s ORNL-1255 010 » ^mm mX BASIG PERFORMANCE CHARACTERISTICS OF THE STEAM TURBINE-COMPRESSOR- JET AIRCRAFT PROPULSION CYCLE By Arthur P. Fraas George Cohen OAK RIDGE NATIONAL LABORATORY CENTRAL RESEARCH LIBRARY CIRCULATION SECTION 4500N ROOM 175 LIBRARY LOAN COPY DO NOT TRANSFER TO ANOTHER PERSON If you wish someone else to see this report, send in name with report and the library will arrange a loan. UCN-7969 (3 9-77) t-fcr OAK RIDGE NATIONAL. LABORATORY OPERATED BY Carbide and carbon chemicals compa A DIVISION OF UNION CARBIDE AND CARBON CORPORATION OAK RIDGE. TENNESSEE * 4E9
Transcript
s
ORNL-1255
010 » ^mm mX
BASIG PERFORMANCE
CHARACTERISTICS OF THE
STEAM TURBINE-COMPRESSOR-
JET AIRCRAFT PROPULSION
CYCLE
By
Arthur P. FraasGeorge Cohen
OAK RIDGE NATIONAL LABORATORY
CENTRAL RESEARCH LIBRARYCIRCULATION SECTION
4500N ROOM 175
LIBRARY LOAN COPYDO NOT TRANSFER TO ANOTHER PERSON
If you wish someone else to see thisreport, send in name with report and
the library will arrange a loan.UCN-7969 (3 9-77)
t-fcr
OAK RIDGE NATIONAL. LABORATORYOPERATED BY
Carbide and carbon chemicals compaA DIVISION OF UNION CARBIDE AND CARBON CORPORATION
OAK RIDGE. TENNESSEE
*
4E9
Index No. ORNL-1255This document contains 37 pages.This is copy^of 152 ,Series A.
Subject Category: Reactors-Research and
Power
BASIC PERFORMANCE CHARACTERISTICS OF THE STEAMTURBINE-COMPRESSOR-JET AIRCRAFT PROPULSION CYCLE
hy
Arthur P. Fraas
and
George Cohen*
OAK RIDGE NATIONAL LABOOperated by
CARBIDE AND CARBON CHEMICALS COMPANYA DIVISION OF UNION CARBIDE AND CARBON CORPORATION
Oak Ridge, Tennessee
Contract No. W-71<-05-eng
♦Formerly with ORNL, presently employed byAEC Cincinnati Operations Office.
lKIimiIiKnIJ,ENEMY svs™s i
3 44St Q3bCH5b b
Distribution, Series
1-59- Carbide anVcarbon Chemicals Company (Y-l^jElrea)6O-69. Argonne Natmnal Laboratory70. Armed Forces Ibecial Weapons Project (S^Jdia)71-78. Atomic Energy oWaission, Washington79' Battelle Memoria^Institute80-82. Brookhaven Nation^ Laboratory83. Bureau of Ships84. Chicago Patent Group185- Chief of Naval Resean86-90. duPont Company91' H. K. Ferguson Company92-94. General Electric Company,'ItokJEdge95-98. General Electric Company, H|£]p.and99' Hanford Operations Office100-104. Idaho Operations Office105. Iowa State CollegeIO6-IO9. Knolls Atomic Power Laborajbry110-112. Los Alamos
113. Massachusetts Institute 0 Technology (Kaufmann)114-115. Mound Laboratory116. National Advisory Comm|ftee for Aero%utics117-118. New York Operations 0fjp.ce119-120. North American AviatiJE, Inc.121. Patent Branch, Washi:ra;on122. Savannah River OperaRons Office123-124. University of Califwnia Radiation Laboratory125-128. Westinghouse ElectjK: Corporation129-137. Wright Air DeveloiJent Center138-152. Technical Informqpon Service, Oak Ridge
Carbide and Carbon ChemicalsJFompany internal distribution as\follows:
1. C. E. Center
2. C. E. Larson
3« W. D. Lavers
4. A. M. Weinberg5. W. B. Humes
6. E. D. Shipley7- R. C. Briant
8. E. H. Taylor9' J. A- Swartout10. K. Z. Morgan,11. C. E. Winter12. J. A. Lane,
13- J- H. Bucl14. A. P. Frg
Issuing Office
Technical Information Department, Y-12 AreaDate Issued: >.,,.;r .
W^r UI952
K. ErgenS. ThompsonW. SavageN. LyonJ. Miller
W. Schroeder
S. BillingtonP. Blizard
E. Clifford
D. Callihan
D. Manly
L. Meem
R. Grimes
F. Poppendiek
Index Nc.
Reactoi
ORNL-1255-Research and Power
56-59.
G. F. Wi*l.icenus
G. Cohen
Gale Young''E. P. WigneiLt. Col. R. E\GreerLloyd P. Smith!Chemistry Libra!Physics LibraryBiology LibraryHealth Physics LibraryMetallurgy LibraryTraining School Libr^X-10 Central Files
4 Steam Turbine-Compressor-Jet Cycle Performancefor Steam Turbine Inlet Temperature and Pressure =900 F and 5000 psia, and Condenser Pressure = 660 psia 25
5 Steam Turbine-Compressor-Jet Cycle Performance forSteam Turbine Inlet Temperature and Pressure = 1200 Fand 7000 psia, and Condenser Pressure = 550 psia 26
6 Steam Turbine-Compressor-Jet Cycle Performance forSteam Turbine Inlet Temperature and Pressure = 1200°Fand 10,000 psia, and Condenser Pressure = 800 psia 27
7 Steam Turbine-Compressor-Jet Cycle Performance forSteam Turbine Inlet Temperature and Pressure = 1500 Fand 7000 psia, and Condenser Pressure = 58 psia 28
8 Steam Turbine-Compressor-Jet Cycle Performance forSteam Turbine Inlet Temperature and Pressure = 1500 Fand 10,000 psia and Condenser Pressure = 90 psia 29
9 Steam. Turbine-Compressor Jet Cycle Performance for 0Steam Turbine Inlet Temperature and Pressure = 1500 Fand 7000 psia and Condenser Pressure = 150 psia 30
10 Working Chart No. 1; Cooling Effectiveness of Condenser 31
11 Working Chart No. 2; R Factor for Condenser;Air A P/P = .05 and M = 0.9 32
12 Working Chart No. 3; R Factor for Condenser;Air A P/P = .10 and M = 0.9 33
13 Working Chart No. 4; R Factor for Condenser;Air A P/P = .20 and M = 0.9 34
14 Working Chart No. 5; R Factor for Condenser;Air Al?/? = .10 and M = 1.5 35
15 Working Chart No. 6; Compressor Air Outlet Temp. 36
16 Working Chart No. 7; Air Enthalpy Rise in Compressorand Condenser ^^^^^^^^^^^^ 37
LIST OF TABLES
Table No. Title Page No.
I Calculated Performance of a Steam-Turbine-Com
pressor-Jet Cycle For a Condenser CoolingEffectiveness of 80$, An Altitude of 45,000 ft,and a Flight Mach No. of 0.9 13
II
III
IV
Calculated Performance of A Steam-Turbine-
Compressor-Jet Cycle for a Condenser CoolingEffectiveness of 80$, an Altitude of 45,000 ft,And a Flight Mach No. of 0.9
Calculated Performance of a Steam-Turbine-
Compressor-Jet Cycle for a Condenser CoolingEffectiveness of 80$, an Altitude of 45,000 ft,and a Flight Mach No. of 1.5
Sample Calculation Sheet
14
15
22
BASIC PERFORMANCE CHARACTERISTICS OF THE STEAM
TURBINE-COMPRESSOR-JET AIRCRAFT PROPULSION CYCLE
Introduction
Recently much interest has been expressed in utilizing the supercritical
water cycle for aircraft nuclear propulsion. One of the most widely-advocated
methods of accomplishing this is to use the compressor-jet propulsion cycle.
This involves adding pressure energy to the air stream in a low compression
ratio blower, then adding heat in a radiator or condenser, and finally allow
ing the air to expand in a jet to generate an impulse for propulsion. The
supercritical steam from the reactor expands through a turbine which drives the
air blower and the feed water pump. The turbine exhaust steam is fed to the
condenser where it loses its heat of vaporization to the air stream from the
blower.
Among the advantages of this cycle is the use of water, a familiar and a
relatively non-corrosive substance, for both coolant and moderator. The dis
advantages include an inherently low specific impulse and the necessity of
developing an entirely new type of aircraft engine.
The purpose of the work covered by this report was to analyze the funda
mental cycle and discover some of the relations among the many basic parameters
involved. In particular, the condenser air inlet face area, the condenser
weight, and the impulse were evaluated per-pound of air flow in terms of the
temperature and pressure of the steam leaving the reactor and the condenser
pressure. This was accomplished for flight at 45,000 feet altitude at Mach
numbers of 0.9 and 1.5.
Reasonable values were assumed for component efficiencies and actual test
data used for the condenser performance. The results should give attainable
performance of the fundamental cycle at the two design points investigated.
Somewhat better performance can probably be obtained through a program of opti
mization of the cycle and equipment. However, the data presented here should
give performance not far from the optimum and hence should be useful for pre
liminary design studies of the system.
Summary of Results
The results of this investigation as summarized in Figure 1 indicate that,
o
for reactor outlet steam conditions ranging from 1000 to 1500 F and pressures
from 5000 to 10,000 psi, the following statements can be made:
1. The specific impulse was found to be low in all cases considered;i.e., from 15 to 20 lb/lb air/sec at a flight Mach No. = 0.9 andfrom 9 to 14 lb/lb air/sec at a flight Mach No. = 1.5.
2. Increasing reactor outlet steam temperature or pressure or condenser pressure effects some improvement in all cases and in allparameters considered; i.e., specific impulse, specific heat consumption, and specific condenser weight and frontal area.
4. Increasing the reactor steam outlet pressure from 5000 to 10,000 psigives very little improvement in performance.
O O CO
m -33
•v JO m co
CO
c JO m n -0
CO
SP
EC
IFIC
IMP
UL
SE
LB
TH
RU
ST
LB
AIR
PE
RS
EC
SP
EC
IFIC
HE
AT
CO
NS
.—B
TU
LB
TH
RU
ST
SP
EC
IFIC
CO
ND
.W
EIG
HT
—L
B
LB
TH
RU
ST
SP
EC
IFIC
CO
ND
.F
RO
NT
AL
AR
EA
-F
T'
LB
TH
RU
ST
0
8
Ram Air
Diffuser*-!-
Air
Compressor-*~2 —
•*- 5 —
Radiator *- 3-
1
Nozzle•*- 0- Ambient
Air
\
Steam
Turbine
Steam
Condenser
1
1 Mechanical Linkage
1
T6
Reactor -H7-Feed
Water Pump
Figure 2
SCHEMATIC FLOW SHEET SHOWING THE MAJOR ITEMSOF EQUIPMENT REQUIRED FOR THE STEAM TURBINE-COMPRESSOR-JET CYCLE;
(The subscripts used in the text of this reportindicate the same points in the cycle as thecorresponding numerals in this diagram.)
Description of Cycle:
While there are many type of aircraft power plant that might be designed
around a steam generating reactor, the type considered here is one in which
the steam is generated at supercritical pressures and fed through the
turbine, condenser, and feed water pump back to the reactor. Modification
of this basic cycle can be made; e.g., a fuel oil burner could be employed
to boost the temperature of the air ahead of the jet nozzle, but such
elaborations were not considered in the cycle performance calculations
made in this study.
The proposed cycle is illustrated in Figure 2. Air compression owing to
ram takes place in the air inlet and diffuser. Further compression takes place
in the turbine-driven axial flow blower, or compressor. The air then flows to
the radiator, or condenser, where it is heated by the exhaust steam from the
turbine. The high velocity resulting from expansion of the air through the
nozzle in discharging to the atmosphere gives an impulse, or thrust.
On the steam side of the cycle, water enters the reactor from the feed pump
at supercritical pressure, i.e., above 3206 psia. The high pressure prevents
boiling in the reactor and preserves sufficient density for effective moderation.
After gaining heat energy in the reactor, the steam drives the turbine and then
transfers its heat of vaporization to the air in the condenser-radiator. The
condensed water is then raised to reactor pressure by the turbine-driven feed
water pump.
There are a multitude of parameters involved in the system. Obviously basic
are the turbine inlet conditions, T^ and P^, and the condenser pressure, Pc
(see Figure 2). No pressure drop is assumed in the condenser on the steam side,
so P^ = Pg. The condenser outlet temperature, Tg, was taken as the saturation
temperature corresponding to P^. (Actually the water would have to be cooled
below this temperature to avoid feed pump cavitation). P7 is assumed equal to
Pij.. 1c may be superheated or saturated with some moisture.
On the air side, the blower compression ratio, P2/p]_> and the air pressure
drop in the condenser, (P2-Po)/P2> must be considered. The nozzle temperature,
T3, is found to be directly related to the heat exchanger cooling effectiveness,
a widely-used heat exchanger performance parameter.
10
The cooling effectiveness,"^. , is normally defined as:
-ft _ Temperature rise in coolantInitial temperature difference
It is usually expressed as a percentage.
Steam
AT,eff
•P
<
TC
Distance from air inlet
Figure 3. Temperature Distribution in Condenser
The application of this expression is quite straight forward when there is no
change in state in a fluid passing through the heat exchanger, or when only
condensation or boiling occur. If superheated steam is fed to a condenser,
however, the peculiar temperature distribution shown in Figure 3 results. In
order to use available heat exchanger performance data, it was necessary to re
define cooling effectiveness for this special case. A reasonable approximation
was taken to be the following:
^ =T3-T2
A. T(1005&)
effective
where
=(T6 -T2) + * h^evUeat ( _ }0 * ^ h total '
The relations are such that selection of T^, P^, P5, (P2 -P3VP2 >a^d T3
identify a cycle. With values of these parameters known, the following can be
evaluated also:
Blower compression ratio
Heat exchanger cooling effectiveness = *X.
o •*• -. -i lb of thrustSpecific impulse =
lb of air per sec
Condenser airflow rate = ^ air per sec—ft air inlet face area
11
Specific condenser area = ft of air inlet face arealb of thrust
Condenser depth in direction of air flow - inches
Specific condenser weight =lb of thrust
h) Specific heat consumption = Btu/lb of thrust
The first step in the study was an attempt to select optimum values for
two of the five identifying variables. If this could be done, these two
parameters could be fixed at their optimum values and the calculations required
would be greatly reduced.
The optimization was accomplished by plotting (b) through (h) against T3
for a particular combination of T^, Pij., and P5. This was done for several
values of (P2 - P^)/P2. The results are presented in Figures 4 to 9-
These plots revealed that a pressure drop across the condenser of
AP/P = .10 seems to be the most reasonable pressure drop. They show that going
to A P/P = .20 reduces the specific area very little, but increases the specific
weight substantially. On the other hand, A P/P = .05 gives a quite severe
increase in specific area, with only a slight decrease in specific weight. The
specific weights for .05 and .10 generally converge in the region of interest.
The plots also revealed a minimum in specific condenser area. This minimum
occurs at practically the same point for each cycle. With the selection of
12
AP/P = .10, the minimum specific area is obtained at approximately 80$
cooling effectiveness. It seems reasonable to select this as the optimum value
for^ .
The identity of the cycle could now be established by T^, Pil, and Pc,
since Ap/P = .10 and ^ = 80$. Selection of >£ = 80$ is equivalent to
selection of To, because the plots reveal a linear variation between the two
parameters.
The next step was to select values for T^ and P^ and vary Pc for each
combination. The principal parameters were then plotted versus Pc in Figure 1
for five different combinations at Mach =0.9 and 1.5. The remaining parameters
are tabulated in Tables I, II, and III.
The lower limit imposed on Pc was that pressure at which the steam con
tained 10$ moisture at the turbine exit. The upper limit was either arbitrarily
taken as 1000 psi, or that pressure at which the heat from the-superheat of
the exhaust steam was 10$ of the total heat given up in the condenser by the
exhaust steam. The heat exchanger data were based on condensing coefficients
and should not be extended into the superheat range. It was felt that the
approximation for cooling effectiveness given on Page 6 should be fairly good
if limited to small amounts of steam superheat at the condenser inlet,
especially since the major temperature drop is from the metal to the air rather
than from the steam to the metal. A special 2-pass condenser would, of course,
be required with the superheated steam coursing across the air outlet end
first before entering the main part of the condenser.
Calculation Methods
The method of performing the calculations can be best explained by
carrying through the entire procedure for an illustrative cycle.
o
CDHo
>>o
C-l
C-3C-5
C-7C-9
B-l
B-3B-5
B-7B-9B-ll
B-13B-15B-17B-19B-21
B-23B-25
pa3
S3 pCO
CO CO-p £CO °H
EH EH
1000
1000
1000
1000
1000
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
CALCULATED PERFORMANCE OF A STEAM-TURBINE-COMPRESSOR-JET CYCLE FOR A CONDENSER COOLINGEFFECTIVENESS OF 80$, AN ALTITUDE OF 45,OOP FT., AND A FLIGHT MACH NO. OF .9
pco co
•H• 10
03 ftCO ICO Pfk 0)
P4 H
CO COp aCO tH
ifP4 Eh
5000
50005000
5000
5000
10000
10000
10000
10000
10000
7000
70007000
5000
50005000
5000
5000
p
to
to coCO °HU CO
CM ft
§ ShCO COCO 10
p flCO (D
=•,. flVOO
1000
8oo6oo300
' 180
1000
8oo550247100
800550247400350247150
120
COpCO
i
uCO(0dCO
OCO O
!*P =rlcd
CO ♦
&VOCO fa
EH EHO
545518486417373
545518
4774003285184774oo
4454324oo
35834l
&uCOa ow p
o
o•H _P -cscd a hmow:
O inII CO
O
U Hco pqto
G OCO P
« P w
6.505.905.234.173.67
4.86
4.554„o6
3.322.80
4.654.123 =553.943.783.483-12
3.00
w•r a; m
p. to Oe a) ^
ft -d
c
p
o
cd
p03CO
uO CO
co ?..p
EHo
co-eK CO ^
43°, 6.6$26°, 3-5$Dry Satd.
5.2$ M7 =7$ M
53°, 7-8$35°, 4.6$5°, 0.7$
5«l$ M8.9$ M
105°,11.3$72°,. 7=0$8°, 0.7$
9=4$120
108°, 8.3$82°, 5 =9$43°, 2.9$29°, 1.9$
0U COCO to
nO ,Q
O H
OOJ•H -P<H U•H I
O COCO COft fc
CO <J
.0180
.0181
.0181
.0192
.0206
.0143
.0148
.0154
.0170
.0200
.0148
.0152
.01780016000162=0172.0188
.0196
ucoCO
ao
o
u•H
CO
3
o3•H
•HOCO
!
1ft CO
CO I3t
.250
.252
.254
.270
.289
.203
.210
.219
.242
.274
.207
.217
.251
.228=230.245.265,277
COw
H
3 °8* <»
uU =H
•H cd
•H ,0O HC0\-ft ,Q
CO H
17o6l17=3517.0816.00
14.95
20.4819.8019.00
17.2514.9419.9019.20
16.7518.3518.10
17.1515.8515.22
1
CO 0p 3cO CO
K P
ss<+H\
•H =H
3 =163-193.243 =253.25
3 =423.423.413.4i3-353 =39
4236404i
3836
333
33
3
3-35
1
pft
aucoCOd wco co
x) a3 oo a
U H
7=917=937=977=987.98
8.088.088.088.088.028.058.098.028.078.088.068.02
8.02
p «2 oo
1
ft ua coCO w
Eh C
u -d
EH O
910
88786l
806
771
91489185779573689886379584o
828800
762748
uoCOco oCO =HU P
|dO 0)
u
HtQPh co
\ CO
Ph Ph
1.471.491.51
1-531 =53
,64,64
1.641.64
1.59,62=64
1.60x.631.64
1.621.60
1 =59
l.
1.
tr1
H
*IT
ii
se
ii
ii
iH
HH
HV
O-JV
Tico
H-JV
J1
U)
H
HH
I-'l
-'H
HH
t-'H
vn
vn
v/iv
_n
vx
iv
nv
jiv
_n
vji
OO
OO
OO
OO
OO
OO
OO
OO
OO
VJ1VJ1-J-J-J
oO
OO
OOOOOOOOO
OOOOOOOOO
OOOOOOOOO
hh
roV
J1V
0V
J1V
OV
J1V
J1V
OV
/1-p
-C
OO
CO
OO
OD
OO
-J
ro
co
ro
co
co
ro
co
co
-p"
vo
ro
vo
ro
vji
vo
ro
vn
oo
oo
oco
oocoo
oco
o
ro
ro
ro
ro
ro
ro
ro
ro
ro
CO-P
"rO
-frV
Jlfo
-p-V
/1-l
jco
vo
-jH
vo
co
ro
-p
-co
hro
HH
co
ro
h-p
-C
DO
to
-ro
HW
CO
vn
OO
OO
OO
OO
O
HH
VOH
yi
—3
OH
-p-
ONVO
CO
CO
-J
VO
CO
•o
I•
••
—•
-
H
OO
OO
OO
OO
OH
HH
HH
rO
HI-'H
CO
on
vo
-Jv
ilO
Co
vn
-p-
vo
-J-j-p
-ro
oro
co
ro
ro
ro
ro
ro
ro
ro
ro
ro
ro
o\-p
-co
vjiro
co
o\ro
hv
oo
ro
oo
-p
-o
co
H
!—"
1—'
1—'
I—•
I—'
I—•
1—'
I—•
I—"
v-n
ON
-P-
On
CO
-p-v
n-j
vo
co
vo
vo
-P"
roo
nv
o-j
rov
nv
nO
roco
vn
-^
Oco
co
co
co
co
co
co
co
co
co
-p-v
ji.p
-vn
vn
-p-
^r-
vji
on
Vn
co
HO
VO
HO
N-JO
CO
CO
CO
CD
OO
CO
CO
CD
CO
HM
MH
ro
on
ro
ro
OC
OC
O-J
OC
OC
OO
CO
—J—
J-J-J—
J—
]-^
-q
CO
ro
vjiH
-p
--jo
co
o\o
ro-p
-co
rov
oco
vn
co
—j
HH
h-1
ON
-4-j
ro
ON
—J
—J
-p
-o
-
h1
t->
i->
H
.0
NO
N-J
-J
On
-P"-j
-p-
co
II
aif
fVJ,
Cy
cle
No
.
T^_,
SteamTemp,
at
Turbine
Inlet-
¥
P^,
SteamPress,
atTurbine
Inlet-psia
Pg,
SteamPress.
Condenser-psia
at
Tg,
Sat
ura
ted
Ste
amT
emp
,in
Co
nd
en
ser-
R=
Rati
oo
fE
nerg
yto
Co
nd
en
ser
to
En
erg
yto
Blo
wer
Ste
am
ou
to
-pT
irrb
•'->
->
$M
ni<5
+,o
rD
egre
esSu
perh
eat
and^
Ahx
jjj/
Ahrjn
Qrp
Specific
Condenser
Area-ft2/lb
air/sec
Specific
Condenser
Weight-lb/lb
air/
sec
Specific
Impulse
lb/lb
air/sec
Airflow
Rate-lb
Air/lb
Steam
Condenser
Depth-
Inches
,Air
Temp,
Condenser
out
•°R
P2/P]_,Compressor
Pressure
Ratio
H
oC
oi*
j
CO
vo
Q
£l
II
I1
11
hh
co
on
-P"
roC
OO
N
td
Wtd
td
cd
td
td
tclcd
bd
ii
tt
it
ii
ii
ro
ro
ro
ro
HH
co
oN
-p
-ro
on
-p
-ro
ocd
o
oo
oo
o1
11
11
HC
OO
N-P
T0
oC
ycle
No
.
h-'
[-•
i-1
}-•
y-1
t-1
vn
vn
vn
vn
vn
vn
oo
OO
OO
OO
Oo
oo
HH
I-'h
-'l
-'H
I-'l
-'H
Hro
ro
ro
ro
ro
ro
ro
ro
ro
ro
OO
OO
OO
OO
OO
OO
OO
OO
OO
OO
\->
Hh-
1h
^^
oo
oo
oo
oo
oo
oo
oo
o
T^
,S
team
Tem
p,at
Tu
rbin
eIn
let-
°F
l_i
HH
Hv
nv
nO
OO
OO
OO
OO
OO
OO
OO
OO
OO
oo
o
11
J1
11
11
1I
vn
vn
vn
vn
vn
oo
oo
oO
OO
OO
OO
OO
OO
OO
OO
OO
OO
OO
OO
OO
OO
OO
O
vn
vn
vn
vn
vn
oo
oo
oo
oo
oo
oo
oo
o
Pli
,S
team
Pre
ss,
at
Tu
rbin
eIn
let-
psia
hro
vn
vo
v".
vn
vn
-F
CO
OC
OO
O—
]
HH
ro
co
p-h
ro
vn
co
oro
vn
-p
-v
nO
O-p
-v
nO
OO
O—
]0
00
—]Q
OO
HH
CO
ON
CO
OC
OO
Oo
oo
oo
oo
Pg,
Ste
amP
ress
,at
Co
nd
en
ser-
psia
roco
ro
co
co
-p-
vo
ro
vo
ro
vn
oo
oo
oC
Oo
co
co
-p-
-p-
-p
-co
p-
-p
-v
nv
n-p
-vn
OC
OrtO
O^
H-P
HO
oO
ro
vn
Oo
O—
0C
Ov
n
co
-p-
-p
-v
nv
n-0
PO
DH
Pco
—J
on
co
vn
Tg,
Sat
ura
ted
Stea
mT
em
p,
inC
on
den
ser-
Op
ro
ro
ro
ro
ro
ro
co
-f^-
ro
-p-v
n_
jco
vo
co
ro-p
-co
co
co
co
co
co
ro
co
-p-
-p-
-p-
O—
i---J
VO
CO
CO
OV
JIC
Oo
roco
co
-p-
oro
ow
no
n
co
-p-v
nv
no
n
on
hro
vo
vn
—J
—J
CO
oo
R=
Rati
oo
fE
nerg
yto
Co
nd
en
ser
to
En
erg
yto
Blo
wer
HW
i-1
co
roco
^i
vo
co
(B
OH
WC
ov
no
oo
oo
oV
j.,«
\#
^\*
Va
HV
OH
H-P
-O
NV
O
-p-
-p-
CO
CO
MO
ro
-p-
co
oro
co
vn
vo
co
ro
co
ov
nv
nco
oo
oo
oo
oo
V>
\d
S*
<w
V>
Va
V»
\»
HrO
Ui
00
\OC
DV
/iO
-P"-
v]
vn
vo
vo
co
-p-v
nH
-J
ON
CO
<r.
;ro
-;-'
'SO
NC
Or<
;o
o
CO
—J
vn
faco
On
..
ct-
••
-j
roft
vn
on
Ste
am
ou
to
fT
urb
i^'-
i-M
m*s
t.or
Deg
rees
Sup
erhe
atan
dA
nsn
/A
hrp0
T
bb
bb
bb
co
ro
co
ro
ro
mO
-p-
-P-—
3H
-J
vn
co
vn
vo
Co
vo
bb
bb
bb
bb
bb
WW
MH
HW
WH
HH
-j
vn
oco
—]
vo
Oo
n-P
--p
-v
nH
ON
ro
vn
Hv
nco
vo
H
bb
bb
bro
ro
h1
hh
vn
HC
O—
]O
N—
]o
nro
ro
co
Sp
ecif
icC
on
den
ser
Are
a-ft
2/l
bai
r/se
c
vn
-p
-v
n-p
-co
co
HH
CO
—]
—]
HO
NC
OO
OJ
-P-
H
°-p--
p-co
Coro
-p-c
oto
roro
ON
ro
vn
hv
oco
vn
co
vn
-p-
vn
-p
-H
ro
vo
vo
-p
-M
-p
--p
-
-p
-co
co
ro
roC
Oo
no
vo
—5
O-p
-co
ov
n
Sp
ecif
icC
on
den
ser
Wei
gh
t-lb
/lb
air
/sec
ON
CO
ON
-4
'VO
H
CO
-p-
H-P
*C
OH
rov
no
On
Ov
n
co
co
vo
HH
—a
oro
CO
-p-
Hco
vo
HO
nro
op
-v
nco
OO
vo
Co
ON
vn
oO
rov
n
\^H
\--
oo
vo
hro
ro
ro—
]-p
-ro
co
vn
HO
N-P
-C
O
Sp
ecif
icIm
pu
lse
lb/l
bair
/sec
-p-
-p-
-p-
-s-
-p
-v
n
CO
CO
—]
co
vo
Oo
co
vn
oco
o
-J
-P
--P
--P
--P
--P
--P
--P
--P
--P
-
C\
CO
co
vo
vo
-J
CO
VO
vo
vo
OO
—J
HH
vn
CO
-p-—
]-P
"
rrp
pp
«»
ei»
o
UJ
Co
co
vn
vn
Air
flo
wR
ate
-lb
Air
/lb
Stea
m
vo
vo
vo
vo
vo
vo
CN
Co
vn
on
—J
CO
OO
ON
rov
nv
n
vo
vo
vo
vo
vo
vo
vo
vo
vo
vo
ON
ON
—J
—]
—J
vn
CO
CO
—J
CO
oo
oro
roo
no
oo
ro
vo
vo
vo
vo
vo
vn
On
ON
vn
vn
OO
OO
NO
n
Co
nd
en
ser
Dep
th-
In
ch
es
-J
~]
-0
-J
-J
CO
co
--j
ro
vn
co
roC
OO
-p-
Hv
nv
n
-O-J
CO
CO
CO
—]
CO
CO
VO
vo
ON
CO
H-P
-O
NV
nH
—]
HC
OO
NO
CO
CO
Ov
nv
n—
jo
vn
—J
CO
CO
VO
vo
vo
roco
oco
OO
NO
-4
OT
o,
Air
Tem
p,
ou
to
rC
on
den
ser
-°R
HH
L->
!-•
h*
h>
co
co
ro
co
co
-p-
I-1
vn
vo
ro
-j
h
HH
h-'t
-'H
HH
h-'t
-'l
-'
co
co
co
co
co
ro
co
co
co
co
OH
-P-
ON
ON
VO
vn
CO
00
CO
\-J
H(_
!|_
l|_
1
ro
co
co
ro
ro
00
oo
vo
vo
P2/P
^,C
ompr
esso
rP
ressu
re
Rati
o
in
arc
av
a
CO r-3
1-3
H 1-3
a u o
l o oo o o H
3
t)
H o w szi
o §
13 o tH fed
o w o o S3 I CO
o o rn
Q
16
Cycle B-3 will be used for this purpose. Its identifying qualities are:
M 0.9 at 45,000 ft
T4 = 1200 F
P^ = 10,000 psi
P^ = P5 = 800 psi
With the assumption of turbine adiabatic efficiency = 80$, it is possible
to specify the conditions and the energy at each point of the steam side of
the cycle.
From extrapolated steam data contained in TAB-78:
h^ = 1447 Btu/lb; S^ = I.396
Using the Mollier Diagram, the enthalpy after isentropic expansion to
condenser pressure is:
h5 » 1179 Btu/lb
A hisent
T5 "
(h4 "h5>isentropic = 268 Btu/lbApplication of the 80$ turbine efficiency gives the true enthalpy drop:
A h = (.8)(1^ -h5)igent = 214 Btu/lb
h5 m h^ -214 = 1233 Btu/lb
From Mollier Diagram at h,- = 1233, P,- = 800 psi:
o
553 F
Saturation temperature at 800 psi is 518 F, so the steam is entering the
condenser with 35 superheat. The water leaves the condenser saturated so:
Tg = 518 F
V6 "
h6 "
.0209 ft /lb
510 Btu/lb
The heat given up in the condenser is:
h^ -h6 = 1233 - 510 = 723 Btu/lb
The feed pump work to return the water to the reactor, assuming 65$
efficiency and incompressibility is:
v6 (P7 - P6)^ -h6 =
(Eff) J
= (=0209)(10,000 -8oo)(i44) = 55 Btu/lb(.65)(778)
A useful parameter is now defined:
R = Heat to condenser
Energy to blower
h5 - h6
(hi^ - h^-th-, - hg) lag - hx
723
214 - 55
(All values of enthalpy so far are per pound of water.)
Turning to the air side of the cycle, standard atmospheric conditions
at 45,000 feet are:
TQ = 393°R; P0 = 2.14 psiaThe Air Tables give the isentropic pressure ratio at Mach = 0.9-
P /P^ = .59126 (Primes represent isentropic)
P^ = 2.14/.59126 = 3.62
]?l-po= 1.48
The diffuser is assumed to achieve 85$ of the isentropic pressure recovery.
Px -P = .85(1.48) = 1.26
= 4.55
*? -H
17
The temperature is the stagnation temperature for Mach =0.9.
o
18
T, 393/.86058 = 457 R; hx = 109.2 Btu/lb of air
It is now possible to select one more condition, To, against which the
major performance parameters may be plotted. To illustrate the procedure, To
is selected as:
o
T, = 891 R
h- = 214.05 Btu/lb
The jet velocity, and therefore the thrust, can be calculated if Po is
determined. It is first necessary to determine the compression ratio of the
blower.
The energy added in the blower and condenser is:
h - hx = 214.1 - 109.2 = 104.9 Btu/lb
Since R is known from the steam side:
(112 - hj) + R(hc, - hx) = h3 - hx
ho - h, 104.9h„ - h. = -2 i = = 18.9 Btu/lb
1 + R 1 + 4.55
h2 = hx + 18.9 » 109.2 + 18.9 = 128.1 Btu/lb
From the Air Tables at this h:
= 536 R
Knowing the blower inlet conditions, and assuming an adiabatic
efficiency = 87$, it is possible to plot Tp against Pp/P-,. This has been
done in Figure 15. Entering this plot at T2 = 536 > P2/Pl is found ^°
be = 1.64.
P2 « 1.64 px = (1.64)(3.4) = 5.58 psia.
It is now necessary to select an air pressure drop in the radiator.
Three different values were used originally, but for this illustration the
optimum will be used:
PQ - Po_£ 2. = 0.10
P3 = °*9 P2 = (°-9)(5.58) = 5.02 psia
Po 5.02
P0 2.14=- 2.35
r = 0.426 = pressure ratio across jet nozzle.
The jet velocity is:
J V m
m = molecular weight
R = 1545
T3 12 gnR J n - 1/(l-r n
n - 1 V
n = 1.4 = -^cv
1 n~TT.6 v/ T_ vj (1 - r nV. = 109
The last term is tabulated in Table 25 of Keenan and Kaye Gas Tables.
V. = (109-6) ^891 (.465) = 1522 ft/secJ
The airplane velocity is:
19
V = Ma = (0.9)(49.1) V393 = 876 ft/sec
The impulse is equal to the change in momentum:
Jt - w/g (Vj -va)W = weight of air, lb
With a weight flow of one pound of air per sec, the specific impulse is:
I «VVa 1522 - 876 lb - sec
= 20.132.2 lb
20
The total heat added per pound of air is:
h, -h, = 214.1 - 109.2 = 104.9 -,, B^U .—3 1 lb of air
