fac tors a f fec t both

radiator area and t h e choice of temperature variables. Envelope curves,

similar t o tha t shown i n figure 4, w i l l be used t o represent. radiator areai

3he value of ? /T which minimizes radiator area f o r any eiven 2 /T ?

2 1 4 1 j w i l l be subsequently called (T , and t h e (T2/T1! l oc i w i l l be

opt shown on the envelope curves.

c c

- 15 ~ - 16 -

Tie design factors which influence radiator a rea a r e turbine in l e t

t.emperature, sink temperature, turbomachinery efficiency, loss pressure

ratio, recuperator effectiveness, gas heat t ransfer coefficient, and sur-

face emissivity.

i s Shown i n f igure 5, where prime radiator area is plotted against

f o r turbine i n l e t temperatures of 1710°, 2160°, and 2500' R.

turbine in l e t temperature from 1710

fac tor of nearly four.

as can be Seen from f igure 5, hundreds or thousands of Square fee t of

rad ia tor area, depending on turbine in le t temperature and System power

level, w i l l be required for Brayton cycle power systems.

radiator area with increasing t.urbine in l e t temperature is due t o t h e in-

crease i n rad ia t ive heat f l ux which is proportional t o t h e fourth power of

radiator temperature. As turbine in l e t temperature increases, there i s a

s m a l l decrease i n t h e optimum values O f Td/Tl and TzjTl. In addition,

t h e choice of

increases.

The e f fec t of turbine i n l e t temperature on radiator area

T4/Tl

Increasing

0 t o 2500° R redeces radiator area by a

Such an a rea reduction i s very Significant since,

The reduction i n

T4/T1 becomes l e s s res t r ic ted as t h e temperature leve l

The e f fec t Of si& temperature on radiator area i s shown i n figure 6,

TgjTL for sink temperatures where prime radiator a7ea is plotted against

of Oo, 400°, and 600' R. Radiator area increases with increasing sink tem-

perature due t o a reduction i n t h e net radiative heat flux; t h e increase i n

a rea becomes qu i t e significant as sink temperature begins t o approach com-

pressor i n l e t temperature. For t h e case shorn i n f igure 6, an increase i n

sink temperature from 0

a rea while fur ther increase from 400' t o 600' R r e su l t s i n a 30 percent increase

0 0 t o 400 R r e su l t s i n a 13 percent increase i n radiator

i n radiator area. The optimum values of T4/Tl and Tz/T1 increase s l i gh t ly

and t h e i r proper choice becomes more c r i t i c a l as sink temperature increases.

The combined ef fec ts of turbine in l e t temperature and sink temperature

on radiator area a re Shown in f i g w e 7, where minimum prime rad ia tor area i s

plotted against turbine in le t temperature for several values of sink tempera-

tu re . Tne radiator areas presented i n t h i s f igure a re the minimum obtainable

( i ~ e ~ , those areas corresponding t o t h e opt ima values of

f o r each combination of turbine in l e t and sink temperatures. As w a s seen

from t h e two previous figures, radiator area decreases with increasing turbine

in l e t temperature and decreasing sink temperature.

perature on radiator area i s seen t o become more significant as turb ine in l e t

temperature decreases. operation at higher turbine in l e t temperatures, aside

from reducing radiator area, has t,he advantage of lessening operating f luc tu-

ations due t o a change i n sink temperature with position i n space.

Ta/Tl and Ta/Tl)

The effect of sink tem-

The effect of turbomachinery efficiency on radiator a rea is Shown i n

figure 8, where prime radiator area i s plotted against

and compressor efficiencies of 0.70, 0.80, and 0.90. A reduction i n t.urbo-

machinery efficiency r e su l t s i n a very significant increase i n radiator area.

As Seen from f igure 8, a reduction i n turbine and compressor e f f ic ienc ies

from 0.90 t o 0.80 r e su l t s i n a twofold increase i n radiator a rea while a

flirther reduction from 0.80 t o 0.70 causes an additional t.hreefold increase

i n radiator area.

crease i n cycle efficiency shown i n figure 3(a).

T4/T1, as Seen from f igure 8, decreases with decreasing turbomachinery ef- 5

ficiency i n order t o of fse t t h e rapid deterioration of cycle efficiency;

T4/Tl for tu rb ine

This increase i n radiator area i s due primarily t o t h e de,-

The optimum value of g a

conseoqently, rad ia tor temperature has decreased, ard $he combined effects

of lower radiator temperature and cycle efficiency cause the large increase

in rad ia tor area. The optimum value of T2/T1 i s seen t o increase with a

redr;ct.ion in turbomachinery efficiency.

The effect of loss pressure r a t i o O n radiator area i s shorn in figure 9,

T4/T1 f o r l o s s pressure r a t io s where prime rad ia tor area i s plotted against

of 0:?3, 9).80, and 0.90. A reduct.ion i n loss pressure r a t i o r e su l t s i n a

large increase i n rad ia tor area. As seen from f igu re 9, a reduction i n

loss p r e s s ~ - e r a t i o from 0.90 t o 0.83 r e su l t s i n a 50 percent increase i n

rad ia tor a x a while a further reduction from 0.80 t o 0.70 causes an additional

55 percent increase i n radiator area. The increase i n radiat.or area and de-

c x a s e i n apd,imm ~T4/T1

s m e reasons as explained above fo r decreasing turbomachinery efficiency.

?be optotinw value of

with decreasing loss pressure r a t i o occlir for the

Tz/Ti decresses with a reduction in loss pressure rat io .

The effect of recuperator elfectiveness on radiator m e a i s shwm in

f i g w e 10, where prime radiator area i s plotted a g a i m t

a t o r effectivenesses of 0, 0.5, and 1. Radiator a rea decreases with in-

creasing effectiveness, and t h e area required f o r 9 = 1 is about 70 perceEt

cf that required for E = 0. The reduction i n rad ia tor area with increasing

effectiveness i s due t o t h e increase i n cycle efficiencg-, a5 showr, i n f ig -

zrs 3(c ' , . Althowh cycle e f f i c i enc j is nolle than doubled as effectiveness

increases from 0 t o 1, t h e decrease i n radiator a rea i s no? proportionately

as grea t because t h e a rea redwtion occurs at t h e high temperature (most

e f f i c i e n t j end of t h e radiator. Due t o t he lnhereritly laFge Size of t h e

radiat.or, even a 20 o r 25 percent reduction i n rad ia tor area, as can be

achieved with recuperator effectivenesses 3f 0.6 t o 0.9, c a ~ resu l t i n enough

T4/Tl f o r recuper-

of a savings t o offset t he a t i ona l veight and pressure drop a t t r ibu tab le

: o a recu2erator. The optimun value of T4/Tl increases only s l igh t ly

w i t h increasing effectiveness; t he optimm value of

Significantly as effectiveness increases. This increase i n T2/Tl i s advan-

tageous since it resu l t s i n a reduction i n the pressure r a t i o requirement for

t h e turbomachinery.

T2/Ts1, however, increases

?he effect of gas heat t ransfer coefficient on radiazor area is s:?om

T4/Tl fo r gas i n figure 11, where prime radiator area i s plotted against

heat t ransfer coefficients of 5, 20, and inf ini ty . The heat t ransfer co-

efficient presented i n t h i s f igure i s the coefficient r e l a t ive t o radiating

area which, according t o equation (lS), i s equal t o t h e coefficient r e l a t ive

t o internal heat. t ransfer area times t h e r a t io of i n t e rca l heat t ransfer area

t o radiating area. For meteoroid protected tube and f i n radiators, t h i s area

r a t i o can be as lou as 0.10 t o 0.25 and, consequently, cause t h e heat. t rans-

f e r coefficient re la t ive t o radiating area t o be qui te low. Radiator area

iicreases Wizh decreasing hear t ransfer coefficient; however, as seen from

figllrf 11, the effect of heat t ransfer coefficient on radiator area is qui te

s m a l l for coefficients in excess of about 20, but becomes significant as t h e

heat t ransfer Coefficient decreases below 20. A reduction i n heat t ransfer

coefficient from 20 t o 5 r e su l t s i n a 40 percent increase i n radiator area.

For those cases where the heat t ransfer coefficient i s qa i t e lm, t he use of

in te rna l fins, which grea t ly increase the r a t i o of in te rna l t o radiating la

area, can be beneficial. The optimum values of riq/T1 and Tz/Tl increases

s l i gh t ly with increasing heat transfe- coefficient.

s

The effect of radiator surface emissivity on radiator area is Shown i n

figure 12, where prime area i s plotted against

0.6, 0.8, and 1.0. Radiator a rea increases with decreasing emissivity Since

the rad ia t ive heat f lux i s d i r ec t ly proportional t o emissivity. A

reduction i n emissivity from 1.0 t o 0.8 r e su l t s i n an 11 percent increase

i n radiator area while a fur ther reduction from 0.80 t o 0.60 cauSeS

additional 23 percent increase i n area. The optimm values of T d T l and

T2/?il

T4/Tl for emissivit ies of

appear t o be nearly independent of emissivity.

It is in te res t ing t o note tha t t h e optimum values of T2/T1 and T&l,

even over the wide range of design fac tors investigated, were generally i n

the rmge of 0.70 t o 0.80 and 0.25 t o 0.55, respectively.

SUMMPXY OF RES7JLTS

This analysis was conducted i n order t o obtain an understanding of t h e

The thermodynmic charac te r i s t ics of Brayton cycles for space application.

characterist ics of interest a r e system performance, as denoted by cycle

efficiency, and a desirable s e t of cycle temperatures. Since t h e radiator

i s t h e largest component and a major weight contributor t o t h e system, mini-

mum prime radiator are8 m s selected as the c r i te r ion for cycle temperature

select ion.

Cycle efficiency and prime radiator area a re functions of several

system design f ac to r s and two independent temperature variables. Cycle

efficiency depends on such design fac tors as turbine and compressor effi-

ciencies, l a s s pressure ratio, and recuperator effectiveness. Radiator

area a l s o depends on the above mentioned design fac tors as well as t h e

additional factors of tvrbine in le t temperature, sink temperature, radiating

surface emissivity, and gas heat t ransfer coefficient. The two independent

temperature variables were turbine exit t o in le t temperature r a t i o and com-

pressor i n l e t .to turbine in l e t temperature ra t io .

A t each r a t i o of compressor in le t t o turbine in l e t temperature there i s

one par t icu lar value of turbine ex i t t o i n l e t temperature r a t i o that maximizes

cycle efficiency and an increase i n compressor i n l e t t o turbine in l e t tem-

perature r a t i o r e su l t s i n a decrease i n t h i s maximum cycle efficiency.

creases i n turbine and compressor efficiencies and lo s s pressure r a t i o re-

sult i n a rapid deterioration of cycle efficiency.

offers a potential twofold increase i n cycle efficiency.

De-

The use of a recuperator

FOP any given s e t Of design factors, a study of radiator area reveals

tha t :

there i s one value of ccsnpressor in le t t o turbine i n l e t temperature r a t i o

t . b t yields a minimum radiator area; (2 ) for each value of the r a t i o of com-

pressor i n l e t t o turbine i n l e t temperature the re i s one value oi turbine

exit t o i n l e t temperature r a t i o tha t yields a minimm radiator area; and

(3) there is one combination of t h e two temperature variables tha t yields

a minimum radiator a rea with respect t o both variables.

area can be reduced by increasing turbine in l e t temperature, turbomachinery

efficiency, loss pressure ratio, recuperator effectiveness, gas beat t ransfer

coefficient, and surface emissivity and decreasing si& temperature.

(1) for each value of t h e r a t i o of turbine ex i t t o in le t temperature

Required rad ia tor

The opzimum values of t h e cycle temperature variables depend upon t h e

particular values of t h e design factors.

those usually eniountered i n a System design, t h e optimum values of turbine

ex i t to i n l e t temperature r a t i o and compressor i n l e t t o turbine in l e t tempera

For design fac tors i n the range of

4 F - t v re r a t i o a re generally i n the range of 0.70 t o 0.80 and 0.25 t o 0.35, 0

respectively.

Y

l-

e w Q

w I-

a

TURBINE

5,

RECUPERATOR

( a 1 SCHEMATIC DIAGRAM

w e 3

o

I

ENTROPY ( b) TEMPERATURE-ENTROPY DIAGRAM

~

REFKRENCES

L k c k a y , E. B e : Powerplant S e a t Cycles for Space V e h i c l e s . Paper 59-104,

Inst. Aero. Sei., 1959.

2. Engl ish, Robert, X , Slone, Henry O., Bernat.ovicz, D a n i e l I., Davison,

Z h e r B., and L i e b l e i n , Sejmour; A 20,000-Kilowatt Nuciear Turbo-

e l e c t r i c Power Supply for Manned Space V e h c i l e s l NASA N i l 0 2-20-59Z, !

1959.

3. Wesliw, G. C., and Brown, X.: Tnermodynamics of Space Power P l a n t s ,

Rep, R59AGT16, Genera l E l e c t r i c Co., Feb. 1959.

4, Lloyd, W. R , r R a d i a t o r Design Study fo r Space Engines . Rep. RSSAGiT417,

General E l e c t r i c Co., May 28, 1958.

F i g u r e 1. - Brayion ?over c y c l e .

- ' . , > .

I . n

.20 .25 .30 .35 .40 COMPRESSOR INLET TO

TURBINE INLET TEMP RATIO, L'T,

I I O y

COMPRESSOR INLET TO TURBINE INLET TEMP

RATIO, T4 / Ti

I O .IO .20 .30 .40 .50

COMPRESSOR INLET TO TURBINE INLET TEMP 0,

1600 I800 2000 2200 2400 2600 TURBINE INLET TEMP, T , , O R

ilB"'" 7.. - i.lfrit or rliihlnr inlet ann a m > tmpcmturer 0" prime F"nl,%fOi Y.FLI.

COMPRESSOR INLET TO TURBINE INLET TEMP

110,-

50

30

.I5 .25 -35 .45

t

I- I O L U

.I 5 .25 .35 .45 COMPRESSOR INLET TO TURBINE INLET TEMP

COMPRESSOR INLET TO TURBINE INLET TEMP

' O r

I O U J .I5 .25 .35 .45

COMPRESSOR INLET TO TURBINE INLET