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Experimental investigation on thermal cracking and convective heat transfer characteristics of aviation kerosene RP-3 in a vertical tube under supercritical pressures
International Journal of Thermal Sciences 146 (2019) 106092
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Experimental investigation on thermal cracking and convective heat transfer characteristics of aviation kerosene RP-3 in a vertical tube under supercritical pressures Si Jiao, Sufen Li *, Hang Pu, Ming Dong, Yan Shang School of Energy and Power Engineering, Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, Dalian University of Technology, Dalian, 116024, PR China
A R T I C L E I N F O
A B S T R A C T
Keywords: RP-3 Supercritical pressures Pyrolysis Heat transfer
This study experimentally investigated the pyrolysis and heat transfer characteristics of a specific EHF (aviation kerosene RP-3) flowing in a vertical upward tube under supercritical pressures (2.5–5.5 MPa). Three wall heat flux conditions, i.e. 700, 950, and 1240 kW/m2 are designed to represent the condition with no significant cracked, mildly cracked, and deeply cracked of fuel, respectively. The results show that the elevated pressure could impact on the reaction pathway of alkanes and alkenes, resulting in a smaller alkene/alkane ratio and less endothermicity. A promoting effect of the elevated pressure and heat flux on the conversion and gas yield is confirmed in this work. Then heat transfer characteristics are analyzed in detail based on the wall temperature and the local (apparent)/average HTC distributions. The buoyancy effect causes the deterioration of heat transfer under high heat flux. The elevated pressure decreases the maximum wall temperature whereas enlarges the range of heat transfer deterioration region. A conclusion could be obtained that the increase of pressure has little effect on alleviating of heat transfer deterioration under rather large heat flux conditions. The average HTCs in the cracked region is twice larger than that in the non-cracked region, indicating that the pyrolysis improves the heat transfer of fuel. Besides, it is found that the influence of pressure on heat transfer characteristic is dominated by the isobaric specific heat capacity and density in the non-cracked region and the cracked region, respectively. Furthermore, the effect of pyrolysis on heat transfer deterioration is investigated. It is found that the strong pyrolysis reaction near the wall is beneficial to lower the wall temperature in the HTD region, and the buoyancy effect is not significantly increased by the further decrease in fluid density caused by pyrolysis.
1. Introduction It is known that the thermophysical properties of fluids vary dramatically within a narrow temperature range across the pseudocritical temperature at supercritical pressures. And these dramatic var iations in thermophysical properties could result in complex and unique flow and heat transfer behaviors. Since the middle of the last century, researchers have begun to widely investigate the heat transfer perfor mance of supercritical fluids, such as water, carbon dioxide and re frigerants [1–3]. Recently, growing interest has been paid on heat transfer characteristics of hydrocarbon fuels at supercritical pressures due to the thermal protection remains to be a big challenge for the development of advanced hypersonic aircraft, rocket and missile en gines, etc. [4–6].
In the thermal protection of hypersonic vehicle engines, the on-board endothermic hydrocarbon fuels (EHFs) working as the coolant and traveling through the cooling channels along the combustion chamber wall has been considered as one of the most effective cooling methods [7]. The temperature of EHFs can be as high as 1000 K and thermal cracking will occur in the latter part of the cooling channels for the se vere heat loading. Thus the heating process of EHFs in cooling channels is complicated and the flow, heat transfer and pyrolysis are coupled with each other. Based on the results from existing researches, the convection heat transfer process of EHFs in the channels can be divided into the noncracked region and the cracked region, and a number of studies have been carried out focusing on these two regions separately. In the noncracked region, researchers carried out experimental and numerical studies on the parametric effects (mass flux, heat flux, pressure,
* Corresponding author. E-mail address: [email protected] (S. Li). https://doi.org/10.1016/j.ijthermalsci.2019.106092 Received 3 April 2019; Received in revised form 3 September 2019; Accepted 3 September 2019 Available online 13 September 2019 1290-0729/© 2019 Elsevier Masson SAS. All rights reserved.
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International Journal of Thermal Sciences 146 (2019) 106092
Nomenclature Bo* Cp d g h I k KvT L m_ P ΔP q Q r R Re
t T U x X
buoyancy parameter isobaric specific heat capacity, J/(kg⋅K) diameter, m gravitational acceleration, m/s2 heat transfer coefficient, kW/(m2⋅K) electric current, A reaction rate, s 1 thermal acceleration parameter length of the heated section, m mass flow rate, g/s pressure, MPa pressure difference, kPa heat flux, kW/m2 heat sink, kJ/kg radius, m resistivity, Ω⋅mm2/m or universal gas constant, Pa⋅m3/ mol⋅K Reynolds number
residence time, s temperature, K voltage, V axial location, m conversion of fuel
Greek symbols β volume compression coefficient, 1/K λ thermal conductivity, W/(m⋅ K) μ dynamic viscosity, Pa⋅s ρ density, kg/m3 Subscript b i in o pc w
diameter, and flow direction, etc.) on heat transfer characteristics [4, 8–11], mechanisms of heat transfer deterioration and enhancement [5, 12], flow and heat transfer instabilities [13], and Nusselt correlations fitting [14,15] of EHFs under supercritical pressure conditions. To point it out particularly, among the above-mentioned issues, the heat transfer deterioration (HTD) occurring at large heat flux and the low mass flow rate conditions was of significant importance to the thermal protection of scramjet engines [16]. The pyrolysis of EHFs in the heat transfer deterioration region is a unique phenomenon compared with other su percritical fluids such as water and carbon dioxide. However, few experimental studies have focused on the effect of pyrolysis on heat transfer in the HTD region. Up to now, the thermal cracking characteristics of EHFs in the cracked region has gain extensive attention, such as the mechanisms of the pyrolysis/coke process [17–19], reaction kinetic model for pyroly sis/coke of EHFs [20–23], and parametric effects (residence time, pressure [24], and additive [25] etc.) on the endothermic chemical re action. For further improvement on the cooling capacity of EHFs, Feng et al. [26,27] carried out numerical studies on the influence of turbu lence and heat and mass transfers on the pyrolysis in the cracked region using a 2D numerical model. Liang et al. [28] experimentally investi gated the heat transfer behavior of n-decane under sub- and supercritical pressure at high pyrolysis ratio and found that relatively low pressure of pyrolysis had great advantages under the condition of relatively high heat flux due to the larger heat transfer coefficients and less coking. Whereas in the non-cracked region, high operating pressure was found to alleviate the heat transfer deterioration. Therefore, the results ob tained from studies in the non-cracked region and the cracked region have their own limitations and may even lead to conclusions contrary to each other. Besides, the comprehensive study on the heat transfer be haviors in cooling channels combining the non-cracked region and the cracked region is rare. In order to obtain a fundamental understanding of the coupled physicochemical processes of EHFs in the regenerative cooling tube. This work carried out experimentally study on the pyrolysis and heat transfer characteristics of a specific EHF (aviation kerosene RP-3) flowing in a vertical upward tube under supercritical pressures (2.5–5.5 MPa). Three wall heat flux conditions, i.e. 700, 950, and 1240 kW/m2 were designed to represent the condition with no signifi cant cracked, mildly cracked, and deeply cracked of fuel through the cooling channels, respectively. Pyrolysis characteristics including the conversion, gas yield, alkene/alkane ratio, as well as endothermicity
bulk fluid inner inlet outer pseudo-critical wall
were studied. Then the distributions of wall temperature and the local (apparent)/average heat transfer coefficient were analyzed in detail. In addition, the effect of pyrolysis on heat transfer in HTD region was discussed. 2. Experimental section 2.1. Material Aviation kerosene RP-3, which is the most popular jet fuel used in the aero engines in China, is used in this work. The aviation kerosene RP-3 was provided by China National Petroleum Corporation and mainly composed of normal paraffin (38.82 wt%), branched paraffin (24.91 wt %), naphthenes (6.79 wt%), aromatics (20.15 wt%), alkenes (4.32 wt%) and others (5.01 wt%). The fuel was checked by a gas chromatographmass spectrometer (GC–MS) and the detailed compositions were listed in Table S1 of Supplementary material. The GC-MS spectra are shown in Fig. 1. 2.2. Experimental apparatus The schematic diagram of the experimental apparatus used in this work is shown in Fig. 2. The experimental apparatus consisted of four subsystems, i.e. oil delivery system, electrically heating system, cooling water circulation system, data acquisition/analytic system. Before each run, the system was purged with nitrogen for 10 min to exhaust the air in the reactor. Then the fuel was pumped into the preheater section at a fixed flow rate of 1 g/s by a high-pressure constant-flow pump (SANO TAC, SP2010). A stainless steel 316L tube (1 mm i.d. � 2 mm o. d. � 900 mm, the chemical mass composition of the tube is given in Table 1) was used as the test section, which was heated by the resistive heat generated by the electric power. Both the preheater and the test section were thermally insulated by a layer of aluminum silicate fiber of 40 mm thick. In the test section, two K-type sheath thermocouples (TC) were inserted into tee couplings at the inlet and outlet to measure the bulk fuel temperature. Twenty K-type TCs were welded on the outside wall of the test tube to measure wall temperatures. Downstream the test section the high-temperature fluid flowed through a water-cooled heat exchanger and was quenched to the room temperature. The system pressure was controlled at target values by a back-pressure value (SSK91 33F-1P), and measured by a manometer (EJA430A). Besides, the pressure drop along the test section was measured by a differential 2
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International Journal of Thermal Sciences 146 (2019) 106092
Fig. 1. GC-MS spectra of RP-3.
Fig. 2. Schematic diagrams of the experimental apparatus. Table 1 Chemical mass composition of stainless steel 316L tube (unit: %). 316L
Table 2 Precision of direct measurements.
C
Cr
Fe
Mn
Mo
Ni
S
Si
Parameter
Unit
Precision
0.014
17.36
Bal.
1.57
2.53
13.96
0.006
0.5
Pressure: P Pressure difference:ΔP Wall temperature: Tw,o Fluid temperature: Tb Electric voltage: U Electric current: I
MPa kPa K K V A
�0.065% (0–14 MPa) �0.065% (0–500 kPa) �0.4% �0.75% �1% �0.5%
pressure transducer (EJA130A), in order to monitor the amount of coke inside the test tube. Following the back-pressure value, a gas-liquid separator was installed, the gaseous and liquid products of cracked fuel were separately collected via sampling valve in 90 s and then weighted by an electrical balance. The composition of the liquid prod ucts and gaseous products were analyzed off-line by a GC–MS equipped with a flame ionization detector and a thermal conductivity detector. The detailed information on bulk fuel temperatures and chemical composition distributions along the tube were obtained by electrically heating different lengths (L ¼ 0.3 m, 0.4 m, 0.5 m, 0.62 m, 0.7 m, and 0.8 m) of the tube with the constant electric current. The precision of the direct measurements are given in Table 2. For each condition, three parallel experiments were performed to ensure the reproducibility of results. Besides, the test section was replaced with a new one for every two conditions to avoid the increase of thermal resistance and pressure drop resulted from the surface carbon deposi tion. Fig. 3 shows the results of reproducibility tests under the same
conditions. The outer wall temperature discrepancy between the two tests under the same conditions is less than 2.2%. The detailed experimental conditions of the current work are given in Table 3. To be specific, three wall heat flux conditions, i.e. 700, 950, and 1240 kW/m2 were designed to represent the condition with no significant cracked, mildly cracked, and deeply cracked fuel, respectively. 2.3. Thermophysical property As the aviation kerosene RP-3 is a complex fuel mixture, it is hard to estimate the thermophysical properties with its real composition. In this paper, a 13-species surrogate model which proposed in our previous 3
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International Journal of Thermal Sciences 146 (2019) 106092
and experimental values is 7.73% and 1.69%. The calculated pseudo-critical temperature of RP-3 kerosene is 658 K, 688 K, 712 K, and 734 K at 2.5, 3.5, 4.5 and 5.5 MPa, respectively, which increases with the increasing pressure. 2.4. Data reduction Based on the one-dimensional thermal conduction equation under the cylindrical coordinate system, the local inner wall temperature Tw,i can be calculated as follow: �� �� 2 � � � φ_ r2o r2i φr _ o ro qloss ro Tw;i ¼ Tw;o (1) ln 2λ λ ri 4λ where λ is the thermal conductivity of the tube, φ_ ¼ π ðd2UId2 ÞL is the in 4
o
i
ternal heat source. The effective heat flux qw can be calculated by:
qw ¼ π 4
Fig. 3. Reproducibility tests of the experimental system under the same conditions.
433
Mass flux (kg/m2⋅s) Pressure (MPa) Inlet Reynolds number Heat flux (kW/m2)
1273 2.5, 3.5, 4.5, 5.5 4360–4500 700, 950, 1240
hx ¼
RP-3
n-octane (2.19%), n-nonane (6.77%), n-decane (11.62%), n-undecane (16.12%), n-dodecane (14.82%), n-tridecane (10.48%), n-tetradecane (3.35%), npentadecane (1.86%), 1-decene (6.54%), 1-methyl-3-isopropylbenzene (5.29%), 1, 3, 5-trime thylbenzene (9.45%), 1-methylnaphthalene (4.71%), 1, 1, 4 -trimethylcyclohexane (6.79%), CH4, C2H4, C2H6, C3H6, C3H8, 1-C4H8, n-C4H10, 1-C5H10, n-C5H12, 1C6H12, n-C6H14, 1-C7H14, n-C7H16
Products
(3)
Tb;x
(4)
Qtotal ¼ Qphy þ Qchem
The total heat absorption could be calculated by the effective heat
Table 4 Surrogate compounds used for estimating thermophysical properties of the fuel. Surrogate compound (mass fraction)
qw Tw;i
The fuel only shows the capacity of physical heat absorption before the pyrolysis. When the fuel temperature is higher enough to pyrolysis, the qw in Eq. (3) contains the chemical heat absorption by cracking re actions, the hx calculated by Eq. (3) has both the effect of convective heat transfer and thermal cracking and was named as the apparent heat transfer coefficients. Thus, the HTCs in the non-cracked region and the cracked region should be calculated by different ways. In the non-cracked region, the inner wall temperature was calculated by Eq. (1), while the bulk fuel temperature in the corresponding position was calculated by interpolating the adjacent bulk fuel temperatures measured by TC. In the cracked region, the Tb,x was obtained by mea surement at x ¼ 0.5 m, x ¼ 0.62 m, x ¼ 0.7 m, and x ¼ 0.8 m. While the Tw,i in the corresponding position was calculated by interpolating the adjacent inner wall temperature. The HTCs calculation method in the non-cracked and cracked region has been summarized in Table 5. Besides the heat transfer characteristics, the heat absorption capacity of fuel was studied in this paper. It is known that the pyrolysis of hy drocarbon fuel is an endothermic progress. Once the RP-3 is cracked, the heat absorbed by fuel consists of both physical and chemical heat ab sorption. There is:
work [13] was used to evaluate the thermophysical properties of RP-3. Furthermore, since many low-molecule-weight species are produced, the compositions of fuel keep changing during the pyrolysis process. Thus, the main products should be contained in the surrogate model. And the final surrogate compounds used for thermophysical properties estimation are given in Table 4. As the surrogate compositions of fuel are determined, the method generally adopted to estimate the thermophysical properties is either using the SUPERTRAPP program or developing property code with the equation of state. Because of the limited number of compounds (less than 20 compounds) could be contained in evaluating the thermo physical properties of the mixture with SUPERTRAPP program. The RKPR equation of state (EoS), a unified form of SRK and PR EoS, was adopted to estimate the density (ρ) of the mixture. The details of RK-PR EoS could be found in Refs. [29,30]. The isobaric specific heat capacity (Cp) of the mixture was calculated by the thermodynamic relations [31]. Based on the present 13-species surrogate model, the calculated critical pressure and critical temperature of RP-3 is 2.15 MPa and 634.13 K while the corresponding measured values of RP-3 is 2.33 MPa and 645.04 K [32], respectively. The relatively error between calculated
Fuel
(2)
qloss
where R(T) and qloss is the electrical resistivity and heat loss of the test tube, respectively. Before the experiments, the tube without fuel was directly heated under various heating power, then the heat loss was gained by fitting with the temperature difference between ambient and tube wall, and the electrical resistivity was gained by fitting with the measured wall temperature. Generally, the heat transfer coefficients represent the convective heat transfer characteristic, which was calculated as following:
Table 3 Detailed experimental conditions. Inlet temperature (K)
I 2 ⋅RðTÞ � d2o d2i ⋅πdi
Table 5 The HTCs calculation method in the non-cracked and the cracked region.
Tb, x
Tw, i
4
Non-cracked region (local heat transfer coefficients)
Cracked region (apparent heat transfer coefficients)
The interpolation of measured Tb, x at two adjacent positions.
The outlet bulk fuel temperature measured at x ¼ 0.5 m, x ¼ 0.62 m, x ¼ 0.7 m, and x ¼ 0.8 m. The interpolation of Tw,i at two adjacent positions.
�� 2 φr _ o Tw;i ¼ Tw;o 2λ � � � � φðr _ 2o r2i Þ ro qloss ro ln 4λ λ ri
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International Journal of Thermal Sciences 146 (2019) 106092
flux of 1240 kW/m2. The ratio decreases with the increases of pressure, which indicates that more alkanes and fewer alkenes are produced at the elevated pressure. It is commonly accepted that pyrolysis of hydrocar bons can be explained by the free-radical mechanisms. The product distribution of hydrocarbons under high pressure and temperature conditions should follow the compromise of competition between the Rice-Kossiakoff mechanism (R–K mechanism) [34] and Fabuss-Smith-Satterfield mechanism (F-S-S mechanism) [35–37]. From the free-radical mechanisms, it could be known that β-scission and hydrogen abstraction reaction often occur together during the pyrolysis process of hydrocarbons, which is the main step to produce alkenes and alkanes, respectively. At high reactant concentration resulted from high-pressure conditions, bimolecular hydrogen abstraction reactions are favored over unimolecular β-scission reactions, which typically have higher activation energies [21,38]. Thus, with the elevated pressure, the yield of alkanes is larger than that of alkenes. Furthermore, the forma tion of alkene is an endothermic process, whereas for alkane it is an exothermic process. From this point of view, elevated pressure has an inhibitory effect on the endothermic capacity of the fuel. This result is consistent with Zhou’s research [24], that the effect of pressure on the endothermicity of n-decane is not a simple effect of promotion or inhi bition and the regularity is different in different temperature ranges. And there will be another intersection in total heat sink curves at higher conversion. In conclusion, the elevated pressure can impact on the reaction pathway of alkanes and alkenes, resulting in a smaller alkene/alkane ratio and less endothermicity. A promoting effect of the elevated pres sure and heat flux on the conversion and gas yield was confirmed in this work.
flux, as shown by Eq. (5). (5)
Qtotal ¼ qw ⋅πd⋅Δl=m_
While the heat absorbed by unreacted fuel and the reaction products comprises the physical heat sink. The Cp of cracked RP-3 (the dot symbol in Fig. 7) could be obtained based on the detailed chemical compositions at outlet of different length heated tube. Thus, the physical heat sink can be calculated by the enthalpy difference, as given by Eq. (6). Z T2 Qphy ¼ Cp ðTÞdT (6) T1
Then, the chemical heat sink was obtained based on Eqs. (4)–(6). According to the error propagation formula and precision of direct measurements, the uncertainty of effective heat flux, inner wall tem perature, and heat transfer coefficient were calculated and summarized in Table 6. 3. Results and discussion 3.1. Pyrolysis characteristics The conversion and gas yield of RP-3 under different conditions are shown in Fig. 4. The gas yield is defined as the mass fraction of the gaseous products to the fed fuel. The pyrolysis conversion is defined as the mass fraction of the reacted fuel to the fed: X¼
1
m m
0
(7)
� 100%
where m is the mass of unreacted RP-3 at the outlet of the test tube. The gas yield was the mass fraction of gaseous product to the fed. As seen in Fig. 4, the thermal cracking of RP-3 begins at approxi mately 790 K, which is similar to the result of Liu et al. [19]. Under the same inlet temperature, heated length, and pressure condition, the conversion of RP-3 increases from 34 � 4% to 62 � 3% as the heat flux increases from 950 kW/m2 to 1240 kW/m2. Previous studies [33] found that a high pressure implies a high reactant concentration which results in a large reaction rate. On the other hand, a high pressure also results in a large fluid density and long residence time. Combining the two factors mentioned above, a lower bulk fuel temperature and higher conversion can be observed when elevating the pressure. The distributions of gas yields with temperature are similar to those of conversions, except that the slope of gas yield - Tb is larger than that of X–Tb in the high fuel temperature region. The reason is that with the increase of temperature, the secondary reactions become strong and lots of gaseous products were generated by the secondary reactions [20]. The variations of the heat sink with bulk fuel temperature at different pressures are shown in Fig. 5. Under the studied conditions, the total heat sink exhibits a growth trend with the increase of pressure and temperature. The difference between total heat sink and physical heat sink is the chemical heat sink provided by the endothermic pyrolysis of RP-3. From Fig. 5, it is obviously that the chemical heat sink is approximately one-third of total heat sink at the outlet of test section. Besides, the chemical heat sink increases with the increasing pressure while the little effect of pressure on physical heat sink was observed. From the previous discussion, it is known that the elevated pressure leads to high conversion of fuel and thus a larger endothermic capacity. Fig. 6 shows the alkene/alkane ratio of products under the wall heat 0
3.2. Heat transfer characteristics Fig. 7 shows the variations of isobaric specific heat capacity and density with bulk fluid temperature. The dash lines represent the isobaric specific heat capacity and density without considering the composition change in the cracked region. The variations of composition caused by pyrolysis lead to a slight decrease of isobaric specific heat capacity and obvious decreases of the density respectively, as shown in Fig. 7. Fig. 8 shows the local outer wall temperature and bulk fuel tem perature variations along the heated tube under different heat fluxes. Under 700 kW/m2 condition, obvious difference were observed in Tw,o when the bulk fuel temperature reached Tpc at different pressures. As the heat flux was increased to 950 kW/m2, local wall temperature peaks appeared at approximately x ¼ 0.385 m under all pressure conditions. At a rather higher heat flux (qw ¼ 1240 kW/m2), significant local peak of wall temperature was observed at x ¼ 0.29–0.34 m and the peak location shifted to the inlet of heated tube. Besides, the magnitude of peak wall temperature increases with the decrease of pressure. Based on the above three cases, it is observed that the position of peak wall temperature shifts towards the tube inlet with the increased heat flux. While the magnitude of peak wall temperature increases as well as the peak location of wall temperature shifts progressively towards the tube inlet with the decrease of pressure. Fig. 9 shows the variation of heat transfer coefficient (HTC) as a function of bulk fluid temperature under different pressures. The dot and star symbol represents the local and apparent HTCs in the non-cracked and cracked region, respectively. It is observed from Fig. 9 that the HTCs have the same trend with the increasing heat flux at all pressure conditions: heat transfer enhancement was observed when approaching the fuel critical temperature, which is in accordance with the previous studies [4]. It is known that when the fuel temperature is near the Tpc, the specific heat of the bulk fluid will increase while both the viscosity and density will decrease and this will therefore enhance the heat transfer. When Tw is much higher than the Tpc, the fluid density, thermal conductivity and specific heat near the wall can be quite low, while
Table 6 Uncertainties in the experimental parameters. Parameters
Uncertainties
Effective heat flux, kW/m2 Inner wall temperature, K Heat transfer coefficients, kW/m2⋅K Conversion/Gas yield, %
�1.29% �10.07% �10.23% �10.00%
5
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International Journal of Thermal Sciences 146 (2019) 106092
Fig. 4. Distributions of conversion and gas yield of RP-3.
Fig. 5. Heat sink (qw ¼ 1240 kW/m2).
with
fuel
temperature
at
different
impairs the heat transfer between the fluid and the wall, and this will therefore deteriorate the heat transfer [39]. At qw ¼ 700 kW/m2, the Tw is only slightly higher than Tpc when Tb is near the Tpc, thus the enhanced effect of Tb prevails over the deteriorated effect of Tw, peaks of local HTC appear at (P ¼ 2.5 MPa) or before (P ¼ 3.5, 4.5, and 5.5 MPa) the bulk fuel temperature reached Tpc. The magnitude of peak HTC reduced with pressure increasing from 3.5 MPa to 5.5 MPa as the isobaric specific heat capacity at Tpc (given in Fig. 7) reduced with increasing pressure. As the heat flux increasing to 950 kW/m2, the enhanced effect of Tb was weakened by the deteriorated effect of Tw, an increase of local HTC in the vicinity of Tpc was obtained and local peak of HTC is less obvious. At relatively high heat flux (qw ¼ 1240 kW/m2), the Tw is much higher than the Tpc, thus the deteriorated effect of Tw overcomes the enhanced effect of Tb, no peak of local HTC was observed. In the cracked region, the apparent HTC under different pressures first decreased and then recovered. This may results from that the increased heat absorption capacity makes the rate of the increase of the fuel temperature slow down while the difference between the fuel temper ature and wall temperature is not affected at the same time, so the wall temperature also has a lower rate of increase when fuel starts to pyrol ysis [40]. The same distributions of fuel and wall temperature has been reported by Liu et al. [19]. As the conversion of RP-3 increase, the fuel density further decrease and a recovery of HTCs could be observed near the tube outlet under 1240 kW/m2. In what follows, the effect of buoyancy and thermal acceleration on heat transfer in the vertical flow is discussed. The dimensionless buoy ancy parameter, Bo* was introduced to evaluate the buoyancy effect on heat transfer and it was defined as
pressures
Bo* ¼
Grq Re3:425 Pr0:8
(8) 2 4
where Grq ¼ βgqλwμρ2 d is Grashof number, β ¼ ρ1
f
ρb ρw
Tw Tb
is the thermal
compression coefficient. Jackson et al. [41] pointed out that the buoy ancy effect is non-negligible and the heat transfer is deteriorated when Bo* is between 6 � 10 7 and 1.2 � 10 6 for upward flow. Liu et al. [5] found that buoyancy may significantly deteriorate heat transfer of n-decane when Bo* larger than 2 � 10 7 for upward flow. Recently, Fu et al. [9] obtained a new limiting value of Bo*＞1 � 10 8 as the criterion to evaluate the influence of buoyancy on heat transfer to supercritical RP-3. The effect of thermal acceleration on heat transfer ability was characterized by the thermal acceleration factor KvT. KvT ¼ Fig. 6. Alkene/alkane ratio of products under different pressures.
4βqw
ρuCp Re
(9)
Fig. 10 shows the variations of Bo* and KvT with bulk fuel 6
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International Journal of Thermal Sciences 146 (2019) 106092
Fig. 7. Variations of isobaric specific heat capacity and density with bulk fuel temperature.
Fig. 8. Local wall temperature and bulk fuel temperature distributions along the heated tube.
temperature under different heat fluxes. The results indicated that KvT is always far less than 6 � 10 7 [5] and the effect of thermal acceleration could be neglected in all of the studied conditions. From the results of Bo*, it is known that the Tw peak (in Fig. 8) and the obvious decrease of local HTCs (in Fig. 9) decrease under qw ¼ 950 kW/m2 and qw ¼ 1240 kW/m2 are mainly caused by the buoyancy effect. As well known, the buoyancy force exerts in the same direction of the flow and the turbulence production in the near-wall region would be reduced (flow laminarization) for upward flow. Consequently, the turbulent shear stress and thus momentum transfer is impaired and results in the deterioration of heat transfer [42]. To point it out particularly, under the relatively high heat flux, increasing pressure can decrease the value of the maximum wall temperature. Whereas the elevated pressure will enlarge the range of heat transfer deterioration region caused by buoyancy. Thus, it can be concluded that the increase of pressure has little effect on alleviating of heat transfer deterioration under rather large heat flux. Furthermore, the average heat transfer coefficient was calculated. In this paper, the average HTC is defined as: h¼
n X hi � Δli i¼1
L
significant increase in velocity, which consequently improves the convective heat transfer. Besides, the thermal cracking of RP-3 is an endothermic process which absorbs heat from fuel, and thus decrease the temperature difference between the bulk and the near wall, which is beneficial for the improvement the convective heat transfer. In the non-cracked region, the average HTC increased as the pressure increases, and the reverse trends were observed in the cracked region under the same heat flux. In previous researches [43], the average HTC was always found to increases with decreasing pressure under normal heat transfer regimes. The opposite trend found in this work might be due to the heat transfer deterioration occurred under the heat flux of 950 kW/m2 and 1240 kW/m2. While in the cracked region, the varia tions of average HTC with pressure is mainly determined by density. Even the total heat sink increases with the elevated pressure (in Fig. 5) in the cracked region, the heat absorption rate shows a reverse trend because of the residence time increases with the elevated pressure in the cracked region as shown in Fig. 12. And as well known the residence time is mainly determined by the local density. From the above analysis, it can be concluded that the influence of pressure on heat transfer characteristic is dominant by the isobaric specific heat capacity and density in the non-cracked region and the cracked region, respectively.
(10)
3.3. Effect of pyrolysis on heat transfer in HTD region
The average heat transfer coefficients of the non-cracked region and cracked region under different pressures are shown in Fig. 11. Obvi ously, the average HTC in the cracked region is significantly larger than that of the non-cracked region, which implies that the pyrolysis of fuel will improve the heat transfer. As stated in the previous section, the obviously decreases of density in the cracked region will lead to a
The apparent kinetic parameters (pseudo frequency factor A and pseudo activation energy Ea) of RP-3 were determined at different pressures, assuming that the pyrolysis reaction follows a first-order ki netic law. Based on the method provided by Jiang et al. [20], the re action rate could be derived from the conversion and residence time in 7
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International Journal of Thermal Sciences 146 (2019) 106092
Fig. 9. Variations of HTCs with bulk fuel temperature.
Fig. 10. Variations of Bo* and KvT with bulk fuel temperature.
each segment of the test tube. Then the apparent frequency factor and the pseudo activation energy were obtained by plotting lnk vs 1000/RT, as shown in Fig. 13. The apparent kinetic parameters of RP-3 pyrolysis were determined by the linear regression analysis method, the results are listed in Table 7. For the high pyrolysis rate near the wall (in Fig. 14) in heat transfer deterioration region, errors could be introduced in estimating the apparent kinetic parameters. The estimated apparent kinetic parameters would be larger than the true values. Based on the apparent kinetic parameters, the reaction rate constants along the tube were calculated. Fig. 14 shows the detailed distributions of reaction rate constant based on the inner wall temperature and bulk fuel temperature at the heat flux of 1240 kW/m2. It can be seen from
Fig. 14 that the reaction rate constant in the near-wall region when HTD happens (x ¼ 0.2–0.4 m) can be larger than 250 s 1, while the maximum of that of bulk fuel was ca. 200 s 1. The pyrolysis products result in decrease of fuel density in the near-wall region, which further increases the density difference on the cross-section. On the other hand, the strong pyrolysis reaction of RP-3 near the wall also provided additional heat sink, which is beneficial for the improvement of the heat transfer. The variations of Bo* without and with considering the pyrolysis in the nearwall region are shown in Fig. 15. The influence of pyrolysis on the dis tribution of Bo* and thus buoyancy effect was small. Therefore, the pyrolysis is beneficial to lower the wall temperature in HTD region. Similar conclusions were drawn by Isaev et al. [44] that the 8
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International Journal of Thermal Sciences 146 (2019) 106092
Table 7 Apparent kinetic parameters. Pressure (MPa)
Temperature (K)
Ea (kJ/mol)
A (s 1)
2.5 3.5 4.5 5.5 5 [20]
790–950 793–947 800–941 799–937 773–977
181.298 188.993 188.774 186.520 217.9
2.94 � 1012 8.21 � 1012 7.97 � 1012 5.48 � 1012 2.8686 � 1014
Fig. 11. Average heat transfer coefficient under different pressures.
Fig. 14. Distributions of reaction rate constants at 1240 kW/m2.
Fig. 12. Distributions (qw ¼ 1240 kW/m2).
of
residence
time
and
heat
absorption
rate
Fig. 15. Variations of Bo* without and with considering the pyrolysis.
Tao et al. [45] conducted a numerical investigation of the pyrolysis ef fects on heat transfer characteristics, it was found that the pyrolysis can lower the maximum value of the wall temperature and shortens the range of HTD region. 4. Conclusions Fig. 13. Arrhenius plot for the pyrolysis of RP-3 under different pressures.
This study experimentally investigated the pyrolysis and heat transfer characteristics of aviation kerosene RP-3 flowing in a vertical upward tube under supercritical pressure ranging from 2.5 MPa to 5.5 MPa and fluid temperature ranging of 433 K–950 K. The major
enhancement of heat transfer under high heat flux is caused by the py rolysis reaction in the boundary layer under high heat flux and fuel temperature conditions, which is a special phenomenon for organics. 9
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conclusions are summarized in the following.
[11] S. Yildiz, D.C. Groeneveld, Diameter effect on supercritical heat transfer, Int. Commun. Heat Mass Transf. 54 (2014) 27–32. [12] F. Sun, Y. Li, B. Sunden, G. Xie, The behavior of turbulent heat transfer deterioration in supercritical hydrocarbon fuel flow considering thermal resistance distribution, Int. J. Therm. Sci. 141 (2019) 19–32. [13] S. Li, Y. Wang, M. Dong, H. Pu, S. Jiao, Y. Shang, Experimental investigation on flow and heat transfer instabilities of RP-3 aviation kerosene in a vertical miniature tube under supercritical pressures, Appl. Therm. Eng. 149 (2019) 73–84. [14] W. Chen, X. Fang, Modeling of convective heat transfer of RP-3 aviation kerosene in vertical miniature tubes under supercritical pressure, Int. J. Heat Mass Transf. 95 (2016) 272–277. [15] L. Zhang, R.L. Zhang, S.D. Xiao, J. Jiang, J.L. Le, Experimental investigation on heat transfer correlations of n -decane under supercritical pressure, Int. J. Heat Mass Transf. 64 (-) (2013) 393–400. [16] S. Zhang, J. Qin, K. Xie, Y. Feng, W. Bao, Thermal behavior inside scramjet cooling channels at different channel aspect ratios, J. Propuls. Power 32 (1) (2015) 57–70. [17] C. Song, W.C. Lai, H.H. Schobert, Condensed-phase pyrolysis of n-tetradecane at elevated pressures for long duration. Product distribution and reaction mechanisms, Ind. Eng. Chem. Res. 33 (3) (1994) 534–547. [18] H. Ghassabzadeh, J.T. Darian, P. Zaheri, Experimental study and kinetic modeling of kerosene thermal cracking, J. Anal. Appl. Pyrolysis 86 (1) (2009) 221–232. [19] G. Liu, X. Wang, X. Zhang, Pyrolytic depositions of hydrocarbon aviation fuels in regenerative cooling channels, J. Anal. Appl. Pyrolysis 104 (10) (2013) 384–395. [20] R. Jiang, G. Liu, X. Zhang, Thermal cracking of hydrocarbon aviation fuels in regenerative cooling microchannels, Energy Fuels 27 (5) (2013) 2563–2577. [21] Z. Jia, H. Huang, W. Zhou, F. Qi, M. Zeng, Experimental and modeling investigation of n-decane pyrolysis at supercritical pressures, Energy Fuels 28 (9) (2014) 6019–6028. [22] Y. Fu, G. Xu, J. Wen, H. Huang, Thermal oxidation coking of aviation kerosene RP3 at supercritical pressure in helical tubes, Appl. Therm. Eng. 128 (2018) 1186–1195. [23] Y. Feng, J. Qin, S. Liu, S. Zhang, X. Li, Y. Cao, H. Huang, A simplification of pyrolytic reaction model of hydrocarbon fuel and its application in simulation of heated channel flow, Int. J. Therm. Sci. 130 (2018) 10–18. [24] W. Zhou, Z. Jia, J. Qin, W. Bao, B. Yu, Experimental study on effect of pressure on heat sink of n-decane, Chem. Eng. J. 243 (4) (2014) 127–136. [25] T. Cordero-Lanzac, A.T. Aguayo, A.G. Gayubo, P. Casta~ no, J. Bilbao, Simultaneous modeling of the kinetics for n-pentane cracking and the deactivation of a HZSM-5 based catalyst, Chem. Eng. J. 331 (2018) 818–830. [26] Y. Feng, Y. Jiang, X. Li, S. Zhang, J. Qin, Y. Cao, H. Huang, Numerical study on the influences of heat and mass transfers on the pyrolysis of hydrocarbon fuel in minichannel, Appl. Therm. Eng. 119 (2017) 650–658. [27] Y. Feng, S. Liu, J. Qin, Y. Cao, Y. Jiang, S. Zhang, Numerical study on the influence of turbulence on the pyrolysis of hydrocarbon fuel in mini-channel, Int. J. Heat Mass Transf. 119 (2018) 768–776. [28] C. Liang, Y. Wang, S. Jiang, Q. Zhang, X. Li, The comprehensive study on hydrocarbon fuel pyrolysis and heat transfer characteristics, Appl. Therm. Eng. 117 (2017) 652–658. [29] M. Cismondi, J. Mollerup, Development and application of a three-parameter RK–PR equation of state, Fluid Phase Equilib. 232 (1) (2005) 74–89. [30] S.K. Kim, H.S. Choi, Y. Kim, Thermodynamic modeling based on a generalized cubic equation of state for kerosene/LOx rocket combustion, Combust. Flame 159 (3) (2012) 1351–1365. [31] H. Meng, V. Yang, A unified treatment of general fluid thermodynamics and its application to a preconditioning scheme, J. Comput. Phys. 189 (1) (2003) 277–304. [32] H. Deng, C. Zhang, X.U. Guoqiang, Z. Tao, K. Zhu, Y. Wang, Visualization experiments of a specific fuel flow through quartz-glass tubes under both sub-and supercritical conditions, Chin. J. Aeronaut. 25 (3) (2012) 372–380. [33] S. Jiao, S. Li, H. Pu, M. Dong, Y. Shang, Investigation of pressure effect on thermal cracking of n-decane at supercritical pressures, Energy Fuels 32 (3) (2018) 4040–4048. [34] A. Kossiakoff, F.O. Rice, Thermal decomposition of hydrocarbons, resonance stabilization and isomerization of free Radicals 1, J. Anal. Toxicol. 65 (1943) 590–595. [35] B.M. Fabuss, J.O. Smith, R.I. Lait, A.S. Borsanyi, C.N. Satterfield, Rapid thermal cracking of n-hexadecane at elevated pressures, Ind. Eng. Chem. Process Des. Dev. 1 (4) (1962) 293–299. [36] B.M. Fabuss, J.O. Smith, C.N. Satterfield, Thermal cracking of pure saturated hydrocarbons, J. Anal. Toxicol. 9 (1964) 157–201. [37] B. Jin, K. Jing, J. Liu, X. Zhang, G. Liu, Pyrolysis and coking of endothermic hydrocarbon fuel in regenerative cooling channel under different pressures, J. Anal. Appl. Pyrolysis 125 (2017) 117–126. [38] F. Domine, P.M. Marquaire, C. Muller, G.M. Come, Kinetics of hexane pyrolysis at very high pressures. 2. Computer modeling, Energy Fuels 4 (1) (1990) 2–10. [39] D. Huang, W. Li, A brief review on the buoyancy criteria for supercritical fluids, Appl. Therm. Eng. 131 (2018) 977–987. [40] J. Qin, S. Zhang, W. Bao, W. Zhou, D. Yu, Thermal management method of fuel in advanced aeroengines, Energy 49 (1) (2013) 459–468. [41] D.M. McEligot, J.D. Jackson, “Deterioration” criteria for convective heat transfer in gas flow through non-circular ducts, Nucl. Eng. Des. 232 (3) (2004) 327–333. [42] W.S. Kim, S. He, J.D. Jackson, Assessment by comparison with DNS data of turbulence models used in simulations of mixed convection, Int. J. Heat Mass Transf. 51 (5) (2008) 1293–1312.
(1) Under the studied conditions, the increases of heat flux lead to a high conversion and gas yields which accompanied with the heat transfer deterioration phenomenon. The elevated pressure was found to increase the conversion and gas yield of fuel, and impacted on the reaction pathway of alkanes and alkenes, resulting in a smaller alkene/alkane ratio and less endothermicity. (2) The heat transfer characteristics were analyzed in detail based on the wall temperature and the local (apparent)/average HTC dis tributions. The buoyancy effect caused the deterioration of heat transfer under rather high heat flux. The elevated pressure decreased the maximum wall temperature whereas enlarged the range of heat transfer deterioration region caused by buoyancy. A conclusion was obtained that the increase of pressure has little effect on alleviating of heat transfer deterioration under rather large heat flux. The average HTCs in the cracked region is twice larger than that in the non-cracked region, which implied the pyrolysis improves the heat transfer of fuel. Besides, it was found that the influence of pressure on heat transfer characteristic is dominated by the isobaric specific heat capacity and density and in the non-cracked region and the cracked region, respectively. (3) The apparent kinetic parameters under different pressures were obtained and the effect of pyrolysis on heat transfer deterioration was investigated. It was found that the strong pyrolysis reaction near the wall was beneficial to lower the wall temperature in the HTD region, and the buoyancy effect was not significantly increased by the further decrease in fluid density caused by pyrolysis. Acknowledgment This work was funded by the National Natural Science Foundation of China (Grant No.51576027), the financial support is gratefully acknowledged. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.ijthermalsci.2019.106092. References [1] W.B. Hall, Heat transfer near the critical point, Adv. Heat Tran. 7 (1971) 1–86. [2] K. Yamagata, K. Nishikawa, S. Hasegawa, T. Fujii, S. Yoshida, Forced convective heat transfer to supercritical water flowing in tubes, Int. J. Heat Mass Transf. 15 (12) (1972) 2575–2593. [3] D. Wang, X. Dai, R. Tian, L. Shi, Experimental investigation of the heat transfer of supercritical R134a in a horizontal micro-fin tube, Int. J. Therm. Sci. 138 (2019) 536–549. [4] W. Li, D. Huang, G.Q. Xu, Z. Tao, Z. Wu, H.T. Zhu, Heat transfer to aviation kerosene flowing upward in smooth tubes at supercritical pressures, Int. J. Heat Mass Transf. 85 (2015) 1084–1094. [5] B. Liu, Y. Zhu, J.J. Yan, Y. Lei, B. Zhang, P.X. Jiang, Experimental investigation of convection heat transfer of n-decane at supercritical pressures in small vertical tubes, Int. J. Heat Mass Transf. 91 (2015) 734–746. [6] A. Urbano, F. Nasuti, Onset of heat transfer deterioration in supercritical methane flow channels, J. Thermophys. Heat Transf. 27 (2) (2013) 298–308. [7] R.F. Faulkner, The Evolution of the Hyset Hydrocarbon Fueled Scramjet Engine, vols. 15–19, 12th AIAA International Space Planes and Hypersonic Systems and Technologies, Norfolk, Virginia, 2011, p. 2003. Dec. [8] C. Zhang, G. Xu, L. Gao, Z. Tao, H. Deng, K. Zhu, Experimental investigation on heat transfer of a specific fuel (RP-3) flows through downward tubes at supercritical pressure, J. Supercrit. Fluids 72 (9) (2012) 90–99. [9] Y. Fu, H. Huang, J. Wen, G. Xu, W. Zhao, Experimental investigation on convective heat transfer of supercritical RP-3 in vertical miniature tubes with various diameters, Int. J. Heat Mass Transf. 112 (2017) 814–824. [10] J. Wen, H. Huang, Y. Fu, G. Xu, K. Zhu, Heat transfer performance of aviation kerosene RP-3 flowing in a vertical helical tube at supercritical pressure, Appl. Therm. Eng. 121 (2017) 853–862.
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[43] D. Huang, B. Ruan, X. Wu, W. Zhang, G. Xu, Z. Tao, P. Jiang, L. Ma, W. Li, Experimental study on heat transfer of aviation kerosene in a vertical upward tube at supercritical pressures, Chin. J. Chem. Eng. 23 (2) (2015) 425–434. [44] G.I. Isaev, I.T. Arabova, G.K. Abdullaeva, F. Mamedov, Heat exchange in organic fluids at supercritical pressure, Heat Transf. Sov. Res. 25 (1993) 175–178.
[45] Z. Tao, X. Hu, J. Zhu, H. Wu, Numerical investigation of pyrolysis effects on heat transfer characteristics and flow resistance of n-decane under supercritical pressure, Chin. J. Aeronaut. 31 (6) (2018) 1249–1257.
11
Contents lists available at ScienceDirect
International Journal of Thermal Sciences journal homepage: http://www.elsevier.com/locate/ijts
Experimental investigation on thermal cracking and convective heat transfer characteristics of aviation kerosene RP-3 in a vertical tube under supercritical pressures Si Jiao, Sufen Li *, Hang Pu, Ming Dong, Yan Shang School of Energy and Power Engineering, Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, Dalian University of Technology, Dalian, 116024, PR China
A R T I C L E I N F O
A B S T R A C T
Keywords: RP-3 Supercritical pressures Pyrolysis Heat transfer
This study experimentally investigated the pyrolysis and heat transfer characteristics of a specific EHF (aviation kerosene RP-3) flowing in a vertical upward tube under supercritical pressures (2.5–5.5 MPa). Three wall heat flux conditions, i.e. 700, 950, and 1240 kW/m2 are designed to represent the condition with no significant cracked, mildly cracked, and deeply cracked of fuel, respectively. The results show that the elevated pressure could impact on the reaction pathway of alkanes and alkenes, resulting in a smaller alkene/alkane ratio and less endothermicity. A promoting effect of the elevated pressure and heat flux on the conversion and gas yield is confirmed in this work. Then heat transfer characteristics are analyzed in detail based on the wall temperature and the local (apparent)/average HTC distributions. The buoyancy effect causes the deterioration of heat transfer under high heat flux. The elevated pressure decreases the maximum wall temperature whereas enlarges the range of heat transfer deterioration region. A conclusion could be obtained that the increase of pressure has little effect on alleviating of heat transfer deterioration under rather large heat flux conditions. The average HTCs in the cracked region is twice larger than that in the non-cracked region, indicating that the pyrolysis improves the heat transfer of fuel. Besides, it is found that the influence of pressure on heat transfer characteristic is dominated by the isobaric specific heat capacity and density in the non-cracked region and the cracked region, respectively. Furthermore, the effect of pyrolysis on heat transfer deterioration is investigated. It is found that the strong pyrolysis reaction near the wall is beneficial to lower the wall temperature in the HTD region, and the buoyancy effect is not significantly increased by the further decrease in fluid density caused by pyrolysis.
1. Introduction It is known that the thermophysical properties of fluids vary dramatically within a narrow temperature range across the pseudocritical temperature at supercritical pressures. And these dramatic var iations in thermophysical properties could result in complex and unique flow and heat transfer behaviors. Since the middle of the last century, researchers have begun to widely investigate the heat transfer perfor mance of supercritical fluids, such as water, carbon dioxide and re frigerants [1–3]. Recently, growing interest has been paid on heat transfer characteristics of hydrocarbon fuels at supercritical pressures due to the thermal protection remains to be a big challenge for the development of advanced hypersonic aircraft, rocket and missile en gines, etc. [4–6].
In the thermal protection of hypersonic vehicle engines, the on-board endothermic hydrocarbon fuels (EHFs) working as the coolant and traveling through the cooling channels along the combustion chamber wall has been considered as one of the most effective cooling methods [7]. The temperature of EHFs can be as high as 1000 K and thermal cracking will occur in the latter part of the cooling channels for the se vere heat loading. Thus the heating process of EHFs in cooling channels is complicated and the flow, heat transfer and pyrolysis are coupled with each other. Based on the results from existing researches, the convection heat transfer process of EHFs in the channels can be divided into the noncracked region and the cracked region, and a number of studies have been carried out focusing on these two regions separately. In the noncracked region, researchers carried out experimental and numerical studies on the parametric effects (mass flux, heat flux, pressure,
* Corresponding author. E-mail address: [email protected] (S. Li). https://doi.org/10.1016/j.ijthermalsci.2019.106092 Received 3 April 2019; Received in revised form 3 September 2019; Accepted 3 September 2019 Available online 13 September 2019 1290-0729/© 2019 Elsevier Masson SAS. All rights reserved.
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Nomenclature Bo* Cp d g h I k KvT L m_ P ΔP q Q r R Re
t T U x X
buoyancy parameter isobaric specific heat capacity, J/(kg⋅K) diameter, m gravitational acceleration, m/s2 heat transfer coefficient, kW/(m2⋅K) electric current, A reaction rate, s 1 thermal acceleration parameter length of the heated section, m mass flow rate, g/s pressure, MPa pressure difference, kPa heat flux, kW/m2 heat sink, kJ/kg radius, m resistivity, Ω⋅mm2/m or universal gas constant, Pa⋅m3/ mol⋅K Reynolds number
residence time, s temperature, K voltage, V axial location, m conversion of fuel
Greek symbols β volume compression coefficient, 1/K λ thermal conductivity, W/(m⋅ K) μ dynamic viscosity, Pa⋅s ρ density, kg/m3 Subscript b i in o pc w
diameter, and flow direction, etc.) on heat transfer characteristics [4, 8–11], mechanisms of heat transfer deterioration and enhancement [5, 12], flow and heat transfer instabilities [13], and Nusselt correlations fitting [14,15] of EHFs under supercritical pressure conditions. To point it out particularly, among the above-mentioned issues, the heat transfer deterioration (HTD) occurring at large heat flux and the low mass flow rate conditions was of significant importance to the thermal protection of scramjet engines [16]. The pyrolysis of EHFs in the heat transfer deterioration region is a unique phenomenon compared with other su percritical fluids such as water and carbon dioxide. However, few experimental studies have focused on the effect of pyrolysis on heat transfer in the HTD region. Up to now, the thermal cracking characteristics of EHFs in the cracked region has gain extensive attention, such as the mechanisms of the pyrolysis/coke process [17–19], reaction kinetic model for pyroly sis/coke of EHFs [20–23], and parametric effects (residence time, pressure [24], and additive [25] etc.) on the endothermic chemical re action. For further improvement on the cooling capacity of EHFs, Feng et al. [26,27] carried out numerical studies on the influence of turbu lence and heat and mass transfers on the pyrolysis in the cracked region using a 2D numerical model. Liang et al. [28] experimentally investi gated the heat transfer behavior of n-decane under sub- and supercritical pressure at high pyrolysis ratio and found that relatively low pressure of pyrolysis had great advantages under the condition of relatively high heat flux due to the larger heat transfer coefficients and less coking. Whereas in the non-cracked region, high operating pressure was found to alleviate the heat transfer deterioration. Therefore, the results ob tained from studies in the non-cracked region and the cracked region have their own limitations and may even lead to conclusions contrary to each other. Besides, the comprehensive study on the heat transfer be haviors in cooling channels combining the non-cracked region and the cracked region is rare. In order to obtain a fundamental understanding of the coupled physicochemical processes of EHFs in the regenerative cooling tube. This work carried out experimentally study on the pyrolysis and heat transfer characteristics of a specific EHF (aviation kerosene RP-3) flowing in a vertical upward tube under supercritical pressures (2.5–5.5 MPa). Three wall heat flux conditions, i.e. 700, 950, and 1240 kW/m2 were designed to represent the condition with no signifi cant cracked, mildly cracked, and deeply cracked of fuel through the cooling channels, respectively. Pyrolysis characteristics including the conversion, gas yield, alkene/alkane ratio, as well as endothermicity
bulk fluid inner inlet outer pseudo-critical wall
were studied. Then the distributions of wall temperature and the local (apparent)/average heat transfer coefficient were analyzed in detail. In addition, the effect of pyrolysis on heat transfer in HTD region was discussed. 2. Experimental section 2.1. Material Aviation kerosene RP-3, which is the most popular jet fuel used in the aero engines in China, is used in this work. The aviation kerosene RP-3 was provided by China National Petroleum Corporation and mainly composed of normal paraffin (38.82 wt%), branched paraffin (24.91 wt %), naphthenes (6.79 wt%), aromatics (20.15 wt%), alkenes (4.32 wt%) and others (5.01 wt%). The fuel was checked by a gas chromatographmass spectrometer (GC–MS) and the detailed compositions were listed in Table S1 of Supplementary material. The GC-MS spectra are shown in Fig. 1. 2.2. Experimental apparatus The schematic diagram of the experimental apparatus used in this work is shown in Fig. 2. The experimental apparatus consisted of four subsystems, i.e. oil delivery system, electrically heating system, cooling water circulation system, data acquisition/analytic system. Before each run, the system was purged with nitrogen for 10 min to exhaust the air in the reactor. Then the fuel was pumped into the preheater section at a fixed flow rate of 1 g/s by a high-pressure constant-flow pump (SANO TAC, SP2010). A stainless steel 316L tube (1 mm i.d. � 2 mm o. d. � 900 mm, the chemical mass composition of the tube is given in Table 1) was used as the test section, which was heated by the resistive heat generated by the electric power. Both the preheater and the test section were thermally insulated by a layer of aluminum silicate fiber of 40 mm thick. In the test section, two K-type sheath thermocouples (TC) were inserted into tee couplings at the inlet and outlet to measure the bulk fuel temperature. Twenty K-type TCs were welded on the outside wall of the test tube to measure wall temperatures. Downstream the test section the high-temperature fluid flowed through a water-cooled heat exchanger and was quenched to the room temperature. The system pressure was controlled at target values by a back-pressure value (SSK91 33F-1P), and measured by a manometer (EJA430A). Besides, the pressure drop along the test section was measured by a differential 2
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International Journal of Thermal Sciences 146 (2019) 106092
Fig. 1. GC-MS spectra of RP-3.
Fig. 2. Schematic diagrams of the experimental apparatus. Table 1 Chemical mass composition of stainless steel 316L tube (unit: %). 316L
Table 2 Precision of direct measurements.
C
Cr
Fe
Mn
Mo
Ni
S
Si
Parameter
Unit
Precision
0.014
17.36
Bal.
1.57
2.53
13.96
0.006
0.5
Pressure: P Pressure difference:ΔP Wall temperature: Tw,o Fluid temperature: Tb Electric voltage: U Electric current: I
MPa kPa K K V A
�0.065% (0–14 MPa) �0.065% (0–500 kPa) �0.4% �0.75% �1% �0.5%
pressure transducer (EJA130A), in order to monitor the amount of coke inside the test tube. Following the back-pressure value, a gas-liquid separator was installed, the gaseous and liquid products of cracked fuel were separately collected via sampling valve in 90 s and then weighted by an electrical balance. The composition of the liquid prod ucts and gaseous products were analyzed off-line by a GC–MS equipped with a flame ionization detector and a thermal conductivity detector. The detailed information on bulk fuel temperatures and chemical composition distributions along the tube were obtained by electrically heating different lengths (L ¼ 0.3 m, 0.4 m, 0.5 m, 0.62 m, 0.7 m, and 0.8 m) of the tube with the constant electric current. The precision of the direct measurements are given in Table 2. For each condition, three parallel experiments were performed to ensure the reproducibility of results. Besides, the test section was replaced with a new one for every two conditions to avoid the increase of thermal resistance and pressure drop resulted from the surface carbon deposi tion. Fig. 3 shows the results of reproducibility tests under the same
conditions. The outer wall temperature discrepancy between the two tests under the same conditions is less than 2.2%. The detailed experimental conditions of the current work are given in Table 3. To be specific, three wall heat flux conditions, i.e. 700, 950, and 1240 kW/m2 were designed to represent the condition with no significant cracked, mildly cracked, and deeply cracked fuel, respectively. 2.3. Thermophysical property As the aviation kerosene RP-3 is a complex fuel mixture, it is hard to estimate the thermophysical properties with its real composition. In this paper, a 13-species surrogate model which proposed in our previous 3
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International Journal of Thermal Sciences 146 (2019) 106092
and experimental values is 7.73% and 1.69%. The calculated pseudo-critical temperature of RP-3 kerosene is 658 K, 688 K, 712 K, and 734 K at 2.5, 3.5, 4.5 and 5.5 MPa, respectively, which increases with the increasing pressure. 2.4. Data reduction Based on the one-dimensional thermal conduction equation under the cylindrical coordinate system, the local inner wall temperature Tw,i can be calculated as follow: �� �� 2 � � � φ_ r2o r2i φr _ o ro qloss ro Tw;i ¼ Tw;o (1) ln 2λ λ ri 4λ where λ is the thermal conductivity of the tube, φ_ ¼ π ðd2UId2 ÞL is the in 4
o
i
ternal heat source. The effective heat flux qw can be calculated by:
qw ¼ π 4
Fig. 3. Reproducibility tests of the experimental system under the same conditions.
433
Mass flux (kg/m2⋅s) Pressure (MPa) Inlet Reynolds number Heat flux (kW/m2)
1273 2.5, 3.5, 4.5, 5.5 4360–4500 700, 950, 1240
hx ¼
RP-3
n-octane (2.19%), n-nonane (6.77%), n-decane (11.62%), n-undecane (16.12%), n-dodecane (14.82%), n-tridecane (10.48%), n-tetradecane (3.35%), npentadecane (1.86%), 1-decene (6.54%), 1-methyl-3-isopropylbenzene (5.29%), 1, 3, 5-trime thylbenzene (9.45%), 1-methylnaphthalene (4.71%), 1, 1, 4 -trimethylcyclohexane (6.79%), CH4, C2H4, C2H6, C3H6, C3H8, 1-C4H8, n-C4H10, 1-C5H10, n-C5H12, 1C6H12, n-C6H14, 1-C7H14, n-C7H16
Products
(3)
Tb;x
(4)
Qtotal ¼ Qphy þ Qchem
The total heat absorption could be calculated by the effective heat
Table 4 Surrogate compounds used for estimating thermophysical properties of the fuel. Surrogate compound (mass fraction)
qw Tw;i
The fuel only shows the capacity of physical heat absorption before the pyrolysis. When the fuel temperature is higher enough to pyrolysis, the qw in Eq. (3) contains the chemical heat absorption by cracking re actions, the hx calculated by Eq. (3) has both the effect of convective heat transfer and thermal cracking and was named as the apparent heat transfer coefficients. Thus, the HTCs in the non-cracked region and the cracked region should be calculated by different ways. In the non-cracked region, the inner wall temperature was calculated by Eq. (1), while the bulk fuel temperature in the corresponding position was calculated by interpolating the adjacent bulk fuel temperatures measured by TC. In the cracked region, the Tb,x was obtained by mea surement at x ¼ 0.5 m, x ¼ 0.62 m, x ¼ 0.7 m, and x ¼ 0.8 m. While the Tw,i in the corresponding position was calculated by interpolating the adjacent inner wall temperature. The HTCs calculation method in the non-cracked and cracked region has been summarized in Table 5. Besides the heat transfer characteristics, the heat absorption capacity of fuel was studied in this paper. It is known that the pyrolysis of hy drocarbon fuel is an endothermic progress. Once the RP-3 is cracked, the heat absorbed by fuel consists of both physical and chemical heat ab sorption. There is:
work [13] was used to evaluate the thermophysical properties of RP-3. Furthermore, since many low-molecule-weight species are produced, the compositions of fuel keep changing during the pyrolysis process. Thus, the main products should be contained in the surrogate model. And the final surrogate compounds used for thermophysical properties estimation are given in Table 4. As the surrogate compositions of fuel are determined, the method generally adopted to estimate the thermophysical properties is either using the SUPERTRAPP program or developing property code with the equation of state. Because of the limited number of compounds (less than 20 compounds) could be contained in evaluating the thermo physical properties of the mixture with SUPERTRAPP program. The RKPR equation of state (EoS), a unified form of SRK and PR EoS, was adopted to estimate the density (ρ) of the mixture. The details of RK-PR EoS could be found in Refs. [29,30]. The isobaric specific heat capacity (Cp) of the mixture was calculated by the thermodynamic relations [31]. Based on the present 13-species surrogate model, the calculated critical pressure and critical temperature of RP-3 is 2.15 MPa and 634.13 K while the corresponding measured values of RP-3 is 2.33 MPa and 645.04 K [32], respectively. The relatively error between calculated
Fuel
(2)
qloss
where R(T) and qloss is the electrical resistivity and heat loss of the test tube, respectively. Before the experiments, the tube without fuel was directly heated under various heating power, then the heat loss was gained by fitting with the temperature difference between ambient and tube wall, and the electrical resistivity was gained by fitting with the measured wall temperature. Generally, the heat transfer coefficients represent the convective heat transfer characteristic, which was calculated as following:
Table 3 Detailed experimental conditions. Inlet temperature (K)
I 2 ⋅RðTÞ � d2o d2i ⋅πdi
Table 5 The HTCs calculation method in the non-cracked and the cracked region.
Tb, x
Tw, i
4
Non-cracked region (local heat transfer coefficients)
Cracked region (apparent heat transfer coefficients)
The interpolation of measured Tb, x at two adjacent positions.
The outlet bulk fuel temperature measured at x ¼ 0.5 m, x ¼ 0.62 m, x ¼ 0.7 m, and x ¼ 0.8 m. The interpolation of Tw,i at two adjacent positions.
�� 2 φr _ o Tw;i ¼ Tw;o 2λ � � � � φðr _ 2o r2i Þ ro qloss ro ln 4λ λ ri
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International Journal of Thermal Sciences 146 (2019) 106092
flux of 1240 kW/m2. The ratio decreases with the increases of pressure, which indicates that more alkanes and fewer alkenes are produced at the elevated pressure. It is commonly accepted that pyrolysis of hydrocar bons can be explained by the free-radical mechanisms. The product distribution of hydrocarbons under high pressure and temperature conditions should follow the compromise of competition between the Rice-Kossiakoff mechanism (R–K mechanism) [34] and Fabuss-Smith-Satterfield mechanism (F-S-S mechanism) [35–37]. From the free-radical mechanisms, it could be known that β-scission and hydrogen abstraction reaction often occur together during the pyrolysis process of hydrocarbons, which is the main step to produce alkenes and alkanes, respectively. At high reactant concentration resulted from high-pressure conditions, bimolecular hydrogen abstraction reactions are favored over unimolecular β-scission reactions, which typically have higher activation energies [21,38]. Thus, with the elevated pressure, the yield of alkanes is larger than that of alkenes. Furthermore, the forma tion of alkene is an endothermic process, whereas for alkane it is an exothermic process. From this point of view, elevated pressure has an inhibitory effect on the endothermic capacity of the fuel. This result is consistent with Zhou’s research [24], that the effect of pressure on the endothermicity of n-decane is not a simple effect of promotion or inhi bition and the regularity is different in different temperature ranges. And there will be another intersection in total heat sink curves at higher conversion. In conclusion, the elevated pressure can impact on the reaction pathway of alkanes and alkenes, resulting in a smaller alkene/alkane ratio and less endothermicity. A promoting effect of the elevated pres sure and heat flux on the conversion and gas yield was confirmed in this work.
flux, as shown by Eq. (5). (5)
Qtotal ¼ qw ⋅πd⋅Δl=m_
While the heat absorbed by unreacted fuel and the reaction products comprises the physical heat sink. The Cp of cracked RP-3 (the dot symbol in Fig. 7) could be obtained based on the detailed chemical compositions at outlet of different length heated tube. Thus, the physical heat sink can be calculated by the enthalpy difference, as given by Eq. (6). Z T2 Qphy ¼ Cp ðTÞdT (6) T1
Then, the chemical heat sink was obtained based on Eqs. (4)–(6). According to the error propagation formula and precision of direct measurements, the uncertainty of effective heat flux, inner wall tem perature, and heat transfer coefficient were calculated and summarized in Table 6. 3. Results and discussion 3.1. Pyrolysis characteristics The conversion and gas yield of RP-3 under different conditions are shown in Fig. 4. The gas yield is defined as the mass fraction of the gaseous products to the fed fuel. The pyrolysis conversion is defined as the mass fraction of the reacted fuel to the fed: X¼
1
m m
0
(7)
� 100%
where m is the mass of unreacted RP-3 at the outlet of the test tube. The gas yield was the mass fraction of gaseous product to the fed. As seen in Fig. 4, the thermal cracking of RP-3 begins at approxi mately 790 K, which is similar to the result of Liu et al. [19]. Under the same inlet temperature, heated length, and pressure condition, the conversion of RP-3 increases from 34 � 4% to 62 � 3% as the heat flux increases from 950 kW/m2 to 1240 kW/m2. Previous studies [33] found that a high pressure implies a high reactant concentration which results in a large reaction rate. On the other hand, a high pressure also results in a large fluid density and long residence time. Combining the two factors mentioned above, a lower bulk fuel temperature and higher conversion can be observed when elevating the pressure. The distributions of gas yields with temperature are similar to those of conversions, except that the slope of gas yield - Tb is larger than that of X–Tb in the high fuel temperature region. The reason is that with the increase of temperature, the secondary reactions become strong and lots of gaseous products were generated by the secondary reactions [20]. The variations of the heat sink with bulk fuel temperature at different pressures are shown in Fig. 5. Under the studied conditions, the total heat sink exhibits a growth trend with the increase of pressure and temperature. The difference between total heat sink and physical heat sink is the chemical heat sink provided by the endothermic pyrolysis of RP-3. From Fig. 5, it is obviously that the chemical heat sink is approximately one-third of total heat sink at the outlet of test section. Besides, the chemical heat sink increases with the increasing pressure while the little effect of pressure on physical heat sink was observed. From the previous discussion, it is known that the elevated pressure leads to high conversion of fuel and thus a larger endothermic capacity. Fig. 6 shows the alkene/alkane ratio of products under the wall heat 0
3.2. Heat transfer characteristics Fig. 7 shows the variations of isobaric specific heat capacity and density with bulk fluid temperature. The dash lines represent the isobaric specific heat capacity and density without considering the composition change in the cracked region. The variations of composition caused by pyrolysis lead to a slight decrease of isobaric specific heat capacity and obvious decreases of the density respectively, as shown in Fig. 7. Fig. 8 shows the local outer wall temperature and bulk fuel tem perature variations along the heated tube under different heat fluxes. Under 700 kW/m2 condition, obvious difference were observed in Tw,o when the bulk fuel temperature reached Tpc at different pressures. As the heat flux was increased to 950 kW/m2, local wall temperature peaks appeared at approximately x ¼ 0.385 m under all pressure conditions. At a rather higher heat flux (qw ¼ 1240 kW/m2), significant local peak of wall temperature was observed at x ¼ 0.29–0.34 m and the peak location shifted to the inlet of heated tube. Besides, the magnitude of peak wall temperature increases with the decrease of pressure. Based on the above three cases, it is observed that the position of peak wall temperature shifts towards the tube inlet with the increased heat flux. While the magnitude of peak wall temperature increases as well as the peak location of wall temperature shifts progressively towards the tube inlet with the decrease of pressure. Fig. 9 shows the variation of heat transfer coefficient (HTC) as a function of bulk fluid temperature under different pressures. The dot and star symbol represents the local and apparent HTCs in the non-cracked and cracked region, respectively. It is observed from Fig. 9 that the HTCs have the same trend with the increasing heat flux at all pressure conditions: heat transfer enhancement was observed when approaching the fuel critical temperature, which is in accordance with the previous studies [4]. It is known that when the fuel temperature is near the Tpc, the specific heat of the bulk fluid will increase while both the viscosity and density will decrease and this will therefore enhance the heat transfer. When Tw is much higher than the Tpc, the fluid density, thermal conductivity and specific heat near the wall can be quite low, while
Table 6 Uncertainties in the experimental parameters. Parameters
Uncertainties
Effective heat flux, kW/m2 Inner wall temperature, K Heat transfer coefficients, kW/m2⋅K Conversion/Gas yield, %
�1.29% �10.07% �10.23% �10.00%
5
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International Journal of Thermal Sciences 146 (2019) 106092
Fig. 4. Distributions of conversion and gas yield of RP-3.
Fig. 5. Heat sink (qw ¼ 1240 kW/m2).
with
fuel
temperature
at
different
impairs the heat transfer between the fluid and the wall, and this will therefore deteriorate the heat transfer [39]. At qw ¼ 700 kW/m2, the Tw is only slightly higher than Tpc when Tb is near the Tpc, thus the enhanced effect of Tb prevails over the deteriorated effect of Tw, peaks of local HTC appear at (P ¼ 2.5 MPa) or before (P ¼ 3.5, 4.5, and 5.5 MPa) the bulk fuel temperature reached Tpc. The magnitude of peak HTC reduced with pressure increasing from 3.5 MPa to 5.5 MPa as the isobaric specific heat capacity at Tpc (given in Fig. 7) reduced with increasing pressure. As the heat flux increasing to 950 kW/m2, the enhanced effect of Tb was weakened by the deteriorated effect of Tw, an increase of local HTC in the vicinity of Tpc was obtained and local peak of HTC is less obvious. At relatively high heat flux (qw ¼ 1240 kW/m2), the Tw is much higher than the Tpc, thus the deteriorated effect of Tw overcomes the enhanced effect of Tb, no peak of local HTC was observed. In the cracked region, the apparent HTC under different pressures first decreased and then recovered. This may results from that the increased heat absorption capacity makes the rate of the increase of the fuel temperature slow down while the difference between the fuel temper ature and wall temperature is not affected at the same time, so the wall temperature also has a lower rate of increase when fuel starts to pyrol ysis [40]. The same distributions of fuel and wall temperature has been reported by Liu et al. [19]. As the conversion of RP-3 increase, the fuel density further decrease and a recovery of HTCs could be observed near the tube outlet under 1240 kW/m2. In what follows, the effect of buoyancy and thermal acceleration on heat transfer in the vertical flow is discussed. The dimensionless buoy ancy parameter, Bo* was introduced to evaluate the buoyancy effect on heat transfer and it was defined as
pressures
Bo* ¼
Grq Re3:425 Pr0:8
(8) 2 4
where Grq ¼ βgqλwμρ2 d is Grashof number, β ¼ ρ1
f
ρb ρw
Tw Tb
is the thermal
compression coefficient. Jackson et al. [41] pointed out that the buoy ancy effect is non-negligible and the heat transfer is deteriorated when Bo* is between 6 � 10 7 and 1.2 � 10 6 for upward flow. Liu et al. [5] found that buoyancy may significantly deteriorate heat transfer of n-decane when Bo* larger than 2 � 10 7 for upward flow. Recently, Fu et al. [9] obtained a new limiting value of Bo*＞1 � 10 8 as the criterion to evaluate the influence of buoyancy on heat transfer to supercritical RP-3. The effect of thermal acceleration on heat transfer ability was characterized by the thermal acceleration factor KvT. KvT ¼ Fig. 6. Alkene/alkane ratio of products under different pressures.
4βqw
ρuCp Re
(9)
Fig. 10 shows the variations of Bo* and KvT with bulk fuel 6
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International Journal of Thermal Sciences 146 (2019) 106092
Fig. 7. Variations of isobaric specific heat capacity and density with bulk fuel temperature.
Fig. 8. Local wall temperature and bulk fuel temperature distributions along the heated tube.
temperature under different heat fluxes. The results indicated that KvT is always far less than 6 � 10 7 [5] and the effect of thermal acceleration could be neglected in all of the studied conditions. From the results of Bo*, it is known that the Tw peak (in Fig. 8) and the obvious decrease of local HTCs (in Fig. 9) decrease under qw ¼ 950 kW/m2 and qw ¼ 1240 kW/m2 are mainly caused by the buoyancy effect. As well known, the buoyancy force exerts in the same direction of the flow and the turbulence production in the near-wall region would be reduced (flow laminarization) for upward flow. Consequently, the turbulent shear stress and thus momentum transfer is impaired and results in the deterioration of heat transfer [42]. To point it out particularly, under the relatively high heat flux, increasing pressure can decrease the value of the maximum wall temperature. Whereas the elevated pressure will enlarge the range of heat transfer deterioration region caused by buoyancy. Thus, it can be concluded that the increase of pressure has little effect on alleviating of heat transfer deterioration under rather large heat flux. Furthermore, the average heat transfer coefficient was calculated. In this paper, the average HTC is defined as: h¼
n X hi � Δli i¼1
L
significant increase in velocity, which consequently improves the convective heat transfer. Besides, the thermal cracking of RP-3 is an endothermic process which absorbs heat from fuel, and thus decrease the temperature difference between the bulk and the near wall, which is beneficial for the improvement the convective heat transfer. In the non-cracked region, the average HTC increased as the pressure increases, and the reverse trends were observed in the cracked region under the same heat flux. In previous researches [43], the average HTC was always found to increases with decreasing pressure under normal heat transfer regimes. The opposite trend found in this work might be due to the heat transfer deterioration occurred under the heat flux of 950 kW/m2 and 1240 kW/m2. While in the cracked region, the varia tions of average HTC with pressure is mainly determined by density. Even the total heat sink increases with the elevated pressure (in Fig. 5) in the cracked region, the heat absorption rate shows a reverse trend because of the residence time increases with the elevated pressure in the cracked region as shown in Fig. 12. And as well known the residence time is mainly determined by the local density. From the above analysis, it can be concluded that the influence of pressure on heat transfer characteristic is dominant by the isobaric specific heat capacity and density in the non-cracked region and the cracked region, respectively.
(10)
3.3. Effect of pyrolysis on heat transfer in HTD region
The average heat transfer coefficients of the non-cracked region and cracked region under different pressures are shown in Fig. 11. Obvi ously, the average HTC in the cracked region is significantly larger than that of the non-cracked region, which implies that the pyrolysis of fuel will improve the heat transfer. As stated in the previous section, the obviously decreases of density in the cracked region will lead to a
The apparent kinetic parameters (pseudo frequency factor A and pseudo activation energy Ea) of RP-3 were determined at different pressures, assuming that the pyrolysis reaction follows a first-order ki netic law. Based on the method provided by Jiang et al. [20], the re action rate could be derived from the conversion and residence time in 7
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International Journal of Thermal Sciences 146 (2019) 106092
Fig. 9. Variations of HTCs with bulk fuel temperature.
Fig. 10. Variations of Bo* and KvT with bulk fuel temperature.
each segment of the test tube. Then the apparent frequency factor and the pseudo activation energy were obtained by plotting lnk vs 1000/RT, as shown in Fig. 13. The apparent kinetic parameters of RP-3 pyrolysis were determined by the linear regression analysis method, the results are listed in Table 7. For the high pyrolysis rate near the wall (in Fig. 14) in heat transfer deterioration region, errors could be introduced in estimating the apparent kinetic parameters. The estimated apparent kinetic parameters would be larger than the true values. Based on the apparent kinetic parameters, the reaction rate constants along the tube were calculated. Fig. 14 shows the detailed distributions of reaction rate constant based on the inner wall temperature and bulk fuel temperature at the heat flux of 1240 kW/m2. It can be seen from
Fig. 14 that the reaction rate constant in the near-wall region when HTD happens (x ¼ 0.2–0.4 m) can be larger than 250 s 1, while the maximum of that of bulk fuel was ca. 200 s 1. The pyrolysis products result in decrease of fuel density in the near-wall region, which further increases the density difference on the cross-section. On the other hand, the strong pyrolysis reaction of RP-3 near the wall also provided additional heat sink, which is beneficial for the improvement of the heat transfer. The variations of Bo* without and with considering the pyrolysis in the nearwall region are shown in Fig. 15. The influence of pyrolysis on the dis tribution of Bo* and thus buoyancy effect was small. Therefore, the pyrolysis is beneficial to lower the wall temperature in HTD region. Similar conclusions were drawn by Isaev et al. [44] that the 8
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International Journal of Thermal Sciences 146 (2019) 106092
Table 7 Apparent kinetic parameters. Pressure (MPa)
Temperature (K)
Ea (kJ/mol)
A (s 1)
2.5 3.5 4.5 5.5 5 [20]
790–950 793–947 800–941 799–937 773–977
181.298 188.993 188.774 186.520 217.9
2.94 � 1012 8.21 � 1012 7.97 � 1012 5.48 � 1012 2.8686 � 1014
Fig. 11. Average heat transfer coefficient under different pressures.
Fig. 14. Distributions of reaction rate constants at 1240 kW/m2.
Fig. 12. Distributions (qw ¼ 1240 kW/m2).
of
residence
time
and
heat
absorption
rate
Fig. 15. Variations of Bo* without and with considering the pyrolysis.
Tao et al. [45] conducted a numerical investigation of the pyrolysis ef fects on heat transfer characteristics, it was found that the pyrolysis can lower the maximum value of the wall temperature and shortens the range of HTD region. 4. Conclusions Fig. 13. Arrhenius plot for the pyrolysis of RP-3 under different pressures.
This study experimentally investigated the pyrolysis and heat transfer characteristics of aviation kerosene RP-3 flowing in a vertical upward tube under supercritical pressure ranging from 2.5 MPa to 5.5 MPa and fluid temperature ranging of 433 K–950 K. The major
enhancement of heat transfer under high heat flux is caused by the py rolysis reaction in the boundary layer under high heat flux and fuel temperature conditions, which is a special phenomenon for organics. 9
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conclusions are summarized in the following.
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(1) Under the studied conditions, the increases of heat flux lead to a high conversion and gas yields which accompanied with the heat transfer deterioration phenomenon. The elevated pressure was found to increase the conversion and gas yield of fuel, and impacted on the reaction pathway of alkanes and alkenes, resulting in a smaller alkene/alkane ratio and less endothermicity. (2) The heat transfer characteristics were analyzed in detail based on the wall temperature and the local (apparent)/average HTC dis tributions. The buoyancy effect caused the deterioration of heat transfer under rather high heat flux. The elevated pressure decreased the maximum wall temperature whereas enlarged the range of heat transfer deterioration region caused by buoyancy. A conclusion was obtained that the increase of pressure has little effect on alleviating of heat transfer deterioration under rather large heat flux. The average HTCs in the cracked region is twice larger than that in the non-cracked region, which implied the pyrolysis improves the heat transfer of fuel. Besides, it was found that the influence of pressure on heat transfer characteristic is dominated by the isobaric specific heat capacity and density and in the non-cracked region and the cracked region, respectively. (3) The apparent kinetic parameters under different pressures were obtained and the effect of pyrolysis on heat transfer deterioration was investigated. It was found that the strong pyrolysis reaction near the wall was beneficial to lower the wall temperature in the HTD region, and the buoyancy effect was not significantly increased by the further decrease in fluid density caused by pyrolysis. Acknowledgment This work was funded by the National Natural Science Foundation of China (Grant No.51576027), the financial support is gratefully acknowledged. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.ijthermalsci.2019.106092. References [1] W.B. Hall, Heat transfer near the critical point, Adv. Heat Tran. 7 (1971) 1–86. [2] K. Yamagata, K. Nishikawa, S. Hasegawa, T. Fujii, S. Yoshida, Forced convective heat transfer to supercritical water flowing in tubes, Int. J. Heat Mass Transf. 15 (12) (1972) 2575–2593. [3] D. Wang, X. Dai, R. Tian, L. Shi, Experimental investigation of the heat transfer of supercritical R134a in a horizontal micro-fin tube, Int. J. Therm. Sci. 138 (2019) 536–549. [4] W. Li, D. Huang, G.Q. Xu, Z. Tao, Z. Wu, H.T. Zhu, Heat transfer to aviation kerosene flowing upward in smooth tubes at supercritical pressures, Int. J. Heat Mass Transf. 85 (2015) 1084–1094. [5] B. Liu, Y. Zhu, J.J. Yan, Y. Lei, B. Zhang, P.X. Jiang, Experimental investigation of convection heat transfer of n-decane at supercritical pressures in small vertical tubes, Int. J. Heat Mass Transf. 91 (2015) 734–746. [6] A. Urbano, F. Nasuti, Onset of heat transfer deterioration in supercritical methane flow channels, J. Thermophys. Heat Transf. 27 (2) (2013) 298–308. [7] R.F. Faulkner, The Evolution of the Hyset Hydrocarbon Fueled Scramjet Engine, vols. 15–19, 12th AIAA International Space Planes and Hypersonic Systems and Technologies, Norfolk, Virginia, 2011, p. 2003. Dec. [8] C. Zhang, G. Xu, L. Gao, Z. Tao, H. Deng, K. Zhu, Experimental investigation on heat transfer of a specific fuel (RP-3) flows through downward tubes at supercritical pressure, J. Supercrit. Fluids 72 (9) (2012) 90–99. [9] Y. Fu, H. Huang, J. Wen, G. Xu, W. Zhao, Experimental investigation on convective heat transfer of supercritical RP-3 in vertical miniature tubes with various diameters, Int. J. Heat Mass Transf. 112 (2017) 814–824. [10] J. Wen, H. Huang, Y. Fu, G. Xu, K. Zhu, Heat transfer performance of aviation kerosene RP-3 flowing in a vertical helical tube at supercritical pressure, Appl. Therm. Eng. 121 (2017) 853–862.
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[43] D. Huang, B. Ruan, X. Wu, W. Zhang, G. Xu, Z. Tao, P. Jiang, L. Ma, W. Li, Experimental study on heat transfer of aviation kerosene in a vertical upward tube at supercritical pressures, Chin. J. Chem. Eng. 23 (2) (2015) 425–434. [44] G.I. Isaev, I.T. Arabova, G.K. Abdullaeva, F. Mamedov, Heat exchange in organic fluids at supercritical pressure, Heat Transf. Sov. Res. 25 (1993) 175–178.
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11