Experimental and Numerical Investigations on n-Decane Thermal

Dec 18, 2013 - ABSTRACT: The flow and heat-transfer behavior of thermal cracking n-decane was investigated experimentally and numerically. An electric...
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Experimental and Numerical Investigations on n‑Decane Thermal Cracking at Supercritical Pressures in a Vertical Tube Yinhai Zhu, Bo Liu, and Peixue Jiang* Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Beijing Key Laboratory of CO2 Utilization and Reduction Technology, Department of Thermal Engineering, Tsinghua University, Beijing 100084, People’s Republic of China ABSTRACT: The flow and heat-transfer behavior of thermal cracking n-decane was investigated experimentally and numerically. An electrically heated vertical tube (2 mm inner diameter) was applied to carry out thermal cracking of supercritical pressure n-decane at various pressures, temperatures, and resident times. The results showed that the second-order reactions increase the formation rates of the light products (especially CH4 and C2H4) for conversions greater than 13%, while the heavy product (C5−C9) formation rates are decreased. A global reaction model is given for n-decane conversions less than 13%, including 18 main product species. A computational fluid dynamics (CFD) model was developed using the real thermal properties and coupled with fuel flow, heat transfer, and wall thermal conduction. Three turbulence models were tried out and then compared to the experimental results. The “SST k−ω model” can better predict the wall temperature than other turbulence models. The predicted fuel and wall temperatures are in good agreement with experimental data. The results also show that ndecane continues to crack with almost half of the n-decane conversion in the connection pipe. Thus, the thermal cracking in the connection pipe should be more carefully analyzed in cracking models.

1. INTRODUCTION Thermal control and cooling are a major consideration for advanced hypersonic flight vehicles. In the vehicle engines, the combustion temperatures and the heat-transfer rates from the hot gas to the combustor chamber wall are both very high. Regenerative cooling with the fuel as the coolant is one feasible solution that uses the sensible heat provided by the fuel. In regenerative cooling, the fuel flows through cooling passages to cool the engine wall before it is injected into the combustion chamber for combustion.1,2 Traditional cooling methods using only the fuel sensible heat will not be sufficient to meet the cooling requirements of advanced aircraft. One potential solution is the use of endothermic fuels to provide extra cooling through endothermic cracking reactions.3−6 Hydrocarbon fuels generally react with dissolved oxygen at temperatures above approximately 150 °C.7 Significant thermal cracking of jet fuel occurs at temperatures above 480 °C.8 Increased fuel conversion will result in more cooling with the formation of more aromatics. Aromatics are known deposition precursors.9 Deposition is undesirable because it can block cooling passages, resulting in system failure. Therefore, mild cracking reactions of fuels are of interest in endothermic fuel regenerative cooling systems. In real fuel systems, the thermal cracking mechanism is quite complex, with the cracking resulting in thousands of chemical reactions. The fuel temperature, pressure, and residence time all strongly influence the cracking reactions. The three main types of thermal reaction models include detailed, lumped, and global mechanisms. Detailed and lumped chemical mechanisms have generally been used in only non-flowing, one-dimensional, analytical models.10−12 Dahm et al.13 proposed a detailed kinetic model with 1175 reactions for n-dodecane based on experimental data for thermal decomposition from 950 to 1050 K. Xing et al.14 investigated the kinetics and product distributions at different temperatures from 663 to 703 K. © 2013 American Chemical Society

The thermal cracking kinetic process was correlated by the pseudo-first-order kinetic equation. Widegren and Bruno15−17 investigated the thermal cracking of RP-1 and RP-2 in stainlesssteel ampule reactors. The global pseudo-first-order rate constants were obtained that approximate the overall rate of decomposition for the fuel. Li et al.18 and Jiao et al.19 used a program named “ReaxGen” to develop detailed mechanisms for large hydrocarbons. The detailed decomposition kinetic models for n-heptane were constructed with 557 reactions, and the detailed decomposition kinetic models for n-decane were constructed with 1072 reactions. However, these kinetic models require detailed reaction pathways and rate constants that are generally unavailable for high carbon number n-alkanes, which make them difficult to use in computational fluid dynamics (CFD) modeling. For low conversion (mild cracking) of normal alkanes, the primary degradation products have been observed to be smaller carbon number alkanes and alkenes.20,21 Mild-cracking experiments have shown that the products form with constant proportions with respect to the other products.20,22 Most past numerical simulations of thermal cracking have used global chemical mechanisms.23 Global models are generally most practical for CFD applications, especially for mild cracking conditions. Ward et al.24,25 further experimentally investigated the reactions in n-decane and n-dodecane flow reactors for mild cracking conditions. A numerical model was developed to calculate the heat and mass transport using a unique global chemical kinetics model based on the proportional product distribution assumption, whereas the heat transfer between the fuel and wall was not included in the CFD model and the wall Received: September 24, 2013 Revised: December 15, 2013 Published: December 18, 2013 466

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Figure 1. Experimental flow reactor test rig: (1) fuel reservoir, (2) two piston pumps, (3) flow meter, (4) preheater section, (5) test section, (6) connection pipe including flange, (7) cooler, (8) back-pressure valve, (9) liquid−gas separator, (10) flow meter, (11) gas sample, and (12) liquid sample.

Figure 2. Schematic of the test section.

temperature was specified as a boundary condition. Hou et al.26 proposed a one-step thermal cracking global reaction model for kerosene using the proportional product distribution assumption. However, the liquid-phase products were not measured, with the liquid products assumed to all be represented by C7H8. Zhong et al.27 studied the thermal cracking of kerosene and developed a one-step lumped model. Their model also did not account for the liquid products. More recently, Jiang et al.28 carried out thermal cracking of supercritical hydrocarbon aviation fuels with variable reactor tube lengths. A modified molecular reaction model consisting of 18 species and 24 reactions was developed to predict thermal cracking, whereas their model assumed that the flow is a one-dimensional plug flow and the turbulence was not considered. Therefore, their model cannot predict the heat transfer between the fuel and wall and provide the information of the wall temperature. Most past simulation models calculate the cracking reaction but do not couple the heat transfer between the fuel and wall. The wall temperature is significant in the regenerative cooling design. The focus of the current work is to develop a CFD model that couples the fuel flow, thermal cracking, and heat transfer between the fuel and wall. n-Decane was chosen as the fuel for the present study because it is a typical hydrocarbon fuel with a similar carbon number and similar properties to commonly used hydrocarbon fuels for aerospace applications. The wall temperature, fuel temperature and pressure, and cracking product distributions were measured for flowing supercritical n-decane. A global reaction model was then obtained, which included 18 vapor and liquid product species.

The reaction model was then incorporated into a CFD model to simulate n-decane thermal cracking with fuel flow, heat transfer, and wall conduction. Three turbulence models were tried out and were validated by comparison to experimental data. The continued thermal cracking in the connection pipe between the test tube and the cooler was also investigated.

2. EXPERIMENTAL SECTION 2.1. Experimental System. The flow reactor experimental test rig is shown schematically in Figure 1. The rig included a fuel supply system, a preheater, a test section, a cooler, and sampling and measurement systems. The fuel supply system consisted of a fuel tank, two high-pressure piston pumps, a fluid regulator, and a bypass valve. n-Decane was used as the fuel. The fuel was pressurized from the fuel tank to a supercritical pressure and fed into the preheater and reactor by the piston pumps. The pumps were used to control the fuel mass flow rate by adjusting the stroke of the plunger piston. The fluid regulator was installed after the pumps to eliminate the pressure fluctuations. The fuel was heated by electric power in the preheater and reactor. Two voltage stabilizers were used to supply constant power inputs. The preheater was made of stainless steel with an inner diameter of 2 mm and a wall thickness of 0.5 mm. The fuel in the test section was heated to thermal cracking conditions. A short 147 mm long connection pipe connected the test section and the cooler to minimize thermal cracking in the connection pipe. The cooler was a pipe heat exchanger with water as the coolant. The fuel was cooled to room temperature with the pressure and then reduced to ambient pressure by the back-pressure valve. We used a vapor−liquid separator especially designed for aviation kerosene. Each experimental data was recorded until the heat and mass 467

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balanced in the separator to increase the separation efficiency. The experimental system took about 2 h to achieve steady. After the separator, gas product samples were collected using a gas bag and then injected into a gas chromatograph (GC, model SP3420A). Ultrahighpurity helium was used as the carrier gas. The residual liquid samples were collected and analyzed off-line using a gas chromatograph with a mass spectrometer (GC−MS, model SHIMADZU GCMS-QP2010 SE). 2.2. Test Section. The test section was a 940 mm long vertical stainless-steel tube with an inner diameter of 2 mm and an outer diameter of 3 mm. The test section was connected to the rig by two sets of flanges, which were thermally and electrically insulated by a layer of mica and two layers of graphite placed between the flanges. Both the test section and the connection pipe were thermally insulated from the environment. The fuel flowed downward. The outer wall temperatures of the test section were measured by 31 micro K-type thermocouples at the locations shown in Figure 2. The test section inlet and outlet fuel temperatures, Tin and Tout, were also measured after mixers. The fluid inlet pressure was measured by a pressure transducer, while the pressure drop through the test section was measured by a differential pressure transducer. 2.3. Uncertainty Analysis. The experimental uncertainty is dependent upon the measurements of the electrical current used to heat, fuel pressure and temperature, wall temperature, fuel flow rate, and product species. The errors of the fuel and wall temperature measurement were dependent upon the K-type thermocouples (accuracy of 0.4%). The errors of the fuel pressure measurement were dependent upon the pressure transducers (accuracy of 0.075% of the full scale). The uncertainty of the pressure is lower than 0.4%. The mass flow rates of the inlet fuel and the total gas products were measured by two Coriolis-type mass flow rate meters (model Siemens MASS2100). The flow meter instructions indicated that the accuracy of the mass flow meters was 0.1%. The error of the electrical current of the power measurement was less than 1.0%. The uncertainty of the electricity heat is approximately 1.3%. The heat loss of the test section was measured and calibrated before the thermal cracking experiments. The heat loss, which depends upon the outer wall temperature, is the total heat dissipated by means of natural convection heat transfer and thermal radiation to the environment. During the heat loss tests, the test section with thermal is vacuumed and heated by electric power. The heat loss under different temperatures is shown in Figure 3. In this study, the outer

uncertainties of the measured mass fraction of all species were lower than 2.5%. All of the product species in Figures 6 and 7 used the data from the second measurement run.

3. CFD MODEL 3.1. Governing Equations. The flow in the pipes was assumed to be governed by the compressible steady-state form of the flow conservation equations. The governing equations for continuum, momentum, energy, and species can be written in the cylindrical (x, r) coordinate system for axisymmetric flow as29 ρv ∂ ∂ (ρu) + (ρv) + =0 ∂x ∂r r

(1)

1 ∂ 1 ∂ (rρuu) + (rρuv) r ∂x r ∂r ⎞⎤ ∂p 1 ∂ ⎡ ⎛ ∂u 2 =− + − (∇ v ⃗ )⎟ ⎥ ⎢rμ⎝⎜ ⎠⎦ ∂x r ∂x ⎣ ∂x 3 1 ∂ ⎡ ⎜⎛ ∂u ∂v ⎟⎞⎤ + + ⎢rμ ⎥ + ρg r ∂r ⎣ ⎝ ∂r ∂x ⎠⎦

(2)

1 ∂ 1 ∂ (rρuv) + (rρvv) r ∂x r ∂r ⎞⎤ ∂p 1 ∂ ⎡ ⎛ ∂v 2 =− + − (∇ v ⃗ ) ⎟ ⎥ ⎢rμ⎝⎜2 ⎠⎦ ∂r ∂r r ∂r ⎣ 3 1 ∂ ⎡ ⎜⎛ ∂u v 2μ ∂v ⎟⎞⎤ (∇ v ⃗ ) + + ⎢rμ⎝ ⎥ − 2μ 2 + r ∂x ⎣ ∂r 3r ∂x ⎠⎦ r

(3)

∂ ∂ (ρuh) + (ρvh) ∂x ∂r ρvh ∂ ⎛⎜ ∂T ⎞⎟ ∂ ⎛ ∂T ⎞ λ ∂T = λ + ⎜λ ⎟ − + + Sh ∂x ⎝ ∂x ⎠ ∂r ⎝ ∂r ⎠ r r ∂r

(4)

∂J ⃗ ∂J ⃗ J⃗ ρvYi ∂ ∂ (ρuYi ) + (ρvYi ) = i + i − + i + Ri ∂x ∂r ∂x ∂r r r (5)

where (∇v)⃗ = (∂u/∂x) + (∂v/∂r) + (v/r). Yi is the mass fraction of species i, and Ji is the diffusion flux of species i. Ri is the net generation rate of species i in the thermal cracking reaction. Sh is the energy source term. The chemical reactions for thermal cracking were modeled using the finite-rate/eddy-dissipation model, which computes both the Arrhenius reaction rate and the mixing reaction rate and uses the smaller of the two.29 The model included one reaction involving 19 species. The rate coefficient, k, was computed using the Arrhenius expression k(T ) = A exp( −E /RT )

(6)

where A is the pre-exponential factor, T is the temperature, E is the activation energy, and R is the universal gas constant. According to Ward et al.,25 A is equal to 1.6 × 1015 and the activation energy E is 63 kcal/mol. The reaction model for the thermal cracking will be introduced in section 4 based on the present experimental data. 3.2. Real Gas Properties. The fuel conditions in this study were all at supercritical pressures. The fluid thermophysical properties at these states are strongly affected by the temperature and pressure, especially in the pseudo-critical region. Therefore, the fluid density, enthalpy, entropy, and

Figure 3. Heat loss under different wall temperatures. wall temperature is within 300−700 °C. The heat loss of the test section is less than 5% of the total power input, and the heat loss of the connect pipe is in the range of 14−18 W. Both the gas chromatograph and GC−MS were calibrated with two external standard mixtures spanning the entire range of products formed in the experiment. A total of 10 replicates of the experimental runs of the two standard mixtures were performed to obtain the relative uncertainties. Reproducibility tests showed that the relative 468

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renormalization-group (RNG) k−ε model, and shear-stress transport (SST) k−ω model,29 were tried out for solving the flow of supercritical pressure fuel. The “enhanced wall treatment” was used to treat the near wall velocity. The first node location in the near-wall mesh was very important, and y+ was kept at approximately 0.7. The inlet boundary conditions were set as the “mass flow inlet” condition with the “pressure outlet” condition at the outlet. The outer wall of the test section was set as adiabatic. The outer wall of the connection pipe was simplified to a constant heat flux boundary condition of 11 550 W/m2 to account for the heat loss. For each simulation, the solution was iterated until the residue for each governing equation was less than 10−3 and the fluctuation of the n-decane mass fraction was within 0.5%.

specific heat were computed as ideal gas properties with departure functions derived from the equation of state. The Peng−Robinson (PR) equation of state was used here because of its wide range of validity and ease of implementation30 p=

RT a − (Vm − b) Vm(Vm + b) + b(Vm − b)

(7)

where R is the universal gas constant and Vm is the volume. The parameters a and b are a = a(Tc)α(T ) b = 0.0778RTc/pc a(Tc) = 0.45724R2Tc 2/pc

4. CHEMICAL REACTION MODEL The thermal cracking behavior of n-decane is affected by the fuel pressure, fuel residence time, and input heat. This study considered various primary flow pressures from 3.1 and 6.3 MPa, fuel inlet mass flow rates from 1.5 to 4 kg/h, and heat inputs to the test section from 350 to 1400 W. The product mass (molar) fraction of species i, yi (xi), was defined as ṁ i ni̇ ; xi = yi = ∑products ni̇ ∑products ṁ i (11)

α(T ) = [1 + m(1 − Tr 0.5)]2 m = 0.37464 + 1.54226ω − 0.26992ω 2

(8)

where Tc is the critical temperature (Tc,C10H22 = 617.7 K), pc is the critical pressure (pc,C10H22 = 2.103 MPa), and ω is the acentric factor (ωC10H22 = 0.4884).31 Tr is equal to T/Tc. The specific heat, cp, was computed from the ideal specific heat, cp,ideal, and the departure specific heat at constant volume, cp,dep, as c p,ideal c p = c p,ideal − (9) MW c p,dep = c v,dep − R − T

(∂V /∂T )2 ∂V /∂T

where ṁ i is the mass flow rate of species i (kg/s) and ṅi is the molar flow rate of species i (mol/s). The mass (molar) fraction of species i, Yi (Xi), was defined as ṁ i ni̇ Yi = ; Xi = ∑fuel mixture ni̇ ∑fuel mixture ṁ i (12)

(10)

where MW is the mean molecular weight (kg/kmol), cv,dep was computed by differentiating the equation for the departure internal energy with respect to T,29 and the partial derivatives of the specific volume were computed by differentiating eq 7. The thermal conductivities and viscosities of both the fuel and the products were calculated using a set of piecewise polynomial correlations based on data from SUPERTRAPP.31 3.3. Mesh and Solution Strategy. The numerical study used the commercial software ANSYS 13.0 FLUENT as the CFD solver. The computational model was modeled in a twodimensional (2D) asymmetric domain, including the test section and the connection pipe, as shown in Figure 4. The grid is made at about 65 000 structured quadrilateral elements.

where ∑fuel mixtureṁ i is the sum of the mass flow rates of all of the species, including the parent fuel, and all of the products. ∑fuel mixtureṅi is the sum of the molar flow rates of all of the species, including the parent fuel, and all of the products. The conversion of n-decane was defined as ṁ C10H22 ε = 1 − YC10H22 = 1 − ∑fuel mixture ṁ i (13) where ṁ C10H22 is the mass flow rate of uncracked n-decane. The variations of the overall and sensible heat sinks with the fuel temperature are shown in Figure 5 for various pressures. The results show that the overall heat sinks at different pressures increase at similar rates with the fuel temperature.

Figure 4. Computational domain.

The nonlinear governing equations were solved using the “pressure-based” solver with the “real gas model”. The secondorder upwind scheme was used to discretize the convective terms. The SIMPLEC algorithm was used for the pressure field. In CFD modeling, the choice of the turbulence model and the wall function is of critical importance to predict the wall temperature. Three turbulence models, standard k−ε model,

Figure 5. Overall and sensible heat sinks at various fuel outlet temperatures. 469

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When the fuel temperature exceeds 560 °C, the endothermic reactions increase, leading to the overall heat sink being greater than the sensible heat sink. The measured maximum overall heat sink increases to 2.7 MJ/kg. Panels a and b of Figure 6 show the variations of the mass fractions of all of the measured vapor and liquid products with

Figure 7. Molar fractions of the products at different n-decane conversions.

The results in panels a and b of Figure 7 show that the second-order reactions begin with n-decane conversions greater than 13%, with the fractions of H2, CH4, and C2H4 significantly increased and those of C5H10, C5H12, C6H12, C6H14, C7H16, and C9H20 significantly decreased. The other product fractions, C2H6, C3H6, C3H8, C4H8, C4H10, C7H14, C8H16, C8H18, and C9H18, remain nearly constant. Thus, the proportional distribution assumption will introduce errors for n-decane conversions greater than 13%. The experimental data were used to develop a one-step global reaction model with constant parameters for n-decane conversions less than 13%.

Figure 6. Species mass fractions of the total fuel mixture for various ndecane conversions.

increasing n-decane conversions. At low n-decane conversions, the formation rate of each product is approximately linear. The formation rate of each product begins to deviate from linear for conversions greater than 13%. The data in Figure 6a show that the formation rates of some of the light vapor products, i.e., CH4 and C2H4, significantly increase at higher n-decane conversions (13% and greater). Figure 6b shows that the mass fractions of the heavier liquid products increase slowly at higher n-decane conversions. This phenomenon can be explained by the second-order cracking reactions. The heavier liquid product formation rates drop below the initial linear rate because they undergo second-order cracking reactions at higher n-decane conversions, while the light product formation rates increase beyond their initial linear rates as more light products formed from these second-order cracking reactions. Figure 7 shows the product molar fractions of all of the cracked n-decane products for different n-decane conversions. Figure 7a shows that CH4, C2H4, and C2H6 are the major species in the vapor products, while olefins are the major species in the liquid products, as seen in Figure 7b. The molar fractions of all of the products are nearly constant at low ndecane conversions, where the second-order n-decane thermal cracking reactions are negligible. Therefore, the product distributions are generally proportional to each another at low n-decane conversions. This result is consistent with other results in the literature.22,24

C10H 22 = 0.0170H 2 + 0.1827CH4 + 0.1980C2H4 + 0.1327C2H6 + 0.0566C3H6 + 0.0372C3H8 + 0.0135C4H8 + 0.0048C4H10 + 0.2015C5H10 + 0.1167C5H12 + 0.0372C3H8 + 0.0135C4H8 + 0.0048C4H10 + 0.2015C5H10 + 0.1167C5H12 + 0.3033C6H12 + 0.0735C6H14 + 0.2611C7H14 + 0.0684C7H16 + 0.2209C8H16 + 0.0130C8H18 + 0.0817C9H18 + 0.0040C9H 20

5. RESULTS AND DISCUSSION The CFD model was used to obtain more detailed information about the flow, temperature, and species distributions in the tube, which are difficult to measure. The six experimental cases shown in Table 1 were selected to compare to simulation results from the CFD model. The fuel and wall temperatures along the test section tube and the connection pipe are obtained with the three turbulence 470

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at 4.2 MPa), as the fuel bulk temperature increases along the tube, the density, viscosity, and thermal conductivity decrease, while the specific heat has a peak at the pseudo-critical temperature, as shown in Figure 9. The decreased thermal conductivity reduces the heat transfer, but the decreased viscosity makes the viscous sublayer thinner, which enhances the heat transfer. The sharp increase of the specific heat significantly enhances the heat transfer because of the increased convection transport capacity. Therefore, the increased rate of the local wall temperature drops at x = 0.25 m, as shown in Figure 8. Figure 10 shows the predicted fuel and wall temperatures along the test section tube and the connection pipe (x > 0.8

Table 1. Cases for Comparison run number

1

2

3

4

5

6

Tin (K) Tout (K) G (kg/h) Q (W) Pin (MPa) Pout (MPa)

624.3 862.79 2.20 591.49 4.20 4.19

625.93 884.32 2.19 648.89 4.20 4.19

627.72 888.56 2.19 663.22 4.22 4.21

664.19 885.87 3.13 826.01 5.30 5.23

666.08 893.63 3.10 865.36 5.28 5.18

666.7 903.06 3.17 939.29 5.28 5.12

models, as shown in Figure 8. The measured fuel temperatures at the test section exit and 31 wall temperatures are also shown

Figure 10. Predicted fuel mixture and wall temperature contours. Figure 8. Comparison of predicted fuel and outer wall temperatures to experimental data (run number 2).

m). The fuel temperature increases gradually at the test section and decreases in the connection pipe. The fuel temperature at the near wall is higher than that at the pipe central locations. For the case of run number 6, the fuel bulk temperature drop is 19.1 K in the connection pipe with consideration of both heat loss from the pipe wall to the environment and the heat absorbed through the endothermic chemical reactions. For the same conditions, the temperature drop is 15.2 K in the connection pipe without the heat loss from the pipe wall to the environment. The n-decane mass fractions along the test section tube and the connection pipe for runs 1−6 are shown in Figure 11. The results show that the present thermal cracking mechanism

in Figure 8. Different from the k−ε models, the SST k−ω model uses a k−ω formulation in the inner parts of the boundary layer. Hence, the SST k−ω model can solve a low-Re turbulent flow without any extra damping functions. Results show that the predicted fuel temperatures by the three turbulence models are very close, while the predicted wall temperatures by the SST k−ω turbulence model agree best with experiments than other turbulence models (other cases calculated but not shown). Thus, the SST k−ω turbulence model is selected in the following CFD studies. The predicted fuel mixture thermal properties and velocity along the tube with the SST k−ω turbulence model are shown in Figure 9. Because the fuel temperatures at the test section entrance are lower than the pseudo-critical temperature (679 K

Figure 9. Fuel mixture thermal properties and velocity along the tube (run number 2), with the SST k−ω turbulence model.

Figure 11. Comparison of predicted C10H22 distributions to experimental data. 471

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agrees reasonably well with the experimental data. The deviation between the predicted outlet n-decane mass fractions and the experimental data is within 3.9%. The results in Figure 11 further show that the predicted outlet n-decane mass fractions are lower than the experimental data at large n-decane conversions and higher than the experimental data at small ndecane conversions. The thermal cracking of n-decane continues after the fuel exits the test tube and flows into the connection pipe, as seen in Figure 12. Although the connection pipe is much shorter than

Figure 14. Predicted CH4 mass fraction distribution contours.

Figure 12. Predicted C10H22 mass fraction distribution contours.

the test tube, almost half of the n-decane conversion is in the connection pipe. The results show that the thermal cracking in the connection pipe between the test tube and the cooler contributes a significant amount to the total thermal cracking and should be included in numerical models. The variations of the mass fraction of two products, CH4 and C5H10, along the tube are shown in Figures 13−16. Both

Figure 15. Comparison of predicted C5H10 distributions to experimental data.

Figure 16. Predicted C5H10 mass fraction distribution contours.

for H2, −34.4% for CH4, and −23.3% for C5H10. Note that the lighter molecular weight products are very little in the cracked mixture. For example, the maximum mass fraction of H2 in the cracked mixture is about 0.013%. Therefore, the absolute error of predicted H2 mass is negligible.

Figure 13. Comparison of predicted CH 4 distributions to experimental data.

product fractions increase along the tube as the n-decane is cracked to produce smaller hydrocarbons. The largest differences between the measured and predicted product mass fractions occur for the H2, CH4, C2H4, C5H10, and C6H12 mass fractions, especially the lighter molecular weight products, because the gas products were difficult to separate and accurately measure. The maximum percent difference is 88%

6. CONCLUSION This work investigates the flow, heat-transfer, and thermal cracking behavior of supercritical n-decane for various pressures, temperatures, and resident times. A total of 18 of the primary cracking product species were measured. The 472

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experiments show that, at low n-decane conversions, the formation rate of each product is approximately linear. The formation rates of the light products (C0−C4) begin to increase for conversions greater than 13%, while the formation rates of the heavy products (C5−C9) decreased. The experimental data were then used to develop a one-step global reaction model with constant parameters for n-decane conversions less than 13%. A CFD model was established to obtain more detailed information about the flow field and species distributions in the tube. The model accounts for the thermal cracking of n-decane at supercritical pressures based on the real gas equation of state and real thermal properties. The model included the flow, heat transfer, and chemical reactions of the fuel and the heat conduction in the tube wall. Three turbulence models were adopted and compared to the experiments. The “SST k−ω model” with “enhanced wall function” can better predict wall temperature than other turbulence models.

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AUTHOR INFORMATION

Corresponding Author

*Telephone: +86-10-6277-2661. Fax: +86-10-6277-0209. Email: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This project was supported by the National Natural Science Foundation of China (51276094), the Science Fund for Creative Research Groups (51321002), and the Defense Industrial Technology Development Program (B1420110113).

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NOMENCLATURE cp = specific heat at constant pressure, J kg−1 K−1 d = diameter (m) E = activation energy (kJ/mol) G = mass flow rate (kg/h) Q = heat input (W) ṁ i = mass flow rate of species i (kg/s) ṅi = molar flow rate of species i (mol/s) p = pressure (Pa) T = temperature (K) u = flow velocity (m/s) x = axial coordinate (m) y+ = non-dimensional wall distance

Greek Symbols

ε = n-decane conversion λ = thermal conductivity (W m−1 K−1) ρ = fuel density (kg/m3) μ = dynamic viscosity (kg m−1 s−1)

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dx.doi.org/10.1021/ef401924s | Energy Fuels 2014, 28, 466−474

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