Zhiliang Lei,Bin Liu,Qin Huang,Kuo He,Zewei Bao*,Quan Zhu,Xiangyuan Li

School of Chemical Engineering,Sichuan University,Chengdu 610065,China

Keywords:Hydrocarbons Supercritical fluid Pyrolysis Rectangular tube Circular tube

ABSTRACT To investigate the effect of regenerative cooling channel geometry on pyrolysis of endothermic hydrocarbon fuel,a series of supercritical pyrolysis experiments of n-decane in the rectangular and circular tubes were conducted.Moreover,sensitivity analysis of production of propylene and methane as well as CFD simulation were also done.The results showed that gas yield and conversion in the circular tube with an inner diameter of 2 mm had a similar tendency with the one of 1.5 mm in inner diameter.The conversion in the circular tube was much less than that in the rectangular tube at the same outlet temperature.The heat sink of the rectangular tube at the same outlet temperature was larger than that of circular tubes,but the temperature at the corner of the rectangular tube was relatively high.According to the experimental data of the test tubes,a correlation between the conversion and the temperature in the rectangular and circular tubes at the same outlet temperature was ftited,providing a reference for the design of regenerative cooling channels.

1.Introduction

Regenerative cooling technology with endothermic hydrocarbon fuel plays an important role in the thermal management of scramjet[1-4].During a regenerative cooling process,the endothermic hydrocarbon fuel is heated to about 1000 K with drastic thermophysical property variations,and hydrocarbon molecules would crack into several smaller molecules,such as CH4,C2H4and C2H6,with the release of chemical heat sink[5].The total heat sink of endothermic hydrocarbon fuels can be increased by enhancing the reaction rate to meet the cooling requirements for future high-performance aircraft.Therefore,it is important to understand the cracking process of hydrocarbon fuels in different cross-sectional shapes.

The pyrolysis process of endothermic hydrocarbon fuel is coupled and complicated.There are many factors that affect the cracking reaction.The reaction temperature,residence time and operating pressure have been studied due to their intense influences on the reaction rate.Cooper and Shepherd[6]have examined the decomposition of JP-10 through thermal and catalytic cracking mechanisms while maintaining the flow path at elevated temperatures and pressures for extended periods of time.The conversion and product compositions were determined as functions of the fuel metering rate,reactor temperature,system backpressure,and zeolite type.Zhong et al.[7]investigated the thermal cracking and the heat sink capacity of aviation kerosene in a heated tube at 780 to 1050 K and 3 to 4.5 MPa for a residence time duration of 0.6-3 s.They found the chemical heat sink does not always increase with the temperature of fuel and a maximum endothermicity occurred at a temperature of fuel approximately 900-960 K.The maximum chemical heat sink was approximately 0.5 MJ·kg-1with a 45%fuel conversion.

The pyrolysis characteristics of endothermic hydrocarbon fuel in the tubes with different diameters have been studied experimentally and theoretically[8-12].Ward et al.[8]obtained the proportional product model in 316 stainless steel circular tube with an inner diameter of 0.5 mm through experiments,and accounted for changes in the chemical composition of a flowing fuel by simulation.Zhu et al.[10]built a one-step model in the stainless-steel tube and explained the distribution of the mass fraction of pyrolysis products at supercritical pressure by simulation.However,most of the literatures focused on the distributions of flow field and pyrolysis in the flow direction.Only several literatures studied the influence factors of radial cracking characteristics.Zhang et al.[13]studied a three-dimensional simulation of propane pyrolysis reactor tube based on a detailed kinetic radical cracking scheme.Large scale of radial nonuniformity in the vicinity of the tube wall was investigated.Feng et al.[14,15]studied the influences of radial heat and mass transfers on the pyrolysis of hydrocarbon fuel in cooling mini-channel using a 2D numerical model.It was found that the conversion of hydrocarbon fuel near wall and in core flow increase and decrease with the increase of heating rate,respectively,which caused the increase in the non-uniformity of conversion at the cross section.Li et al.[16]studied the effect of cooling channel geometric structures on the thermal cracking behaviors of HF-1 in the channels with the same cross-sectional area under 3.5 MPa.

For the design of regenerative cooling channels,channel geometry is one of the most important factors.Different cross-sectional dimensions would lead to different distributions of pyrolysis products and conversion in the cross section.Therefore,it is a challenge to apply the simulation and experimental results obtained from circular cooling tubes to the design of rectangular cooling channels.However,there is a little previous literature on the effect of cross-sectional shape of cooling channels on pyrolysis experimentally.In addition,the quantitative relationship between conversion and various factors,such as cross section shape,bulk fluid temperature,wall temperature and residence time needs to be further investigated.In this study,the thermal cracking characteristics of n-decane in the rectangular and circular tubes were investigated experimentally and theoretically.Furthermore,effects of temperature and residence time on conversion in the tubes with different cross-section dimensions were discussed,and a quantitative relationship in the conversion between the rectangular and circular tubes were established.

2.Experimental Apparatus

As shown in Fig.1,an experimental apparatus was built to investigate the thermal cracking characteristics of n-decane in the rectangular and circular tubes under a constant pressure of 3.5 MPa.Three stainlesssteel SS304 tube reactors shown in Fig.2 and listed in Table 1 were used as heating reactor.In Table 1,2R represented the rectangular tube with a width of 1 mm and a height of 2 mm,while 2C and 1.5C represented the circular tube with an inner diameter of 2 mm and the one with an inner diameter of 1.5 mm,respectively.To investigate the effect of the fuel outlet temperature on the pyrolysis process,five tube lengths,i.e.,1034 mm,1134 mm,1234 mm,1334 mm and 1560 mm,were conducted in our experiments.Accordingly,the fuels in the five tubes were heated to 861 K,878 K,890 K,898 K and 923 K,respectively.The mass flow rate of n-decane in the reactor was maintained by the highpressure constant flow pump and the mass flow rate was kept constant at 1 g·s-1.In each experiment,the gas and liquid components of fuel were collected and analyzed,respectively.A detailed description of the feeding,sampling and analysis systems can be found in our previous work[17,18].

The fuel temperatures at the inlet and outlet of the tubes were measured using a thermocouple inserted into the flow of fuel.The maximum measurement temperature of the thermocouple can be up to 1073 K and the accuracy is±0.5%.Meanwhile,the wall temperature distribution along the tube was monitored by K-type thermocouples welded on the outside surface of the tube.The measuring range is 233-1373 K and the accuracy is±0.4%.To reduce the heat loss,the tube reactor was covered with the thermal insulation materials(aluminum silicate).This insulation schema would also diminish the temperature fluctuation of thermocouples and guarantee the accuracy of the temperature measurements.

Fig.2.Scheme of rectangular and circular tubes:a—width;b—height;c,c1,c2—wall thickness;R—radius.

The uncertainty of conversion is dependent upon the measurements of the mass flow rate and product species.The mass flow rate of the inlet fuel was measured by a Micro-Motion CMF101 mass flow meter with an uncertainty of less than±0.1%.The mass flow rate of the liquid products was measured by an electronic balance with an uncertainty of less than 0.1 mg.The gas products were analyzed online by gas chromatography.The small molecule hydrocarbons were measured using an Agilent HPAl/S capillary column(50 m×0.53 mm×5.0 μm)combined with a flame ionization detector.Hydrogen was detected by a thermal conductivity detector(stationary phase TDX-101).The liquid products were identified using a Perkin Elmer GC Clarus 680.According to experimental uncertainty analysis based on Moffat's experiment error transfer procedure[19],the relative uncertainties of the measured mass fraction of all species were lower than 2.5%,and the relative uncertainty in total heat sink was estimated to be±5%.

3.Numerical Analysis

3.1.Physical model and boundary conditions

In order to ensure that the simulation conditions are consistent with the experimental setups,the heat flux,which has been deducted the heat loss,is used as the thermal boundary condition of the wall.The heat flux of heated surface is calculated based on the experimental electrical heating method by Eq.(1).

Fig.1.Schematic of the experimental apparatus for fuel pyrolysis:1,fuel tank;2,high-pressure constant flow pump;3,filter;4,needle valve;5,Coriolis mass flowmeter;6,K-type thermocouples;7,pressure transmitters;8,adjustable power supplies;9,data acquisition system;10,water-cooled condenser;11,back pressure controller;12,gas-liquid separator;13,liquid collector;14,Perkin Elmer GC Clarus 680;15,wet gas flowmeter;16,gas chromatography.

Table 1 Parameters of channel geometries in the experiments

The heat loss could be described as a polynomial function of surface temperature[12].In our experiments,the heat loss was caused by natural convective heat transfer,thermal radiation of the outer wall with environment and thermal conduction of insulation materials,whose effect was included in the correlation coefficients of fitting functions.The fitted equations of heat loss in the 2R,2C and 1.5C were presented as follows:

Circular(2C):

Therefore,the heat flux of heated surface in the 2C,1.5C and 2R was calculated and presented in Table 2.

In order to verify the simulation method,the tubes with a length of 1560 mm in the 2C,1.5C and 2R were chosen to carry out the numerical simulation of the heating tube reactor.In the experiments,the heating length of the tube with a length of 1560 mm was gradually shortened by moving the front copper clamp with constant electric current,and similar methods were used by Jiang et al.[20]and Zhou et al.[21].It was found that the bulk fluid temperatures at the position of 1034 mm in the 2C,1.5C and 2R were 766 K,752 K and 861 K,respectively,which were close to the cracking temperature of n-decane.Since the present study focused on the effects of channel cross section size on the distribution of temperature and conversion in the pyrolysis zone,the rectangular and circular tubes at 1034 to 1560 mm(cracking section with 526 mm in length)were studied to verify the simulation.Fig.3 showed the computational domain of one fourth of the rectangular tube with a width of 1 mm and a height of 2 mm.Fig.4 presented the computational domain of the circular tube with the inner diameter 2 mm and the inner diameter 1.5 mm.Lengths of the inlet and outlet unheated sections were both 150 mm.The inlet section shown in Figs.3 and 4 was adopted so that the fuel flow became fully developed before the fuel was heated.The outlet unheated section was included to eliminate the effect of pressure outlet boundary condition on the numerical results.

3.2.Thermophysical property and pyrolysis reaction model

The density(ρ),specific heat capacity(cp),thermal conductivity(λ)and dynamic viscosity(μ)of the n-decane and the cracked products were calculated by linear interpolation according to the data of NIST SUPERTRAPP[22].The thermal cracking occurred when n-decane was heated to approximately 770 K[23].Molar mass,state standard enthalpy and entropy were adopted by referring to NIST SUPERTRAPP.The massweighted-mixing-law provided by the commercial CFD software was used to calculate the thermophysical properties of the mixture[24].

According to Ward's PPD model[25],the cracking process could be approximated as an overall reaction,which could be expressed as:

Eq.(4)is the first order reaction kinetics model.According to the Arrhenius expression,the reaction rate constant can be expressed as:

where activation energy Ea=263.7 kJ·mol-1and pre-exponential factor k0=1.6×1015s-1,universal gas constant Rm=8.314 J·(mol·K)-1.

3.3.Solution strategy

The above model and property evaluation methods have been implemented using a commercial CFD package,ANSYS Fluent 14.5.The shear stress transport k-ω(SST k-ω)turbulence model was adopted to simulate the turbulent flow in the present study.The pressurebased solver was chosen to solve the governing equations with pyrolysis.Pressure-velocity coupling used the SIMPLE algorithm.The equations were discretized with the second-order upper difference scheme.The appropriate convergence criteria for the continuity,energy and other equations were less than 10-3,10-6,and 10-5,respectively.For the cases,the difference between inlet and outlet mass flow rates was less than 0.001%,and the fluctuations of the fluid outlet temperature and velocity were little.

3.4.Simulation verification

In order to better understand the experimental phenomena,the experimental conditions in Table 2 were simulated to explain the effects of geometric structure on cross section temperature and conversion.Before performing detailed numerical studies,the grid-independence analysis and numerical method validation were conducted to ensure the accuracy of the present numerical calculations.Five sets of computational grids were tested,which were 1652×25,2478×38,3304×50,4130×63,and 4956×75(axial×radial)for the circular tube with an inner diameter of 2 mm respectively.When increasing the meshes from 3304×50 to 4130×63,the relative numerical errors interms of the bulk fluid temperature,the average wall temperature and conversion were 0.001%,0.002%and 0.014%,respectively.Decreasing the meshes from 3304×50 to 2478×38 resulted in the relative numerical errors of 0.002%,0.05%and 0.18%,respectively.Finally,the grids of 3304×50(axial×radial)were adopted for the calculations hereinafter.For other tubes,the number of the grids in the axial direction remained 3304,while the number of the grids in the r/Y and Z directions was proportion to the length of computational domain.Therefore,the grid systems of 1.5C and 2R were 3304×38(axial×radial)and 3304×50×25 in the X,Y and Z directions,respectively.

Table 2 Experimental boundary conditions for simulation

Fig.3.3D computational domain of the rectangular tube:(a)geometry of the X-Y plane and(b)geometry of the Y-Z plane.

Table 3 showed the comparisons of the simulated and experimental outlet conversion and outlet temperature.From Table 3,the maximum relative errors between experimental and numerical values of fluid outlet temperature and conversion were 2.31%and 8.16%,respectively.The relative error was higher because of the effect of a secondary reaction which occurred under a higher conversion.Although the maximum relative error reached 8.16%,it was meaningful for engineering analysis in this study.Therefore,the present numerical model was reliable.

The bulk fluid temperature is defined by Eq.(6).

3.5.Numerical analysis of n-decane pyrolysis in the outlet cross section

To better understand the differences in conversion between the rectangular and circular tubes,temperature and conversion distributions in the outlet cross section of the channels should be well investigated.Fig.5a and c presented the variations of temperature and conversion along the diameter direction in the outlet cross section of the circular tube.It was found that the maximum temperature difference along the diameter in the 2C was 10 K higher than that in the 1.5C,and the maximum difference in the conversion in the 2C was 1.6 times as high as that in the 1.5C.

Fig.5b and d showed the variations of temperature and conversion along different lines in the outlet cross section of the rectangular tube.The temperature profiles in the rectangular tube were approximately parabolic along different lines.The distributions of temperature and conversion had a large change in the range of 0%-20%and 80%-100%(within the boundary layer).From Fig.5b,local high temperature occurred at the corner of the rectangular channel,and the maximum temperature at the corner with the outlet average temperature of 944 K reached 1020 K,which closed to the maximum temperature limit of the tube material.

4.Results and Discussion

4.1.Heat sink,gas yield and conversion in different tubes

The heat sink is one of the key indicators of the endothermic hydrocarbon fuels to meet the cooling requirements for future highperformance aircraft.The total heat absorbed by fuel was the difference between resistance heat UI and heat loss Qlosswhich was related to surface temperature.The total heat sink of n-decane was calculated by Eq.(7).

Fig.4.2D axisymmetric computational domain of the circular tube:(a)the inner diameter 2 mm circular tube and(b)the inner diameter 1.5 mm circular tube.

Table 3 Comparisons of conversion and fluid temperature between simulation and experimental results at outlet

The total heat sink of the n-decane under different experimental conditions was shown in Fig.6.It can be found that the total heat sink increased as the temperature of fuel increased.When the pyrolysis reaction takes place,the heat sink of hydrocarbon fuel includes physical and chemical heat sinks.The cracking conversion of fuel directly affects its chemical heat sink,and the higher the conversion is,the higher the chemical heat sink reaches[11].From Fig.7,the cracking conversion and gas yield increased gradually with the increase of temperature,and the proportion of chemical heat sinks in the total heat sink also rose.Therefore,the total heat sink exhibited a growth trend as the temperature of fuel increased.From Fig.6,the total heat sink of a rectangular tube at the same outlet temperature was larger than that of circular tubes.The total heat sink of the fuel was affected by the conversion and gas products.The changes in the shape of the tube influenced the chemical reaction path.Different chemical reaction paths lead to different conversion rates and product components,and further influence the chemical heat sink.

The conversion and gas yield of the n-decane under different experimental conditions were shown in Fig.7.As expected,elevated temperature could positively influence conversion and gas yield,because higher temperature can make the scission of the C--C bonds easier,thus generating more free radicals and accelerating the overall reaction rate[26,27].From Fig.7,gas yield and conversion in the circular tube with an inner diameter of 2 mm(2C)had a similar tendency with the one of 1.5 mm in inner diameter(1.5C),and the conversion in the 2C was 1.41-2.10 times(their arithmetic mean was 1.8,which was closer to 1.6 times in Section 3.5)as high as that in the 1.5C with the temperature range of 861 K-923 K.The conversions in the rectangular tube at 861 K and 923 K were 1.47 and 1.88 times larger than the circular tube with an inner diameter of 2 mm,respectively.The difference in conversion between the rectangular and the circular tubes can be explained by the residence time and temperature distribution.From Fig.5b,the maximum temperature in the rectangular tube was much higher than that of the circular tubes at the same outlet temperature.Therefore,the conversion in the rectangular tube was greater than that in the circular one.

Fig.5.Variations of temperature and conversion along the different lines in the outlet cross section of the(a,c)circular tubes and(b,d)rectangular tube.

Fig.6.Heat sink as a function of bulk fluid temperature in the rectangular and circular tubes.

4.2.Gas products in different tubes

Fig.7.(a)Gas yield and(b)conversion as a function of bulk fluid temperature in the rectangular and circular tubes.

Fig.8 showed the molar fractions of methane,ethane and propylene for different temperatures.From Fig.8,the increase in propylene slowed down after 900 K in the rectangular tube.The following was explained by the sensitivity of the reaction.Fig.9 showed the sensitivity analysis of production of propylene at 880 K,3.5 MPa and methane at 900 K,3.5 MPa using CHEMKIN-PRO program and the mechanisms in the literature[23].The C1-C3 small-molecule alkane is mainly subjected to hydrogen extraction reaction of alkyl radicals,and the alkyl radicals are also easily formed into olefins by β-cleavage.It was found through the sensitivity analysis that the consumption and formation of propylene and methane were mainly through the reversible reaction(aC3H5+CH4?C3H6+CH3).From Fig.9,a small amount of methane would be consumed to produce propylene at 880 K,while propylene would be consumed to generate methane at 900 K.Due to the relatively high temperature near the wall of the rectangular tube,more propylene would be consumed to generate methane in the rectangular tube,so the distribution of methane increased rapidly after 900 K in the rectangular tube,as shown in Fig.8.

4.3.Effects of geometric structure on the residence time

As mentioned in the Introduction,the residence time had a significant impact on conversion.Therefore,the effects of geometric structure on the residence time need to be studied.

The electrical heating tube reactor tube was divided into j segments.The real residence time of cracking fuel flowing in jth segment of the tube reactor can be calculated as:

The cracking fuels have approximately equal average densities(ρ)under the same temperature and pressure.According to Eq.(8),the cross-sectional area(A)was regarded as a dominant factor affecting the residence time under the same flow rate and the same tube length,as was presented in Eq.(9).

The residence time ratio of the rectangular tube with a width of 1 mm and a height of 2 mm(2R)to the 2C(f1)was defined as follows:

According to Section 4.1,the average conversion in the 2C was 1.8 times as high as that in the 1.5C,which was the same as the residence time ratio calculated by Eq.(9)under the same condition.It indicated that the conversion in different circular tubes with varying diameters was mainly affected by the residence time.For the rectangular tube,the residence time ratio(f1)calculated by Eq.(10)was 0.64 under the same flow rate and the same tube length.That was to say,the residence time of the 2R was smaller than that of the 2C,but according to Section 4.1,the rectangular tube had a higher conversion compared with the 2C,which mainly depended on the cross-sectional temperature distribution.It showed that in addition to the residence time,the temperature distribution of the cross-section was also a key factor affecting the conversion for the rectangular tube.

4.4.Relationship between conversion and temperature

The Arrhenius expression showed that there was a correlation between the reaction rate and the temperature,and there should be a similar relationship between the conversion and the temperature in the rectangular tube.In this study,the temperature distribution characteristics in the cross section were represented by the difference between wall temperature and fluid temperature.The difference between wall temperature and fluid temperature was defined as follows:

Fig.9.Absolute rate of(a)propylene at 880 K,3.5 MPa and(b)methane at 900 K,3.5 MPa in the flow reactor tube.

The temperature difference ratio of the 2R to the 2C(f2)was defined as follows:

The relationship between conversion and fluid temperature in the 1.5C was obtained by fitting the experimental data:

According to Section 4.1,conversion in the 2C had a similar tendency with the 1.5C and the average conversion in the 2C was 1.8 times as high as that in the 1.5C.Therefore,the relationship between conversion and fluid temperature in the 2C was obtained by multiplying Eq.(13)by 1.8:

Table 4 presented the calculated values of f2.By multiplying Eq.(14)by f1and f2,the relationship between the conversion and the temperature in the rectangular tube was given as follows:

Fig.10 showed the comparisons between the experimental data and the fitting results.From Fig.10,the maximum relative error between the results calculated by Eq.(15)and the experimental data in the rectangular tube was less than 17.5%,which means the developed relationship can be a reference for the design of rectangular cooling channels.In this way,we can estimate the conversion of the rectangular tube by using the wall temperature and the fluid temperature of the rectangular tube and the temperature difference of the circular tube.

5.Conclusions

The effect of geometric structure of regenerative cooling channels on thermal cracking of n-decane was investigated by experiments and simulations in the rectangular and circular tubes.It can be seen from the presentation above:

Table 4 Calculated values of temperature difference ratio between the rectangular tube with a width of 1 mm,a height of 2 mm and the circular one with an inner diameter of 2 mm

1)Numerical simulation results presented the differences of the conversion and temperature distributions between the rectangular and circular tubes in the cross sections.The distribution of temperature and conversion had a large change within the boundary layer in the rectangular tube.The heat sink of a rectangular tube at the same outlet temperature was larger than that of circular tubes,but the maximum temperature limit of the tube material would most likely occur at the corner of the rectangular channel.

2)The experiment results showed that gas yield and conversion in the circular tube with an inner diameter of 2 mm had a similar tendency with the one of 1.5 mm in inner diameter.The conversion in the rectangular tube with a width of 1 mm and a height of 2 mm was 2.47-3.16 times as high as that of the one with an inner diameter of 2 mm.The distribution of methane increased rapidly after 900 K in the rectangular tube.In addition to the residence time,the temperature distribution of the cross-section was also a key factor affecting the conversion in the rectangular tube.Based on the experimental data,the quantitative relationship between the conversion and temperature was proposed in the rectangular tube,which can be a reference for the design of rectangular cooling channels.

Fig.10.Comparison of fuel conversion as a function of bulk fluid temperature between the experimental data and the fitting results.

Nomenclature

A cross-sectional area,m2

A2cross-sectional area in the 2C,m2

A1×2cross-sectional area in the 2R,m2

a width of the rectangular tube,m

b height of the rectangular tube,m

c,c1,c2 wall thickness,m

cpspecific heat at constant pressure,J?kg-1?K-1

Eaactivation energy,kJ?mol-1

f1residence time ratio of the 2R to the 2C

f2temperature difference ratio of the 2R to the 2C

I heating electric current,A

K reaction rate,s-1

k0pre-exponential factor,s-1

l length of the tube,m

Qlossheat loss,W

Qsinktotal heat sink,kJ?kg-1

q heat flux,MW?m-2

R radius,m

Rmuniversal gas constant,8.314×10-3kJ·mol-1·K-1

r r-axis coordinate,m

S surface area,m2

T temperature,K

t time,s

t1residence time in the 1.5C,s

t1×2residence time in the 2R,s

t2residence time in the 2C,s

U heating electric voltage,V

u velocity,m·s-1

X x-axis coordinate,m

Y y-axis coordinate,m

y conversion,wt%

Z z-axis coordinate,m

ΔT2difference between wall temperature and fluid temperature in the 2C,K

ΔT1×2difference between wall temperature and fluid temperature in the 2R,K

λ thermal conductivity,W?m-1?K-1

μ dynamic viscosity,kg·m-1·s-1

ρ density,kg·m-3

1.5C circular tube with an inner diameter of 1.5 mm

2C circular tube with an inner diameter of 2 mm

2R rectangular tube with a width of 1 mm and a height of 2 mm

Subscripts

f bulk fluid

i inner

j segments

loc local

loss heat loss

o outer

w wall

Acknowledgments

This work was financially supported by the National Natural Science Foundation of China(Grant No.91741201 and Grant No.91641121).