http://ppr.buaa.edu.cn/

H O S T E D B Y

www.sciencedirect.com

Propulsion and Power Research

Propulsion and Power Research 2015;4(4):202–211

2212-540X & 2015 NaCC BY-NC-ND licenshttp://dx.doi.org/10.10

nCorresponding aut

E-mail address: m

Peer review under r

ORIGINAL ARTICLE

Model validation and parametric studyof fluid flows and heat transfer of aviationkerosene with endothermic pyrolysisat supercritical pressure

Keke Xua,b, Hua Menga,n

aSchool of Aeronautics and Astronautics, Zhejiang University, Hangzhou, Zhejiang 310027, ChinabCollaborative Innovation Center for Advanced Aero-Engine, Beijing 100191, China

Received 28 January 2015; accepted 15 June 2015Available online 28 November 2015

KEYWORDS

Supercritical pressures;Hydrocarbon fuel;Convective heat trans-fer;Fuel pyrolysis;Regenerative cooling

tional Laboratory foe (http://creativecom16/j.jppr.2015.10.00

hor. Tel.: þ86 571 8

enghua@zju.edu.cn

esponsibility of Nat

Abstract The regenerative cooling technology is a promising approach for effective thermalprotection of propulsion and power-generation systems. A mathematical model has been used toexamine fluid flows and heat transfer of the aviation kerosene RP-3 with endothermic fuel pyrolysis ata supercritical pressure of 5 MPa. A pyrolytic reaction mechanism, which consists of 18 species and 24elementary reactions, is incorporated to account for fuel pyrolysis. Detailed model validations areconducted against a series of experimental data, including fluid temperature, fuel conversion rate,various product yields, and chemical heat sink, fully verifying the accuracy and reliability of the model.Effects of fuel pyrolysis and inlet flow velocity on flow dynamics and heat transfer characteristics ofRP-3 are investigated. Results reveal that the endothermic fuel pyrolysis significantly improves the heattransfer process in the high fluid temperature region. During the supercritical-pressure heat transferprocess, the flow velocity significantly increases, caused by the drastic variations of thermophysicalproperties. Under all the tested conditions, the Nusselt number initially increases, consistent with theincreased flow velocity, and then slightly decreases in the high fluid temperature region, mainly owingto the decreased heat absorption rate from the endothermic pyrolytic chemical reactions.& 2015 National Laboratory for Aeronautics and Astronautics. Production and hosting by Elsevier B.V.

This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/).

r Aeronautics and Astronautics. Production and hosting by Elsevier B.V. This is an open access article under themons.org/licenses/by-nc-nd/4.0/).2

7952990.

(Hua Meng).

ional Laboratory for Aeronautics and Astronautics, China.

Model validation and parametric study of fluid flows and heat transfer 203

1. Introduction

In propulsion and power-generation systems, such as thescramjet and advanced gas turbine engines, the combustionchamber is exposed to high heat load from chemical reac-tions and aerodynamic heating. To ensure engine reliabilityand durability, the regenerative cooling technology, whichuses a hydrocarbon fuel as the coolant, is needed foreffective thermal protection [1,2].

During the regenerative cooling process, the engine fuelis circulated in micro cooling channels surrounding thecombustion chamber prior to fuel injection and burning,generally under supercritical pressures. As the fuel tem-perature increases and reaches the trans-critical region, itsthermophysical properties experience drastic variations andproduce strong influences on the supercritical-pressure fluidflows and heat transfer processes. In addition, as the fueltemperature further rises to around 750 K, thermal crackingof the fuel occurs, a phenomenon known as endothermicpyrolysis, which can further increase the heat-absorbingcapacity of a hydrocarbon fuel and benefit the subsequentcombustion process [3].

In the open literature, many experimental studies have beencarried out on high pressure pyrolysis of hydrocarbon fuels. Yuand Eser [4,5] studied thermal decomposition of C10-C14

normal alkanes and their mixture under near-critical andsupercritical conditions. A modified free radical mechanismwas proposed to explain the product yields, and a first-orderreaction mechanism was developed. Zhong et al. [6] conductedexperiments to analyze thermal cracking and heat-absorbingcapacity of RP-3 at supercritical conditions. Results showedthat the chemical heat sink of RP-3 varies with temperature,with a maximum value between 900 K and 960 K, dependingon the residence time. Abraham et al. [7,8] developed a real-time quantification infrared method to identify and quantify thepyrolytic products of hydrocarbon fuels. DeWitt et al. [9]studied the effect of fuel type on the pyrolytic reactivity anddeposition propensity under supercritical conditions. Jiang et al.[10] recently conducted a series of experiments using anelectrically heated micro tube to obtain variations of the localproduct concentrations and fluid temperature of RP-3. Adetailed reaction mechanism consisting of 18 species and 24chemical reactions was proposed to describe the endothermicfuel pyrolysis.

A number of numerical studies have also been carried outfor fundamental understanding of supercritical-pressurefluid flows and heat transfer of hydrocarbon fuels withpyrolysis. Sheu et al. [11] conducted numerical studieson thermal cracking of Norpar-13 under near- and super-critical conditions. A three-step lumped pyrolytic mechan-ism was employed to account for chemical reactions. Num-erical results showed that the endothermic pyrolytic reac-tions could effectively reduce the fuel and wall temperature.Ward et al. proposed a one-step proportional product distri-bution (PPD) model for thermal cracking of n-decane andn-dodecane [12] and investigated pressure effects on fluidflows and heat transfer of n-decane with mild thermal

cracking [13]. Zhu et al. [14] developed a similar globalreaction mechanism of n-decane and applied it for numer-ical studies. Ruan et al. [15] recently simplified the generalPPD model proposed by Ward et al. [12] by grouping thehigh-molecular-weight alkane or alkene species together,and applied the reduced reaction mechanism for efficientnumerical simulations of fluid flows and heat transfer of n-decane with endothermic pyrolysis.

In these existing studies, since simplified reaction mec-hanisms were used to account for the endothermic pyrolysisof hydrocarbon fuels, the numerical models are thus onlyapplicable for studying supercritical-pressure heat transferwith mild thermal cracking of the hydrocarbon fuels(generally less than 25% of fuel conversion). The applic-ability and accuracy of these models need further impr-ovement.

In this paper, a mathematical model has been used tostudy supercritical-pressure fluid flow and heat transfer ofthe aviation kerosene RP-3 with endothermic pyrolysis.A complete set of conservation equations of mass, momen-tum, energy, and species mass fractions are numericallysolved, with accurate calculations of thermophysical pro-perties. A detailed reaction mechanism of RP-3, whichcontains 18 species and 24 elementary reactions [10], isincorporated to account for fuel pyrolysis. Detailed modelvalidations are conducted against a series of experimentaldata, including the fluid temperature, fuel conversion rate,various product yields, and chemical heat sink. The modelis applicable over a wide range of operating conditions andis also capable of providing detailed and accurate numericalresults. Comprehensive numerical studies have been carriedout to analyze the effects of fuel pyrolysis and inlet flowvelocity on the supercritical-pressure fluid flows and heattransfer of RP-3 in a micro cooling tube under a constantwall temperature and at a supercritical pressure of 5 MPa.

2. Mathematical model

2.1. Conservation equations

In the present numerical study of fluid flows and heattransfer of RP-3 with fuel pyrolysis at a supercriticalpressure, the following conservation equations of mass,momentum, energy, and species mass fractions are solved:

∇∙ ρu-

� �¼ 0 ð1Þ

∇∙ ρu-u-

� �¼ �∇pþ ∇∙τ ð2Þ

∇∙ ρu-et

� �¼∇∙ λ∇Tð Þ�∇∙ pu

-� �

ð3Þ

∇∙ ρYi u-

� �¼ �∇∙ ρYi u

-d;i

� �þ Si ð4Þ

The relevant variables are defined in the nomenclature. Inthese equations, the effect of gravity on fluid flows and heattransfer is neglected because of the small size of the cooling

Nomenclature

C constant in the turbulent modelc heat capacity (unit: J/(kg �K))et total energy (unit: J/kg)Gk turbulent generation termk turbulent kinetic energy (unit: J/kg)p pressure (unit: Pa)S source term (unit: kg/(m3 � s))T temperature (unit: K)u velocity (unit: m/s)Y species mass fraction

Greek letters

ε turbulent dissipation rate (unit: m2/s3)

λ thermal conductivity (unit: W/(m �K))μ viscosity (unit: N � S/m2)ρ density (unit: kg/m3)σ turbulent Prandtl numberτ viscous stress tensor (unit: N/m2)

Subscripts

b averaged parameterd diffusioni speciesk turbulent kinetic energyp constant pressuret turbulent valueε turbulent dissipation rate

Keke Xu, Hua Meng204

tube. The viscous dissipation term is also neglected due tothe relatively low flow velocity. The source term, in Eq. (4),results from the endothermic pyrolytic chemical reactions.The standard k-ε turbulent model, along with an enha-

nced wall treatment, is employed to handle the turbu-lent fluid flows. The conservation equations are as follows:

∇∙ ρu-k

� �¼∇∙ μþ μt

σk

� �∇k

� ��ρεþ Gk ð5Þ

∇∙ ρu-ε

� �¼∇∙ μþ μt

σε

� �∇ε

� �þ C1

ε

kGk�C2ρ

ε2

kð6Þ

2.2. Pyrolytic reaction mechanism

The detailed pyrolytic chemical reaction mechanism ofRP-3 proposed by Jiang et al. [10] is used to take intoaccount fuel pyrolysis. It consists of 18 species and 24elementary reactions. A trace species in the reaction mech-anism, styrene, is ignored in the present model due to itsnegligible mass fraction (less than 1% in weight), andits mass is included in RP-3. Therefore, a total of 16 con-servation equations of species mass fractions are num-erically solved in the mathematical model.

2.3. Thermophysical property calculation

During the fluid flows and heat transfer process, thethermophysical properties of the fuel mixture undergostrong variations at supercritical pressures. Therefore, it’sa prerequisite to accurately calculate the variations withtemperature, pressure and species fractions. In our priornumerical studies [16–19], a general framework has beenestablished for this purpose. The extended correspondingstates principle is employed to calculate the thermodynamicand transport properties of the fuel mixture, with a purehydrocarbon fuel, propane, chosen as the reference material.The binary mass diffusivity at high pressures is evaluated in

two steps. First the empirical correlation proposed by Fuller[20] is applied to obtain the binary mass diffusivity at lowpressures, and then a simple corresponding state methoddeveloped by Takahashi [21] is used to taken into accountthe pressure effects.

Surrogate models suggested by Jiang et al. [10] for RP-3and the lumped products of C5þ, CC5þ, and CnH2n-6, aslisted in Table 1, are used in the present study for propertycalculations. The critical pressure and temperature of RP-3are around 2.3 MPa and 646 K, according to experimentalmeasurement [22]. The predicted critical pressure and temp-erature from the surrogate model are 2.21 MPa and 667 K.The relative errors are -3.9% and 3.6% for the criticalpressure and temperature, respectively.

The chemical reaction mechanism and thermophysicalproperty evaluation methods are implemented into thecommercial CFD package, Fluent, through its user codingcapability, thus establishing a mathematical model andcomputational software for numerical studying of fluidflows and heat transfer of RP-3 with endothermic pyrolysisat supercritical pressures. More details of the mathematicalmodel can be found in Ref. [23].

3. Results and discussion

3.1. Model validations

Detailed model validations are conducted in this sectionagainst two sets of experimental data of Jiang et al. [10]. Asshown in Figure 1, the turbulent fluid flows and heat transferof RP-3 with endothermic pyrolysis in a micro cooling tubeare numerically simulated using the previously developedmathematical model and computational software. In thecalculations, the tube diameter is 1 mm, with two tubelengths of 0.635 m and 0.870 m used in test 1 and test 2,respectively. A constant heat flux is imposed on the tubesurface. The constant fuel temperature, mass flow rate, andoperating pressure are specified at the tube inlet. Outflow

Figure 1 Schematic configuration of the cooling tube.

Table 2 Operating parameters used in model validations.

TubelengthL/m

InlettemperatureT0/K

Massflux m/(g/s)

Inletpressurep0/MPa

Heat fluxqw/(kW/m2)

Test 1 0.635 298.15 0.392 5 442.3Test 2 0.870 298.15 0.793 5 583.9

Figure 2 Variations of bulk fluid temperature.

Figure 3 Variations of fuel conversion rate.

Table 1 Surrogate compounds for property evaluations [10].

Surrogate compounds Mole fraction

RP-3 n-decane 0.25n-dodecane 0.50n-tridecane 0.12n-butyl-cyclohexane 0.13

C5þ pentene 0.40hexene 0.60

CC5þ cyclohexane 0.50cyclopentane 0.50

CnH2n-6 benzene 1

Model validation and parametric study of fluid flows and heat transfer 205

boundary conditions are specified at the tube outlet. Theother operating parameters are listed in Table 2, consistentwith the experimental set-ups in Ref. [10]. Two computa-tional meshes of 2540� 50 for test 1 and 3480� 50 for test2 in the x- and r- directions, respectively, are chosen for thepresent studies, based on our previous numerical work [15].

Figure 2 shows variations of the calculated bulk fluidtemperature in the heated section for the two different cases.The bulk fluid temperature is defined as

Tb ¼ZAρu-cpTdA

ZAρu-cpdA

�ð7Þ

The fluid temperature initially increases rapidly, butthe increasing rate slows down in the high temperatureregion, due to the endothermic chemical reactions. Thenumerical results are compared with experimental data[10], showing very good agreements. The maximumrelative errors are only 5.5% and 2.2% for the two testcases, respectively.

Figure 3 shows variations of the predicted fuel conver-sion rate, along with the measured experimental data. Thefuel conversion rate is defined as:

Yb ¼ 1�ZAρu-YRP�3dA

ZAρu-dA

�ð8Þ

Thermal cracking of RP-3 mainly occurs at aroundx¼300 mm for case 1 and x¼450 mm for case 2. At bothlocations, the bulk fluid temperature reaches around750 K, as shown in Figure 2. The calculated resultsmatch the experimental data very well. At the thermalexit, the relative errors between the calculated andexperimental data are only 5.9% and 3.08% for the twotest cases, respectively.

Detailed species yields from the endothermic pyrolysis ofRP-3 are shown in Figure 4. Mass fractions of the lightproducts, such as methane and ethane, increase monotoni-cally along the heated section. Mass fractions of the heavyproducts, such as C5þ and CC5þ, initially increase with fuelpyrolysis, but then decrease as more fuel is thermallycracked. This is caused by the secondary chemical reactionsin the detailed pyrolytic chemical reaction mechanism.Excellent matches between the numerical results andexperimental data can be clearly observed in Figure 4(a)-(d) for the light species, but relatively larger deviationsoccur between the two sets of data for the two lumpedspecies, C5þ and CC5þ, mainly in the transition regions. In

Keke Xu, Hua Meng206

the pyrolytic chemical reaction mechanism of RP-3 [10],since C5þ and CC5þ are used to represent two groups ofrelatively heavy species, the chemical reactions for them aresimplified and thus may not be very accurate.The numerically calculated heat sink, which directly

indicates the potential cooling capacity of RP-3, is com-pared with the analytical result in Figure 5. The heat sinkinitially increases linearly with temperature, but once thebulk fluid temperature exceeds 800 K, it shows a rapid rise,

Figure 4 Variations of species yields from fuel pyrolysis. (a)

attributable to the extra heat absorbing capacity of thehydrocarbon fuel through endothermic chemical reactionsin the high temperature region. Again, the calculated valuesare consistent with the analytical data [10].

In this section, detailed model validations have beencarried out against a series of experimental data, includingthe bulk fluid temperature, fuel conversion rate, variousproduct yields, and chemical heat sink, fully verifying theaccuracy and reliability of the mathematical model.

CH4, (b) C2H4, (c) C2H6, (d) C3H6, (e) C5þ and (f) CC5þ.

Figure 5 Variations of the fuel heat sink.

Table 3 Operating parameters usedfor parametric study.

Parameters Values

Inlet pressure, p0/MPa 5Wall temperature, Tw/K 950Inlet temperature, T0/K 300Inlet velocity, u0/(m/s) 0.5–4

Figure 6 Variations of bulk fluid temperature with and withoutpyrolysis.

Figure 7 Variations of surface heat flux with and without pyrolysis.

Model validation and parametric study of fluid flows and heat transfer 207

3.2. Effects of fuel pyrolysis and inlet velocity

In this section, the model is applied to study effects of thefuel pyrolysis and inlet flow velocity on fluid dynamics andheat transfer characteristics of RP-3 in a micro cooling tubeat a supercritical pressure of 5 MPa. The tube diameter is1 mm, with a total length at 800 mm. An inlet section of150 mm is thermally insulated to ensure a fully develo-ped flow before heat transfer starts, and an outlet sectionof 150 mm is also thermally insulated to avoid effects ofthe outflow boundary conditions on numerical results. Themiddle section with a tube length of 500 mm is heatedwith a constant wall temperature of 950 K for the purposeof fundamental studies. Results calculated using different

thermal boundary conditions are discussed in Ref. [23]. Inthe present study, the flow velocity, varying from 0.5 m/s to4 m/s, is prescribed at the tube inlet. The detailed operatingparameters are listed in Table 3.

Figure 6 shows variations of the bulk fluid temperaturecalculated with and without consideration of fuel pyrolysis.The inlet flow velocity is 0.5 m/s. At the thermal exit, theendothermic pyrolytic chemical reactions lead to around40 K decrease in the bulk fluid temperature. In this case, thefuel conversion rate at thermal exit is approximate 80%, asdiscussed later in this section.

Variations of the surface heat flux, with and withoutconsideration of fuel pyrolysis, are shown in Figure 7. Inthe current case with a constant wall temperature, it is moreappropriate to use the surface heat flux to elucidate theeffects of fuel pyrolysis on the convective heat transfer [15].Because of the endothermic chemical reactions, the surfaceheat flux is significantly increased. Particularly at the ther-mal exit, at which point 80% of RP-3 is thermally cracked,the surface heat flux with fuel pyrolysis increases nearly 10times, comparing with that without fuel pyrolysis. It shouldalso be noted that the sudden increase of the surface heatflux from x/D¼150, as clearly observable in Figure 7, iscaused by strong variations of thermophysical properties ofthe cracked fuel mixture in the trans-critical region whenthe fluid temperature rises from a subcritical to supercriticalstate. More detailed discussion is provided in Ref. [23].

The effects of inlet flow velocity on fluid flows, fuelpyrolysis, and heat transfer are further analyzed. Figure 8shows variations of the bulk fluid temperature and surfaceheat flux at different inlet flow velocities. As the inletvelocity increases, the bulk fluid temperature decreases,while the surface heat flux increases significantly. Thisphysical phenomenon is attributable to the improved heattransfer performance at a high flow velocity.

Figure 9 presents variations of the fuel conversion ratealong the heated section at different inlet flow velocities.The thermal decomposition of RP-3 weakens as the flowvelocity increases. At the thermal exit, the fuel conversionrate drops from 80% to 13% as the inlet flow velocity

Figure 8 Variations of (a) bulk fluid temperature and (b) surface heatflux at different inlet flow velocities.

Figure 9 Variations of fuel conversion rate at different inletvelocities.

Figure 10 Variations of (a) volumetric endothermic heat absorptionrate, (b) equivalent surface heat flux from fuel pyrolysis, and (c) ratioof equivalent surface heat flux to total wall heat flux at different inletflow velocities.

Keke Xu, Hua Meng208

increases from 0.5 m/s to 4 m/s. This is mainly due to thedecreased fluid temperature, as shown in Figure 8(a).Variations of the volumetric heat absorption rates from

fuel pyrolysis at different inlet flow velocities are presentedin Figure 10(a). The general trend is that the endothermicvalue initially increases significantly with the increase of thefluid temperature, and then it starts to decrease in the hightemperature region, caused by the decrease of RP-3 con-centration [23]. It is observed that the maximum value of

the volumetric endothermic value increases as the inlet flowvelocity increases, because of the increased mass flow rate.

To quantitatively compare the endothermic heat absorp-tion rate with the total surface heat flux at the tube wall, anequivalent endothermic surface heat flux can be defined[15]. Variations of the equivalent endothermic surface heatflux at different inlet flow velocities are shown in Figure 10(b). By directly comparing the results in Figures 10(b) and 8(b), it is found that the surface heat flux from the endo-

Figure 11 Variations of (a) fluid density, (b) constant-pressure heatcapacity, and (c) fluid viscosity at different inlet flow velocities.

Model validation and parametric study of fluid flows and heat transfer 209

thermic pyrolytic chemical reactions amount to more than60% of the total wall heat flux in the high fluid temperatureregion for all the cases. Therefore, fuel pyrolysis plays adictating role in supercritical-pressure heat transfer in thehigh fluid temperature region.

During the supercritical-pressure heat transfer process, as thefluid temperature increases and many low-molecular-weightproducts are produced, the thermophysical properties of thefluid mixture exhibit strong variations. Figure 11 showsvariations of the fluid density, constant-pressure heat capacity,and fluid viscosity at different inlet flow velocities. These

properties are calculated using the bulk fluid temperature. Thefluid density experiences drastic decrease at various inlet flowvelocities. The constant-pressure heat capacity reaches a max-imum value in the trans-critical region when the fluid tempera-ture transits from the subcritical to supercritical state.

The decrease in fluid density along the heated sectionleads to the significantly increased flow velocity, as shownin Figure 12, in which detailed velocity distributions in theflowfield and velocity variations in the axial and radialdirections are provided. In the case with an inlet flowvelocity at 4 m/s, the maximum velocity at the thermal exitcan reach more than 40 m/s. The corresponding variationsof the Reynolds number at different inlet flow velocities arepresented in Figure 13. The Reynolds number is quite smallat the tube inlet. For example, with an inlet flow velocity at0.5 m/s, the Reynolds number is only 286 at the inlet of theheated section, but it rapidly increases in the heat transferprocess prior to fuel pyrolysis. This is caused by thecombined effects of the increased flow velocity and thesignificantly decreased fluid density and viscosity(Figure 11(a) and (c)). Therefore, the fluid flow and heattransfer process transits from the laminar to turbulent state.

Figure 14 presents variations of the heat transfer coeffi-cient, the Nusselt number, at various inlet flow velocities.This parameter initially increases, consistent with theincreased flow velocity and thus enhanced heat transfer,but it slightly decreases in the high fluid temperature region,mainly owing to the decreased heat absorption rate fromfuel pyrolysis, as shown in Figure 10. As discussed early inthis section, a supercritical-pressure heat transfer process ofRP-3 is dictated by the endothermic pyrolytic chemicalreactions in the high fluid temperature region.

4. Conclusions

In this paper, a mathematical model has been used toexamine fluid flows and heat transfer of the aviationkerosene RP-3 with endothermic pyrolysis at a supercriticalpressure. A complete set of conservation equations of mass,momentum, energy, and species mass fractions are numeri-cally solved, with accurate calculations of thermophysicalproperties. A detailed reaction mechanism, containing 18species and 24 elementary reactions, is incorporated toaccount for endothermic decomposition of the hydrocarbonfuel. The model is applicable over a wide range of operatingconditions.

Detailed model validations have been carried out againsta series of experimental data, including the fluid tempera-ture, fuel conversion rate, various product yields, and heatsink. Good matches between the numerical and experi-mental results clearly verify the accuracy and reliability ofthe mathematic model.

Effects of the endothermic fuel pyrolysis and inlet flowvelocity on fluid flows and heat transfer of RP-3 in acircular cooling tube have been investigated under aconstant surface temperature of 950 K and at a supercritical

Figure 12 Detailed distributions of velocity magnitude at inlet velocities of (a) 0.5 m/s and (b) 4 m/s, (c) velocity variations along axial directionat r¼0 mm and (d) velocity variations along radial direction at x/D¼500.

Figure 13 Variations of Reynolds number at different inletvelocities.

Figure 14 Variations of Nusselt number at different inlet velocities.

Keke Xu, Hua Meng210

Model validation and parametric study of fluid flows and heat transfer 211

pressure of 5 MPa. Results reveal that the endothermicpyrolytic chemical reactions significantly improve the heattransfer process, particularly in the high temperature region.The equivalent surface heat flux from the endothermic fuelpyrolysis amounts to more than 60% of the total wall heatflux at the thermal exit under all the tested conditions.During the supercritical-pressure heat transfer process, theflow velocity significantly increases, and the correspondingReynolds number also increases but mainly prior to fuelpyrolysis. This is caused by the drastic variations of vari-ous thermophysical properties. As a result, the fluid flowand heat transfer process transits from the laminar to turb-ulent state. The heat transfer coefficient, the Nusseltnumber, initially increases, consistent with the increasedflow velocity, and then slightly decreases in the high fluidtemperature region, mainly owing to the decreased heatabsorption rate from fuel pyrolysis.

Acknowledgements

This work was supported by the Zhejiang ProvincialNatural Science Foundation of China (R1100300) and theNational Natural Science Foundation of China (11372277).

References

[1] W.R. Wagner, J.M. Shoji, Advanced regenerative coolingtechniques for future space transportation systems, AIAA 75-1247, 1975.

[2] D.R. Sobel, L.J. Spadaccini, Hydrocarbon fuel coolingtechnologies for advanced propulsion, Journal of Engineeringfor Gas Turbines and Power 119 (2) (1997) 344–351.

[3] X. Fan, G. Yu, J. Li, X. Lu, X. Zhang, C.J. Sung,Combustion and ignition of thermally cracked kerosene insupersonic model combustors, Journal of Propulsion andPower 23 (2) (2007) 317–324.

[4] J. Yu, S. Eser, Thermal decomposition of C10-C14 normalalkanes in near-critical and supercritical regions: productdistributions and reaction mechanisms, Industrial Engineer-ing Chemistry Research 36 (3) (1997) 574–584.

[5] J. Yu, S. Eser, Kinetics of supercritical-phase thermaldecomposition of C10-C14 normal alkanes and their mixtures,Industrial Engineering Chemistry Research 36 (3) (1997)585–591.

[6] F. Zhong, X. Fan, G. Yu, J. Li, C.J. Sung, Thermal crackingand heat sink capacity of aviation kerosene under super-critical conditions, Journal of Thermophysics and HeatTransfer 25 (3) (2011) 450–456.

[7] G. Abraham, N. Gascoin, P. Gillard, M. Bouchez, Real-timemethod for the identification and quantification of hydro-carbon pyrolysis products, part I: development and validationof the infra red technique, Journal of Analytical and AppliedPyrolysis 91 (2) (2011) 368–376.

[8] N. Gascoin, G. Abraham, P. Gillard, M. Bouchez, Real-timemethod for the identification and quantification of hydro-carbon pyrolysis products, Part II: application to transient

pyrolysis and validation by numerical simulation, Journal ofAnalytical and Applied Pyrolysis 91 (2) (2011) 377–387.

[9] M.J. DeWitt, T. Edwards, L. Shafer, D. Brooks, R. Striebich,S.P. Bagley, M.J. Wornat, Effect of aviation fuel type onpyrolytic reactivity and deposition propensity under super-critical conditions, Industrial Engineering Chemistry Research50 (18) (2011) 10434–10451.

[10] R. Jiang, G. Liu, X. Zhang, Thermal cracking of hydrocarbonaviation fuels in regenerative cooling microchannels, EnergyFuels 27 (5) (2013) 2563–2577.

[11] J.-C. Sheu, N. Zhou, A. Krishnan, Thermal cracking ofNorpar-13 under near-critical and supercritical conditions,AIAA 98–3758, 1998.

[12] T.A. Ward, J.S. Ervin, R.C. Striebich, S. Zabarnick, Simula-tions of flowing mildly-cracked normal alkanes incorporatingproportional product distributions, Journal of Propulsion andPower 20 (3) (2004) 394–402.

[13] T.A. Ward, J.S. Ervin, S. Zabarnick, L. Shafer, Pressureeffects on flowing mildly-cracked n-decane, Journal ofPropulsion and Power 21 (2) (2005) 344–355.

[14] Y. Zhu, B. Liu, P. Jiang, Experimental and numericalinvestigation on n-decane thermal cracking at supercriticalpressures in a vertical tube, Energy Fuels 28 (1) (2013) 466–474.

[15] B. Ruan, H. Meng, V. Yang, Simplification of pyrolyticreaction mechanism and turbulent heat transfer of n-decane atsupercritical pressures, International Journal of Heat andMass Transfer 69 (2014) 455–463.

[16] H. Meng, G.C. Hsiao, V. Yang, J.S. Shuen, Transport anddynamics of liquid oxygen droplets in supercritical hydrogenstreams, Journal of Fluid Mechanics 527 (2005) 115–139.

[17] H. Meng, V. Yang, A unified treatment of general fluidthermodynamics and its application to a preconditioningscheme, Journal of Computational Physics 189 (1) (2003)277–304.

[18] Y.Z. Wang, Y.X. Hua, H. Meng, Numerical study ofsupercritical turbulent convective heat transfer ofcryogenic-propellant methane, Journal of Thermophysicsand Heat Transfer 24 (3) (2010) 490–500.

[19] Y.X. Hua, Y.Z. Wang, H. Meng, A numerical study ofsupercritical forced convective heat transfer of n-heptaneinside a horizontal miniature tube, The Journal of Super-critical Fluids 52 (1) (2010) 36–46.

[20] B.E. Poling, J.M. Prausnitz, O.C. John Paul, The Propertiesof Gases and Liquids, McGraw-Hill, New York, 2001.

[21] S. Takahashi, Preparation of a generalized chart for thediffusion coefficients of gases at high pressures, Journal ofChemical Engineering (Japan) 7 (6) (1975) 417–420.

[22] N. Wang, J. Zhou, Y. Pan, H. Wang, Determination ofcritical properties of endothermic hydrocarbon fuel RP-3based on flow visualization, International Journal of Thermo-phys 35 (2014) 13–18.

[23] K. Xu, H. Meng, Modeling and simulation of supercritical-pressure turbulent heat transfer of aviation kerosene withdetailed pyrolytic chemical reactions, Energy Fuels 29 (2015)4137–4149.