THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS
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Copyright © 1986 by ASME
Impact of Higher Freeze Point Fuels
on Naval Aircraft Operations
R. A. KAMIN
Project Engineer
Naval Air Proplsion Center
Trenton, NJ
P. M. McCONNELL
Project Engineer
Boeing Military Airplane Company
Seattle, WA
ABSTRACT
P
Density of Fluid
Refinery process studies have indicated that the
relaxation of the JP-5 freeze point specification is a
viable means of increasing jet fuel availability. The
Naval Air Propulsion Center is investigating the impact of higher freeze point fuels on naval aircraft
operations. Six fuels, with freeze points ranging
from -55 ° F to +10 ° F, were tested in two instrumented
external fuel tanks. Thirty hours of flight test and
one hundred hours of wind tunnel test data have been
accumulated. This information is being used in
conjunction with laboratory and bench scale test data
to support the development of a three dimensional
computer code. This code will predict fuel cool down
and hold-up (unpumpable frozen fuel) for any fuel tank
geometry during a mission. Initial results indicate
that the current JP-5 freeze point specification of
-51 ° F is conservative and could be safely relaxed.
V
Kinematic Viscosity
NOMENCLATURE
C
Specific Heat
g
Gravity Vector
H
Specific Enthalpy of Fluid
K
Thermal Conductivity of Fluid
L
Tank Length
P
Fluid Pressure
T
Temperature of Fluid
T ref
Reference Temperature
t
Time
✓
Velocity Vector
Volumetric Coefficient of Fluid Expansion
INTRODUCTION
Although the current glut in the petroleum market
has temporarily eased the fears caused by the oil
embargos of the 1970's, recent forecasts has predicted
potential shortages of Aviation Turbine Fuel (ATF)
within the next few decades. The underlying factors
behind these predictions are the increasing use of
heavier, high sulfur, lower yielding crudes and the
increased competition from other middle distillate
products. The region of specific concern to the Navy
is the United States West Coast, Petroleum Administration Defense District Five (PADD 5). Due to its
extensive processing of lower quality crudes, this
region, in which 42% of all current Naval Aviation
Turbine Fuel (JP-5) is produced (Reference 1), is and
will continue to be susceptible to potential production shortfalls.
The Navy, in response to the potential fuel shortage, has given a high priority to investigating methods
of increasing JP-5 availability. A recent study has
indicated that JP-5, due to its tight specifications
(60 ° C flash point and -46 ° C freeze point) and minimal
demand (23,500,000 barrels/year), is a specialty
product currently being produced by only 20% of the
available refinery capacity. One recommendation of
this study identified the relaxation of the JP-5
freeze point specification as a means of increasing
availability. Potential increases in the Maximum
Theoretical Yield of JP-5 per barrel of crude obtainable from the relaxation of the freeze point specification to the commercial (Jet A) specification of -40 ° C,
range from 45% to 757 (Reference 2) depending on the
crude source (Table 1). However before any specification change is considered, the potential impact on
aircraft performance must be evaluated. This investigation is necessary because of the concern that the
higher freeze point fuels may form solid-wax precipitates during high altitude, long duration missions.
These precipitates could cause plugging of filters and
Presented at the International Gas Turbine Conference and Exhibit
Dusseldorf, West Germany—June 8-12, 1986
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withdrawal tubes or cause malfunctions in the boost
and ejector-scavenger pumps.
bulk of the internal thermocouples were placed within
five centimeters of the tank's skin in order to obtain
an abundance of data in the area where the greatest
temperature gradients were theoretically predicted to
occur. The data from the thermocouples were passed to
a pulse code modulator (PCM) encoder and stored on a
magnetic tape located in the tank's tailcone section.
Data retrieval was accomplished by transmitting the
signals from the magnetic tape through a decoder into
a HP9826 computer.
TABLE 1 EFFECT OF FREEZE POINT RELAXATION
ON
MAXIMUM THEORETICAL YIELD OF JP-5
MAXIMUM THEORETICAL YIELD FOR CRUDE SOURCE
FREEZE
POINT
C
-46
CURRENT
MED GRAN
HI SULFUR
MEXICAN
70
LT GRAV HEAVY CR AV MED GR AV V HEA V GRAY
HI SULFUR HI SULFUR HI SULFUR HI SULFUR
ALASKAN
CA OS
ARABIAN
CA
11.5
12.5
10.3
SPEC
0.0
-40
L2.3
16_7
12.5
15.9
11_7
% INCREASE
OVER CURB
SPEC
76
45
45
53
46
SKIN THERMOCOUPLES
DATA ACQUISITION
SYSTEM
CONSTANT GO C FL ASH POINT
The Navy's program to evaluate the impact of using
higher freeze point fuels is divided into four phases.
Phase One of the program consists of obtaining actual
fuel cool down and hold-up (unpumpable frozen fuel
within the tank) data. This data is necessary to
verify the mathematical computer model to be developed
in Phase Two of the program. The model developed will
be capable of predicting the fuel cool down and holdup for any given fuel tank flying a particular mission
profile through known temperature conditions. Phase
Three of the Navy's program will be performed concurrently with Phases One and Two and will investigate
the pumpability and flowability of fuels at and below
their freeze point. The majority of this effort will
be performed in an aircraft fuel system simulator
composed of actual fUel system components. The fourth
and final phase of the program will use the computer
model developed in Phase Two to analyze all possible
naval aircraft missions to determine the limit to
which the freeze point specification can be safely
relaxed.
This paper focuses on Phases One and Two of the
Navy's program. The results of the flight and wind
tunnel tests as well as the development and initial
simulations of the mathematical computer model will be
discussed.
FRONT THERMOCOUPLE
TREE
REAR THERMOCOUPLE
TREE
FIGURE 1 INSTRUMENTED FUEL TANK
rc
01
• 032
• 0.35
C 1.53
O 298
L
FRONT THERMOCOUPLE TREE
FIGURE 2
F 4.13
G GAG
H 10 49
I 11 43
• 11.75
• L5 24
2160
23.81
N 24. 7 7
(
1• N!
L6i il
REAP THERMOCOUPLE
TREE
INTERNAL THERMOCOUPLE POSITIONS
EXTERNAL FUEL TANK INSTRUMENTATION
Although considerable effort has been spent to
obtain fuel temperature profiles in wing tank simulators, a relatively small amount of in-flight fuel
temperature data has been recorded. Therefore, the
first goal in Phase One of the Navy's program was to
obtain in-flight fuel temperature data. Two external
fuel tanks, the 300 gallon AERO-1D and the 150 gallon
FPU-3A, were chosen to be instrumented because of
their wide use within the system and the number of
potential aircraft on which they can be flown. In
addition, the fuel tanks' three dimensional temperature
gradients, due to their cylindrical geometry, would
present an excellent test in which to verify the
accuracy of the model.
Each fuel tank was instrumented with a total of
sixty-five thermocouples. Seventeen thermocouples
were placed along the outside skin of the tank, while
the remaining forty-eight were mounted on two teflon
trees placed inside the tank (Figure 1). Each tree
consisted of twenty-four thermocouples placed in a
pattern of concentric circles along the major horizontal and vertical axes of the tank (Figure 2). The
FLIGHT TEST
The 300 gallon AERO-1D external fuel tank was
flight tested for thirty hours on the in-board station
of an A-6E aircraft. The A-6E was chosen because its
capabilities of high altitude, long duration, and low
airspeed flight would expose the tank to an extremely
low temperature environment. A total of ten missions
were flown, each exposing the fuel tank to altitude
soak conditions for approximately three hours.
Although each mission differed slightly, they were all
within the approximate range of: 1) airspeed - .5 to
.7 mach, 2) altitude - 33,000 to 40,000 feet, and
3) outside air temperature - -48 ° C to -62 ° C. Eight
of the missions were flown using MIL-T-5624 specification JP-5 in the fuel tank while the remaining two
missions were flown with Navy Distillate Fuel (F-76).
F-76, with a -7 ° C freeze point and a -18 ° C pour point,
was selected as a test fuel in order to obtain temperature profiles for a fuel having a different composition
than JP-5 as well as to investigate the temperature
profiles of a fuel as it undergoes freezing during
2
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flight. The minimum fuel temperature recorded during
the flight tests was -43°C. This temperature was recorded at a location of .32 centimeters from the
bottom skin of the tank. The outside air temperature
recorded during this time was -62 ° C, which corresponds
to the MIL-STD-210 1% worldwide extreme low temperature condition at 30,000 feet (Reference 3).
Some trends observed during the flight tests agree
with results obtained in earlier wing tank simulator
and bench scale testing. First and most prominent is
that the fuel cool down rate is inversely proportional
to the distance from the tank's skin (i.e., slower
cool down rates towards the center of the tank). This
observation supports the theoretical explanation that
the convective flow currents created by the density
changes of the cooling fuel within the tank cause the
heavier, denser, colder fuel to settle in stagnant
regions at the bottom of the tank. Secondly, the cool
down rates exhibited by the flight tests could be
divided into three distinct regimes; the tank skin,
the bulk fuel located in the center of the tank, and
the stagnant fuel layer located in the bottom third
of the tank. These regimes could be further broken
down into two segments of the mission, ascent (first
fifteen to twenty minutes) and altitude soak (high
altitude low airspeed portion of the mission). For
an average JP-5 test the skin cool down rate was
calculated to be 2.8 ° C/min during the ascent portion
of the mission and .09 ° C/min during the altitude soak.
In contrast, the bulk fuel cool down rate was .11 ° C/
min during ascent and .28°C/min during the altitude
soak. The rates for the stagnation layer were
typically between those of the skin and the bulk fuel
and were .44 ° C/min during ascent and .30 ° C/min during
the altitude soak. Although the numbers themselves
changed for each particular mission, the pattern they
followed during both ascent and altitude soak remained
constant. Thirdly, the F-76 profile of fuel temperature versus axial location (Figure 3) became increasingly parabolic during the mission. This change in
profile did not occur in the JP-5 case (Figure 4) and
was attributed to the freezing of the F-76 during the
mission. Although there was no way to verify this
assumption, similar profiles have been observed during
the freezing of fuels in experimental wing tank
simulators (Reference 4).
In addition to the expected phenomenon, some unexpected results were obtained from the flight tests.
First, the fuel in the rear of the tank was approximately 5 ° C to 10 ° C cooler than the fuel in the front
of the tank. This temperature difference appears
shortly after flight and continues through the
altitude soak portion of the mission. Although the
exact reason for this difference was not known, it was
strongly believed to be due to the 4 ° to 6 ° positive
angle of attack the tank experienced during flight
(Reference 5). Similar phenomenon have been recently
observed during cool down tests performed in cylindrical test tank having a 10 ° angle of inclination
(Reference 6). The flow of cold fuel to the rear of
the fuel tank could present a potentially serious
problem because the fuel withdrawal tube is located
in the rear of the tank and would therefore be highly
susceptible to blockage by frozen fuel. A second
unexpected result was that the measured fuel temperature versus time plots showed relatively large spikes
at seemingly random times (Figure 5), thus suggesting
that localized regions of warm or cold fluid were
circulating in directions other than the expected
main pattern of flow.
1
7
AV—
17
0 MINUTES
—111- 90 MINUTES
60 MINUTES
r to__ --
-120 MINUTES
"
?-4
•
-
2 -
-
CALL IL- 11-'ERAI
FIGURE 3 FUEL TEMPERATURE VS DISTANCE FROM BOTTOM SKIN
FOR F-76 TEST FUEL
14 20
I
11-- 0 MINUTES
30 MINUTES
60 MINUTES
--,0,120 MINUTES
7
I 1,7,
c
N
-
✓ 10.4.
H
E
26
46
Ala
FUEL. TLMPERA .FIkt:'7F:'.
FIGURE 4 FUEL TEMPERATURE VS DISTANCE FROM BOTTOM SKIN
FOR JP-5 TEST FUEL
411----TC*1 152 CM FROM SKIN
--11- TC#4 4.1 CM FROM SKIN
-10.--TC#G LB CM FROM SKIN
E
E
-404-
20
4 66
4
1A0 140 1 -
TIME (MINUTES.'
FIGURE 5 FLIGHT TEST TEMPERATURE PROFILES
FOR LOWER REAR THERMOCOUPLE RAKE
WIND TUNNEL TESTS
Although the flight tests provided a tremendous
wealth of useful data, they left several questions
unanswered. Therefore, in order to attempt to resolve
these questions, the 150 gallon FPU - 3A external fuel
tank was tested in a sea level engine test cell designed to operate similarly to a wind tunnel. These
tests allowed the instrumented fuel tank to be
operated in a strictly controlled environment using
test fuels having higher than specification freezing
points. In addition, the amount of fuel hold-up
encountered could be measured at the end of each
mission. The fuel pod was situated in the test cell
3
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with a 0 ° angle of attack and surrounded with a
cylindrical ducting. The size of the outer ducting
was designed in order that the external heat transfer
coefficient encountered during a flight of approximately .5 mach airspeed, 35,000 feet altitude and
-55 ° C outside air temperature could be simulated
during the testing (Reference 7). Six fuels, JP-5,
F-76, and four fuels meeting all JP-5 specifications
except the freeze point (freeze points ranged
from -39 ° C to -44 ° C), were tested over four distinct
missions, with the severest being a three hour cold
soak at -65 ° C. Air, fuel, and skin temperature
measurements were taken approximately every three
minutes during the test. At the completion of the
test, the tank was pressurized according to aircraft
operating procedures (10 - 15 psig) and the fuel was
withdrawn from the tank until cessation of flow. The
tank was then warmed to ambient conditions and the
remaining fuel was removed. The amount of remaining
fuel removed after warm-up was recorded as the fuel
hold-up for the test.
The fuel cool down rates obtained for the six test
fuels exhibited the same general profiles as those in
the flight test. Also, the parobolic nature of the
fuel temperature versus axial tank position profile
of the wind tunnel test fuels undergoing freezing
approximately matched the F-76 profiles from the
flight tests. Unlike the flight tests however, the
wind tunnel tests showed no three dimensional cooling
gradients. The temperatures recorded by the front
thermocouple tree were approximately equal to those
recorded by the rear thermocouple tree. This result
supports the theory that the angle of attack that the
300 gallon tank experienced during flight was responsible for producing the three dimensional gradients
observed during the flight tests. Another difference
between the flight test and the wind tunnel test was
the difference in temperature between the bottom and
side tank skins. In the wind tunnel test the tank
sides, where the theoretical maximum convective flow
occurs, were approximately 10 ° C to 17 ° C warmer than
the tank bottom. In the flight test however, the
temperature difference was only 3 ° C to 8 ° C. The exact
cause for this difference has not been verified, but
there is a strong possibility that the sloshing and
vibration the tank had experienced during the flight
was responsible for altering the expected theoretical
convective flow patterns.
The most important result obtained from the wind
tunnel tests was the surprising degree of pumpability
of the test fuels at temperatures 15 ° C to 41 ° C below
their respective freeze points. Subject to test
conditions of -65 ° C for a test duration of 2 to 3
hours, 65% of the F-76 in the tank was pumpable at a
fuel temperature 41 ° C below its freeze point, 73% of
Test Fuel #4 was pumpable at a fuel temperature 19 ° C
below its freeze point, 83% of Test Fuel #3 was
pumpable at a fuel temperature of 18 ° C below its
freeze point, 85% of Test Fuel #2 was pumpable at a
fuel temperature 17 ° C below its freeze point and 99%
of Test Fuel #1 was pumpable 15 ° C below its freeze
point (Table 2). In each case the fuel temperature
was measured approximately .32 centimeters from the
bottom of the tank. These results directly contradict
both the pour point and Shell Cold Flow Test analyses
which predicted 100% hold-up (0% flowability) for each
fuel at the measured wind tunnel test temperatures.
However, both the Shell Cold Flow and the pour point
tests are subjected only to gravity induced flow and
not the 10 to 15 psig pressure force used to pump the
fuel from the instrumented tank. Similarly, previous
work performed in wing tank simulators have shown
a higher degree of hold-up at tests conditions less
severe than those encountered during the wind tunnel
testing (Reference 8). A possible explanation for the
difference in hold-up is the manner in which the fuel
was withdrawn. In the wing tank simulator, the fuel
was withdrawn via gravity drain or suction pump. This
method of fuel withdrawal pulls the colder frozen fuel,
located in the bottom of the tank, towards the drain.
This makes the drain highly susceptible to being
blocked by frozen fuel and trapping the warmer liquid
fuel located in the center of the tank. In contrast,
the fuel was withdrawn from the instrument fuel tank
by pushing, with 10 to 15 psig air, it through a
standpipe that has an opening located .32 centimeters
from the bottom of the tank. It is postulated that the
air pressure causes the warmer bulk liquid fuel to
create a path through the colder frozen fuel and allow
the liquid fuel in the center of the tank to exit.
Since the fuel's behavior could not be seen within the
fuel tank, this hypothesis is only conjecture and must
he substantiated with further experimentation.
Additional work is planned to investigate the pumpability of fuel at low temperatures using a cold flow
test cylinder, containing plexiglass end walls, capable
of fuel withdrawal via gravity drain, suction pump or
pressurization.
,
TABLE 2
WIND TUNNEL TESTING
FUEL HOLD-UP
FUEL
FUEL HOLD-UP
DEGREES C BELOW
FREEZING POINT
F-76
35
41
PER CENT
TEST FUEL 41
15
17
TEST FUEL #2
15
TEST FUEL #3
17
18
TEST FUEL #4
27
19
ANALYTICAL MODEL
Although the measurement of fuel temperatures
within an aircraft fuel tank under actual flight
conditions would be the ideal method for assessing the
impact of using higher freeze point fuels, the number
of tests required to provide an accurate analysis would
be costly and time consuming. Therefore the only
practical method to approaching this problem was to
develop a mathematical computer model capable of predicting fuel cool down and hold-up for any given fuel
tank flying a particular mission profile at known
temperature conditions. However, developing a model
to predict the cool down and freezing of jet fuels is
a highly complex and difficult analytical problem.
This complexity is due to the turbulent, unsteady
boundary conditions and the extremely high Rayleigh
numbers (10 12 ) encountered during a flight. Due to
these complexities, the accuracy of any model developed
must be verified by actual test data before being
universally accepted. For modeling purposes the
phenomenon of fuel cool down was divided into two
distinct regimes: external heat transfer (between tank
skin and the atmosphere) and internal heat transfer
(between the tank skin and the fuel). The governing
theoretical equations to calculate the heat transfer
4
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ments would be beneficial in the final model. This
would create an additional margin for safety in the
evaluation of the effects of higher freeze point fuels
on aircraft operations.
Although the PHOENICS code successfully predicted
the fuel temperatures obtained within the strictly
controlled wind tunnel environment, the code encountered problems in predicting the fuel temperatures recorded during the flight tests. Even though the test
data clearly indicated that the fuel experienced three
dimensional cooling gradients, only a two-dimensional
analysis was performed during initial flight test
simulations in order to reduce computational costs.
Along the tank's horizontal centerline, predicted
results were approximately 2 ° C lower than the measured
values. Predicted values in the area between the
tank's centerline and one inch from the bottom of the
tank were 6 ° C to 7 ° C above the measured values. At
positions less than one inch from the bottom of the
tank skin the predicted values were within 1 ° C of the
measured temperatures. Some factors which may have
attributed to the difficulty in modeling the flight
test were the slosh and vibration experienced by the
fuel, the internal tank structures (i.e., ribs and
baffles) and the angle of attack of the fuel tank
during flight. All of these three dimensional effects
are currently not modeled by the PHOENICS code and are
being investigated to determine the effect of modeling
each would have on the solution.
In addition to modeling the cool down rates of the
fuel, work has been initiated to develop the PHOENICS
code to predict the amount of fuel that freezes and
becomes unusable (hold-up) during a mission. The predicting of fuel freezing in aircraft tanks is virtually
an unexplored field in the area of numerical simulation.
The approach taken to model this phenomenon was to
treat the liquid as a single phase continuum with an
appropriately large viscosity representing the fuel.
This approach appeared to be valid since at very low
Rayleigh Numbers ( 10 3 ) the bouyant fluid motions are
very small and fall within the creep flow range
(Ra 10 3 ); in such flows, discernable velocity boundary
layers are absent. In this case the governing
equations are reduced to
in these regimes are:
MASS:
=
(1)
MOMENTUM (NAVIER-STOKES):
DY
Dt
1
— VP - 154(T- T
—
(2)
ENERGY:
DH DP u a
PDt Dt
'
(3)
The above equations are non-linear, coupled elliptic,
differential equations which apply to the entire flow
domain. No assumptions concerning the core configuration or location of pure conduction regimes are required. The fluid density was assumed in all terms
except for the bouyancy force terms in the momentum
equation that drive the natural convection (Boussinesq
approximation). This assumption is valid when large
density variations are not encountered in the fluid
and was appropriate for the environmental temperature
variations and fuels being considered (Reference 9).
A one dimensional computer code was previously
developed to predict fuel cool down rates in wing
tanks (Reference (10)). However, this code was
determined to be inadequate to model the complex heat
transfer phenomenon encountered within the instrumented, cylindrical fuel tanks. After an extensive search
of the multi-dimensional heat transfer computational
codes currently available, the three dimensional
general purpose, PHOENICS (Parabolic, Hyperbolic, or
Elliptic Numerical - Integration Code Series) code
was determined as the best available code to solve the
problem. The PHOENICS code consists of a centralized,
versatile, economical system capable of simulating a
large number of fluid-flow, heat transfer and chemicalreaction equations. The centralized code is surrounded by a number of satellite codes specifically
tailored by each user to provide additional properties
and support equations needed by the central code as
well as to retrieve the desired results (Reference
11).
The first test of the PHOENICS code was to model
the temperature profiles of JP-5 obtained in the 150
gallon FPU-3A fuel tank undergoing a long duration,
low temperature wind tunnel test (-65 ° C for three
hours). Since the wind tunnel data exhibited very
few three dimensional effects, the simulation was performed in two dimensional slices to reduce computational costs. In order to initially avoid the complexities of modeling fuel freezing, the simulation
was terminated before the fuel reached the freezing
phase. Inputs to the model were outside air temperature, air velocity, initial fuel temperature, tank
geometry, and fuel quantity within the tank. Output
values from the code were the fuel temperatures versus
time and location. The predicted temperatures along
the tank's horizontal centerline were all within 1 ° C
of the measured fuel temperatures. Predicted values
in the area of the centerline to approximately one
inch from the bottom of the tank were within 2 ° C of
the measured values. At positions less than one inch
from the bottom of the tank the predicted values
were approximately 3 ° C to 4 ° C colder than the measured
values. Although code modifications are being made to
improve these results, the predicting of the fuel
temperatures slightly colder than the actual measure-
at
(pCT +L) =V.KVT
(4)
where the latent heat, L, is released over a range of
temperatures rather than at a specific freeze point
(Reference 9). Work on this simulation is only in its
initial stages of development and results have not yet
been correlated with wind tunnel or laboratory data.
CONCLUSION
Although the Navy's program to increase the availability of JP-5 through the relaxation of the freeze
point specification is still in progress, many favorable indications are apparent. First, the data obtained during the flight tests demonstrated that even
under the severe temperature conditions encountered the
minimum fuel temperature measured was 3 ° C above the
current specification. Secondly, the data obtained in
the wind tunnel tests demonstrated the pumpability of
fuels at temperatures well below their freeze and
pour points. Although both the flight and wind tunnel
tests didn't simulate actual Naval missions, they
exposed the fuel tanks to a temperature environment as
severe as may be expected during most naval aircraft
missions. Therefore, the data gathered to date gives
credence to the theory that the current JP-5 freeze
5
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point specification is conservative and can be
safely relaxed without effecting aircraft operations.
REFERENCES
1.
Ricciardelli, J. N., "Physical and Chemical
Properties of JP-5 Fuel," 1980-1983, NAPC-PE-105,
December 1984.
2.
Liberman, M., and Taylor, W. F., "Effect of
Refinery Variables On The Properties and
Composition of JP-5," RL.2PE80, June 1980.
3
Kamin, R. A., "Effects of Higher Freezing Point
Fuels on Naval Aircraft Operations Phase I: InFlight Temperature Measurements," Air Force/Navy
Science and Engineering Symposium, November 1984.
4
Massman, L. A., McConnell, P. M., "Analysis of
Aircraft Fuel Tank Temperatures," AFAPL-TR-82-2083,
June 1982.
5.
A-6 Flight Conditions and Configuration
Characteristics, NADC-AM-7106.
6.
McConnell, P. M., "Development and Use of a Fuel
Tank Fluids Characteristics Mathematical Model,"
Final Report (To be published).
7.
Ulrich, R., "Fuel Tank/Wind Tunnel Testing,"
Personnel Correspondence, August 1984.
8.
Mehta, H. K., Armstrong, R. S., "Detailed Studies
of Aviation Fuel Flowability," NASA CR 174938,
June 1985.
9.
McConnell, P. M., Owens, S. F., and Kamin, R. A.,
"Prediction of Fuel Freezing In Airplane Fuel
Tanks of Arbitrary Geometry," PHOENICS Users
Conference, September 1985.
10. McConnell, P. M., et al, "Heat Transfer In
Airplane Fuel. Tanks at Low Temperatures," ASME
Paper No. 83-HT-102, 1983.
11. Spalding, D. B., "A General Purpose Computer
Program For Multi-Dimensional One and Two Phase
Flow," Mathematics and Computers in Simulation,
North Holland Press: Vol XXIII 267-276 (1981).
6
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