Kinetic Modeling of Thermal Oxidation and Coking Deposition in

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Kinetic Modeling of Thermal Oxidation and Coking Deposition in Aviation Fuel Xinyan Pei, Lingyun Hou,* and Zhuyin Ren School of Aerospace Engineering, Tsinghua University, Beijing 100084, China ABSTRACT: Aviation fuel is also employed as a coolant in advanced aircraft engines, and the associated formation of deposits in heat exchange systems involves a complex combination of physical processes and chemical reactions. On the basis of our previous experimental results, a pseudodetailed chemical kinetic and global deposition mechanism of the aviation kerosene RP-3 under supercritical pressure was developed. This mechanism involves three bulk reactions and three wall deposition reactions and considers temperature gradients, oxygen consumption, and flow regimes. The fluid−thermal−solid interactions in a tube were simulated in conjunction with the above mechanism, and experimental results obtained at various levels of dissolved oxygen were used to validate the simulation. It was found that this model is able to accurately predict the total amounts of deposition and oxygen consumption, as well as the deposit profile along the tube. The effects of air saturation and of low levels of dissolved oxygen on coking deposition were compared, and a decrease in the dissolved oxygen concentration was shown to effectively reduce coke deposition. The contribution of the temperature gradient was assessed on the basis of predictions of local coking deposition, and the rates of wall reactions were determined to be far slower than those of bulk reactions.

1. INTRODUCTION In next-generation engines, aviation fuel will not only be burned in the combustor but also used as a coolant to ensure sufficient cooling. However, dissolved oxygen and other oxygenated compounds can react with the fuel to form insoluble particles and surface deposits over the temperature range of 150−450 °C. The formation of such deposits within the flow stream in a heat exchange system involves a complex series of physical processes and chemical reactions. Typically, the extent of oxidative coke deposition will vary with temperature,1 flow regimes,2−4 convective heat transfer,5,6 fuel additives,7,8 and surface materials.9,10 Hazlett11 concluded that any mechanism for oxidation deposition must address three factors. These include the sequence of free radical chain reactions between dissolved oxygen and chemical compounds in the fuel that leads to the formation of deposits, the major participating species and precursors associated with the deposition of compounds containing oxygen, sulfur, and nitrogen, and the fact that only a minuscule amount of the original fuel is responsible for insoluble species. Katta et al.12 developed a nine-step kinetic deposition model, although this model was not entirely successful at predicting peak depositions in the certain areas. On the basis of this model, Ervin et al.13 focused on surface deposition in cooled regions, while Zabarnick et al.14 and Ervin et al.15 developed a 17-step pseudodetailed mechanism incorporating the effects of oxygen consumption on deposition. Doungthip et al.16 added the catalytic deposition reactions at the walls to the model to improve predictions of the dissolved oxygen consumption rate. Kuprowicz et al.17 further refined the model and extended it to 21 steps by adding reactions involving phenols, reactive sulfur species, dissolved metals, and hydroperoxides, and also by considering the decomposition reactions of hydroperoxides. Ervin and Zabarnick et al. 5,13,17−19 performed much research concerning the thermal stability of hydrocarbon fuels and oxidation deposition mechanisms. © XXXX American Chemical Society

The mechanisms in previous works were largely based on conditions involving air-saturated fuels or static test systems. In addition, the effects of different inlet dissolved oxygen concentrations on deposition at high temperatures have not been explored. The ability to predict oxidative deposition remains unsatisfactory because details of the oxidation and deposition processes are still not fully understood. To gain a better understanding of the kerosene oxidation and coking processes, the present work developed an oxidative deposition mechanism for RP-3 fuel based on previously reported experimental data.4,6,20 Because of the complicated fluid flows, heat transfer, and chemical reactions in cooling systems, three-dimensional fluid−thermal−solid interactions were simulated using a pseudodetailed chemical kinematic mechanism. On the basis of this mechanism, the effects of different inlet dissolve oxygen concentrations were studied numerically.

2. NUMERICAL SECTION The heat flux in the heat exchanger within an engine is transferred through the interface from the outer wall of a steel tube to the fuel. This process eventually leads to thermal equilibrium based on significant convective heat transfer, complex chemical reactions, and supercritical flow. Accordingly, the fluid−thermal−solid interactions were simulated using the Ansys Fluent package21 in conjunction with a user-defined program of thermal physical properties by establishing fluid and solid domains. These simulations involved a set of conservation equations including mass, momentum, energy, and species transport, as follows: ∇·(ρv ⃗) = 0

(1)

Received: October 31, 2016 Revised: January 7, 2017 Published: January 9, 2017 A

DOI: 10.1021/acs.energyfuels.6b02869 Energy Fuels XXXX, XXX, XXX−XXX

Article

Energy & Fuels

Figure 1. A comparison of experimental and calculated RP-3 thermal properties.

∇·(ρvv⃗ ⃗) = −∇p + ∇·τ ̿

(2)

∇·(v (⃗ ρE + p)) = ∇·(ke∇T − ΣhiJi ⃗ + (τ ̿ ·v ⃗)) + SE

(3)

∇·(ρYv i ⃗) = −∇· (ρYv i d,⃗ i) + Si

(4)

flow, whereas the RNG theory provides an analytically derived differential formula for effective viscosity that accounts for low Reynolds number effects. Therefore, the RNG k−ε model,27 based on the renormalization group method, with full buoyancy effect and enhanced wall treatment was selected as the turbulence model to simulate the transition flow, which has been successfully applied in solving the heat transfer process of supercritical flow in many studies.28−30 The effects of buoyancy are determined by a nonzero gravity field and a nonzero temperature (or density) gradient. In the RNG k−ε turbulence model, the generation of turbulence due to buoyancy is given as

Here, ρ is the density, v ⃗ is the velocity vector, p is the static pressure, τ ̿ is the stress tensor, E is the total energy (including the internal and kinetic energies), ke is the effective conductivity, T is the temperature, Ji⃗ is the diffusion flux of species i, Yi is the mass fraction of species i, and SE and Si are the heat and species source terms related to thermal oxidation reactions. In the solid domain, only the heat conduction equation is solved, as ∇·(λ∇T) = 0, and the conditions at the fuel/solid interface are coupled at the same temperature and heat flux. Chinese No. 3 (RP-3) kerosene was chosen as the model fuel for use in this study.20 An indirectly electrically heated S316 tube was employed to simulate a heat exchanger in which thermal oxidative deposition reactions occur at the supercritical pressure of 3 MPa. The thermal physical properties of aviation kerosene are temperature dependent, and in the simulation the bulk temperature of the fuel increases as it moves along the tube. The components of aviation kerosene were determined using a three-component surrogate model based on the gas chromatography−mass spectrometer analysis.22 The thermal physical properties were calculated by weighting the proportional average of three kinds of components, that is, paraffin, cycloalkanes, and benzenes. The calculated results for these properties are compared to experimental data23−26 in Figure 1. At a fuel temperature close to the critical point, small changes in pressure or temperature result in large variations in the thermal properties, and the fuel becomes a supercritical fluid with gas-like diffusivity, density, and viscosity above its pseudocritical temperature. Because of the properties of the supercritical flow, the Reynolds numbers of fluid have a large variation from inlet to outlet of the tube with a transition from laminar to turbulent flow during the heat exchanging. The standard k−ε model is suitable for a high Reynolds number

μ ∂T

G b = βgi Prt ∂x , where Prt is the turbulent Prandtl number for t

i

energy and gi is the component of the gravitational vector in the ith direction. β is the coefficient of thermal expansion, which is 1

defined as β = − ρ

( ∂∂Tρ )p.

Three different grid densities were employed to ensure the grid independence of the solutions. With a distribution of 390 000 nodes, the computed results were found to be only minimally sensitive to further grid refinement. The mesh near the wall, however, was refined, and the value of the dimensionless wall distance, y+, near the wall of less than 1 was used so as to ensure an enhanced wall treatment. The SIMPLEC pressure-based solver was employed in conjunction with a skewness correction factor of 1. When the normalized error residual for each of the calculated variables was reduced by 6 orders of magnitude below its maximum, the solution was considered to have converged. The experimentally determined outer wall temperature profile obtained from a previous study was fitted with a polynomial equation and used as a boundary condition along the tube in the model. The inlet mass flow rate and the temperature profiles were set to 1 g/s and 20 °C, respectively, while the dissolved oxygen concentration in the normal case was set to 10 ppm. B


Article

Energy & Fuels Table 1. Global-Kinetic Deposition Mechanism Model Parameters for RP-3 pre-exponential A

reaction no.

activation energy E (J/kg mol)

reaction order α

Bulk Fuel Reactions V1 V2 V3

F + O2 → P P→S P → IN

0.083 500 2

W1 W2 W3

F→D IN → D P→D

2 × 10−11 10 480

2 × 10+05 4.1861 × 10+07 8.4 × 10+06

[F][O2] [P] [P]

Wall Reactions 8.6 × 10+06 5 × 10+07 8.5 × 10+07

[F][dT/dX]0.7 [IN] [P]

Here, ω̇ r,s is the rate of the surface reaction, Qr is the heat of the surface reaction, and T is the temperature. In our previous studies, it was concluded that a large quantity of oxidation deposits was generated in the zone associated with high temperature gradients.20 Micrographs of normal oxidative deposits and the deposition in the high temperature gradient section are compared in Figure 2. The normal oxidative deposit

3. REACTION MECHANISM As the chemical kinetics associated with the autoxidation of kerosene and the subsequent formation of surface deposits are extremely complex, the thermal oxidative and coking deposition of kerosene RP-3 was simplified to six pseudodetailed reactions, as shown in Table 1. Reactions V1−V3 occur in the bulk fuel, while W1−W3 take place on the wall surface. The rates for these reactions were presumed to be governed by Arrhenius −E expressions, ω̇ = A exp RT , based on a combination of previously proposed thermal oxidation mechanisms12,31 and our own experimental data.4,6,20 The kinetic mechanism was restricted to temperatures in the range over which oxidation reactions occur, from 150 to 450 °C. In Table 1, F represents the RP-3 fuel, O2 is the dissolved oxygen in the fuel that stimulates the chain reaction oxidation processes, P is the precursor representing the primary product leading to deposits, and S, IN, and D are the bulk solute, the bulk insoluble materials, and the surface deposits, respectively. In the case of the first step of the fuel reaction (V1), a global reaction form was assumed, the rate of which was defined by −E ω̇v1 = A v1 exp RTv1 [F][O2 ], where [F] and [O2] are the concentrations of the fuel and dissolved oxygen, respectively. The dissolved oxygen was primarily consumed in this step, stimulating the oxidation reactions that produce deposition precursor compounds containing oxygen, such as alcohols, aldehydes, and organic acids. Thus, reaction V1 was sensitive to the level of dissolved oxygen in the fuel. Because the deposition rate decreases with increases in the temperature and in the consumption of dissolved oxygen, the function of the second fuel reaction (V2) was to limit the concentration of precursors at high temperatures by producing bulk solute species. In experimental deposition trials, some insoluble species have been observed after filtration through a 0.45 μm membrane, and so, in reaction V3, the precursors transit to bulk insoluble compounds that subsequently form deposits on the wall. The extent of deposit formation on the inner surface of the tube was governed by three wall reactions, and the total deposition rate was determined by the sum of these wall reactions. Given that coking reactions occur on the wall surfaces, the surface boundary conditions for species and energy were set as follows.

( )

( )

ρDi

λs

∂Yi ∂n

∂T ∂n

= Wi ∑ (bir − air )ωṙ ,s w

= w

r

∑ Q rωṙ ,s r

Figure 2. SEM micrographs of the inner surface deposition.

seems to be composed of amorphous and flocculent particles, which has been also observed in some previous experiments.15,32 It is noteworthy that there are not only quantitative but also morphological differences in these deposition layers, which indicates varying deposition mechanisms. In this work, the term (dT/dX)c was added to the Arrhenius expression for the reaction rate, and a reaction order (c) of 0.7 was obtained

(5)

(6) C


Article

Energy & Fuels from regression fitting of the experimental data. The deposits formed by the bulk insoluble material are sensitive to the flow conditions because to some extent they depend on a physical process. A laminar sublayer of very slow-moving fluid is formed adjacent to the inner wall as a result of the high viscosity of the fuel. The resulting long residence time, as well as other factors such as temperature, pressure, and surface roughness, lead to the deposition of bulk insolubles, as represented by reaction W2. The precursors within the fuel are transported to the wall surface as a result of convective fluid motion and molecular turbulent diffusion, and so the formation of deposits primarily depends on the precursor characteristics. A simple model of the deposition resulting from precursors is represented by the wall reaction W3.

4. RESULTS AND DISCUSSION The numerical simulation was validated on the basis of assessing the experimental bulk fuel temperatures measured at the outlet as a function of heat flux. In Figure 3, the error

Figure 3. Comparison of experimental and calculated fuel temperatures at the outlet.

between the predicted values and previously obtained experimental data is seen to be less than 3%. The details of the setup and measurements used to obtain these experimental data have been reported separately in our previous works.4,6,20 The predictions of total deposition mass and oxygen consumption are compared to the previous experimental data in Figure 4. The dissolved oxygen concentrations in the fuel were set to 10 ppm (the normal air-saturated level), 1 ppm (low level), or 32 ppm (high level) at the inlet of the tube. In Figure 4a, the total deposition mass was found to decrease with a drop in the dissolved oxygen concentration at the inlet. The prediction at the normal oxygen level matches the experimental data well, while the predicted deposition at the high level is somewhat lower than the experimental value (by 1.6%), and the deposition is more severely underestimated (by 23%) in the simulation involving a low level of oxygen. Bulk dissolved oxygen levels were measured at the inlet and outlet of the experimental tube section, and Figure 4b provides the experimental and numerical mass fractions of dissolved oxygen at the tube exit for different inlet dissolved oxygen concentrations, which demonstrates the consumption of

Figure 4. Comparison between the experimental and numerical results for deposition and oxygen concentration.

dissolved oxygen in reaction V1. It is shown that the overall predicted dissolved oxygen behavior agrees reasonably well with the measurements. The difference between numerical and experimental data in dissolved oxygen is similar to that for total deposition mass, which reflects the importance of dissolved oxygen in the oxidation deposition reaction in the simulation model. The low and normal dissolved oxygen concentrations represent typical inlet values in an actual cooling system. As shown in Figure 5, the trend of the deposition rate plot moving along the tube generally follows that of the experimental data, indicating the reliability of the present kinetics mechanism. The simulated deposition rates (in kg/m2·s) were converted to the total mass amount of deposition by multiplying the rate by the internal surface area of the tube and the duration of the test. The variations in the local deposition rate result from the wall D


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Energy & Fuels

Figure 5. Comparison of the experimental and calculated deposition rates along the tube.

Figure 7. Species distributions along the tube.

inlet, accompanied by a decrease in the precursor species caused by reaction V2. In Figure 8, the rates of wall reactions are seen to be far less than those of the bulk reactions, because the rate of reaction V1

reaction W1. In contrast, the numerical results for deoxidization tend to underestimate the deposition in some positions as compared to the experimental data; this error results from the special deposition mechanism under deoxygenated condition. Comparing the SEM micrographs in Figures 2a and 6, the

Figure 8. Plots of the reaction rates along the tube axis. Figure 6. SEM micrographs of the inner surface following a deoxidization experiment.

gradually decreases along the tube as a result of the reduction of dissolved oxygen. After the middle of the tube, associated with the relativity high temperature regime, the wall reaction W1 is dominant. The local variations in deposition are ascribed to the wall reaction W3. Figure 9 provides data for the flow field in the normal case. In Figure 9a, the simulation predicts an inhomogeneous distribution of wall temperatures similar to the experimental scenario, such that the temperature near the tube surface is higher than that at the tube center. This asymmetric distribution results from the effects of gravity and buoyancy lift, as compared to the temperature contour without gravity and buoyancy lift in Figure 9b. The flow is strongly influenced by buoyancy, depending on the magnitude of the local Reynolds number. In Figure 9c, the specific heat is evidently enhanced near the pseudocritical temperature according to the characteristics of a supercritical fluid. In Figure 9d, as the fuel flows through the tube, the velocity close to the wall is lower than that near the tube center. Thus, the fuel resides for a

material obtained under deoxygenated conditions appears looser than that in the air-saturated case. These deposits are formed by traces of oxygenated species, which are present at concentrations less than 2% in the initial fuel. In addition, the micrographs show a microscopic needle structure, attributed to the coking originating from C−S−H components.33 Much more research will be necessary to determine the differences in the deposit formation mechanisms in fuels with different levels of dissolved oxygen. When assessing the formation of surface deposits along the tube, it is helpful to visualize the distribution of species in the flow field, especially in the case of dissolved oxygen consumption. In Figure 7, the simulated dissolved oxygen mass fraction undergoes a significant decrease from the beginning of the inlet, and gradually drops moving along the tube. Under these conditions, the production of bulk soluble material is delayed until a distance of 300 mm from the tube E


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Energy & Fuels

Figure 9. Distribution of the flow field for the normal case.

deposition will be taken into account in the future modification of the model.

relatively long time span in the high temperature region close to the wall, resulting in enhanced deposition reactions.

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5. CONCLUSION A kinetic model for the thermal oxidation and deposition of RP-3 kerosene fuel was developed on the basis of multistep volume reactions and global surface reactions, taking into consideration the temperature gradient. The results of this simulation were found to be consistent with experimental deposition data acquired at three dissolved oxygen concentrations, including data for the total surface deposition mass, the dissolved oxygen concentration at the outlet, and the fuel temperatures and deposition rate along the tube. This outcome demonstrates the reliability of the kinetics mechanism and the simulation model. The temperature gradient plays an important role in predictions of local coking deposition, and its incorporation improves the predictive accuracy of the model. The rates of wall reactions are evidently far less than those of bulk reactions, and there is a large temperature gradient and low velocity region near the boundary layer of the wall. Finally, decreases in the dissolved oxygen concentration were found to effectively reduce the extent of coke deposition. The influence of deposition layer on the heat transfer and the effects of the different materials and roughness of the tube on coke

AUTHOR INFORMATION

Corresponding Author

*Tel.: +86-10-62772157. E-mail: [email protected]. ORCID

Lingyun Hou: 0000-0001-9013-9265 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial assistance provided by the National Natural Science Foundation of China (91641114) and the Tsinghua University Initiative Scientific Research Program (20131089265) is gratefully acknowledged.

■

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Kinetic Modeling of Thermal Oxidation and Coking Deposition in

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