AFRL-PR-WP-TP-2002-202
`
`ENDOTHERMIC HEAT-SINK OF
`HYDROCARBON FUELS FOR
`SCRAMJET COOLING
`AIAA 2002-3871
`
`H. Huang, D.R. Sobel, and L.J. Spadaccini
`
`JULY 2002
`
`Approved for public release; distribution is unlimited.
`
`Copyright © 2002 by UTRC
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`4. TITLE AND SUBTITLE
`ENDOTHERMIC HEAT-SINK OF HYDROCARBON FUELS FOR
`SCRAMJET COOLLNG
`AIAA 2002-3871
`
`6. AUTHOR(S)
`H. Huang, D.R. Sobel, and LJ. Spadaccini
`
`7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)
`United Technologies Research Center
`411 Silver Lane
`East Hartford, CT 06108
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`Air Force Research Laboratory
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`This report contains copyrighted material.
`Proceedings of 38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit; July 7-10, 2002,
`Indianapolis, IN.
`14. ABSTRACT (Maximum 200 Words)
`Storable liquid hydrocarbon fuels, such as JP-7, JP-8+100, and JP-10, that can undergo endothermic reactions may
`provide sufficient heat sink to enable hypersonic flight without having to resort to cryogenic fuels. The objective of this
`research is to develop and demonstrate the endothermic potential of these fuels for hypersonic scramjet cooling. A high-
`pressure bench-scale reactor was used to determine the overall heat sinks (including endotherm), endothermic reforming
`products, and coking rates for the fuels. A baseline fuel, n-octane, was also investigated for comparison. Tests were
`conducted in catalyst-coated tubes that simulate a single passage in a practical catalytic heat exchanger/reactor under
`representative flow conditions.
`
`15. SUBJECT TERMS
`endothermic fuels, heat sink, coking, thermal management
`
`16. SECURITY CLASSIFICATION OF:
`
`a. REPORT
`Unclassified
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`b. ABSTRACT
`Unclassified
`
`c. THIS PAGE
`Unclassified
`
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`OF ABSTRACT:
`SAR
`
`18. NUMBER OF
`PAGES
`14
`
`19a. NAME OF RESPONSIBLE PERSON (Monitor)
`Tim Edwards
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`(937) 255-3524
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`GE-1027.002
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`

`
`ENDOTHERMIC HEAT-SINK OF HYDROCARBON FUELS
`
`2002-3871
`
`FOR SCRAMJET COOLING
`
`H. Huang, D. R. Sobel, and L. J. Spadaccini
`
`United Technologies Research Center
`East Hartford, CT 06108
`
`Abstract
`Storable liquid hydrocarbon fuels, such as JP-
`7, JP-8+100, and JP-10, that can undergo endothermic
`reactions may provide sufficient heat sink to enable
`hypersonic flight without having to resort to cryogenic
`fuels. The objective of this research is to develop and
`demonstrate the endothermic potential of these fuels for
`hypersonic scramjet cooling. A high-pressure bench-
`scale reactor was used to determine the overall heat
`sinks (including endotherm), endothermic reforming
`products, and coking rates for the fuels. A baseline fuel,
`n-octane, was also investigated for comparison. Tests
`were conducted in catalyst-coated tubes that simulate a
`single passage in a practical catalytic heat
`exchanger/reactor under representative flow conditions.
`Performance evaluations were primarily based on
`endotherm measurements and coke deposition.
`Adequate heat sink capacities have been demonstrated
`for JP-7 and JP-8+100 at elevated pressures using a
`simple, inexpensive zeolite cracking catalyst. Although
`the JP-10 provided an attractive heat sink, its high
`carbon-to-hydrogen ratio leads to significant
`coking/fouling problems and potential poisoning of the
`catalyst, even at relatively low temperatures. The
`results are directly applicable to the selection of fuels
`and the design of fuel-cooled thermal management
`systems for hypersonic scramjet applications.
`Introduction
`High heat sink fuel cooling technology can be
`applied to enhance engine performance over the entire
`spectrum of flight regimes. For hypersonic flight, it
`provides the only means for meeting the cooling
`requirements with storable fuels; for advanced fighter
`aircraft, it provides an identifiable path to achieving
`
`IHPTET performance goals with current materials; and, for
`lower-speed military and commercial aircraft, it can
`increase growth potential and play a key role in emissions-
`reduction strategies.
`Although cryogenic fuels, such as. liquid methane
`and liquid hydrogen, can provide sufficient cooling, they
`require large vehicles (because of their low densities) and
`present cost, logistics, operational and safety problems. By
`contrast, conventional liquid hydrocarbon fuels may offer
`the required cooling capacity without the problems
`associated with cryogenic fuels. For example, paraffinic
`liquid hydrocarbon fuels have significant sensible heat sink
`capacities for supersonic aircraft applications and may
`undergo endothermic chemical cracking on a catalyst for
`hypersonic missile applications [1,2].
`The total heat sink of a hydrocarbon fuel comes
`from the physical heating of the fuel (raising its
`temperature and thereby its sensible enthalpy) and a heat-
`absorbing (endothermic) chemical reaction. Nixon and his
`co-workers [3,4] first demonstrated that the selective
`dehydrogenation of methylcyclohexane (MCH) on a
`platinum/alumina catalyst can provide a total heat sink of
`nearly 900 Btu/lb. MCH, the first-generation endothermic
`fuel, offers sufficient heat sink for cooling a Mach 4 to 6
`aircraft, but is much more expensive than current aviation
`fuels, requires an expensive platinum catalyst, and presents
`significant logistics problems. On a practical path to realize
`the hydrocarbon fuel cooling technologies, Sobel and
`Spadaccini [2] first investigated the endothermic potential
`of liquid hydrocarbon fuels with inexpensive and readily
`available catalysts under operating conditions simulative of
`high-speed flight applications. High heat sink capacities
`and desirable reaction products were demonstrated in their
`study for pure paraffinic (e.g., n-heptane) and blended
`normal paraffinic (e.g., Norpar 12) fuels in coated-tube
`
`Copyright©2002 by UTRC. Published by the American Institute of Aeronautics and Astronautics, Inc. with
`permission.
`
`1
`American Institute of Aeronautics and Astronautics
`
`GE-1027.003
`
`

`
`reactor configurations. At temperatures above
`approximately 1000 F, the sensible heat sink can be
`supplemented by a heat absorbing chemical reaction as
`the fuel undergoes thermal and catalytic cracking
`reactions that reform it into a mixture of lighter
`hydrocarbons and hydrogen [2], which can then be
`burned in the engine. The coke deposition mechanism
`in this high temperature regime is characterized by
`pyrolysis. In this process, the catalyst can serve to
`enhance the endothermic reaction rate and improve the
`selectivity of the reaction for the preferred products that
`may have shorter ignition delay times and more rapid
`burning rates and may also reduce the coke formation.
`The starting temperature for the endothermic reactions
`is on the order of 1000 F and depends primarily on the
`catalyst and the fuel composition. It is also a function of
`fuel flow rate and residence time.
`Endothermic fuel cooling technology can be
`implemented in a practical thermal management system
`in two different ways: direct cooling, which refers to
`the incorporation of the heat exchanger into the
`structure of a hot component, such as a scramjet
`combustor, an augmentor, or a turbine exit guide vane;
`and indirect cooling, wherein ram air or compressor
`bleed air is cooled by the fuel in a nearby heat
`exchanger, and then used to cool the hot components.
`This indirect cooling, "cooled cooling air", allows a
`substantial increase in engine pressure ratio, with
`corresponding improvement in the thrust-to-weight
`ratio [5,6], and thermal efficiency. In both ways, the
`cooling capacity of conventional hydrocarbon fuels is
`limited by a temperature constraint necessary to limit
`coke deposition [7].
`The principal engine operability issue that will
`affect hydrocarbon fuel cooling technology is coke
`formation. In hypersonic applications, duty cycles are
`short, but requirements for maximizing heat sink lead to
`very high fuel temperature operation (>1300 F) and the
`potential for accelerated coking. The extent to which
`the benefits of high heat sink cooling technology can be
`realized is directly related to our ability to mitigate
`against coke formation.
`
`To assess the relative potential of various fuels
`for high-speed flight applications, it is important to
`compare directly the performance, i.e., the heat sink
`capacity and coking limits, in a simulation of scramjet
`regenerative cooling. Within this effort, several
`candidate fuels, namely JP-7 (baseline fuel), JP-8+100,
`JP-10, and n-octane (reference fuel), were tested using a
`single-tube reactor rig under representative flow
`conditions that simulate a single passage in a practical
`catalytic heat exchanger/reactor. The total (physical +
`chemical) heat sinks of these fuels were determined,
`and the coke deposition resulting from extended
`
`duration tests were measured. In addition, the compositions
`of the products from the endothermic cracking were
`analyzed using both GC (Gas Chromatograph) and GC/MS
`(Gas Chromatograph/Mass Spectrometer).
`
`Fuel Selection
`JP-7 and JP-8+100 were chosen as the primary
`fuels in this study. These multi-component kerosene-type
`fuels are defined by their physical properties and broad
`composition guidelines (e.g., aromatics limit) rather than
`specific chemical compositions. Many of the defining
`characteristics can be found in the CRC Handbook for
`aviation fuels [8]. JP-7 is a military jet fuel with low
`volatility and high thermal stability. The fuel specifications
`for JP-7 require that aromatics comprise less than 5 percent
`of the fuel (as determined by ASTM D-1319), the
`remainder of the composition being saturated species, i.e.,
`normal-, iso-, and cyclo-paraffins. JP-8+100 is
`representative of a class of military and commercial
`aircraft gas-turbine fuels with improved thermal stability.
`
`The design of the experiments and interpretation
`of the data require the ability to estimate thermodynamic
`and physical properties. To enable this, simple models
`were used to represent the complex fuel blends. Based on
`GC/MS analyses, 6-component and 11-component
`mixtures, as listed in Table 1, were selected to simulate
`analytically the more complex JP-7 and JP-8+100,
`respectively. These simulations allow computations of the
`physical and thermodynamic properties of the jet fuels
`using the NIST SUPERTRAPP program [9].
`
`Table 1: Jet Fuel Simulations
`
`JP-7
`
`Component
`
`n-undecane
`n-dodecane
`n-tridecane
`n-tetradecane
`n-pentadecane
`ethytcyclohexane
`
`Molar
`Fraction
`
`Component
`
`JP-8
`Molar
`Fraction
`
`Component
`
`Molar
`Fraction
`
`0.122
`0.289
`0.368
`0.031
`0.018
`0.172
`
`methylcyclohexa ne
`meta-xytene
`n-octane
`n-decane
`butylbenzene
`isobutylbenzene
`
`0.075
`0.070
`0.130
`0.156
`0.055
`0.055
`
`t-butytbenzene
`n-dodecane
`1 -methylna p hthale ne
`n-tetradecane
`n-hexadecane
`
`0.055
`0.175
`0.052
`0.112
`0.065
`
`Unlike the fuels described above, n-octane and
`JP-10 are single-component hydrocarbon fuels. n-Octane is
`a reference fuel studied for comparison. JP-10 is a missile
`fuel with high energy density and, therefore, is well suited
`to volume-limited applications. Furthermore, because of its
`attractive thermophysical properties (e.g., viscosity,
`freezing point), it is the most widely used missile fuel.
`However, its mission capability is limited by the extent to
`which it can be used as the primary coolant in a vehicle
`thermal management system. The benefits for expanding
`this mission capability through the development of the
`endothermic potential of JP-10 are therefore clear.
`
`American Institute of Aeronautics and Astronautics
`
`GE-1027.004
`
`

`
`Experimental Apparatus
`The high-pressure bench-scale test apparatus is
`shown schematically in Figure 1. Fuel is introduced
`into the reactor at supercritical pressure using a flow
`control system with a high-pressure fuel reservoir. The
`tests were run with or without a fuel preheater,
`depending on what types of heat sink data were sought.
`For determining the physical heat sink from ambient to
`1000 F, the preheater was turned off. For all tests
`involving endothermic reactions (i.e., > -1000 F), the
`fuel was first preheated to approximately 700 F
`(supercritical) in order to reduce the reactor length
`requirement.
`
`Fuel reservoir
`
`Control volume
`
`Back-pressure
`regulator
`
`Figure 1: Bench-Scale Reactor Test Rig
`Resistive heating was used to allow a direct
`measurement of the overall heat sink capacity of the
`fuels by performing an energy balance on the control
`volume depicted in Figure 1. With this method, heat is
`supplied by the imposition of an electric current
`through the reactor tube itself. The electrical power
`input, Qi„, is converted to heat and transferred to the
`fuel on the inside of the reactor and, by natural
`convection, to the environment on the outside. The
`portion of heat lost to the environment through natural
`convection, Qenn is minimized by insulation and
`accounted for through multi-point calibrations without
`fuel flow prior to a given test. (The heat losses were in
`the range of 3 to 8 percent of the total power input,
`depending on the reactor wall temperatures and fuel
`flowrate.) The overall heat sink of the fuels, Qsmk, can
`be computed by
`
`where H-mk, and Hexil are the fuel enthalpies at the reactor
`inlet and exit, respectively, and ril the fuel mass flowrate.
`The overall heat sink of fuel (QSM) can be further divided
`into that which results in raising the temperature of the
`fuel/products (sensible heating, AHsens) and that which is
`absorbed in the reaction (endotherm, AHe„do). The net
`endotherm can then be computed as
`MIend0=(Hex„-Hinle,)-MI;
`
`(3)
`
`and sensible heat sink computed as a function of the fuel
`temperatures measured at the reactor inlet (Tj„iet) and exit
`(Texu)- For the purpose of sensible enthalpy calculation, the
`fuel composition is treated as constant.
`
`All reactors were coated with an inexpensive
`zeolite cracking catalyst using a ceramic-like binder. In
`addition to the fuel temperature measurements at the
`reactor inlet and exit, the fuel pressures were also
`measured at the reactor inlet and exit to correlate reactor
`performance. A differential pressure gauge was used to
`measure and track-in-time the reactor pressure drop, which
`is indicative of coke deposition. Since the coated-wall
`reactor tubes were generally small diameter to simulate
`practical heat exchanger reactor passages, only tube outer
`wall temperatures were measured along the reactor.
`Downstream of the reactor, the products were quenched in
`a water-cooled heat exchanger and the liquid and gaseous
`products were collected in an on-line biphase sample
`collector for compositional analysis. The liquid and
`gaseous components were separated and analyzed using
`both a cryocooled Hewlett Packard Gas
`Chromatograph/Mass Spectrometer system and a fast-
`response MTI Micro Gas Chromatograph.
`
`To determine the extent of carbon deposition, the
`reactor tubes were removed from the rig at the test
`completion, rinsed with hexane and dried in a vacuum
`oven. The tubes were then cut into 2-in. lengths and the
`carbon accumulated in each section was assessed using a
`LECO RC-412 Carbon Determinator which quantifies
`carbon deposition by measuring carbon dioxide produced
`in a controlled carbon burn-off.
`
`Results And Discussion
`(!) Fuel Heat Sink
`The overall heat sink (i.e., physical + chemical)
`and estimated endotherms (chemical only) of JP-7, JP-
`8+100, JP-10 and a reference fuel, n-octane, are shown in
`Figures 2-5. The sensible enthalpy changes of the fuels
`were estimated using the NIST computer program
`SUPERTRAPP. The SUPERTRAPP computations were
`carried out based on the temperature measurements at the
`reactor inlet and exit, and the fuel simulations in Table 1.
`
`t^sink z£in z^e)
`
`Thermodynamically, the cooling capacity is
`defined as an enthalpy change of fuel between the inlet
`and exit. The enthalpy change can be calculated by
`
`H„ Hir
`
`m
`
`(2)
`
`American Institute of Aeronautics and Astronautics
`
`GE-1027.005
`
`

`
`The test conditions are described in Table 2. As
`mentioned above, the wall temperatures were measured
`along the reactor and the data showed similar wall
`temperature distributions for different fuels. The peak
`wall temperatures were located about 1 to 2 inches from
`the exit (due to wall conduction), and found to be 100
`to 150 F higher than exit fuel temperatures. All the tests
`were run to the maximum operating temperatures where
`the tests were limited by coking deposition. The overall
`heat sink data at the highest temperature for each fuel in
`Figures 2-5 represent a short-duration test with
`subsequent reactor plugging at that temperature.
`Therefore, these highest temperature points should not
`be used for design purposes.
`
`Table 2: Test Conditions
`
`E 400
`"3
`
`Parameter
`Catalyst coatinq
`Pressure
`Fuel flowrate
`LHSV
`
`Condition
`
`zeolite
`600 psia
`4.8 lbm/hr
`3000 1/hr
`
`-"
`0 * .-"""
`
`,•*"'"'
`
`.... -• -•- ."•"
`
`- Data I :
`PJiyslcall :
`
`0 200 «0
`
`1000 1200 1400 1600 1800
`
`Comparison of the total heat sinks (on a mass
`basis) among these fuels at the flow conditions tested
`indicates that:
`
`• There are no significant differences in physical heat
`sink among these fuels, except for JP-10, which has
`slightly lower physical heat sink on a mass basis than
`the other fuels.
`
`lwWntetl
`
`"*• '
`
`•'...
`
`.~ /•
`
`• Data :
`Physical 1
`
`1200 1400
`
`I 400
`
`m
`i"
`
`V ***
`
`,-# a»*
`
`1000 1100
`
`1200 1300 1400 1500 1600
`
`Tibet, F
`
`Figure 3: Heat Sink of JP-8+100
`
`a
`^ .... "
`
`1 15-mln. \
`|caktng last]
`
`r.-*'
`
`.-.•
`
`'
`
`I ■ Data I
`I—Physical |
`
`0 200 400 600 800 1000 1200 1400 1600
`Tfuel, F
`
`JL
`
`1300
`Tfuel, F
`
`1300
`
`Tfuel. F
`
`1400 1500
`
`Figure 2: Heat Sink of JP-7
`
`Figure 4: Heat Sink of JP-10
`
`• At a given temperature, JP-7 has the highest overall
`heat sink, followed by n-octane and JP-8+100. JP-10 has
`the lowest heat sink.
`
`• Compared to JP-8+100, JP-7 has the lower coke
`formation rate, probably due to its low olefin, low
`
`American Institute of Aeronautics and Astronautics
`
`GE-1027.006
`
`

`
`Gaseous and Liquid Products Analysis
`The GC analysis results of the gaseous product
`samples taken at 5 min. for JP-8+100, JP-10, and n-octane
`at the temperatures listed in Table 3 are shown in Figure 6.
`Although the primary species of gaseous products obtained
`are the same with all the fuels tested, differences in the
`species distributions among the fuels are quite significant.
`The GC/MS chromatographs of the JP-8+100 liquid
`product samples are illustrated in Figure 7. Comparisons
`between the unreacted and reacted fuel liquid products
`show substantial shifts in the composition to lower
`molecular weight species in all the tests. The analyses also
`indicate that no species with molecular weights higher than
`those of the unreacted fuel components were being formed
`as a result of the reaction. Chromatographs of the liquid
`product samples for the other fuels (namely, JP-7, JP-10,
`and n-octane) were observed and the results indicate
`similar substantial shifts to lower molecular weight
`species.
`
`Table 3: Summary of the 15-min. Tests
`JP-10
`15
`1286
`1120
`233
`13.2
`
`JP-7
`15
`1334
`1468
`462
`14.1
`
`JP-8+100
`15
`1282
`1250
`354
`9.9
`
`Fuel
`Runninq time, min
`Tfuel(exit), F
`Tolal heat sink: H - H(77F), Btu/lbm
`Endothemn. Btu/lbm
`Total coke deposition, mg
`
`n-Octane
`15
`1205
`1072
`176
`6.4
`
`[coking l«rj
`
`/
`
`••*
`
`_.^-
`
`^.- -•-
`
`200 400
`
`| • Data |
`j Physical 1
`
`1000 1200 1*» 1600
`
`§ 300
`
`? 500
`
`1300
`
`Tfuel. F
`
`Figure 5: Heat Sink of n-Octane
`aromatics, low sulfur, and/or high cyclo-paraffinic
`contents. Therefore, JP-7 can operate at the higher
`temperature and provides the higher heat sink.
`
`• JP-8+100 has slightly lower endotherm than that of
`n-octane or JP-7 at the same temperatures due to its
`higher aromatics content. Aromatics are not cracked
`(thermally or catalytically) under the conditions tested.
`The chemical heat sink (endotherm) and
`physical properties are a function of product
`distribution. Furthermore, the extent to which the
`benefits of the endothermic technology can be realized
`is directly related to our ability to mitigate against coke
`formation. Therefore, tests with durations simulative of
`a high-speed flight mission (15 min.) were conducted at
`constant temperatures for each of the fuels. During
`these 15-min. tests, gaseous and liquid product samples
`were collected at the 5-min. point for composition
`analysis. Also, the reactor tube was removed from the
`rig at the completion of each test for coke deposition
`assessment. The running temperatures of the extended-
`duration tests were selected to be approximately 100-
`150 F below the highest temperatures achieved in the
`heat sink tests to permit running the extended-duration
`tests without flow restriction. The test conditions and
`key results are summarized in Table 3. The single-point
`heat sinks of the fuels in the extended-duration tests for
`coking deposition assessment were also illustrated in
`Figures 2-5 and labeled as "15-min. coking test". The
`detailed results of these tests are discussed below.
`
`CH4 C2H4 C2H6 C3H6 C3H8 C4H8 C4H10
`
`Figure 6: Gaseous Products of Reacted Fuels
`
`Coke Deposition
`The principal heat exchanger operability issue that
`will affect fuel cooling capacity is coke formation. The
`coke deposition on the surface of the heat exchanger can
`degrade its performance by increasing both thermal
`resistance and fuel pressure drop. More critically, the coke
`deposition may lead to system failure by blocking the fuel
`passages. To address these concerns, 15-min tests were
`conducted at a constant test condition.
`
`The coke deposit distributions along the reactor
`for the fuels tested are illustrated in Figure 8. In general,
`the coke deposition increases with increase in fuel and wall
`
`American Institute of Aeronautics and Astronautics
`
`GE-1027.007
`
`

`
`UnreactedJP-8+100
`Liquid Products
`
`dodecane
`undecane
`
`tridecane
`
`15 20 25
`Retention Time
`Figure 7: JP-8+100 Liquid Products
`
`• Substantial endotherms are achievable with JP-7 and
`JP-8+100 using inexpensive zeolite catalysts in
`representative-size passages.
`
`• Under the same temperatures, there are no significant
`differences in physical heat sink among the liquid
`hydrocarbon fuels of JP-7, JP-8+100, and n-octane. JP-10
`shows a slightly lower physical heat sink on a mass basis
`than the other fuels.
`
`• Although the JP-10 provided an attractive heat sink, its
`high carbon-to-hydrogen ratio leads to significant coking
`problems and potential poisoning of the catalyst, even at
`relatively low temperatures.
`
`Acknowledgment
`
`• JP-7 (1334 F)
`*JP-8*100(1282F)
`* rvocUm (1205 F)
`■JP-10(12B6F>
`
`m #
`« • : ;
`
`•
`
`t
`
`I
`
`«
`
`.
`•
`
`Axial Position, x/L
`
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`This paper is based on work performed for the Air
`Force Research Laboratory, Propulsion Directorate under
`Contract F33615-97-D-2784, administered by Dr. Tim
`Edwards of the Fuels Branch, Turbine Engine Division.
`This work was partially funded by the NASA Advanced
`Propellants program, managed by Mr. Michael L. Meyer of
`NASA/Glenn Research Center. The authors gratefully
`acknowledge the test support provided by Mr. David
`McHugh.
`
`Figure 8: Coke Deposition Distribution
`temperatures. As shown in Figure 8, the maximum coke
`depositions in the reactors for all the fuels tested are in
`the range of 0.4 to 1.6 mg/cm2, equivalent to 8 to 33 \x.m
`of coke thickness (assuming coke density of 1 g/cm3 of)
`on the inside wall of the tube, representing less than a 5
`percent restriction of the flow cross-sectional area at the
`point of maximum coke build-up under the indicated
`test conditions.
`
`Conclusion
`Storable liquid hydrocarbon fuels, such as JP-7
`and JP-8+100, that undergo endothermic reactions can
`provide sufficient heat sink to enable hypersonic flight
`without having to resort to cryogenic fuels. The
`endothermic heat sink capacities of the fuels (viz., JP-7,
`JP-8+100, and JP-10) were demonstrated under
`operating conditions simulative of hypersonic scramjet
`cooling applications. Performance evaluations were
`primarily based on overall heat sink (including
`endotherm) measurements and coke deposition. The
`results are directly applicable to tine selection of fuels
`and the design of fuel-cooled thermal management
`systems for hypersonic vehicles.
`Based on the results of the current research,
`the following specific conclusions may be made:
`
`References
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`American Institute of Aeronautics and Astronautics
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`
`

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`7
`American Institute of Aeronautics and Astronautics
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