Efficient utilization of heat sink of hydrocarbon fuel for regeneratively cooled scramjet

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Applied Thermal Engineering 33-34 (2012) 208e218

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Applied Thermal Engineering

journal homepage: www.elsevier .com/locate/apthermeng

Efficient utilization of heat sink of hydrocarbon fuel for regeneratively cooledscramjet

Wen Bao, Xianling Li, Jiang Qin, Weixing Zhou, Daren Yu*

School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, PR China

a r t i c l e i n f o

Article history:Received 20 May 2011Accepted 28 September 2011Available online 6 October 2011

Keywords:Heat sinkHydrocarbon fuelChemical reactionHeat transferScramjet

* Corresponding author.E-mail address: [email protected] (D. Yu).

1359-4311/$ e see front matter � 2011 Elsevier Ltd.doi:10.1016/j.applthermaleng.2011.09.036

a b s t r a c t

Heat sink (cooling capacity) of limited hydrocarbon fuel is not rich for the regenerative cooling ofscramjet. It is therefore very important to use the heat sink of fuel efficiently. This paper focuses on theeffect of operating conditions of cooling system on the heat sink use of hydrocarbon fuel. Consideringthe coupling among flow, heat transfer and chemical reaction, a one-dimensional model is developed toevaluate the heat sink use of endothermic hydrocarbon fuel. The model is validated by comparing thecalculated results with the experimental data measured through an electrical heating flow reactor, inwhich thermal cracking takes place for n-decane. Using the developed model, the effect of maximumallowable temperature of metal wall material, flow velocity and uneven heat flux distribution ofscramjet has been evaluated by simulating some typical operating conditions, and some conclusions aredrawn to assist the fundamental understanding of heat sink use of endothermic hydrocarbon fuel. It isbelieved that the present investigation will provide a useful reference for the design of cooling systemof scramjet.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Supersonic combustion ramjet (scramjet) is an advanced pro-pulsion plant which usually works in high Mach number region(Ma � 5) and provides power for hypersonic air-breathing flightvehicles [1,2]. Thermal protection is a key element for successfulscramjet applications. For example, the total temperature ofexternal air of scramjet reaches a temperature as high as 4950 K atMa 12, so the metal material of engines could not withstand sucha high temperature [3,4]. Since the carriage of special coolantwould result in enormous mass and volume penalties, regenerativecooling using hydrocarbon fuel as a coolant has been considered asone of the most efficient cooling methods. In this way, hydrocarbonfuel flows through the cooling channel to cool the engine wallbefore it is used for combustion [5e7].

However, scramjet is reaching a practical heat transfer limitbeyond which physical heat sink (cooling capacity) provided by thesensible heat transfer of fuel is no longer adequate. One solution isto use chemical heat sink obtained from an endothermic hydro-carbon fuel, which absorbs heat through chemical reactions [8,9].Then, a large number of investigations have been conducted to

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increase the chemical heat sink of fuel by adding catalysts orinitiators [10e12]. Although endothermic reaction can be used tofurther increase the heat sink potential by providing additionalchemical heat sink, the total quantity of heat sink is still not richenough. For instance, previous studies have indicated that the flowrate of coolant will exceed the stoichiometric flow rate during theflight at a speed above a certain Mach number [13,14]. This meansthat the heat sink of fuel may be even insufficient. Considering theenormous mass and volume penalties, it is unexpected to carrymore fuel for cooling, and this is why many studies focus on themethods which can be used to increase the chemical heat sink offuel. Besides the aspect for increasing heat sink of fuel, it is also veryimportant to use the limited heat sink of fuel efficiently. Forexample, some work has been done to improve the use of heat sinkof fuel by inhibiting coking to increase the allowable temperature ofhydrocarbon fuel [15].

For the purpose of efficient use of heat sink, it is necessary to getthe laws governing the use of heat sink under different operatingconditions. Operating temperature of fuel affects the use of heatsink of hydrocarbon fuel, but it is not enough to correlate thetemperature of fuel with the use of heat sink only, because there isa strong coupling among chemical kinetics, flow and heat transferunder supercritical conditions [8,16,17]. More specifically, thevariation in the chemical composition of a flowing hydrocarbonfuel affects the flow and heat transfer of fuel by changing the

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Nomenclature

A pre-exponential factor, s�1

Ab base area of unit length of cooling channel, mACS effective cross-sectional area of metal wall of cooling

channel, m2

Af fin surface area of unit length of cooling channel, mAinner inner wall surface area per unit length of cooling

channel, mAt overall surface area for unit length of cooling channel,

mC specific heat of metal wall material, J/kg/KCp constant-pressure specific heat of hydrocarbon fuel, J/

kg/Kd hydraulic diameter of cooling channel, mEa activation energy, J/molf friction factorh specific enthalpy, J/kgH distance between non-heated surface of cooling

channel and hot gas, mmk reaction rate, s�1

L length of cooling channel, mM metal wall mass per unit length of cooling channel, kg/

mNu Nusselt numberp pressure, PaPr Prandtl numberq heat flux generated by engine, W/m2

qf heat flux between fluid and inner wall surface ofcooling channel, W/m2

Qw heat absorbed per unit length metal wall of coolingchannel, W/m

R universal constant, J/mol$KRe Reynolds numbert time, sTf bulk fuel temperature, KTw metal wall temperature, Ku flow velocity, m/sx axial coordinate, mY mass fraction of cracking product/mass conversion of

fuela heat transfer coefficient, W/m2/Kd absolute roughness, mdb width of channel base, mmdr width of channel fin, mmdw wall thickness between hot gas and coolant, mmhf fin effectivenessht overall fin surface efficiencyl thermal conductivity of hydrocarbon fuel, W/m/Klw thermal conductivity of metal wall material, W/m/Kmf fuel dynamic viscosity at bulk fuel temperature, Pamw fuel dynamic viscosity at metal wall temperature, Pa sr fuel density, kg/m3

Subscriptsx ¼ 0 at inlet of cooling channelt ¼ 0 at initial timex ¼ L at outlet of cooling channel

W. Bao et al. / Applied Thermal Engineering 33-34 (2012) 208e218 209

properties of fuel, such as density, dynamic viscosity and so on.Meanwhile, the flow and heat transfer in the cooling channel alsoaffect the chemical reaction by reaction time and reaction rate. Thestrong coupling will determine the ultimate use of chemical heatsink. Therefore, an in-depth study on the heat sink use of hydro-carbon fuel is necessary by taking into consideration the couplingamong flow, heat transfer and chemical reaction. Based on theunderstanding above, the specific motivations of this paper aregiven in section 2.

2. Motivations

The cooling system of scramjet can be considered as a heatexchanger, and its operating conditions provide some specificconstraints that limit the use of heat sink by affecting the flow, heattransfer and chemical reaction of fuel. Then, the following are thespecific aspects of operating conditions of cooling system whichneed to be taken into consideration.

1) The temperatures of metal wall and fuel can not exceed themaximum allowable temperature of metal wall material(MATMWM), otherwise the metal material will melt. There-fore, MATMWM restricts the use of heat sink by imposing anupper limit on the temperature rise of fuel.

2) The temperature difference between flowing fuel and metalwall of cooling channel is indispensable for the convective heattransfer of fuel. When MATMWM is fixed, the temperaturedifference will further limit the temperature rise of fuel. It isbeneficial for the use of heat sink to increase the flow velocityto enhance heat transfer, since the temperature difference forconvective heat transfer can be reduced by increasing heattransfer coefficient. Nevertheless, increasing flow velocity

will reduce residence time, which is not conducive to the useof chemical heat sink. The two conflicting effects exist simul-taneously, so the effect of flow velocity on the use of heat sinkbecomes complex.

3) Scramjet has an uneven heat flux distribution, which even hasa peak with 10w20 times higher than the lowest value. Theuneven heat flux distribution determines the heat transferalong the flow path of fuel in the cooling channel, which affectsthe chemical reaction of fuel through the reaction rate deter-mined by the fuel temperature. Meanwhile, the heat transferaffects the flow of fuel by changing the properties of hydro-carbon fuel, and the flow will further affect the chemicalreaction through reaction timewhich is also the residence timeof fuel in the cooling channel. Thus, it is necessary for the use ofchemical heat sink to consider the uneven characteristic of heatflux distribution.

Considering the three aspects above, this paper focuses on theeffect of MATMWM, flow velocity and uneven heat flux distributionon the heat sink use of hydrocarbon fuel. A one-dimensional model,which considers the coupling among flow, heat transfer andchemical reaction, is developed to evaluate the use of heat sink ofendothermic hydrocarbon fuel as follows.

3. Modeling of cooling process of endothermic hydrocarbonfuel in scramjet

The model of the cooling process of endothermic hydrocarbonfuel in scramjet consists of three parts: hydrocarbon fuel flowaccompanied by heat transfer and chemical reaction in coolingchannel, heat flux boundary provided by scramjet, boundary andinitial conditions.

Fig. 2. Rectangular cross-section of single cooling channel.

W. Bao et al. / Applied Thermal Engineering 33-34 (2012) 208e218210

3.1. Modeling of hydrocarbon fuel flow accompanied by heattransfer and chemical reaction in cooling channel

Cooling channel with a rectangular cross-section is usually usedfor the thermal protection of scramjet. Fig. 1 gives a schematicdiagram of scramjet to illustrate how the heat flux generated by theengine is injected into hydrocarbon fuel through the metal wall ofcooling channel. Fig. 2 gives a schematic diagram of the rectangularcross-section of a single cooling channel. Assuming that the flow ofcoolant in the cooling channel is one-dimensional, the coolingprocess of endothermic hydrocarbon fuel in scramjet can bemodeled based on the assumption that the following factors can beignored:

1) Variations of fuel properties and flow velocities in the radialdirection;

2) Kinetic energy and heat generated by the viscous effect ofhydrocarbon fuel;

3) Gravitational energy of hydrocarbon fuel;4) Axial heat conduction of hydrocarbon fuel;5) Radial temperature difference between inner surface and outer

surface of metal wall of cooling channel.

In order to avoid phase change and improve heat transfer, it isnecessary to maintain a supercritical pressure for hydrocarbon fuel.Although a sharp phase transformation does not occur undersupercritical pressure, physical properties such as density, specificheat and thermal conductivity can change substantially. Thespecific description of hydrocarbon fuel flow accompanied by heattransfer is given as follows.

Mass conservation equation can be expressed as

vr

vtþ vru

vx¼ 0 (1)

With hydraulic diameter d used to characterize the coolingchannel, energy conservation equation can be given by

v

vtðrhÞ þ v

vxðruhÞ ¼ 4

d$qf (2)

Heat flux qf injected into hydrocarbon fuel through the metalwall of cooling channel can be expressed as

qf ¼ a$�Tw � Tf

�(3)

Heat transfer coefficient a can be given by

a ¼ l

d$Nu (4)

Fig. 1. Schematic diagram of scramjet with cooling channel.

Up to now, there is no heat transfer correlation of hydro-carbon fuel under supercritical pressure which is generallyacknowledged, especially under the operating condition withchemical reaction. In this paper, a heat transfer correlation isadopted as

Nu ¼

8><>:

0:027$Re0:8$Pr0:333$�mfmw

�0:14

Tf � 800 K

0:024$Re0:83$Pr0:4$�mfmw

�0:1

Tf>800 K

(5)

Eq. (5) is obtained according to reference [18] and the modifi-cations based on the measured data at the experimental facilityshown in section 4.1. Re and Pr in Eq. (5) are expressed as

Re ¼ jruj$dm

(6)

Pr ¼ Cpml

(7)

Wall temperature Tw can be determined by

C$M$vTwvt

¼ Qw � qf $Ainner þ lw$ACS$v2Twvx2

(8)

where Qw can be given by

Qw ¼ q$ðdr þ dbÞ (9)

Effective surface area Ainner in Eq. (8) can be expressed

Ainner ¼ Atht (10)

where ht is the overall fin surface efficiency, and At is the overallsurface area for unit length of cooling channel, including the finsurface area of unit length of cooling channel (Af) and the basearea of unit length of cooling channel (Ab). They can be calculatedby

At ¼ Af þ Ab (11)

Af ¼ 2$ðH � dwÞ; Ab ¼ db (12)


ht ¼ Ab þ hf Af (13)
Ab þ Af
Fin effectiveness hf in Eq. (13) can be expressed as

hf ¼ thðmH0ÞmH0 (14)

m ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2a=lwdr

q; H0 ¼ ðH � dwÞ þ dr=2 (15)

Momentum conservation equation can be expressed as

v

vtðruÞ þ v

vxðjruj$uÞ ¼ �vp

vx� 12$fd$ðjruj$uÞ (16)

where expression jruj$u instead of ru2 is used to reflect themomentum direction of fluid flow. Friction coefficient f can begiven by

f ¼( 64=Re Re � 2320

0:11$�d

dþ 68

Re

�0:25

Re>2320(17)

There are different kinds of hydrocarbons, such as alkanes,cycloalkanes, benzenes and so on. As a typical long straight chain n-alkane, n-decane (C10H22) is used to run the present investigation. Itis one of the main ingredients of China NO.3 aviation kerosene [7].The chemical reaction of hydrocarbon fuel mainly includes thermalcracking, catalytic cracking, induced cracking and so on. Thermalcracking usually occurs at a fuel temperature above approximately500�S, and it is a promising endothermic reaction, especially in thestage of mild thermal cracking [8]. Thermal cracking is relativelysimple to use, because there is no any need to add catalyst andinitiator which are indispensable for catalytic cracking and inducedcracking respectively. Considering the characteristics above, thispaper focuses on the investigation of thermal cracking of n-decane.

Strictly speaking, thermal cracking of hydrocarbon fuel is nota true first order reaction process. However, supercritical-phasethermal decomposition of n-alkanes can be represented well byan apparent first order kinetics [16,19,20]. Global chemical mech-anism, without any need to know detailed reaction pathwayswhich are generally unavailable for high carbon number n-alkane,is practical for flow simulation [8]. Using a first-order chemicalkinetics and a global chemical mechanism, the conservationequation of cracking products for n-decane can be expressed as

v

vtðrYÞ þ v

vxðruYÞ ¼ r$ð1� YÞ$k (18)

Fig. 3. Product mass fraction

where Y is the mass fraction of thermal cracking products. Takinginto account the conservation of mass before and after reaction, Ycan also be considered as mass conversion of reactant. In addition, kis the reaction rate, and according to Arrhenius expression, it can beexpressed as

k ¼ A$e�Ea=RTf (19)

As shown in Fig. 3, by ignoring some minor ingredients, anaverage cracking product distribution is obtained for n-decanebased on themeasured results at the experimental facility shown insection 4.1. It is necessary to indicate that, due to the limitation ofexperimental conditions, the present mass conversion of fuel is lessthan 40%. Previous thermal cracking experiments indicate that theproducts form at constant proportions with respect to the otherproducts [8,16]. Thus, this paper predicts the cracking products bytaking the advantage of the characteristic of proportional productdistribution and assuming that the products of n-decane form atconstant proportions as given in Fig. 3.

Since there are twenty-one equations and twenty-sevenunknown variables in above sections, it is necessary to add sixadditional equations to form a complete system. These supple-mentary equations representing the properties of hydrocarbon fuelcan be expressed as

p ¼ pðr;h; YÞ; tf ¼ tf ðr; h; YÞ (20)

mf ¼ m�p; Tf ; Y

�; mw ¼ mðp; Tw; YÞ; l ¼ l

�p; Tf ; Y

�Cp ¼ Cp

�p; Tf ; Y

�(21)

The properties of n-decane above are obtained through calcu-lations using software Aspen Plus, with the effect of chemicalreaction on properties reflected by incorporatingmass conversion Yinto these supplementary equations. Aspen Plus is a popular soft-ware with several databases containing physical, chemical, andthermodynamic data for a wide variety of chemical compounds aswell as thermodynamic models, and it has been widely used forsimulations of chemical systems. Through the calculations ofproperties, a database considering the decomposition of n-decaneis formed, and can be called whenever it is necessary to runsimulations.

3.2. Heat flux boundary provided by scramjet

The heat absorbed by hydrocarbon fuel is generated byengine, so heat flux can be considered as a boundary for theoperation of cooling system. Compared with the inlet, isolator,

distribution of n-decane.

Fig. 4. Heat flux distribution along combustor for operating condition of Ma 6.


and nozzle of scramjet, combustor has the highest heat fluxdistribution, and this paper chooses the heat flux of combustor asboundary to investigate the cooling process of hydrocarbon fuel.As shown in Fig. 4, a typical heat flux distribution for the oper-ating condition of Ma 6 is presented based on the experimentaldata measured from a combustor, which is part of the direct-connected wind tunnel facility of Hypersonic TechnologyResearch Center of HIT. The characteristic of heat flux shown inFig. 4 has a strong representation for other operating conditions,although the magnitude and the spatial location of heat flux peakcan vary with different operating conditions. To simplify theanalysis, all the calculations in section 5 are based on the heatflux distribution shown in Fig. 4.

3.3. Boundary and initial conditions

Cooling channel can be regarded as a hydrodynamic system,and then a kind of boundary conditions commonly used for thesimulations of hydrodynamic systems are employed to solve theproposed model. The detailed boundary conditions include themass flow flux at the inlet of cooling channel (ru)x¼0, the fuel

Fig. 5. Electrical heating experimental

temperature at the inlet of cooling channel Tx¼0, the fuel massconversion at the inlet of cooling channel Yx¼0, the pressure at theoutlet of cooling channel px¼L and the wall temperature at the inletof cooling channel (Tw)x¼0.

The initial conditions are determined on the basis of the fuelflow state at the start time of the simulation. Assuming that theinitial states are at t ¼ 0, there are five initial conditions needed tobe given. They are initial axial density distribution rt¼0, initial axialmass flow flux distribution (ru)t¼0, initial axial distribution of(rh)t¼0, initial axial wall temperature distribution (Tw)t¼0 and initialfuel mass conversion distribution Yt¼0. All these initial conditionsare given in the form of vectors, and are different from boundaryconditions which consist of scalars.

In this paper, a time-marching method, which means that thesteady state can be reached as long as time is long enough, is usedto obtain the steady state for a given operating condition, and theanalyses for the use of heat sink will be performed based on theobtained steady-state results.

4. Model validation

Three aspects of the present model need to be validated. Thefirst one is the heat transfer with substantial changes in the prop-erties of hydrocarbon fuel. It can affect the heat sink use of fuel bydetermining the temperature difference between metal wall andfuel, when MATMWM is fixed. The second one is the total heat sink(composed of physical and chemical heat sink) and the massconversion of fuel (representing chemical heat sink), which are thecore indexes used for the evaluation of heat sink use. The last one isthe ability of the model to reflect the coupling among chemicalreaction, flow and heat transfer, which is the basic feature ofendothermic reaction of a flowing hydrocarbon fuel. The coolingchannel with hydrocarbon fuel flowing through is essentially a tubewith heat injected into, and so, the present model can be validatedby comparing the calculated results with the experimental dataobtained at an electrical heating tube facility.

4.1. Experimental facility

As shown in Fig. 5, a coriolis-type mass flow meter is used tomeasure the mass flow rate flowing through the reactor tube,which is used to simulate the cooling channel of engine. The reactor

system used for model validation.

Fig. 7. Variation of total heat sink and mass conversion of fuel with outlet fuel


tube, heated electrically by passing a direct current through itself, isa circular tube made of 1Cr18Ni9-type stainless steel. The innerdiameter and wall thickness of the test section are 1 mm and0.5 mm respectively. Heat sink of fuel can be calculated using thevoltage and current applied to the test section. The temperatureand pressure of fuel are measured at the inlet and outlet of reactortube via thermocouples and pressure transducers respectively. Thewall temperatures of reactor tube are measured through nine skinthermocouples spot-welded on the tube wall, which are equallyspaced along the test section. Behind the back pressure valve, a gaschromatograph (GC) with mass spectrometer (MS) is used toanalyze the compositions of cracking products. These facility andresearch instrumentation data are recorded on the facility’s datasystem at the rate of one sample per second.

Considering the measurement errors caused by K-type ther-mocouples, the data acquisition board of IMP and the radial loca-tion of thermocouple used for wall temperature measurement, theuncertainty for measured fuel temperature and wall temperatureare �0.58 K and �7.3 K respectively. Considering the measurementerrors of voltage and current, the uncertainty for heat sinkmeasurement is �6.5%. In addition, the uncertainty for massconversion measurement of fuel is �10%.

temperature.

4.2. Comparisons between calculated results and experimentalresults

Firstly, calculation results for heat transfer, total heat sink andmass conversion of fuel based on the proposed model arevalidated. The following are the operating parameters used for thepresent validation: L ¼ 1 m, d ¼ 1 mm, M ¼ 0.05 kg/m, C ¼ 510 J/kg/K. The five boundary conditions are (ru)x¼0 ¼ 1250 kg/m2/s,px¼L ¼ 3.5 MPa, Tx¼0 ¼ 285 K, Yx¼0 ¼ 0 and (Tw)x¼0 ¼ 285 K. A time-marching method is used to obtain the steady state, and then theinitial conditions can be given approximately. During the experi-ments, the electrical power is increased by changing the voltageand current applied to the reactor tube when all the other condi-tions are set. Some measured data are shown in Figs. 6 and 7, withthe corresponding calculated results given for comparison.

As shown in Fig. 6, under condition No. 1, outlet fuel tempera-ture is relatively lower and no chemical reaction occurs. Under

Fig. 6. Axial distribution of wall temperature and fuel temperature along reactor tube.

condition No. 2, a chemical reaction can be seen through the vari-ation trend of fuel temperature near the outlet of tube. As a whole,the calculated wall temperatures are in good agreement with themeasured ones under these two operating conditions. As shown inFig. 7, the total heat sink increases linearly until the fuel tempera-ture reaches 930 K. A rapid rise in the total heat sink appears whenthe outlet fuel temperature is higher than 930 K. The massconversion of hydrocarbon fuel also demonstrates a rapid risewhen the fuel temperature is higher than 930 K, which means thechemical reaction of hydrocarbon fuel occurs. As a whole, it can beseen clearly that the calculated total heat sinks and mass conver-sions are in good agreement with the measured ones.

If the residence time of fuel in the reactor tube varies while allthe other conditions remain unchanged, the chemical reaction willstill be affected, which can be seen through the variations of totalheat sink and mass conversion of fuel. This phenomenon reflects

Fig. 8. Variation of total heat sink with fuel temperature at outlet of tube.

Fig. 9. Variation of mass conversion with fuel temperature at outlet of tube.

Fig. 10. Axial distribution of fuel temperature.


the coupling among chemical reaction, flow and heat transfer.Based on the understanding, this section testifies the ability of themodel to reflect the coupling among chemical reaction, flow andheat transfer by changing the length of reactor tube to achievea different residence time. The following are the operatingparameters used for the present validation: d ¼ 1 mm,M ¼ 0.05 kg/m, C ¼ 510 J/kg/K. The five boundary conditions are(ru)x¼0 ¼ 1250 kg/m2/s, px¼L ¼ 3.5 MPa, Tx¼0 ¼ 285 K, Yx¼0 ¼ 0 and(Tw)x¼0 ¼ 285 K. Two reactor tubes are used for these experiments,one is 1 m long, and the other is 1.5 m long. The comparisonsbetween the calculated results and themeasured data are shown inFigs. 8 and 9.

As shown in Figs. 8 and 9, when other conditions are the same,the operating conditionwith 1.5m long reactor tube has a relativelyhigher total heat sink and mass conversion than that for theoperating condition with 1 m long reactor tube. That’s because therelatively longer reactor tube increases the residence time of fuelused for chemical reaction. Through the comparisons shown inFigs. 8 and 9, it can be seen that the calculated total heat sink andmass conversion of fuel are in good agreement with the measuredones, which indicate that the proposed model can reflect thecoupling among chemical reaction, flow and heat transfer well. Allthe validations above prove that the proposedmodel can be used toevaluate the heat sink use of hydrocarbon fuel for scramjet.

5. Evaluations and discussions

The effect of MATMWM, flow velocity and uneven heat fluxdistribution on the heat sink use of hydrocarbon fuel can be eval-uated through some typical operating conditions, which have the

Table 1Parameters used for simulations.

ConditionNo.

Massflow flux(kg/m2/s)

Fuel temperatureat inlet ofchannel (K)

Flow direction offuel in channel

dr/dw/H(mm)

1 850 285 From outlet to inletof combustor

1.2/1.2/2.4


1.2/1.2/2.4

use limit of heat sink. In subsequent calculations, these typicaloperating conditions are obtained by keeping other conditionsunchanged and reducing the mass flow rate of fuel so that thehighest wall temperature reaches MATMWM. Based on the heatflux boundary shown in Fig. 4, specific evaluations can be done asdetailed below.

5.1. Effect of MATMWM

Considering the use of nickel alloy for thewall material, 1100 K ischosen as MATMWM. Two operating conditions are simulated toshow the effect of MATMWM. One operating condition has thehighest wall temperature of 1100 K; the other one has the highestfuel temperature of 1100 K for comparison. The specific parametersfor the two simulations are listed in Table 1.

Fig. 11. Axial distribution of total heat sink and mass conversion of fuel.

Fig. 12. Minimum allowable mass flow flux and maximum fuel temperature versusMATMWM.


ConditionNo.

Flow velocityat inlet ofchannel (m/s)

Fuel temperatureat inlet ofchannel (K)


dr/dw/H(mm)

1 2.6 285 From outlet toinlet of combustor

1.2/1.2/1.8

2 0.65 285 From outlet toinlet of combustor

1.2/1.2/3.6


As shown in Fig. 10, the highest wall temperature reaches theMATMWM of 1100 K under operating condition 1. Under thiscircumstance, themass flow rate of fuel can not continue to reduce,otherwise the wall temperature will become too high and themetal material can melt. Under the operating condition, as shownin Fig. 11, the mass conversion of fuel can only reach 84.5%, whichindicates that not all the chemical heat sink can be used as a resultof the wall temperature constraint. Under operating condition 2, asshown in Fig. 11, the highest mass conversion still can not reach100% although the outlet fuel temperature has increased to 1100 K,which further demonstrates the necessity for evaluation of thelimit on the use of heat sink. In addition, it can be seen throughFig. 11 that chemical heat sink of fuel would play an important rolein a high temperature stage of fuel (corresponding to the spatialrange of 0 m� x� 0.44 m), since it can keep a rise in total heat sinkas shown in Fig. 11 with a slow rise in fuel temperature as shown inFig. 10 so that thermal protection would benefit from it. In order tofurther show the effect of MATMWM, some calculation results aregiven in Figs. 12 and 13 when MATMWM varies.

Fig. 13. Allowable use limit of heat sink and mass conversion versus MATMWM.

As shown in Fig. 12, the minimum allowable mass flow fluxdecreases as MATMWM increases, especially in the MATMWMrange of 1000 Ke1150 K. The decline of minimum allowable massflow fluxes indicate that heat sink has been usedmore efficiently byincreasing MATMWM. Meanwhile, the variations for maximumallowable fuel temperature shown in Fig. 12, maximum allowabletotal heat sink, maximum allowable physical heat sink andmaximum allowable mass conversion of fuel shown in Fig. 13 alsocome to the same conclusion. It should be pointed out in particularthat the increase of MATMWM from 1000 K to 1150 K will haveamost significant effect on the improvement of the use of heat sink,which can be seen through the rapid rise in total heat sink, physicalheat sink and mass conversion shown in Fig. 13.

5.2. Effect of flow velocity

When MATMWM remains unchanged, the temperature differ-ence between fuel and metal wall can be reduced by increasing theflow velocity of fuel to enhance the heat transfer, which is beneficialfor the use of heat sink of fuel. Meanwhile, it is also not conducive tothe use of heat sink since the residence time would be reduced bythe increasing flow velocity. By changing H only, two operatingconditions with the same mass flow rate at the inlet of channel aresimulated to show the effect of flow velocity on the use of heat sink.The specific parameters used for the two simulations are listed inTable 2, and some calculation results are given in Figs. 14e17.

As shown in Fig. 14, operating condition 1 has a relatively higherheat transfer coefficient than that for operating condition 2,

Fig. 14. Axial distribution of heat transfer coefficient.

Fig. 15. Axial distribution of fuel temperature.

Fig. 17. Maximum allowable mass conversion and physical heat sink versus flowvelocity at inlet of channel.


because the flow velocity at the inlet of channel is increased from0.65 m/s (under operating condition 2) to 2.6 m/s (under operatingcondition 1). Under the two operating conditions, both the highestwall temperatures reach the MATMWM of 1100 K. Under operatingcondition 1, the fuel temperature can rise higher than that underoperating condition 2, which can be seen through Fig. 15. Althoughoperating condition 1 has a relatively higher rise in fuel tempera-ture, the total heat sink still has no obvious increase; morespecifically, both operating conditions have just nearly the sametotal heat sink of 3.47 MJ/kg. In order to illustrate this result, theaxial distributions of flow velocity and reaction rate of fuel areplotted as shown in Fig. 16.

As shown in Fig. 16, under operating condition 1, the relativelyhigher reaction rate caused by the relatively higher fuel tempera-ture is beneficial for the occurrence of chemical reaction. However,the relatively higher flow velocity for operating condition 1reduces the residence time which is needed for the occurrence of

Fig. 16. Axial distribution of flow velocity and reaction rate of fuel.

chemical reaction. Combining the two conflicting effects, there islittle variation in the total heat sink under these two operatingconditions. The results indicate that the use of total heat sink cannot be necessarily improved by increasing flow velocity, althoughphysical heat sink can be increased by reducing the temperaturedifference of convective heat transfer between metal wall andflowing fuel. The results also demonstrate the coupling character-istic among chemical reaction, flow and heat transfer. In order toshow the effect of flow velocity more clearly, Fig. 17 gives thevariations of maximum allowable mass conversion of fuel andmaximum allowable physical heat sink with flow velocity. It can beknown through the two curves that the decrease in mass conver-sion and the rise in physical heat sink cause little variation in totalheat sink.

5.3. Effect of uneven distribution of heat flux

A temperature of 1100 K is still chosen as the MATMWM. Fouroperating conditions are simulated to show the effect of unevendistribution of heat flux, and specific parameters are listed inTable 3.

All the analyses in this section are based on the followingcomparisons: 1) comparison between operating condition 1 andoperating condition 2, which have different flow directions. 2)comparison between operating condition 1 and operating condi-tion 3, which have different flow directions and minimum allow-able mass flow fluxes. 3) comparison between operating condition3 and operating condition 4, which have different heat flux distri-butions. All the results of comparison are given in Figs. 18e21.


ConditionNo.

Mass flowflux(kg/m2/s)

Fuel temperatureat the inletof channel (K)


dr/dw/H(mm)


1.2/1.2/2.4

2 850 285 From inlet to outletof combustor

1.2/1.2/2.4


1.2/1.2/2.4


1.2/1.2/2.4

Fig. 18. Axial distribution of fuel temperature. Fig. 20. Axial distribution of heat flux.


As shown in Fig. 18, under operating condition 2, the fueltemperature at the outlet of channel is lower than that underoperating condition 1, and this phenomenon indicates that chem-ical reaction absorbs more heat under operating condition 2. Thevariation of flow direction essentially means the variation of thedistribution of heat flux. In order to further show the effect of heatflux distribution, Fig. 19 gives more typical comparison betweenoperating conditions 1 and 3. The highest wall temperatures underboth operating conditions reach MATMWM. The minimum allow-able mass flow flux under operating condition 3 is 40 kg/m2/ssmaller than that under operating condition 1, which indicates thatthe heat sink of fuel under operating condition 3 can be used moreefficiently. Obviously, this conclusion can also be drawn from thecomparisons for total heat sink and mass conversion of fuel shownin Fig. 19. It should be pointed out that the two curves for operatingcondition 3 shown in Fig. 19 have been reversed along the axiallocation of combustor for comparison.

A more general comparison is made between operating condi-tion 3 and operating condition 4. As shown in Fig. 20, there is an


even heat flux distribution under operating condition 4, and itsmagnitude is the average value of heat flux under operatingcondition 3. The highest wall temperatures under both operatingconditions 3 and 4 reach MATMWM. The minimum allowable massflow flux under operating conation 3 is 75 kg/m2/s smaller thanthat under operating condition 4, whichmeans that the heat sink offuel under operating condition 3 can be used more efficiently.Obviously, this same conclusion can also be drawn from thecomparisons for total heat sink and mass conversion of fuel shownin Fig. 21.

Through Figs.19 and 21, it can be seen that the most efficient useof heat sink is achieved under operating condition 3. A significantcharacteristic of operating condition 3 is that the fuel flows throughthe district with higher heat flux first, and then it can reachcracking temperature rapidly. So, there will be enough time for theoccurrence of chemical reaction, which means that it is beneficialfor the efficient use of heat sink to make the fuel flow through highheat flux district first.



6. Conclusions and prospects

Considering the coupling among flow, heat transfer and chem-ical reaction, this paper focuses on the effect of operating condi-tions of cooling system on the heat sink use of endothermichydrocarbon fuel. A one-dimensional model of cooling channelwith endothermic hydrocarbon fuel flowing through is proposedfor the evaluation of the use of heat sink. Through simulationsunder typical operating conditions, it can be seen that operatingconditions have significant impact on the heat sink use of hydro-carbon fuel. As a result of MATMWM constraint, the temperaturerise of hydrocarbon fuel is restricted, and then the mass conversionof fuel may be less than 100%, so not all the chemical heat sink canbe used under any conditions. The growth in flow velocity bringsabout improvement to the use of physical heat sink, but the use oftotal heat sink of hydrocarbon fuel has only little change, since theuse of chemical heat sink is reduced correspondingly. The unevenheat flux distribution of scramjet has its effect on the use ofchemical heat sink of hydrocarbon fuel, since a longer time can begot for the occurrence of chemical reaction as the hydrocarbon fuelflows through the high heat flux district of scramjet first, which canresult in a higher mass conversion of hydrocarbon fuel. In a word, itis necessary for the design of cooling system of scramjet to increaseMATMWM and make the hydrocarbon fuel flow through the highheat flux district of scramjet first to improve the use of heat sink ofhydrocarbon fuel.

A further evaluation for the use of heat sink needs to be done bytaking into consideration a change in heat flux boundary caused bythe cooling process. Under transient operating conditions, the useof heat sink of hydrocarbon fuel may be different from that understeady conditions, and it also needs to be investigated further.

Acknowledgements

The authors would like to acknowledge the support of theNational Science Funds for Distinguished Young Scholar of China,No. 50925625. The authors’ special thanks also go to Zhenjian JIA,Chaoyi DENG and Bin YU of Hypersonic Technology ResearchCenter of HIT for their help with the experiments.

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Efficient utilization of heat sink of hydrocarbon fuel for regeneratively cooled scramjet