ORNL-1976.txt

 

 

 

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AEG RESEARCH AND DEVELOPMENT R

   
    
     

CENTRAL REIFAECH LIBRARY

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STEADY-.STATE CONTROL CHARACTERISTICS OF

CHEMICAL-NUCLEAR AIRCRAFT POWER FL@
a

C. B. Thompson

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ORNL 1976
C 85 = Reactors - Aircraft Nuclear
Propulsion Systems

Thsdoc met on i1stsof 44 p g s

Copy? of 135 ¢ pies Ser A

Contract No W 7405-eng 26

AIRCRAFT NUCLEAR PROPULSION PROJECT

STEADY STATE CONTROL CHARACTERISTICS OF CHEMICAL NUCLEAR

AIRCRAFT POWER PLANTS

C B Thompson*

DATE ISSUED

FEB 29 1956

Minneapolis Honeywell Regulator Company Aeronautical Division

OAK RIDGE NATIONAL LABORATORY
Operated by
UNION CARBIDE NUCLEAR COMPANY
A Division of Union Carbide and Cerbon Corporation
Post Ofi e Box P
Ock Ridge Tenne ee

 
 

 

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3 4456 03LL0OO7? 3

 
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ORNL 1976

C 85 - Reactors = Aircraft Nuclear

¥ Propulsion Systems
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Assistant Secrgtary of the Air Forgé R&D

Atomic EnergfgCommission Wasjifngton

Bureau of Aerdnautics

Bureau of Aerqautics GeneraffRepresentative
Chicago Operafgons Office g

Chicago Patent¥sroup

Chief of Naval Besearch #

Convair GeneralfDynamigf Corporation

Director of Labokatoriesf{WCL )

Director of Requitemengs (AFDRQ)

Director of Resedgch ghd Development (AFDRD ANP)
Directorate of Sysgenss Management (RDZ ISN)
Directorate of Sys®ihs Management (RDZ 1SS)
Equipment Laboratfky (WADC)

General Electric @dpany (ANPD)

Hartford Area Of

Headquarters AY Fogke Special Weapons Center
Lockland ;""J tficel

Los Alamos Sgientific & aboratory

Materials La@bratory Pifins Office (WADC)

National Ad@ sory Com '“‘33 tee for Aeronautics Cleveland
National Ad¥isory Commfgtee for Aeronautics Washington
North Ameggican Aviation fnc (Aerophysics Division)
Nuclear Revelopment Corgpration

Patent BFanch Washingtor

Powerj lant Laboratory (W&DC)

Prattgfnd Whitney Aircraft Bvision (Fox Project)
-_ -'- Corporation 4

Sch¥ol of Aviation Medicine

USRF Project RAND

University of California Radiatn Laboratory Livermore
Wright Air Development Center (§COS! 3)

Technical Information Extension Qak Ridge

Division of Research and Development AEC ORO

 
 

CONTENTS

Summary
Introduction

Detailed Power Plant Descriptions — Component Characteristics
Circulating Fuel Reactor
G E X 61 Turbojet Engine
Allison J 71 Turbojet Engine
Steady State Power Plant Performance Characteristics — Nuclear Power Only
Operation
Control Rod Throttling
Reactor Fuel Flow Throttling
NaK Flow Throttling
NaK Bypass Throttling
Air Bypass Throttling
More Complex Throttling Arrangements

Static Stability Characteristics of @ Demand Sensitive Reactor—Turbojet Combination
Coupling Between Engines in a Multiengine Installation

Nuclear Power Source Control Requirements
Manua! Operation at Flight Conditions Where Radiator Capacity Is Excessive
Manual Operation at Radiator Design Flight Conditions
Manual Operation at Flight Conditions Where Radiator Capacity |s Inadequate

Automatic Control Requirements During Operation in the Power Range
Appendix A — Radiator Design Procedure
Appendix B — Steady State Performance Calculations

Appendix C — Static Stability Caleculations

 

0 b W W N

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STEADY STATE CONTROL CHARACTERISTICS OF
CHEMICAL NUCLEAR AIRCRAFT POWER PLANTS

C B Thompson

SUMMARY

It seems reasonable to believe that the simplest
control system for the nuclear power source In a
combination chemical nuclear aircraft power plant
wtll result if nuclear power delivery during normal
operational use can be throttled by variation of a
single control quantity Studies to date of the
steady state off design point performance charac
teristics of two such power plants indicate that
sattsfactory power control can be obtained by by
passing NaK around the engine radiators alone f
full range NaK bypass valves can be built and if
the fuel temperature at the inlet of the reactor
core can be allowed to rise as high as the design
point mean fuel temperature If the fuel tempera
ture at the inlet to the reactor core must be limited
to some value less than the design point mean
fuel temperature the control rod must also be
moved as power delivery 1s varied Possibilities
for throttling reactor power delivery by individual
variation of reactor fuel flow control rod position
NaK flow”and radiator air bypass percentage were
also considered but each of these altemate
schemes 1s unsatisfactory

Study of the static stability charactenistics of a
demand sensitive reactor turbojet load combination
indicates that such a power plant should operate
stably in the high power range
erating conditions
stability of such a power plant 1s questionable
and appears to depend on the throttling scheme
used In the example considered here the NaK
bypass throttled power plant was stable at low
power part load operating points while the air

At part load op
however the inherent static

 

bypass throttled power plant was not stable

The various engine loads are cross coupled
through their common reactor power source If
the power delivered to one engine 1s varied the
power delivered to the other engines also changes
When NaK bypass throttling 1s used and the con
trol rod position is constant the magnitude of the
coupling effect appears to be relatively small |f
rod motion with total power level changes 1s re
quired however cross coupling between engines
will be more pronounced and may be large enough
to make tedious the independent manual adjust
ment of power delivery to each load

Automatic control requirements for the nuclear
heat source can be determined by considering how
the flight engineer might perform typical power
plant maneuvers without the help of automatic con
trol equipment Study of the manual operations
required indicates that the addition of automatic
control equipment for the NaK bypasses 1s very
desirable if not essential to limit movement of
the valves 1n such a way as to maintain the retum
line NaK temperatures between their upper and
lower limits at all times Automatic control equip
ment i1s also required for the rod 1f the fuel tem
perature at the inlet of the reactor core must be
held below the design point mean fuel temperature
Such equipment might withdraw the rod to main
tain the mean fuel temperature at as high a level
as possible as limited by the requirements that
both the core fuel inlet temperature and the core
fuel outlet temperature be less than or equal to
thetr maximum allowable values
&XW, M .
! x

INTRODUCTION

Most of the control system thinking by the ORNL
ANP grouphas quite naturally been directed toward
the problems associated with controlling a circu
lating fuel reactor which delivers power to a heat
dump type of load This work 1s of major concern
since a large part of the ANP effort at ORNL 1s
now being devoted to the ART

The control system for the ultimate reactor—
turbojet engine power plant will obviously be dif
ferent from the control system for the ART power
plant because both a reactor control system and a
properly mated set of chemical turbojet controls
will be required The effectiveness of the ART In
clearing up problems associated with controlling
the large aircraft power plant depends largely on
how well the inherent differences between the con
trol requirements of the ART and those of large
arrcraft power plants are understood The work
described in this report was carried out to provide
some of the information required for studying these
differences

The ultimate power plant will consist of one
large reactor coupled to a number of turbojet
engines (the number ranging from two to six de
pending on the type of aircraft being propelled)
The overall steady state performance charac
teristics of such power plants when manually con
trolled at part power off design operating condi
tions must be thoroughly understood before con
trol system requirements can be determined This
report 1s concemed chiefly with the over all
steady state manual control characteristics of the
following two power plants

L oad

Powe Souce

60 Mw ART type reactor

and chemical burners

60 Mw ART type reactor

and chemical burners

2 GE X 61 turbojet engtne

4 Al sonJ 71 t rbojet

eng nes

These combinations were selected primanly be
cause of the availability of performance data 1t1s
not believed that they necessarily represent usable
systems  They are considered here merely as
vehicles for studying control problems

Detailed charactenistics of each of the com
ponents of the above power plants are summarized
in the next section Steady state part load per
formance characteristics derived from these data
are then discussed and the effects of potential

throttling parameter variations are described The
static stability of a demand sensitive reactor
power source-—turbojet engine load combination 1s
then considered and coupling effects between
engines in a multiengine power plant are invest
gated Finally the actions required of the power
plant operator In carrying out typical power plant
maneuvers without the help of automatic control
equipment are outlined to show what types of
equipment are needed

The symbols employed in the calculations are
defined below

NOMENCLATURE
A,, = frontal rea of rad tor fl'2
IR
AHX = hezat ton fe urf ce ae | heat e changer
ft

AR = heat t nsfer surf e area n radiate ff2

C = spec fc heatof r Bt /Ib °F

Cg = spec fc he t of ulat ng fuel Btu/Ib °F
Cy = spec fic heat of NaK cool nt Bt /b °F
FN = eng ne net thr st output |b
g = grav tational constant
M = fl ght M ch n mbe
N = eng ne otor peed rpm
P = powe Mw
P = powe del ve ed pe engne b lan ed load

%

Mw
PN = power del vered to Nth eng ne Mw
PT = total eactor powe Mw

P = total pe sue at nlet of exh t no le
T6 2
Ib/ ft

P0 = ambient tatic pre ve Ib/ §12
Pl = power delivered to engine No 1 Mw
P - = Prandtl numbe of fuel
R = gas constant for air ft/°R
T = mean reactor fuel temperat e °F
FC = fuel temperature at inlet of rea tor core °F

T
Ty = fuel tempe ature at outlet of e ctor ore °F
T

NC = NaK temperat re at nlet of heat exchange
o
F

2 % %*flz v fiw_i-%

 
T‘m NaK tempe ature at outlet of d tor °F

TNH = N K tempe atu e at outlet of heat exchanger
( nlet of radiater) °F

TT3 = total temperature t omp e sor o tlet °F

TT4 = total temperatue at let of turbine °F

TT6 = total temper ture at iniet of exhaust nozzle
°F

Up = over all heat transfe ocefficient of r d ator

Bt /hr ft2 OF

UHX = over all heat tr nsfer coefficient fuel to NaK
heat exchanger Btu/hr f2 OF

Va = aft velo 1ty fps
4 =€ng ne ar flow Ib/ sec
waD = direct a1 flow r te through adiater pe

engine 1b/ se

W.gp = bypass o1 flow rote per eng ne Ib/sec

WF =re to fuel flow rate b/ sec
N = tot | NaK flow rate Ib/ sec
Wangp = NaK bypass flow te per eng ne Ib/sec

=
f

Mux = heat exchanger effect veness

Np =r diator effectiveness

fr = s ostyoff el Ib/ft se

By = v scosity of NaK b/ ft se

P = average density of a1 In

Pr = density of fuel 1b/ fta
py = density of NaK b/ 2

 

= drect N K flow rate th o gh adiate pe

ND
engine lb/se
WNe = NaK flow rate pe engi e b/ e
X = fr ct on of tot | re ctor power del ve ed to
each engine
y = specific heatr toforar
APR = adi tor p essure d op Ib/ ft2
AT = log mean tempe ature d ffe ence for the heat
m
exch nger
ATa = air temperature difference (TTA - TTS)
ATF = fuel tempe t e dffeence (T, - TFC)
ATN = NaK temperature diffe ence (T, - Ty )

adiator b/ f'r3

DETAILED POWER PLANT DESCRIPTIONS — COMPONENT CHARACTERISTICS

Detailed performance characteristics of each
power plant component must be known before the
over all composite behavior of a power plant can
be calculated Each of the components of the two
power plants under consideration 1s described in
this section

CIRCULATING FUEL REACTOR

An early version of the 60-Mw ART circulating
fuel reactor 1s used here as a basis for control
studies Design values for several important re
actor and heat exchanger quantities and fuel and
NaK physical properties used are tabulated below

Design power Mw 60

Core fuel outlet temperature °F 1600

Mean core fuel temperature °F 1450

Core fuel inlet temperature °F 1300

Fuel flow rate Ib/sec 702
Temperature coefficient of reactivity -55x 102

(Ak/E)/F

Heat exchanger NaK nlet tempe a
ture °F
Heat exchanger NaK outlet tempera
ture °F
Total NaK flow rate |b/sec
Total heat exchanger heat transfer
area ft2
Over all heat transfer coefficient at
des gn po nt Btu/hr ft2 °F
Fuel Reynolds number n heat ex-
changer at design po nt
Heatexchanger effect veness at
des gn point
NaK Reynolds number 1n heat ex
changer at design point
Detailed heat exchanger parameters
Bundles
Tubes per bundle
Diameter of tubes 1n
Spacing between tubes mils
Tube length ft

1100

1500

569
1388

1023

3180

08

125 000

24

132

30
6 67
Equivalent diameter (fuel) 1n 0 1328
per bundle
Free flow area (fuel) In 2 per 3852
bundle
Fuel and NaK physical properties
(from ART design meeting Jan 7
1955)
Cp Btu/Ib°F 0 27
CN Btu/ib °F 025
fp (at 1450°F) Ib/ft sec 379 x 103
gy Ib/ft sec 011x 10-3
Pry (at 1450°F) 2 475
Y 200
Py Ib/ft> 46

The heat exchanger design described above was
obtained from M M Yarosh This design was
prepared some time before detailed heat transfer
tests were run and before final heat exchanger
designs were completed Heat transfer coefficient
estimates fuel property estimates and the design
power rating have all been changed since the
design described in the above table was made
Hence the heat exchanger used here 1s not the
same as the heat exchanger currently planned for
the ART However the external performance char
actenistics of the design considered here and the
current design do not appear to be different enough
to change any of the general conclusions drawn
from this work

The variation of the over all heat transfer coef
ficient of the reactor heat exchanger with changes
in fuel flow rate NaK flow rate and mean reactor
fuel temperature must be known if the part load
steady state performance characternistics of the
power plant are to be calculated The vanation of
this coefficient with changes in fuel flow rate has
been estimated for a mean reactor fuel temperature
of 1450°F and a midrange NaK flow rate (320
Ib/sec) by use of a procedure suggested by
Yarosh The result 1s plotted in Fig 1 Average
temperature changes and NaK flow rate changes
also affect the over all heat transfer coefficient
but these effects are thought to be relatively small
for NaK flow rate and average temperature varia
tions 1n the normal safe operating range

 

15 D Goodlette et al Second Summary Report —
Nuclear Powered Seaplane Feasibility Study ER 6621
(Oct 27 1954)

w
1200
1100

1000

w
o
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800
700
600
500
400
300
200

100

 

o

0 100 200 300 400 500 600 700 800
REACTOR FUEL FLOW W (ib/ )

OVERALL HEAT TRANSFER COEFFICIENT Uy (Bt /h it

Fig 1 Variation of the Over All Heat Transfer

Coefficient of the Main Heat Exchanger with Reactor
Fuel Flow
320 Ib/sec

1450°F NaK flow

Mean temperature

G EX 61 TURBOJET ENGINE
The G E X 61 turbojet engine 1s described briefly

below !

Static thrust output per engine at sea level 23 600
(SL) maximum nterburning b

Static thrust output per eng ne at sea level 33000
maxtmum interburning and afterburning Ib

Static thrust output per eng ne at sea level 6 780
w th 30 Mw power 1nput |b

Max mum allowable powe nput pe eng ne 103 5
SL tatc mitay Mw

Max mum turb ne nlet temperatu e °F 1800

Rated a rflow per engine SL static |b/sec 325

Design pressure ratio 8 451

Part load engine performance data that describe
the variation of the turbojet load imposed on the
reactor at off design operating conditions are re
quired for over all power plant steady state per
formance determination The curves of Figs 2
through 5 show how pertinent off design steady
state X-61 engine parameters vary with net thrust
output at various altitudes and flight speeds for
power inputs less than 30 Mw These curves were
calculated from the corrected quantity data of
Goodlette ! Net thrust output and required power
input were calculated from

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~ 35 000 ft MACH O 75
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0 1 2 3 4 5 6 7 8 9

NET THRUST OUTPUT £ (lb 10)

Fig 2 Variation of Steady State Power Input Required with Net Thrust Output for the G E X 61 Engimne
Exhaust nozzle open

© ol

1800

ORN L D 69

 

1700

 

 

1600

1500 S

35 000 ft MACH 0O 75\7/
1400

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1300 / |
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1200 / % sL Mw—/
1100 o~ // //
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SL STATIC

300 / // //
800 A X

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700 /
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NET THRUST QUTPUT £, (Ib X 10%)

 

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1000

 

STEADY STATE TURBINE INLET TEMPERATURE ( F)

 

 

 

 

 

 

 

 

 

 

 

 

 

600

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~
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Fig 3 Vanation of the Steady-State Turbine Inlet Temperature with Net Thrust Output for the G E
X 61 Engine Exhaust nozzle open
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ENGINE AIR FLOW ' [(Ib/
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60

 

0 1 2 3 4
NET THRUST QUTPUT F~ {lb 10}

wn
[¢]
=~
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Fig 4 Vanahon of the Steady State Engine Air Flow with Net Thrust Output for the G E X 61 Engine

Exhaust nozzle open
.

-
850

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800

 

750

 

TC0

 

650
SL MACH 03\

 

600
15 000 ft MACH O 92\

550
35000 ft MACH 0 92\ )/ __j’

 

 

 

COMPRESSOR OUTLET TEMPERATURE ( F)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

500 e ] | e
450 A//
=1

35000 ft MACH O 75 / |

400 \ - —
SL STATIC
350 /// N |
/ \45 000 ft MACH O 45
300 —
250
0 1 2 3 4 5 6 7 8 9

NET THRUST OUTPUT (Ib 103)

Fig 5 VYanation of the Steady State Compressor Qutlet Temperature with Net Thrust Output for the
G-E X 61 Engine Exhaust nozzle open

6

 
The value for C, was assumed to be constant at 0 26

E5RR

 

 

No zle
coe'?f‘s; ent Gross thrust for full nozzle expansion Ram drag
K—Jfi r N A N
5 1
(2) FN = 0975 Wa\/TTé 2}/R/g()/—]) 1 -(—P——/—I;-)-m W Va/g
T ° 0

The value for y was assumed to be constant at
135

A hypothetical radiator was designed for the
X 61 engine by use of the procedure and basic
data outlined in Appendix A which were obtained
from R D Schultheiss This radiator was de-
signed to transfer 30 Mw of nuclear power to the
engine load imposed during cruise at 35000 ft
Comparison of the total thrust available from two
X 61 engines operating at 30 Mw power input at
35000 ft with the total thrust required by a repre
sentative seaplane airframe shows that such an
aircraft might be expected to cruise at about

Mach 0 87
o TABLE 1

Flight conditions

 

Radiator and X 61 engine match point and de
sign data are shown in Table 1 The varniation of
the over all heat transfer coefficient of this radia
tor with changes in airflow per unit frontal area s
shown in Fig 6 The over all heat transfer coef
ficient also varies with changes in the NaK flow
rate and the mean temperature of the radiater but
these effects are thought to be small in the normal
operating region

The engine performance curves discussed pre
viously (Figs 2 through 5) were worked out for a
normal combustion chamber pressure loss between

RADIATOR AND ENGINE MATCH POINT VALUES
35000 ft Mach 0 87 nuclear power only

 

G E X-61 Engine Allison J 71 Eng ne

 

Net thrust output [b per engine

Number of engines

Nuclear power 1nput required Mw per engine
NaK temperatures °F

NaK flow ate b/ ec pe eng ne
Compressor outlet temperature °F

Eng ne a flow lb/ ec

Turbine inlet temperature °F

Engine speed ¥ of rated

Exhaust noz le area

Radiator heattransfer area ft2

Over all heat transfer coefficient Btu/hr ft2 °F
Radiator frontal area 12

Radiator depth In

Rough estimate of radiator pressure drop 7 of

compressor discharge pressure

5500 2750

2 4

30 15

1500 to 1100 1500 to 1100
2845 142 2

487 454

132 4 657

1311 1286

926 932

Open 87 77 closed
9018 4883

315 26 8

16 12

19 4 14

66 18

 
the compressor and turbine Strictly speaking the
increase in pressure loss resulting from the add:
tion of a radiator causes all the equilibnum operat
ing charactenstics of the engine (Figs 2 through
5) to shift Recalculation of the new steady state
operating characteristics 1s a major job however
which requires engine component performance maps
which are not available

The effects of radigtor pressure drop on steady
state engine performance are therefore neglected
in the calculations that follow This should not
cause serious errors 1n final conclusions because
the radiator pressure drop in this case appears to
be relatively small The overall trends being
sought should still manifest themselves

ALLISON J 71 TURBOJET ENGINE

 

OVERALL HEAT TRANSFER COEFFICIENT ¢, (Bt /h f12 F}

4 6 10 12 14 16 18 20 22 24 26
° 2 ° » The J 71 power plant was considered in addition
AIRFLOW PER SQUARE FCOT FRONTAL AREA W /A'M.,[(lb/ }/ft ]

to the X 61 power plant described in the preced
ing section because the available X 61 perform

Fig 6 Vanation of the Over All Heat Transfer ance data are not conststent in the low power
Coefficient of Radiator with Changes in Air Flow operating region the compressor power required

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

per Unit Frontal Area does not agree with the turbine power available at
¢
1300
1200
TURBINE
INLET 7 /
\ Mp
100 \% //
1000 \\ L~
900 / B .
p\R‘:\"o\N
28 — ~ 800 e 140
24 — 2 700 - 120 7
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. £ / / ;
220 |— 600 100
o = / - =
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216 — 500 e 80 §
o P =
RE
& pOWER /1 TEMPERMU &
5 porarte /SSOP‘ OUTLE «
212 [~ 400 &" COMPRE 60
« - g
';’ 8 M— 300 fw—— s 40 w
Q /
a
4 — 200 20
ot 100 0
3000 3500 4000 4500 5000 5500 6000 6500

ENGINE SPEED ( pm}

Fig 7 Steady State Performance Characteristics of the Allison J 71 Turbojet Engine ot Sea Level
(SL) Static conditions exhaust nozzle open

 
equiltbrium points Preliminary estimated per
formance data on an early version of the Allison
J 71 engine were used so that reactor turbojet
behavior in the low power operating range could
be studied The J71 engine 1s roughly half the
size of the X-61 engine Its full power SL static
pressure ratio 1s about 8 5 to 1

Pertinent performance characternistics of th:s

engine at SL static conditions are plotted in
Fig 7 Radiator and engine match point values
and design data are summarized in Table 1 The
basic procedure and data used in designing this
radiator are outlined in Appendix A The variation
of the over all heat transfer coefficient of the J 71
engine radiator with changes in airflow per unit
frontal area 1s shown in Fig 6

 

STEADY STATE POWER PLANT PERFORMANCE CHARACTERISTICS - NUCLEAR
POWER ONLY OPERATION

The steady state performance characteristics of
the two power plants under consideration during
operation on nuclear power only can be calculated
by combining the component charactenstics sum
marized in the preceding secton Figure 8 1s a
schematic didgram showing the parts of the power
plants under consideration and the nomenclature
used Of particular interest 1s the behavior of
such power plants when throttling in each of the
five ways listed below 1s attempted

Contral Rod Throttling
Variable

Constont at rated values

Mean reactor fuel temperature
Reactor fuel flow and NakK
flows

Air ond NoK bypasses Closed

Reactar Fuel Flow Throtthing

Vartable

Constant at rated values

Reactor fuel flow
Mean reactor fuel temperature
and NaK flow rates

A r and NaK bypa se Clo ed

NaK Flow Th ottling
VYariable

Constant at rated values

NaK flow rates
Mean reactor fuel temperature
and reactor fuel flow rote

Aw and NaK bypasses Closed

NaK Bypass Throtthing
Yariable

Constont at rated values

NaK bypass percentage

Mean reactor fuel temperature
reactor fuel flow rate and
NoK flow rates

Air bypasses Closed

Ar Bypass Throttling
Variable

Constant at rated values

Air bypass percentage

Mean reactor fuel temperature
reactor fuel flow rate and
NaK flow rates

NaK bypasses Closed

The behavior of the hypothetical reactor-X 61
power plant when throttled in each of these ways
1s described in the following paragraphs

CONTROL ROD THROTTLING

The behavior of the reactor-X 61 power plant
when throttling by control rod motion 1s attempted
at a typtcal off design flight condition 1s shown
in Fig 9 A sample calculation illustrating the
procedure used to determine these curves is In
cluded in Appendix B At this flight condition
the radiators have more heat transfer surface area
than 1s required for transferring 30 Mw to each
engine |f the power transferred to each engine s
to be limited to the maximum allowable value of
30 Mw one or more of the potential control quanti
ties generally must be reduced with decreasing
altitude

Figure 9 shows that the mean reactor fuel tem
perature must be reduced to about 1260°F 1f power
delivery 1s to be limited to 30 Mw during flight
at 15000 ft and Mach 0 45 Under these cond:
tions the reactor NaK inlet temperature drops to
about 900°F Operation of the system at such a
low NaK temperature at the inlet of the main heat
exchanger 1s unsafe because of the possibility of
focal cold spot formation and fuel freezing The
situation becomes more unsafe 1f an attempt s
Myy HEAT EXCHANGER EFFECTIVENESS

mi\l K PUMP

Tre COLD FUEL

TEMPERATURE |

we COLD N K
TEMPERATURE

P POWER DELIVERED
TO OTHER ENGINE

_—m
A TOTAL 7 pot FUEL Tuw HOT N K
POWER TEMPERATURE

 

TEMPERATURE
o

Wye TOTAL N K FLOW un K BYPASS VALVE
RATE PER ENGINE

 

TF AVERAGE FUEL TEMPERATURE =

T, RADIATOR EFFECTIVENESS

4, N K BYPASS
g
FLOW RATE

P POWER DELIVERED
TO FIRST ENGINE

o DwG 9 S

     
  

T  COMPRESSOR
DISCHARGE TEMPERATURE

AIR BYPASS VALVE

Wyp DIRECT N K
FLOW RATE
THROUGH RADIATOR

w AIR FLOW RATE
" THROUGH BYPASS

 

 

W  AIR FLOW
THROUGH RADIATOR

(N

W TOTAL AIR FLOW RATE

7 TURBINE INLET
TEMPERATURE

Fig 8 Partial Schematic Diagram of Reactor Turbojet Power Plant

made to reduce power delivery to each engine be
low 30 Mw When the rod i1s inserted far enough
to throttle power delivery to only 25 Mw for ex
ample the core fuel inlet temperatire 1tself drops
to below 1000°F

From the curves of Fig 9 it 1s apparent that
the thrust output of the power plant cannot be
throttled safely by moving only the reactor control
rod Control rod throttling 1s also unsuitable f
independent variations in power delivery to each
of the engines are to be made since motion of the
control rod affects all engines in the same way

REACTOR FUEL FLOW THROTTLING

The behavior of the power plant when 1t is
throttled by reactor fuel flow variation with all
other quantities at their design point values s
shown 1in Fig 10 At the 15000 ft Mach 0 45
flight condition reactor fuel flow must be reduced
to roughly 60% of its rated value to himit power
delivery to each engine to 30 Mw When this is
done the fuel temperature at the outlet of the

10

reactor rises to 1700°F and the NaK temperature
at the inlet of the reactor falls to 900°F Operation
at these temperatures 1s unsafe if not impossible
Further reduction in fuel flow does reduce the
power delivered to each engine and reduces the
engine thrust outputs but as the fuel flow 1s
reduced the fuel outlet temperature continues to
rise and the fuel and NaK inlet temperatures con
tinue to fall

Thus reactor fuel flow alone 1s very unsuitable
as a primary power control parameter  Virtually
all the critical steady state temperature variations
which result when such a scheme s used are
unsafe and independent adjustment of power
delivery to each load 1s not possible

NaK FLOW THROTTLING

The behavior of the power plant when it is
throttled by NaK flow variation alone 1s shown in
Fig 11 The NaK flow must be reduced to 42% of
its rated value to limit power delivery to each

engine to 30 Mw at the 15 000 ft Mach 0 45 flight
ON DWG 8 ©
1500

 

 

 

 

 

 

~ R

=

3 X 1400 ;

W P PER ENGINE /7

2 0l /

W 20 1300 /, , 6000
o /

ul

g / ) A /

W FH 74

Yool 1200 A4 5000
5

@ v

& /

Z ol noo - 4000
o / a2

1000 /

 

TEMPERATURE ( F)

900

 

800

 

/ 1000

700

 

 

 

 

 

 

 

 

600
800 200 1000 1100 1200 {300
AVERAGE FUEL TEMPERATURE 7. ( F}

Fig 9 Steady State Performance of Reactor and
Two G E X 61 Engines Altitude 15000 ft Mach
0 45 reactor power delivery throttled by moving the
control rod

condition  Such a NaK flow reduction with all
other quantities at thewr rated values causes the
NaK temperature at the inlet of the reactor to drop
to around 640°F which is far below the 1050°F
safe lower limit  Further reduction in NaK flow
does reduce power delivery but 1t causes the
return line NaK temperature to drop still lower
Thus NaK flow alone 1s not a suitable power
control quantity because the NaK temperature at
the inlet of the reactor drops rapidly to dangerously
low values as the flow rate 1s reduced Some
means of protection against return line NaK under
cooling must be added if power delivery 1s to be
throttled safely by NaK flow rate reduction

NaK BYPASS THROTTLING

When the reactor—X 61 power plant 1s throttled
by bypassing NaK around the radiators the thrust
output of each engine and the reactor power de
livered to each engine vary as shown in Figs 12
through 14 Fuel and NaK temperatures vary with
power delivery as shown in Fig 15

O L R DWG9

7000

6000

|7
o

~ & 1600 5000
£ PER ENGINE

4000

n

o

T
TEMPERATURE
o B O
o
3 8 8

o

3000

NET THRUST £, (ib}

 

o
[

2000

POWER DELIVERED PER ENGINE 72 (M )

1000

 

0

0 10 20 30 40 50 80 70 80 90 100

FUEL FLOW (¥ OF RATED)

Fig 10 Steady State Performance of Reactor and
Two GE X 61 Engines Altitude 15000 ft Mach
0 45 reactor power delivery throttled by varying the
reactor fuel flow

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

L]
o G
1800 7000
TH
1600 - 6000
-t NH
/fif
1400 5000
Jd/ 7
—_ I —_
= - / o
=30 200 4000 =
Q L W
w g /(PER ENGINE
e | g ’ z
w20 & ooo 3000 £
o = z
a p =
[a] z
w
o
& o 80C 2000
5
w
o
o
) e
z 0 600 A 1000
& / we
/|
400 0
0 20 40 60 80 100

N K FLOW (¥ OF RATED)

Fig 11 Steady State Performance of Reactor and
Two G E X 61 Engines Altitude 15000 ft Mach
0 45 reactor power delivery throttled by varying the
NaK pump speeds

11
ORNLM 9149

N K FLOWING THROUGH BYPASS (7))
100 90 80 70 60 50 40 30 20 10 0

 

 

 

 

 

 

 

 

 

 

SL STATIC
6
T 15 000 ft MA(|3H 045
] SL' MACH 03 L——
’.-—-—_______—
A L=
’ / LT
_z 35000 ft MACH 075
/!
7 /

 

NET THRUST £, (Ib X 103)
O

 

 

 

 

2 FH
//L\as 000 ft MACH 092
!

 

 

 

 

 

 

 

 

 

 

 

 

0

 

o 10 20 30 40 50 60 70 80 90 100
N K FLOWING THROUGH RADIATOR (¥ OF RATED)

Fig 12 Net Thrust Output per Engine at Various
Flight Conditions for Reactor and Two G E X 61
Engines Reactor power delivery throttled with
radiator NaK bypasses

Adequate throttling can be obtained through the
use of NaK bypass valves alone if the fuel tem
perature at the inlet of the reactor core can be
allowed to rise as high as the design point mean
fuel temperature Power delivery and thrust out
put are relatively insensitive to changes in the
NaK bypass percentage in the 50 to 0% bypass
range Hence full range NaK bypass valves are
required If power delivery 1s to be throttled in this
manner

AIR BYPASS THROTTLING

The behavior of the hypothetical reactor-X 61
engine power plant when 1t s throttled by by

12

P

L
ORNL LR DWG 9150

 

15 000 fi MACH 0O 82

£ {5 00 ft MACH © 45
SL MACH 03\ {/ 35 000t MACH O 92
7

 

 

100

 

 

 

 

/ / —
’
SL STATICL. //<~35 000ft MACH 075
80 J 7
70

 

Cy
Wl

 

~

T

 

 

THRUST OUTPUT (¥ OF MAXIMUM)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

100 8O 60 40 20 0
N K FLOWING THROUGH BYPASS (/)

Fig 13 Per Cent of Maximum Thrust Output At
tainable with Nuclear Power Only vs Per Cent NoK
Bypassed Around Radiator Reactor and two G E
X 61 engines

passing air around the engine radiators 1s shown
in Figs 16through 18 Fuel and NaK temperatures
vary with power delivery as shown in Fig 15

These curves show that power plant thrust out
put can also be throttled safely through the use
of air bypasses alone 1f the fuel temperature at the
inlet of the core can be allowed to rise as high
as the design point mean fuel temperature

MORE COMPLEX THROTTLING ARRANGEMENTS

It seems reasonable to believe that the simplest
over all power plant control system will result
when nuclear power delivery 1s throttled by varia
tion of the fewest possible control quantities
The steady state performance characteristics dis
cussed In the preceding paragraphs indicate that
power plant thrust output modulation through varia
tion of a single control quantity — NaK bypass
percentage or air byposs percentage — appears to
be possible if the fuel temperature at the inlet of
the reactor core can be allowed to rise as high as
the design point mean fuel temperature
o—

N K FLLOWING THROUGH BYPASS (/)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6oqoo 90 B8O TO 60 S50 40 30 20 40 0O
| 160 90 80
o &
50
6
= 40 —_ SL STaTIC
Q "2 5
¥ SL STATIC AND 35000 f1 MACH 092 o
5 MACH 03 | \\ =
& 30 —— ’ — = &
o 15000 ft // e T T - 15000 ft MACH 045 —L__ |
Lt - =
& MACH 0 92 —1 = a 4
o //;‘- /y( 35000 ft MACH 0 75 5
o / o
Y 20 —
= id 0 SL MACH 03 ~
o 74 2
o 15000 ft MACH 045 T3
o —
3 L |
10 Z
& / / /
2
0
{
0O 10 20 30 40 50 60 70 8O 90 100 0O {0 20 30 40

N K FLOWING THROUGH RADIATCR (/)

Fig 14 Variation of Reactor Power Delivered to
Each Engine with Per Cent NaK Bypassed Around
Radiator Reactor and two G E X 61 engines

1700

600

1500

1400

TEMPERATURE ( F)

1300

1200

1100

o
ORNL LR DWG 9153

AIR FLOWING THROUGH BYPASS (7))

70 60 50 40 30 20

10

¢

 

 

 

 

 

 

\7
L,

092

 

 

 

|
15 000 ft MACH
//

35 000 ft MACH 092

 

"~ 35 000 £t MACH O

75

 

 

 

 

 

 

 

 

 

 

 

 

 

50 60 70

80

AIR FLOWING THROUGH RADIATOR (7 )

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

POWER DELIVERED PER ENGINE £ (Mw)

T
0 52
TEMPF—EE-‘.U/RE/—“/
TLET
7 FUE v -]
/
[ e 7N K OUTLET TEMPERATURE __
NH
//_
:"--.._.___--
s
\\ “-—__..______/:E REACTOR ,'NLET
TEM
\ PER“TURE
--._____-
\ - N
\fr ,
v
\Er »
é‘.g,pe
\’P“TU
\’?E
‘-\
4 g 12 16 20 24 28

32

90

Fig 16 Net Thrust Output per Engine
power delivery throttled with air bypasses
and two G E X 61 engines

100

Reactor
Reactor

Fig 15 Variations of Reactor Fuel and NaK Temperatures with Power Delivery per Engine Reactor
and two G E X 61 engines throttied by NaK bypass or by air bypass

13
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7 -
ORNL LR DWG 9154
100 1 7 /
SL MACH O 3———__| / / /
90 I I =z /
SL STATIC——“/.é/ / ///
80 | | / /
3 15 000 ft / /
2 MACH O 92— /
2 70 # /
= ' / /
= A
o 60
o 15 000 ft
x~ MACH O 45—
— //
D
Q.
5 40 /-
o 35000 ft MACH O 92
";,,) 30 / | | 1 |
2 Y | T ]
& ~—~—35 000 ft MACH O 75
F 20
10

 

 

 

 

 

 

 

 

 

 

 

 

o
100 20 B8C 70 60 50 40 30 20 10 0
AIR FLOWING THROUGH BYPASS (7)

Fig 17 Per Cent of Maximum Thrust Output At

tainable with Nuclear Power Only vs Per Cent Air

Bypassed Reactor and two G-E X 61 engines

If the fuel tempesature at the inlet of the core
mustbe limited to some value less than the design
point mean fuel temperature the control rod must
also be moved as power delivery 1s changed If
the fuel temperature at the inlet of the reactor core
is to be held at 1350°F or less in the reactor—X 61
power plant for example rod insertion is required
when total power delivery 1s reduced to below

40 Mw

As the development of the full scale aircraft
power plant progresses 1t ts likely that many

14

ORNL LR DWG 9155

AIR FLOWING THROUGH BYPASS (7))

100 90 80 70 60 50 40 30 20 10 o
50

 

 

15000 ft MACH O 45

l
15000 ft MACH 0 92

40

 

 

SL MACH 0 3
30 B

 

r e
it
/
SL STATIC —] /
20 /

 

NN
AN
NN\

 

 

 

 

POWER DELIVERED PER ENGINE £ {Mw)

\35 000 ft MACH O 92

35 000 ft MACH O 75

 

 

 

 

 

 

 

 

O

 

0 10 20 30 40 50 60 70 80 90 100
AIR FLOWING THROUGH RADIATOR (7 )

Fig 18 Vanation of Reactor Power Delivered to
Each Engine with Per Cent Air Bypassed Reactor
and two G E X 61 engines

situations will arise in power plant design or
operation which will make the use of more complex
throttiing arrangements seem desirable  Diffi
culties 1n building full range NaK bypass valves
for example may make the use of a more compl
cated throttling arrangement imperative However
the effect of increasing the complexity of the
control system on the reliability of the over all
power plant should be considered carefully before
such changes are made
o

STATIC STABILITY CHARACTERISTICS OF A DEMAND SENSITIVE

REACTOR-TURBOJET COMBINATION

Stable operation of a reactor—turbojet engine
combination 1s not assured by a large negative
reactor temperature coefficient of reactivity Such
a characteristic does undoubtedly simplify the con
trol of the reactor but the demand characteristic
of a turbojet load and the demand sensitivity char
acteristic of a reactor having a large negative
temperature coefficient of reactivity are not neces
sarily compatible

The turbojet load imposed on the nuclear heat
source (airflow and radiator inlet temperature)
varies 1n a complicated way with the power de
livered to 1t Changes in power delivery to
such a load cause the load characteristics
themselves to change Changes in load charac
teristics however can cause further changes in
reactor power delivery because the large negative
temperature coefficient of reactivity makes the
reactor load sensitive |f it 1s possible for a sub
sequent change in power delivery to reinforce an
original power disturbance the reactor load com
bination can walk or run away The possi
bility for an instability of this type does not exist
when the reactor 1s coupled to a heat dump type
of load because the load characteristics are
externally adjusted by blower speed and louver
and bypass opening variation Changes in these
external load adjustments do cause the reactor
power level to change but changes in the reactor
power level cannot in turn cause further changes
in the load This 1s an important basic difference
between the two load types

The static stability of a demand sensitive reactor
power source and a turbojet load can be studied
from plots showing how the steady state power
available from the radiator and the steady state
power required to run the engine vary with engine
speed when the reactor throttling quantities are
constant  Such plots obviously do not provide a
complete picture of the stability of the over all

 

1

power plant but it does seem that an unstable
intersection between a steady state nuclear power
available curve and the steady state engine power
required curve 1s a definite indication of trouble

Steady state power required and power available
curves for the reactor—J 71 system at SL static
operating conditions are shown in Figs 19 and 20
for air and NaK bypass throttling (sample cal
culations are included in Appendix C) All the
potential reactor control quantities with the ex
ception of the bypasses are constant at their
rated values The awr and NaK bypasses are con
stant along given power available curves at the
values shown

The intersections between the curves of power
available at a constant air bypass setting and
engine power requited are unstable i1n the low
speed range The steady state power avatlable
rises faster than the power required as the engine
speed increases (air flow and compressor discharge
temperature increase)

Idle speed for the J 71 engine 1s around 3000
rem  Net thrust output at this speed i1s down to
about 3% of the rated SL static value Stable
operation at speeds corresponding to less than
maximum nuclear power input (5050 rpm 23% of
rated SL static net thrust output) does not appear
to be possible when the reactor—J 71 power plant
1s throttled by bypassing air around the radiators
This apparent difficulty is a serious disadvantage
of the air bypass throttling arrangement When the
power plant 1s throttled with NaK bypasses the
nuclear power available curves intersect the engine
power required curve stably in the low speed region
The power plant behaves differently in each case
because of basic differences in the effect of each
throttling quantity on radiator performance

The power available from the reactor supplying
a number of balanced loads s related to the various
engine radiator and reactor parameter values by
the following expression

 

e_

W pCang + (1 = ny3)/myxWyC

(Tg =~ Tr3)
NeCN = 1/2XWCp v

15
ORNL LR DWG 9247

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

26 //
/|
24 /'l
/ 0/ NKBYPA
22 //—_ 7 —{._. >
/
POWER AVAILABLE /
20 T ——— POWER REQUIRED //
/
. 18 > //
2 7/
3 / £
w 16 e ——— 50/ N K BYPASS |
O
7
= L
w A
- 14 - //, 60 / N K BYPASS —
E:_, " » / ",/
-

z /// -
- / .—”

© 7/ ===

-—:’————-—_'—
/" 75 / NaK BYPASS
-

8

6

4

2

3000 3500 4000 4500 5000 5500 6000 6500

ENGINE SPEED { pm)

Fig 19 Steady State Power Delivered with NaK Bypass Percentage Constant Steady State Engine
Power Required vs Engine Rotor Speed Reactor and four Allison J 71 engines at SL static conditions
exhaust nozzle open fuel and NaK pump speeds constant at rated values

When the fuel and NaK flows are constant at their
rated values the last two denominator terms are
small and tend to cancel The power delivered to
each load then is approximately

Destabil z ng Stab | ing
term term

—
(4) Pe = WaDnR (TFuv - TTB) Ca

The second term in the equation describes the
stabilizing effect of the increase in compressor
outlet temperature which results when engine speed
Increases This effect alone would cause the
power delivered at a constant mean reactor tem
perature to decrease |f power delivery to an
engine decreases with an increase in engine speed
static stability at least will be assured because
the power required increases with increasing speed

16

 

The first term 1n the power delivery expression
describes the destabilizing effect of the increase
i air flow which results when engine speed in
If the NaK flow rate i1s constant the
effectiveness of the radiator (p,) decreases as
air flow increases but not so rapidly Hence the
product (WaDqR) increases with increasing air
flow This product for the hypothetical J 71 radi
ator 1s plotted vs air flow for several constant NaK
flow rates in Fig 21

creases

The raptd increase in engine air flow with speed
at low speeds causes W_.png to increase faster
than (Tg,, - T.,) decreases Hence the power
delivery curves rise with increasing speed at low
speeds At higher speeds however the effect of
the increase in radiator inlet temperature pre
dominates (as the compressor outlet temperature
moves closer to the mean fuel temperature) and
0% AR BYPASS

309 AIRBYPASS

45% AR BYPASS

60 AIR BYPASS

POWER PER ENGINE (Mw)

POWER AvalLABLE
———— POWER REQUIRED

 

3000 3500 4000 4500 5000 5500 6000 6500
ENGINE SPEED ( pm}

Fig 20 Steady State Power Delivered with Air Bypass Percentage Constant Steady State Engine
Power Required vs Engine Rotor Speed Reactor and four Allison J 71 engines at SL static conditions
exhaust nozzle open fuel and NaK pump speeds constant at rated values

ORNL—-LR DWG 9219

 

 

 

 

 

 

 

 

110
100
30
{00 97 NoK FLOW DIRECT
O NaK BYPASS
BO
/
//
70 ——

50 9% N K FLOW DIRECT
507 N K BYPASS

T
L LT

 

\

A

 

 

 

 

 

RADIATOR PERFORMANCE PARAMETER W, 7,
s R

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

50
/’//_; — | 407 N K FLOW DIRECT
_— 607 N K BYPASS

’ =

20 ///‘_ 25 7 NoK FLOW DIRECT

7 759 NoK BYPASS

20

10

0

0 10 20 30 40 50 60 7O 80 90 100 HO 120 430 140 450 160 170

RADIATOR AIRFLOW u;,a {(ib/ )

Fig 21 Radiator Performance Parameter for the Allison J 71 Engine 17
the W png product rises less rapidly  These
effects cause power delivery to reach a peak and
begin to fall in the high speed range The increase
in radiator inlet temperature with increasing speed
thus causes the steady state power curves to inter
sect stably in both cases at high engine speeds
in spite of the destabilizing effect of increasing
air flow with speed

The relative flatness of the curves showing the
variation of the power available with the NaK by
pass percentage constant at low speeds can be
explained from the W_,5. plot in Fig 19 and
from Eq 4 the power delivered equation The
differences in the performance characteristics of
the air bypass and NaK bypass throttling arrange
ments lie in the behavior of the W _,n. product
as engine arr flow changes since the (T | - Trs)
term varies with speed in the same way in both

cases

The power delivery curves rise most

W, p curves are flattest
of an engine air flow change on reactor power de
livery 1s minimized when the variation of W, pn
with changes in air flow 1s minimized

slowly with increasing speed when the W.plg Vs

The destabilizing effect

R

A study of Fig 19 leads to the conclusion that

W, png varies least with changes in air flow when
the air flow through the radiator 1s high and when
the percentage of NaK flowing through the bypass

1s large  Both these requirements are met best
at part load points by the NaK bypass throttling
arrangement

The behavior of the NaK bypass throttled power

plant at 35000 ft and Mach 087 1s shown in
Fig 22 The very large amount of NaK bypassing
required to throttle the engines at this flight con
dition causes the nuclear power delivery curves

ORNL LR DWG 9220

 

 

 

POWER DELIVERED

 

 

—=——-—  POWER REQUIRED

 

 

 

80 / N K BYPASS
\‘_

- 1

 

 

 

 

POWER PER ENGINE (Mw)
o

90 / N K BYPASS

 

 

 

 

 

- 95 /o N K BYPASS

 

 

 

 

 

 

 

 

 

 

 

3000 3500 4000 4500

5000

ENGINE SPEED { pm)

5500

6000 6500

Fig 22, Steady-State Power Delivered with NaK Bypass Percentage Constant Steady State Engme
Power Required vs Engine Rotor Speed Reactor and four Allison J 71 engines at 35000 ft Mach O 87

exhaust nozzle open fuel and NaK pump speeds constant at rated values

18
to be quite flat This bears out the conclusion
drawn in the preceding paragraph heavy flow of
NaK through the bypass results in flat power
delivery curves

All the nuclear power delivery variations con
sidered so far have been worked out for constant
fuel and NaK pump speeds [t might be desirable
in the interests of simplicity to drive these pumps
at engine speed This aggravates the static
stability problem however since increasing the
pump speeds with engine speed causes power
delivery to rise faster with increasing engine
speed than when the pump speeds are constant

The behavior of the NaK bypass throttled power
plant at SL static conditions when various com
binations of pumps are engine driven 1s shown in
Fig 23 (Pump flow rates were assumed to be
proportional to pump speed ) Driving one or more
pumps at speeds proportional to engine speed
destroys most of the apparent natural static sta
bility of the NaK bypass throttled power plant

Thus from steady state considerations 1t seems
that a turbojet—demand sensitive reactor combina
tion should operate stably in the high power range
At part load operating conditions however the
stability of such a power plant appears to depend

 

 

 

 

 

L
ORNL LR DWG 9224
26
24
22
POWER AVAILABLE
20

 

POWER REQUIRED

18

 

 

 

 

 

12

 

POWER PER ENGINE {(Mw)
o
L
%

\

 

 

o /Q

 

 

 

 

 

 

 

 

 

 

 

6000

a"‘
==

g

6

4

2

3000 3500 4000 4500 5000 5500

ENGINE SPEED (rpm)
Fig 23 Steady State Power Delivered with 60% NaK Bypassed Steady State Engine Power Required

vs Engine Rotor Speed

(1) Pump speeds constant at rated values (2) NaK pump speeds constant fuel

pumps engine-driven (3) fuel pump speeds constant NaK pumps engine driven (4) fuel and NaK pumps

engine driven

19
on the throttling scheme used Relatively speaking
use of a NaK bypass throttling arrangement seems
from steady state considerations at least to result
in more stable power plant operation than does
use of an air bypass throttling arrangement In the
example considered the NaK bypass throttled
power plant was stable at normal part load operating
points when the fuel and NaK pump speeds were
constant  while the air bypass throttled power
plant was not  Whether or not a NaK bypass
throttled system will be stable in other power plant
combinations 1s difficult to say A detailed check
in each particular situation will no doubt be re
quired

If the *hucl®ar power source~turbojet engine load

combination 1s not inherently stable or If the
natural stability 1s not adequate the stability
characteristics can be improved by adding the
proper control equipment Static power plant
stability in the cases considered here for example
would be achieved if some sort of power level
control system were added to the nuclear heat
source to maintain nuclear power delivery to each
engine constant at some preset adjustable value
The power available from the reactor would then
be independent of changes In engine speed or
air flow and compressor outlet temperatures and
the power available vs speed curves would be
horizontal lines

 

COUPLING BETWEEN ENGINES IN A MULTIENGINE INSTALLATION

All the steady state performance characteristics
considered so far have been worked out for
balanced load operation where power delivery to
each engine 15 the same |t 1s also interesting to
consider the effects of coupling between engines
when the power distribution to the various engines
i1s not symmetrical assuming for the moment that
the reactor design and load connection arrangement
will allow unbalanced operation  The various
engine loads are not completely independent They
are cross coupled through their common power
source |f the power delivered to one engine s
varied through manipulation of the NaK bypass of
that engine the power delivered to the other
engines also changes Power delivery to the other
engines changes because variation in power de
livery to one load causes the reactor outlet tem
perature to change The power delivered to any
given engine load 1s related to the reactor outlet
temperature by

(5) Py = (Tpy = Tra) x

1
IV pCang + (1 = Mx)/ M x¥neCn

 

092 The results which are plotted in Fig 24
show how the per cent of full nuclear power de
livered to an engine load with a constant NaK by
pass setting varies with power delivery to a
second engine load In the event of complete
failure of the second engine the power delivered

OR L DWG
110

100

35 Q00 ft

[0

80

70

60

50

40

30

POWER DELIVERED TO ENGINE NO { {¥ OF RATED)

 

20
0 10 20 30 40 50 60 7O BO 90 400 410

POWER DELIVERED TO ENGINE NO 2 (¥ OF RATED)

Fig 24 Steady State Coupling Between Engines

Reactor and two G E X 61 engines altitude 35 000
ft Mach 0 92 No 1 engine NaK bypass constant at
9 5% No 2 engine NoK bypass varied from 9 5 to
100%

The magnitude of the cross coupling effect when
the control rod posttion 1s constant has been de
termined for the NaK bypass throttled reactor-X 61
engine power plant operating at 35 000 ft at Mach

20
to the first engine drops to 93% of its rated value
If this lost power is to be regained the bypass on
the first engine must be readjusted if possible or
the control rod must be withdrawn slightly

Cross coupling between engines can be eliminated
by the addition of automatic control equipment
When the control rod position 1s constant and NaK
bypass throttling 1s used however the magnitude

of the coupling effect does not appear to be great
enough to justify much complication of the control
system for i1ts elimination If rod motion with
total power level changes 1s required cross
coupling between engines will be more pronounced
than in the example considered here and the
coupling effects between engines may be so large
that independent manual power delivery adjustments
to each load will be tedious

 

NUCLEAR POWER SOURCE CONTROL REQUIREMENTS

Automatic control requirements for the nuclear
heat source In a combination chemical nuclear
aircraft power plant of the type discussed in the
preceding sections can be determined by con
sidering how the flight engineer might perform
typical power plant maneuvers without the help
of automatic control equipment
altitudes flight speeds and ambient temperatures
at which such o power plant might be operated
can be grouped into three categories for purposes
of discussion those flight conditions at which
the radiators are (1) larger than they need be
(2) yust large enough and (3) too small to transfer
rated nuclear power to each engine If the radi
ators are designed to transfer rated nuclear power
to each engine at the nuclear cruise flight condition
(Mach 09 at 35000 ft in the example considered
here) excess radiator capacity 1s generally avail
able during flight at altitudes below the nuclear
cruise design altitude and the radiators will
generally be too small to transfer rated nuclear
power to each engine during operation at altitudes

The numerous

above the nuclear cruise design altitude

Manual operation of the nuclear part of the
reactor—X 61 power plant in each of these situ
ations 1s described in the paragraphs which follow
Throttling by means of radiator NaK bypass valves
i1Is assumed and fuel and NaK flow rates are
assumed to be constant at their rated values
Startup and shutdown problems ground handling
problems and sodium coolant temperature control
problems are not considered

MANUAL OPERATION AT FLIGHT CONDITIONS
WHERE RADIATOR CAPACITY IS EXCESSIVE

The radiators will generally be large enough to
transfer more than rated nuclear power to each

engine load at altitudes below the design nuclear
cruise altitude Power plant maneuvers which
might be performed in this operating range include
engine startup operation on nuclear power only
and operation on chemical plus nuclear power

The engines will probably be started on chemical
power only The higher turbine inlet temperatures
obtainable with the chemical power sources should
result in the lowest possible engine firing speeds
and cranking powers The chemical power sources
are also more maneuverable than the nuclear power
source which probably will be advantageous during
the critical starting and accelerating period

Once the engines have been started nuclear
power delivery can be imitiated by diverting NaK
through the engine radiators It 1s assumed that
the reactor has already been brought critical and
ts known to be delivering power at some low level
Care must be exercised in closing the NaK bypass
valves to avoid transient undercooling of the NaK
returning to the reactor  Enough hot NaK must
be allowed to flow through the bypass valves to
ensure that the return line NaK temperatures will
remain above their lower limits at all times

Full closure of the NaK bypass valves is not
permissible even during steady state operation
at flight conditions where excess radiator capacity
1s available Rated nuclear power s delivered
to each engine in the reactor—X 61 power plant
during static operation at sea level, for example
when only 45% of the total rated NaK flow passes
through the radiators (Figs 12 through 15) If
the NaK bypass valves ar= fully closed at such
operating conditions exces. power demands will
be set up and return line NaK undercooling and
reactor fuel overheating will result

Care must also be exercised in opening the NaK

21
bypass valves to reduce nuclear power delivery
The return line NaK temperature should not be
allowed to rise above the value at which isothermal
idling of the reactor i1s desired when power de
livery has been reduced virtually to zero Limiting
the return line NaK temperature rise during load
removal ensures that the load will be removed
slowly enough to prevent reactor overheating

If the reactor design 1s such that the fuel tem
perature at the inlet of the reactor core must be
limited to some value less than the design point
mean fuel temperature control rod withdrawal s
required as nuclear power delivery is increased
Since the reactor fuel inlet temperature approaches
the mean fuel temperature as power delivery is
reduced the rod must be inserted to lower the
mean fuel temperature during operation at low
powers If the reactor fuel inlet temperature 1s
to be maintained below the design point mean fuel
temperature  Subsequent rod withdrawal to raise
the mean fuel temperature to the design point
value cannot be initiated until some load has been
reapplied

[f operation on chemical plus nuclear power 1s
desired engine fuel flows and exhaust nozzle
areas must be controlled Control requirements
for the turbojet section of the power plant during
operation on chemical plus nuclear power will
not be considered here For purposes of this
discussion it 1s assumed that the automatic control
equipment required 1s available

Each time chemical power delivery to the engines
I1s varied or the engine exhaust nozzle areas are
changed the rate of nuclear heat delivery will
also change The changes In compressor outlet
temperatures and in air flow resulting from the
changes in chemical fuel flows or nozzle areas
upset previously established heat transfer balances
in the radiators  |f nuclear power delivery 1s to
be held constant NaK bypasses must be readjusted
each time the engine thrust outputs are changed
during operation on chemical plus maximum nuclear
power

Continuous readjustment of the bypass valve
positions 1s also required if nuclear power delivery
I1s to be maintained constant as the aircraft alt
tude and flight speed change since the engine
air flows and compressor outlet temperatures are
clso functions of the engine inlet total tempera
ture total pressure and flight Mach number The
demand sensitivity of the reactor makes continual

22

 

NaK bypass readjustment necessary if power de
livery 1s to be held constant as the load charac
teristics change Constant power delivery to a
turbojet load is not necessarily desirable except
when nuclear power only flight at the highest
speed possible i1s to be maintained Operation In
this manner will probably be required for a large
percentage of the time during typical missions

MANUAL OPERATION AT RADIATOR
DESIGN FLIGHT CONDITIONS

The manual control operations required in the
execution of typical power plant maneuvers at
flight conditions when the radiators are |ust large
enough to transfer rated nuclear power to each
engine are quite simtlar to those described in the
preceding section except that full closure of the
NaK bypass valves 1s now permissible during
steady state operation  Return line NaK under
cooling and overheating must be guarded against
during transients but the radiators are not large
enough to cause undercooling during steady state
operation at such flight conditions Full nuclear
power delivery to each engine results when the
bypasses are fully closed Rod control require
ments are the same as those discussed in the
preceding section Rod withdrawal or insertion
during power level changes 1s required if the fuel
temperature at the inlet of the reactor core must
be held below the design point mean fuel tempera
ture

MANUAL OPERATION AT FLIGHT CONDITIONS
WHERE RADIATOR CAPACITY IS
INADEQUATE

Radiator capacity will be inadequate at some
flight conditions because the engine air flows
and compressor outlet temperatures are such that
the available heat transfer surface area 1s not
sufficient to transfer rated nuclear power During
dash for example only 71% of rated nuclear power
can be delivered to each engine in the X 61 power
plant even though the NaK bypasses are fully
closed and the mean reactor fuel temperature s
at its design point value This operating condition

1s described in Table 2

Since rated nuclear power 1s not being delivered
the fuel temperature at the outlet of the reactor
core 1s less than the T600°F upper limit  Some
increase 1n nuclear power delivery thus can be
effected by further withdrawal of the control rod
 

TABLE 2. DASH OPERATION (55 000 ft Mach 2 0) OF G E X 61 ENGINE

 

Tg

at Des gn Po nt Yalue TFH at Maximum Va]ue%

 

TFGV °F
Tey °F
Tec °F
NaK byp 7

Pump speeds

Nuclea power delivered per engine Mw

Chemical power delivered per eng ne Mw

Total power del vered per engine Mw

Chemical power reduct on effected by

moving control rod 7

R
1450 1489
1557 1600
1343 1378
0 0
R ted Rated
214 223
40 9 400
623 623
22

 

to raise this temperature  The operating con
ditions described in the last column of Table 2
prevail after such action 15 taken Nuclear power
delivery to each engine s increased to 74% of
rated power and chemical fuel consumption s
reduced by about 2 2% under these conditions

If the fuel temperature at the inlet of the core
must be limited to 1350°F however rod withdrawal
to the extent shown in the last column of Table 2
1s not permissible and the potential advantages
to be gained n raising the mean fuel temperature
during operation at such a flight condition are
not so great as those described in this column

The discussion 1n the preceding paragraphs
leads to the conclusion that some sort of automatic
control equipment to raise the reactor mean fuel
temperature to its maximum allowable value during
operation at radiator hmited flight conditions 1s
desirable but that equipment performing this
function alone 1s not essential to power plant
operation The potential advantages to be gained
do not appear to be great enough to justify much
complication of the control system unless such
equipment 1s also needed for other reasons such
as controlling rod withdrawal during power In
creases

AUTOMATIC CONTROL REQUIREMENTS
DURING OPERATION IN THE
POWER RANGE

The foregoing discussion indicates that some
sort of automatic control equipment Is required
for the NaK bypasses Automatic control equip

ment 1s also required for the control rod if the
fuel temperature at the inlet of the reactor core
must be held below the design point mean fuel
temperature  |f the reactor can be designed to
operate 1sothermally at the design point mean fuel
temperature however a reasonably conventional
manual type rod control will probably suffice

Movement of the NaK bypasses must be limited
to maintain the return line NaK temperatures be
tween their upper and lower himits at all times
The lower limit for steady state operation i1s the
temperature at which rated nuclear power 1s de
livered to each engine  The upper limit 1s the
temperature at which steady state isothermal re
actor 1dling 1s desired

In simplest form the controls for the NaK bypass
valves might be remote positioning servos with
return line NaK temperature overrides and under
rides to limit bypass valve openings to those
values that will result in temperatures in the safe
range Further studies of reactor and engine con
trol integration may show that a more complex
arrangement 1s needed

If the reactor cannot be operated i1sothermally at
the design point mean fuel temperature rod inser
tion with power reduction 1s required to limit the
core inlet fuel temperature rise Rod withdrawal
with increasing power delivery 1s required either
to restore the mean fuel temperature to its design
point value or to raise the reactor fuel outlet
temperature to its maximum value The discussion
in the preceding section showed that a slight
advantage would be gained during the dash if the

23
 

ve

MEASURED CORE FUEL
INLET TEMPERATURE

 

 

 

THERMOCOUPLE THERMOCOUPLE SIGNAL
AMPLIFIER B

 

 

 

 

 

 

INSERT (NEGATIVE ERROR)

AMPLIFIER (POSITIVE ERROR)

 

 

RELAY WITHDRAW _I
l
|
i

 

 

{l; SERVO
INSERT

 

 

 

—_— SERVO

{ WITHDRAW
A

 

ROD DRIVE
INTER OCKS AND
PERMISSIVES

 

 

}
|

INSERT

 

 

MAXIMUM ALLOWABLE CORE FUEL CORE FUEL INLET
INLET TEMPERATURE (4350 F) TEMPERATURE ERROR
¥
MAXIMUM ALLOWABLE CORE FUEL CORE FUEL OUTLET
OUTLET TEMPERATURE (4600 F) TEMPERATURE ERROR
+ —

MEASURED CORE FUEL
QUTLET TEMPERATURE

 

RELAY WITHDRAW
AMPLIFIER (POSITIVE ERROR) |

I
(NEGATIVE ERROR) {
I

 

 

 

 

 

THERMOCOUPLE THERMOCQUPLE SIGNAL
AMPLIFIER o

 

 

 

Fig 25 Schematic Diagram of Rod Servo

DWG

ROD
DRIVE
rod were withdrawn to raise the fuel outlet tem
perature to its maximum value rather than to raise
the mean temperature to its design point valuve
Hence one simple type of rod control for the
reactor—X 61 power plant would be one which
operates as follows
1 withdraws the rod if the reactor core fuel inlet
temperature 1s less than 1345°F and the reactor
core fuel outlet temperature i1s less than 1590°F
2 inserts the rod i1f the reactor core fuel inlet
temperature exceeds 1355°F or the reactor
core fuel outlet temperature exceeds 1600°F

The basic form of such a control system is out
ltned in Fig 25 Further study may show that
additional stabilizing signals are required but
this question will not be considered here The
diagram 1s intended to be schematic only and
does not necessartly represent the best way to
do the |ob

The fuel temperatures resulting from the use
of such a control scheme are shown in Fig 26
Either the core fuel inlet temperature or the core
fuel outlet temperature 1s held at i1ts upper limit
at all times Operation with the fuel outlet tem
perature at its maximum value 1s possible only
when power delivery exceeds 83 4% of the rated
valve The fuel inlet temperature limiting require
ment does not allow the maximum fuel outlet
temperature to be reached when power delivery 1s
less than 83 4% of rated power

ACKNOWLEDGMENTS

The writer wishes to express appreciation for

help received from A P Fraas M M Yarosh and

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

L
ORNL LR DWG 14493
1700
4600 -
REACTOR FUEL OUTLET
TEMPERATURE 7
H>/

1500 =
0 /
w 1400 <
o
D
'_
<
g 7
o REACTOR FUEL INLET
= 1300 [~ EMPERATURE 7. — ]
e ¢

1200

1100

1000

0 20 40 60 80 100
TOTAL REACTOR POWER DELIVERY
( / OF RATED TOTAL POWER)

Fig 26 Fuel Temperature Yariations Resulting

from Use of Rod Servo

R D Schultheiss of ORNL and from J Bendot of
The Glenn L. Martin Company

25
B AR
 

APPENDIX A

RADIATOR DESIGN PRCCEDURE

The basic radiator unit from which the engineradiators discussed in this report were composed,
was designed by R D Schultheiss A sketch of this unit 1s shown

This umit has 776 ft2 of heat transfer area and the vaniation of
its over all heat transfer coefficient U, with changes in air flow
per untt frontal area W /A, 1s as shown in Fig 6 The pro
cedure followed in assembling a hypothetical radiator for the X 61
engine is outlined below

2 Fr

1 An engine radiator design point flight condition 1s chosen,
and the engine load requirements at this flight condition are
determined  The 35000 ft Mach 087 nuclear power only cruise
flight condition was chosen as the radiator engine design point
for the reactor—X 61 power plant and the accompanying load re 6
quirements are shown below

 

o
-
—

=

 

 

=

TNC (1100°F) ¢e———rr~re—— TNH (1500°F)
P_ = 30 Mw
Wa = 13241b/ e
TT3 (487°F) ——~r~r———> TT4 (1311°F)

2 The required value for the product U,A, (total heat transfer area—over all heat transfer
coefficient) 1s then calculated as follows
(1100 - 487) - (1500 - 1311)

Log mean temperature difference = = 360°F

In (1100 — 487)/(1500 - 1311)

 

P, 28 425
RUR AT T 360

 

= 78 9 Btu/sec °F

3 The engine air flow per unit frontal area of the radiator Wa/A/R 1s calculated from W,

 

which 1s known and A which 1s determined from the engine design In this case A, was
arbitrarily chosen as 16 ##2 so
W
132 4
T 2L 8 275 lb/sec ft2
Ap 16

4 A value for U, 1s read from the curve in Fig 6 with the use of W/A/R found In step 3
and the required heat transfer surface area A, 1s calculated

 

Ug = 315 Btu/hr ft2 °F
U,A
R 78 9)(3600
a, R UBICEO _ 9415 42
U, 315

27
28

5 Next a number of the basic radiator units are stacked to provide
the required frontal area  Four units are needed in this example
Since each basic unit contains 776 ft2 of heat transfer area the
stacked array contains 3104 ft2 of heat transfer surface The array
must therefore be lengthened to provide the required over all heat
transfer surface Since a 6 67 in deep stacked unit contains 3104 f+2

and since 9018 ft2 1s required the depth must be increased to H

 

 

-—90]8 667 =194
3104 0 00T A
(N
The pressure drop can be estimated by multiplying the calculations V
of Schultheiss by the proper ratios  Under the following operating
conditions
Wa
= 579 Ib/sec ft2 p = 00434 radiator depth = 6 67 in
R

Schultheiss has calculated that the pressure drop of this type of radiator s
AP, = 28 5n H,0

At other operating conditions the pressure drop 1s estimated to be

wa/AfR 0 0434\ /radiator depth
AP, = 285
579 P, 6 67

For the G E X 61 case

 

AP, = 8216 H,O = 4268 Ib/ft2

At the design point (described in step 1) this pressure drop 1s (426 8/6470) = 6 6% of the com
pressor discharge pressure The same procedure was used In assembling the hypothetical Allison
J 71 radiators

 
APPENDIX B

STEADY STATE PERFORMANCE CALCULATIONS

Control parameter values required to yield given engine thrust outputs during steady state
operation at specified flight conditions can be determined by working backwards through the
engine and reactor performance characteristics The engine [oad imposed on the reactor (as
described by power compressor outlet temperature turbine inlet temperature and airflow) is first
determined from Figs 2 through 5 When these load quantities are known and when values for all
but one of the unknown potential throttling quantities are specified the value which the remaining
unknown throttling quantity must have in order to meet the load conditions can then be calculated
by use of one of the procedures outlined below For purposes of tilustration it 1s assumed In
each case that the throttling quantity value required to deliver 4000 Ib of thrust output per engine
during flight at 15 000 ft at a speed of Mach 0 45 1s to be determined

Example 1 — Control Rod Throttling
The engine load quantities resulting when 4000 Ib of thrust 1s delivered during flight at
15 000 ft and Mach 0 45 are (from Figs 2 through 5)

T,y = 411°F W_ = 157 Ib/sec Tre = 931°F

a

P, = 22 5Mw = 21 300 Btu/sec

Effectiveness values for both the heat exchanger and the engine radiators will be required for
calculation of the unknown quantities Te , Tey Tpe Tyy Tne These effectiveness values
depend on the fluid flow rates and the over all heat transfer coeffictents which are also functions

of the flow rates

- e(UHXAHX/WNCN)[(WNCN/WF CF)_I]

 

TI =
- 1 — (WyC\/WoChp) Uk Aux/ Wy Cy) Wy Cy/ W Cp)-1]

(UgAp/W, C ) [(W,C /WyCy)-1]
— e

 

n =
R 1 — (W,C,/WNCy) e(URAR/WaCa)[(Waca/WNCN)-I]

Since the flow rates in the main heat exchanger are constant at design point values in this
example the heat exchanger effectiveness 1s 0 8 as shown on page 3 The effectiveness of the
radiator at this operating condition 1s found by substituting the foliowing values into the effec
tiveness expression

 

W, = 157 Ib/sec A = 9018 ft2
Ve 157
U, = 336 Btu/hr ft2 °F from = — = 98l and Fig 6
R T
W, = 2843 Ib/sec C, =02 Cy = 025

This substitution shows that the radiator effectiveness 7, 1s 0768
Values for all the unknowns desired can now be determined from the following series of cal
culations

29
NaK Temperature at Outlet of Heat Exchonger (Tyy) — By definition

 

TT4 - TT3
Mg =
TNH - TT3
or
Tra = Tr3 931 - 411
Tyg = ———+ Ty =—————+ 411 = 1088°F
e 0 768
NoK Temperature at Inlet of Heat Exchanger (Tye) -
T T T T e g o 20 790°F
Tnve = Tnuw = Tyn = Tne) = Typ - neCn - (284 3)(0 25) -
Fuel Temperature at Outlet of Reactor Core (T ) = By definition
TNH - TNC
Tx =
Tey = Tnc
or
T Tow 7 TNe MBI iexer
FH = Y INc =g " =
MHx 08
Fuel Temperature at Inlet of Reactor Core (Tre) -
T T (T T.) =T e | 42 600 938°F
FC — FH ~— FH ~ FCc/ — FH ~ WFCF - "—(7—02)(62_7)_

Twice the power delivered to one engine 1s used in the above expression since reactor power

delivery to two engine loads has been assumed

Thus 1f 4000 Ib of thrust 1s to be delivered by each engine during flight at 15000 ft and
Mach 0 45 the control rod must be set to lower the mean fuel temperature to 1051°F f throttling

Is to be by means of control rod motion alone

Example 2 - Reactor Fuel Flow Throttling

The engine load quantities at the 15 000 ft Mach 0 45 4000 1b thrust output flight condition
were given in the preceding example The radiator effectiveness in this case 1s also the same

as the effectiveness calculated in example 1 (ngp = 0768) since the air and NaK flow rates are

the same It 1s assumed in this example that the control rod i1s adjusted to hold the mean fuel

temperature at 1ts design point value Tp = 1450°F

The unknown quantities to be calculated are We Ty T T and T,

FC NH

c The unknown

NaK temperatures are the same as those calculated in example 1 since the load characteristics
are the same and the radiator effectiveness 1s the same The fuel flow rate required to satisfy

heat balances in the main heat exchanger can be calculated as outlined below
The power transferred from the main heat exchanger is

AT),

 

Pr= WCplTpy - Tp ) = 2ch,< + Tye = Tp >

THx

30

 
|f the power delivery to the two engines 1s the same

P

T 299 80 6
P, =——= 027V, + 790 — 1450 ) = W, - 1783
2 Ty x Tux

 

 

Since P_ is known from the engine load requirements and 7, 1s a function of W (since the
NaK flow rate 1s constant) the above expression might be solved directly for W_ However the
complexity of the 5, to W relationship mokes solution by trial and error more attractive One
procedure for solving this equation involves assuming a value for W calculating the associated
value of Myx and calculating a value for P, The process 1s repeated unti| the calculoted power
per engine Is equal to the required power per engine At the 15000 ft Mach 0 45 4000 Ib thrust
output flight condition W, = 125 Ib/sec satisfies the power delivery requirement

Fuel temperatures are then calculated from

 

 

Pr 42 600
Tey - Tpe = = = 1257°F

WoCp  (125)(027)

Tey = Tec 1257 .
Toy = Th +—é—~:14so+ = 2079°F

Tpy - TFC 1257 o
Tpc = Tp ——— = 1450 - = 822°F

Example 3 ~ NaK Flow Throttling

The engine load quantities are again the same as those shown in example 1 since the aircraft
flight condition and engine thrust outputs desired are the same In this example the fuel flow

rate W, and the mean fuel temperature T  are constant at their rated values (702 Ib/sec
and 1450°F respectively)

The unknown quantities to be calculated In this case are W, Tpy Tg( Tyy and Ty
The reactor fuel temperatures are found easily from

P

 

 

- . T 42 600 _ 224°F
rr = Tre T T ooz
Tey -~ Tec 224 o
Tenw = Tk +___2_——:]450+ - e
Toy - Trc 224 .
Tee = Tg -T2 7 1430 T2 1338°F

The NaK flow rate needed for delivering the power required by each engine at the specified
load conditions can be found by a trial and error process The right trial 1s outlined below
A value for W 1s assumed and the resulting n, . 1s calculated If Wy 151554 1b/sec
Tyx 'S 10 as calculated from the known fuel flow rate the over-all heat transfer coefficient
and the assumed NaK flow rate The resulting NaK temperatures are then calculated From the
definition of main heat exchanger effectiveness
T - T P
L 7 21 3%

NC - = 1012°F

FH

31
and

 

T T (T T,.) =T e 1012 + 21 3% 1562°F
- + - = Tyc + = e =
NH NC NH NC W..Cn (155 4)(0 25)

An alternate expression for the radiator effectiveness 1s
o e(URAR/WaCa)[(ATN/ATa)-1]
Mg =
U,An/W C YL(AT /AT )1
| ary SRR Y CITAT /AT )]

Substitution of the following quantities into this expression yields a value for radiator effective
ness which exists when the NaK flow rate 1s 155 4 Ib/sec as was originally assumed

 

 

 

W
a 157 2
= — = 98] Up = 336 Btu/hr 12 °F (Fig 6)
A 16
ATy 1092 2 10 UrAr (33 6)9018) -
AT, 520 W,C,  (157)(0 26)(3600)

1 - 22 063(2 10-1)
g = = 0 450
1 - 210 62 063(2 10-1)

 

The radiator effectiveness required to satisfy the load requirement 1s

TT4 = TTB 520 0 45
'[]R = = =
TNH - TT3 1562 - 411

 

If these two effectiveness calculations had not yielded the same result a different NaK flow
rate would have been assumed and the calculations would have been repeated

Example 4 — NaK Bypass Throttling

The engine load quantities are again the same as those shown in example 1 and in this case
the fuel flow rate total NaK flow rate main heat exchanger effectiveness and mean fuel tem
perature are assumed to be constant at their rated values

The unknown quantities to be calculated are WNBP] WND| Tey Tpe Tyw Tye and Tyhe

Fuel Temperature at Qutlet of Reactor Core (TFH) -

Tpy - Tec 224
+ ————— = 1450 + T= 1562°F

T = Tg >

FH

Fuel Temperature ot Inlet of Reactor Core (Teo) -

TFH - TFC 224

To - =T - — - 1450 - 2 - o
e = Tray > 5 — = 1338°F

32
NaK Temperature at Inlet of Heat Exchanger (T, ) ~ From the definition of heat exchanger
effectiveness

T - T

 

Tne = Tpn = AT 1562 - fi = 1189°F
Ty x 08
haK Temperature at Outlet of Heat Exchanger (T ) -
Tng = Tne + Tnp = Tne) = Tye + - = 1189 + 210
W eCn (284 3)(0 25)

T,y = 1189 + 299 = 1488°F

NaK Temperature at Outlet of Radiator (7, . ) ~ Values for the following constants are first
obtained

Trs = Tra 931 - 411 0 453
nR = = =
Tyy - T, 1488 - 411

 

Url (33 6)(9018)
W.C_ (157)(0 26)(3600)

 

= 2063

Substitution of these constants into the alternate radiator effectiveness expression given in
example 3 yields

2 063 TNy ~Tye V(Tps-Tri)l-11

0483 =

 

2 Ty, -T AT =T =1}
1 - UTyy = Tye Ty = Trglle 063t TNy -Tye T -Trazl-1

Solving for (T, — Tye M Tpy = Trs)

TNH TNC

Try -

= 190
T3

Thus
Tye = Tayg - 190(Tp, - Tpy) = 1488 — 1 90(931 — 411) = 500°F
at the outlet of the radiator
Direct NaK Flow Rate per Engine Through Radiator Wyp) -

Wyp = e 213% 859 Ib/
ND S T T T, )Cy | (1488 — 500)(025) "

 

NoK Bypass Flow Rate per Engine (W ,,) —

Wygp = Wne = Wyp = 2843 = 859 = 198 4 Ib/sec

33
34

or
198 4

00 = 69 8%
843 6

 

Example 5 « Air Bypass Throttling

The engine load quantities are given in example 1 and the fuel flow rate NaK flow rate heat
exchanger effectiveness and mean fuel temperature are assumed to be constant at ther rated
values

The unknowns to be calculated in this case are Wagp Yap Tey Tpe Tyy ond Ty~ The
fuel and NaK temperatures are the same as those calculated in example 4 and are repeated here
for reference

T = 1562°F T = 1338°F T

FH FC Ny = 1488°F Tye = 1189°F

The remaining unknowns W.pand W_p, are calculated in the following way

Direct Radiator Air Flow Rate per Engine (W,p) = The raaiator effectiveness 1s

TT4 - TTS

TNH = TTS

Mg =

Radiator power delivery i1s

Pe = waCa(TT4 - TT3)

Combination of these expressions yields

Y . Pe . 21 300 75 8
DR = C (Tym - Tra)  (026)(1488 — 411)

 

 

The W png product 1s also given by

1 - e(URAR/WaDCa)[(WaDCa/WNCN)—I]
= W

 

waDnR aD

1o e o URAR Wap CAHapCo Wy C) 1]

This expression might be solved for W_,, (inserting the known value of W, png product from
above) since the NaK flow rate 1s constant and the over all heat transfer coefficient Up ts a
function of W_,,  The complexity of the right side of the above expressions makes direct solution
difficult however The value of W,p resulting in a W_pn. product of 75 8 can be found graphi
cally by plotting the right side of the above expression for W.png as a function of W_,  Such
a plot 1s shown in Fig B 1 This plot shows that the required W,.png value (75 8) results when
¥ p 's 83 Ib/sec

a

Bypass Air Flow Rate per Engme (W ;) -

w =W, - W_p

aBP 157 — 83 = 74 Ib/sec

 

74
% air bypass = x 100 = 47%
157
240

220

200

@
o

4160

140

120

100

80

60

RADIATOR PERFORMANCE PARAMETER Wa‘!?R

40

20

ORNL LR DWG 9224

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

/
/,
/,/
]
//
40 80 {20 160 200 240 280 320 360

RADIATOR AIRFLOW %D {ib/s )

Fig B 1 (Performance Parameter for X 61 Engine Radiator

400

35
36

e APPENDIX C

STATIC STABILITY CALCULATIONS

The steady state power delivered by the reactor is related to the engine load quantities in the
following way

]

(CH P =
/W pCang + (1 = 03 )/ W

e

 

(TF v T'ra)
voCn — 1/2XW_C,,
Condition 1 ~ Variation of steady state power delivery with changes in engine speed when
reactor control quantities are constant and throttling 1s by air bypass with pump speeds constant

In this case the quantities listed below are constant at the values shown in the reactor—J 71
engine power plant

MTyx = 08 X =025

Wye = 1422 Ib/sec We = 702 Ib/sec
Cy = 025Bt/Ib°F Cp = 027 Bt/Ib °F
€, = 026 Btu/Ib °F Tre, = 1450°F

Substitution of these values into Eq C 1 yields

1
P, =
(3846/W_,n.) — 0003517

 

(C 2) (1450 — T..)

The W_,n, product 1s a function of the total engine air flow which is a function of speed
(Fig 7) and the air bypass percentage The variation of W.png with W_. at rated NaK flow 1s
shown in Fig 21 Steady state compressor outlet temperature variation with speed 1s shown in

Fig 7 Substtution of values for W,png and T..; at each speed into Eq C 2 yields the power
delivery curves of Fig 20

Condition 2 = Vanation of steady state power delivery with changes in engine speed when
reactor control quantities are constant throttling 1s by NaK bypass and all pump speeds are
constant

Equation C2 applies in this case also  The value for W_, is the same as that for W, (the
total engine air flow) Variations of the W,png product with W_. at constant NaK bypass per
centages are shown in Fig 21 The variations of T..5 and W_ with engine speed are shown in
Fig 7 Substitution of these values into Eq C 2 yields the constant NaK bypass power delivery
curves of Fig 19

Condition 3 ~ Variation of steady state power delivery with changes in engine speed when
reactor control quantities are constant throttling 1s by NaK bypass and one or more pump
speeds are proportioned to engine speed

Equation C 1 applies to this case The vaiue for W.p is equal to that for W _ (the total engine
air flow) the variation of W, 5, with radiator air flow 1s shown 1n Fig 21 variations of W, and
T..3 with engine speed are shown in Fig 7 and heat exchanger effectiveness values are calcu
lated from the fuel and NaK flow rates and the heat exchanger effectiveness equation given on
page 29

In calculating the power delivery curves of Fig 23 it was furthermore assumed that the mean
fuel temperature T._ _ was held constant at 1450°F at all times by rod motion 1f necessary

 
and that the pump flows were proportional to the pump speeds Thus

702
F = %N
142 4
Ne = T5ean

Substitution of these expressions into Eq C 1 yields the desired relationship between power
delivery and engine speed which 1s plotted for various pump drive combinations in Fig 23

37