Influence of Chemical Mechanisms on Spray Combustion

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Influence of Chemical Mechanisms on Spray Combustion Characteristics of Turbulent Flow in a Wall Jet Can Combustor Farzad Bazdidi-Tehrani, Sajad Mirzaei, and Mohammad Sadegh Abedinejad Energy Fuels, Just Accepted Manuscript • Publication Date (Web): 02 Jun 2017 Downloaded from http://pubs.acs.org on June 3, 2017

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Influence of Chemical Mechanisms on Spray Combustion Characteristics of Turbulent Flow in a Wall Jet Can Combustor

Farzad Bazdidi-Tehrani* Sajad Mirzaei Mohammad Sadegh Abedinejad School of Mechanical Engineering, Iran University of Science and Technology, Tehran 1684613114, Iran *Address

correspondence to Professor Farzad Bazdidi-Tehrani, E-mail: [email protected],

Phone number: + 98 21 7749 1228, Fax number: + 98 21 7724 0488

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Abstract The objective of present paper is to assess the influence of different chemical mechanisms on non-premixed combustion of kerosene liquid fuel in a gas turbine model combustor. Simulation of two-phase reacting flow is performed employing realizable 𝑘 − 𝜀 turbulence, laminar flamelet combustion and discrete ordinates radiation models in a structured finite volume grid. An Eulerian-Lagrangian approach is applied to model spray of liquid fuel. Distributions of mean axial velocity, temperature, scalar dissipation rate, mixture fraction, mass fraction and the rate of formation of carbon dioxide, water vapor and nitrogen monoxide are compared for three different cases (three different chemical reaction mechanisms). Results depict that minimum deviations concerning the mean axial velocity and mean temperature are observed for case A which consists of 17 species and 26 reaction steps. Maximum scalar dissipation rate is shown for case B comprising 21 species and 30 reactions steps due to a higher mixture fraction variance. By enhancing the laminar scalar dissipation rate, mean temperature is reduced against mixture fraction. The reaction development and energy release rates are slower for case C including 16 species and 26 reactions steps. Concentrations of predicted 𝑁𝑂 and 𝐶𝑂2 for three cases are different due to the predicted temperature differences. The thermal 𝑁𝑂 formation rate is higher for case A then C and last of all B. Keywords: Model Combustor, Chemical Mechanisms, Turbulence, Reactive Flow, Flamelet


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1. Introduction There are several complex issues in the study of liquid-fueled gas turbine combustor including reactive flow, injection, turbulent flow, multiphase flow, combustion chemical mechanisms, convection and radiation heat transfer, and their interactions with each other. Achieving optimum reaction species and temperature distributions in the modeling of a reactive flow depends on the application of efficient chemical mechanisms. Yan et al.1 have investigated the combustion characteristics of a replacement fuel for kerosene. They have introduced a simplified chemical mechanism containing 62 rudimentary reaction steps and 36 species for n-decane as a one-component substitute fuel. The replacement fuel with a simplified mechanism has been adopted in the simulation of premixed combustion of kerosene. The standard 𝑘 − 𝜀 turbulence model and eddy dissipation concept (EDC) model are used to simulate the reactive turbulent flow. They have also designed an experimental setup to validate their simulations. Comparison of predicted distributions of species concentration and temperature with experimental data has shown that n-decane can be applied as a substitute for kerosene. Also, it has been concluded that the simplified mechanism can properly predict the kerosene combustion characteristics. Zettervall et al.2 have presented a new mechanism with 65 irreversible reactions and 22 species for kerosene. It has been applied in the laminar flame simulation (flamelet model) and exhibits a proper performance in predicting the characteristics of combustion such as flame propagation, ignition and extinction of flame over a wide range of equivalence ratios, temperature and pressure. A two-dimensional numerical study of a model combustor has been performed by Mardani and Fazlollahi-Ghomshi3. The transported probability density function (TPDF) and EDC models are employed for the turbulence-chemistry interaction. A reduced mechanism with 104 reactions and 22 species has been employed for signifying the chemical reactions. Their results show a reasonable prediction accuracy considering a lower computational cost as


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compared with a costly 3-D simulation. However, some characteristics of flow field are missed as compared with the large eddy simulation (LES) approach. Also, it has been shown that the TPDF model leads to proper predictions of flame structure and concentrations of species near the combustor entrance. However, the EDC model provides a more accurate prediction in the downstream of flow field. Zeinivand and Bazdidi-Tehrani4 have numerically studied the impact of position and number of air jet holes on 𝑁𝑂𝑋 pollutants and combustion features in a model combustion chamber. The realizable 𝑘 − 𝜀 and eddy dissipation models are employed for simulating the combustion of kerosene. It has been shown that a reduction in the 𝑁𝑂 concentration and an improvement in the thermal power take place with enhancing the axial distance of jet holes from the fuel nozzle. In addition, with growing the jet holes number, both 𝑁𝑂 concentration and thermal power rise. The rate of 𝑁𝑂 formation is dependent more on the jet position rather than jet number. By increasing the distance of jets from the fuel injector, the outlet temperature profile gets more uniform. Nevertheless, an increase in the holes number leads to a less uniform profile of outlet temperature. Also, Bazdidi-Tehrani and Zeinivand5 have carried out a reactive flow modeling using diesel oil for the prediction of turbulent flow characteristics and temperature profiles in a model combustor. It has been reported that the realizable 𝑘 − 𝜀 model predicts the jet flow characteristics better than the standard 𝑘 − 𝜀 type of RANS models. Moreover, the βpresumed probability density Function (βPDF) model shows the distribution of temperature more accurately than the eddy dissipation model (EDM), particularly in regions close to the walls. Further, by not considering the presence of thermal radiation, a failure in the prediction of NO species concentration occurs. Apte and Moin 6 have numerically simulated a reactive flow in a realistic gas turbine combustor employing the flamelet combustion model and the LES approach. Their major work has been the investigation of sub-grid scale models for calculating the droplet dynamics containing 4 ACS Paragon Plus Environment

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break-up and evaporation. Torkzadeh et al.7 have simulated the non-premixed flame in a gas turbine combustion chamber with the aim of optimizing the design process of a real can-type combustor. The steady flamelet and SST 𝑘 − 𝜔 models have been applied to carry out a multiobjective optimization on the basis of pattern factor, pollutant (𝑁𝑂 and 𝐶𝑂) emission, combustion efficiency and minimization of entropy generation. A combination of the flamelet model, enthalpy and mixture fraction probability density function has been suggested by Wen Ge and Gutheil8 for combustion modeling of methanol injection. A chemical mechanism with 168 reactions and 23 species is implemented for generating the flamelet library of methanol-air. Some numerical results such as mass fraction of methanol, temperature and velocity of continuous phase are verified with the available experimental data. The results show that the mixture fraction and enthalpy are perfectly correlated and the energy consumption of the local spray vaporization leads to a deviation from the correlation. Niu and Piao9 have simulated the kerosene combustion in a scramjet combustion chamber employing the flamelet model. The atomization of the liquid fuel has been adopted in the Eulerian–Lagrangian approach. Their computational results display good agreement with the experimental data. Also, a reduction of combustion efficiency has been shown with an increase of equivalence ratio. Combustion of kerosene and bio-kerosene (a mixture of kerosene and rapeseed oil methyl ester) has been investigated experimentally by Dagaut and Gail10. The experiments have been implemented in a jet stirred reactor (JSR) at 10.0 𝑎𝑡𝑚 pressure in a temperature range of 740 to 1200 𝐾 and for equivalence ratios from 0.5 to 1.5. The species concentrations of reactants, products and stable intermediates are the outcomes of their experimental study. They have modeled the combustion of above-mentioned fuels under the given conditions by using a chemical mechanism including 263 species and 2027 reactions. The numerical results illustrate that employing the considered chemical mechanism gives an acceptable picture in the


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combustion simulation of kerosene and bio-kerosene. The results of experiment and simulation reveal that bio-kerosene has a little more reactivity, as compared with kerosene. Also, the ignition delays of bio-kerosene and kerosene are predicted almost similarly. Molnar and Marek11 have developed a simplified kinetic mechanism for methane and Jet-A fuels. These mechanisms reveal a correlation of kinetic time as a function of temperature, pressure and initial air/fuel ratio. The equations of kinetic time for fuel, 𝐶𝑂 and 𝑁𝑂𝑋 are achieved for both fuels. The results demonstrate that the methane and Jet-A chemical kinetic time correlations for 𝑁𝑂𝑋 and fuel are fairly robust. Kundo et al.12 have presented three simplified mechanisms of Jet-A and propane in order to apply to the combustion CFD codes to evaluate the concentrations of 𝑁𝑂𝑋 . The three kinetic mechanisms include 12, 16, and 17 species and 11, 23, and 26 reaction steps, respectively. The actual entire 𝑁𝑂𝑋 and 𝑁2 𝑂 concentrations are achieved by employing the 17 species reduced mechanism. They have employed the 𝑘 − 𝜀 turbulence model to simulate a premixed combustion at 1.0 to 2.0 𝑎𝑡𝑚 pressure. Comparison of the computed and experimental measurement of 𝑁𝑂𝑋 concentration has been done by using 16 species kinetic mechanism. The 17 species mechanism is applied for calculating the influence of 𝑁2 𝑂 reactions on the formation of 𝑁𝑂𝑋 . It is shown that the detailed mechanism has good agreement with the experimental data and the determination of 𝑁2 𝑂 concentration plays a significant role in the formation of 𝑁𝑂. Samuelsen's research group13-15, from 1981 to 1993, have carried out and reported numerous experimental works on a cylindrical model combustor. Over those years, several topics encompassing distribution and position of primary and secondary air holes, various fuels, mean temperature and velocity distributions, droplet size, 𝑁𝑂𝑋 and soot concentrations have been investigated. In the above reviewed articles, various combustion models such as eddy dissipation concept, equilibrium non-premixed, and flamelet models have been applied for the simulation of 6 ACS Paragon Plus Environment

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reactive flow. However, none of these works has been dedicated to the investigation of the effects of fuel kinetics and chemical reaction mechanisms on the reactive flow modeling within a gas turbine model combustion chamber. In the present study, the influence of three distinct chemical reaction mechanisms of kerosene fuel on the combustion characteristics within a model combustion chamber is assessed. In the simulation of the reactive two-phase flow, the realizable 𝑘 − 𝜀 turbulence, laminar flamelet combustion, and discrete ordinates radiation models are applied. Spraying liquid fuel droplets into a swirling air environment is modeled via an Eulerian–Lagrangian approach. The present boundary conditions conform with the available experimental conditions14 for all the three chemical mechanisms. After verifications of the present simulation results using the existing experimental data14, the accuracy of these mechanisms is evaluated. Verifications of the results are carried out employing the mean axial velocity profiles and mean temperature distributions, at three different axial positions of the model combustor. A variety of simulations provides comparisons of flame scalar dissipation rate, mixture fraction, mass fraction, and the formation rate of carbon dioxide, water vapor, kerosene, and nitrogen oxide species at different sections of the model combustion chamber for the three chemical mechanisms. 2. Numerical Method Description 2.1. Continuous Phase The governing equations of turbulent reactive flow include mass, momentum, energy and chemical species mass conservation. The general form of these equations in the Cartesian coordinates, assuming steady-state and incompressible conditions, is outlined as in equation 1. 𝜕 𝜕 𝜕 (𝜌𝑈Ψ) + (𝜌𝑉Ψ) + (𝜌𝑊Ψ) 𝜕𝑋 𝜕𝑌 𝜕𝑍 =

(1)

𝜕 𝜕Ψ 𝜕 𝜕Ψ 𝜕 𝜕Ψ (ΓΨ )+ (ΓΨ )+ (ΓΨ ) + 𝑆Ψ1 + 𝑆Ψ2 𝜕𝑋 𝜕𝑋 𝜕𝑌 𝜕𝑌 𝜕𝑍 𝜕𝑍


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Where, 𝛹 represents dependent variables including mass, momentum, turbulence kinetic energy, turbulence energy dissipation rate, enthalpy, and species’ mass fractions. The two 𝑆Ψ1 and 𝑆Ψ2 terms signify the source and sink terms for gas phase and droplets phase, respectively. 2.2. Discrete Phase Gas phase is considered as a continuous phase and is modeled employing an Eulerian approach. In the zone near the fuel injector, because of spraying the liquid droplets in the micro-scale range with a volume fraction less than 10% of that of gas phase, a dilute discrete phase is produced. In order to model this discrete phase, a Lagrangian approach16 is applied. In the vicinity of the fuel injector, a discrete phase is developed for which a Lagrangian approach is used for modeling. The development of this phase is due to injection of droplets with the order of magnitude of micrometers and a volumetric fraction of less than 10% of the gas phase volumetric fraction. The droplets path line is acquired from the equation of motion17: 𝑑𝑢 ⃗𝑝 = 𝐹𝐷 (𝑢 ⃗ −𝑢 ⃗ 𝑝) 𝑑𝑡

(2)

The left-hand side term represents a droplet’s inertia showing the mass resistance to velocity and direction variation. The right hand-side term represents the drag friction force. The equilibrium temperature model is used for modeling the droplet temperature. It is assumed that no temperature variation takes place within the droplet and the droplet temperature is homogenous18. Therefore, the droplets domain is not discretized and, consequently, the computation cost is decreased. The evaporation rate

𝑑𝑚𝑝 dt

is calculated using the mass transfer

relation written for the droplet’s vicinity area17: 𝑑𝑚𝑝 = 𝜋𝑑𝑝 𝜌∞ 𝐷𝑖,𝑚 𝑆ℎ𝐴𝐵 𝑙𝑛(1 + 𝐵𝑚 ) 𝑑𝑡

(3)


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where, 𝑑𝑝 , 𝜌∞ , 𝐷𝑖,𝑚 , 𝑆ℎ𝐴𝐵 , and 𝐵𝑚 represent droplet diameter, gas phase density, vapor diffusivity constant through the gas phase, Sherwood number, and Spalding mass transfer number, respectively. The droplet temperature is updated based on the thermal equilibrium equation (equation 4-a). When the temperature of droplet reaches the fuel boiling point, the equation 4-b (boiling rate) is employed. Also, 𝑇∞ , 𝜆∞ , ℎ , 𝑇𝑝 , 𝑐𝑝,𝑝 , and ℎ𝑓𝑔 represent continuous phase temperature, conduction heat transfer coefficient of the gas phase, convection heat transfer coefficient, droplet temperature, droplet’s specific heat at constant pressure and phase change heat consecutively. 𝑚𝑝 𝑐𝑝,𝑝

𝑑𝑇𝑝 𝑑𝑚𝑝 = ℎ𝐴𝑝 (𝑇∞ − 𝑇𝑝 ) − ℎ 𝑑𝑡 𝑑𝑡 𝑓𝑔

(4-a)

𝑑(𝑑𝑝 ) 𝐶𝑝,∞ (𝑇∞ − 𝑇𝑝 ) 4𝜆∞ = (1 + 0.23√𝑅𝑒𝑑 ) × 𝑙𝑛 [1 + ] 𝑑𝑡 𝜌𝑝 𝐶𝑝,∞ 𝑑𝑝 ℎ𝑓𝑔

(4-b)

The fuel is injected through the chamber via an air-blast fuel injector at a 300 𝐾 temperature, 110 𝑚/𝑠 relative velocity and with 60 degrees of cone angle. Considering that the volumetric fraction of the droplets does not exceed 0.001, there is no need to account for the droplets collision. In other words, the influence of droplets over each other is negligible. Yet the discrete phase affects the main phase and this should be accounted for within the continuous phase equations as a source term. For more information about the discrete phase modeling and its governing equations, references19-21 are quite useful. 2.3. Turbulence Model According to the previously reported studies4-5, 22-23, the realizable 𝑘 − 𝜀 model is employed presently for modeling the turbulent flow within a model combustion chamber. The realizable 𝑘 − 𝜀 model provides a sufficient compliance with the physics of turbulent flows. It is also


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likely to deliver an excellent performance for flows comprising boundary layers under strong adverse (positive) pressure gradients, separation, recirculation and rotation. The transport equations regarding this turbulence model are explained by Shih et al.24 which are depicted in equations 5 and 6. 𝜂 parameter represents the ratio of turbulence characteristic time to flow field characteristic time. Also, 𝑘 and 𝜀 denote kinetic energy and dissipation rate, successively. 𝐺𝑘 specifies the generation of turbulence kinetic energy owing to the mean velocity gradients. 𝜕𝑘 𝜕𝑘 𝜕 𝜇𝑡 𝜕𝑘 + 𝜌𝑢𝑖 = [(𝜇 + ) ] + 𝐺𝑘 − 𝜌𝜀 𝜕𝑡 𝜕𝑥𝑖 𝜕𝑥𝑖 𝜎𝑘 𝜕𝑥𝑖 𝜕𝜀 𝜕𝜀 𝜕 𝜇𝑡 𝜕𝜀 𝜌 + 𝜌𝑢𝑖 = [(𝜇 + ) ] + 𝜌𝐶1 𝑆𝜀 − 𝜌𝐶2 𝜕𝑡 𝜕𝑥𝑖 𝜕𝑥𝑖 𝜎𝑘 𝜕𝑥𝑖

𝐶1 = 𝑚𝑎𝑥 [0.43,

(5) 𝜀2 𝜇𝜀 𝑘+√𝜌

𝜂 𝑘 ],𝜂 = 𝑆 𝜂+5 𝜀

𝑆 = √2𝑆𝑖,𝑗 𝑆𝑖,𝑗 , 𝜇𝑡 = 𝜌𝐶𝜇 𝐶2 = 1.9, 𝜎𝑘 = 1.0,

(6-a)

(6-b)

𝑘2 𝜀

(6-c)

𝜎𝜀 = 1.2

(6-d)

2.4. Combustion Model In the present work, the chemical reactions in the model combustion chamber are modeled using the laminar flamelet model25. The turbulent and non-premixed combustion flows are correlated via the 𝛽𝑃𝐷𝐹 26. In the flamelet combustion model, it is assumed that a turbulent non-premixed flame consists of a statistical set of laminar thin flames (flamelets)27. The flamelet equations are formulated as mass fraction equation and temperature equation transferred to the mixture fraction system (equation 7 and 8). In these equations, 𝑌𝑖 , 𝑐𝑝,𝑖 , 𝑐𝑝 , 𝑆𝑖 , 𝐻𝑖 , and 𝜒 represent the mass ratio of species 𝑖, the specific heat of species 𝑖, the mixture mean


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specific heat, the source term of reaction rate, the specific enthalpy of species 𝑖 and the scalar dissipation rate, respectively. 𝜕𝑌𝑖 1 𝜕 2 𝑌𝑖 = 𝜌𝜒 2 + 𝑆𝑖 𝜕𝑡 2 𝜕𝑓 𝜌

(7)

𝜕𝑐𝑝 𝜕𝑇 1 𝜕 2 𝑇 1 1 𝜕𝑌𝑖 𝜕𝑇 = 𝜌𝜒 2 − ∑ 𝐻𝑖 𝑆𝑖 + 𝜌𝜒 [ + ∑ 𝑐𝑝,𝑖 ] 𝜕𝑡 2 𝜕𝑓 𝑐𝑝 2𝑐𝑝 𝜕𝑓 𝜕𝑓 𝜕𝑓 𝑖

(8)

𝑖

For acquiring the flame scalar dissipation rate distribution, the mixture fraction conservation equation is solved for opposite flow non-premixed flames via a similar method. The scalar dissipation rate is computable based on the mixture fraction and reaction rate at each point by the following expansion. 2

𝜌 3 (√ ∞⁄𝜌 + 1) 𝛼𝑠 χ(𝑓) = 𝑒𝑥𝑝(−2[𝑒𝑟𝑓𝑐 −1 (2𝑓)]2 ) 4𝜋 𝜌 2√ ∞⁄𝜌 + 1

(9)

Species and temperature are defined by integrating equations 7 and 8 for different quantities of scalar dissipation rates. In these equations, temperature and species mass fraction at steadystate are functions of mixture fraction and non-equilibrium quantity of scalar dissipation rate, indicating the effect of flow field on the flamelet structure. 𝑌𝑖 = 𝑌𝑖 (𝑓, χ)

(10)

𝑇 = 𝑇(𝑓, χ) Thermo-chemical quantities that are produced from the flamelet form a database. These quantities are non-linear functions from the mixture fraction and for acquiring their average, knowing the average mixture fraction is not enough and the fluctuations should also be considered. The influence of turbulence fluctuations on these amounts is taken into account by


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employing 𝛽𝑃𝐷𝐹. Values of mixture fraction and its variance are acquired by solving the transport equations as follows: 𝜕 𝜕 𝜕 𝜇𝑡 𝜕𝑓 ̅ (𝜌̅ 𝑓)̅ + (𝜌̅ 𝑢̅𝑗 𝑓 )̅ = [ ] 𝜕𝑡 𝜕𝑥𝑗 𝜕𝑥𝑗 𝜄𝑡 𝜕𝑥𝑗

(11)

2 ̅̅̅ ́2 𝜕 ̅̅̅2 𝜕 𝜕 𝜇𝑡 𝜕𝑓 𝜕𝑓 ̅ ̅̅̅ 2 (𝜌̅ 𝑓́ ) + (𝜌̅ 𝑢̅𝑗 𝑓́ ) = [ ] + 𝐶𝑔 𝜇𝑡 ( ) − 𝐶𝜒 𝜌̅ 𝜒̅ 𝜕𝑡 𝜕𝑥𝑗 𝜕𝑥𝑗 𝜄𝑡 𝜕𝑥𝑗 𝜕𝑥𝑗

(12)

The mean scalar dissipation rate, 𝜒̅ , is obtained from flow equations, based on one criterion that is described below:

𝜒̅𝑠𝑡 = 𝜒̅ ,

𝜀 2 𝜒̅ = 𝑐𝜒 ̅̅̅ 𝑓́ 𝑘

(13)

In these equations, 𝑘 and 𝜀 as before represent turbulence kinetic energy and it’s dissipation rate, respectively, and 𝐶𝜒 coefficient is generally assumed to be equal to 2

28

. Further

descriptions of the flamelet model are available in references25, 29. 2.5. Chemical Reaction Mechanisms of Combustion The chemical reaction mechanism is a series of real events that occurs by converting reactant molecules to products. Each of these real events makes a primary step that shows a collision of separate molecules or a decomposition of large molecule into simpler molecules. An intermediate or final species may be created from each step of reaction. Intermediate species is produced in one primary step and decomposed in an ensuing step and, thus, it is not emerged in the final reaction. Net chemical reactions and elementary reactions have two significant differences30: The law of elementary reaction rate can be achieved by examination. For instance, a bimolecular process conforms the rate law of second order.


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𝑅𝑎𝑡𝑒 = 𝐾𝐴𝐵 [𝐴][𝐵]

(14)

Elementary reactions mostly include reactive or unstable species while they are not appeared in the equation of net reaction. The mechanism in which a primary step is pursued by other steps is called multi-step reactions. Decomposition of NO2 into NO and O2 (see Table 1) is an example of a mechanism that consists of two elementary steps. NO3 is a transient intermediate species and it is not emerged in the net reaction. If all the steps proceed with comparable rates, the net reaction would not show that two distinct elementary steps are contained on experiments rate law. A great difference in rates of steps makes a completely different kinetics with more complexity. Thus, it requires some simplifying approximations (such as rate determining step, rapid equilibrium and steady-state assumptions) to improve our understanding of the experimental reaction kinetics. [Insert Table 1.] Table 1. Chemical mechanism of decomposition of nitrogen dioxide into nitric oxide and oxygen30 The process of hydrogen oxidation is used in all the present three chain mechanisms, which will be discussed in Tables 3, 4 and 5. Some of the main elementary steps for 𝐻 radical formation is shown in Table 2. The hydrogen oxidation reaction does not happen at room temperature when the two gases (hydrogen and oxygen) are simply mixed. It occurs slowly in the temperature range of 500 to 600 ℃. However, under the condition of spark ignition or heating at 700 ℃, the mixture explodes. The same as other combustion reactions, the mechanism of this reaction is very complicated and changes partly with the conditions. It should be noted that reaction numbers (3) and (4) cause an over-production of hydrogen radicals. Thus, by the activation of each of the mentioned reactions, one new chain process is


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initiated effectively. It results in an exponential increase of the overall rate, which eventually leads to an explosion. [Insert Table 2.] Table 2. Chemical mechanism of oxidation of hydrogen gas30 In the present paper, three different chemical reaction mechanisms are utilized for modeling the kerosene fuel combustion, according to Tables 3, 4, and 5. In all the three mechanisms, particular attention is paid to the NO formation. Also, the model combustor’s operating conditions (i.e., operating pressure: 1 atm) is in accordance with the chemical mechanism operating conditions. The major differences between these mechanisms lie in the number of species, number of reactions, reaction activation energy, and pre-exponential factor or frequency factor. Assumed specifications for the three modeling cases (A, B and C) are listed in Table 6. In case A, the kerosene combustion is simulated using a 26 reaction chemical mechanism with 17 independent species. In case B, a closer condition to the equilibrium chemical mechanism is utilized in comparison with case A. That is, 21 independent species and 30 chemical reactions. In case C, the combustion simulation is performed using a similar mechanism to case A, consisting of 26 chemical reactions and 16 independent species. The main difference between cases A and C is related to the dissimilar Arrhenius model coefficients for each reaction of the mechanism. The second mechanism (case B) includes more species and intermediate reactions, as compared with the other two mechanisms (cases A and C). Considering that increasing the flamelet number and scalar dissipation rate leads to higher computational time and cost, the most optimum case is applied for constructing the flamelet from each of the chemical mechanisms. [Insert Table 3.] Table 3. First chemical reaction mechanism12 (case A) 14 ACS Paragon Plus Environment

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[Insert Table 4.] Table 4. Second chemical mechanism31 (case B) [Insert Table 5.] Table 5. Third chemical mechanism11 (case C) [Insert Table 6.] Table 6. Specifications of three different modeling cases It should be mentioned that at a scalar dissipation rate more than the last scalar dissipation rate, the flame is extinguished29, 32. 2.6. Radiation Heat Transfer Modeling In the reactive flow, because of the presence of a relatively high temperature region, thermal radiation is the dominant heat transport mechanism to the adjacent surfaces. The integrodifferential radiative transfer equation (RTE) for an emitting, scattering and absorbing medium, at location 𝑟 and in the direction 𝑠, is specified as33: 𝑑𝐼(𝑟, 𝑠) 𝜎𝑇 4 𝜎𝑠 4𝜋 2 (𝛼 )𝐼(𝑟, + + 𝜎𝑠 𝑠) = 𝛼𝑛 + ∫ 𝐼(𝑟, 𝑠́ )Φ(𝑠. 𝑠́ )𝑑Ώ 𝑑𝑠 𝜋 4𝜋 0

(15)

The solution to equation 15 is quite complicated33 and various numerical techniques have been developed for this purpose. The discrete ordinates model (DOM)

33-35

is presently employed

due to acceptable levels of accuracy and computational costs. It also allows to compute the non-gray radiation using a gray-band model. Assuming a constant absorption coefficient reduces the computational accuracy due to the permanent variations of pressure, temperature and species concentration during the process of combustion. Therefore, the weighted sum of gray gases model (WSGGM), proposed by Smith et al.36 is implemented for acquiring the


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absorption coefficients of various combustion gases. Further information regarding DOM and WSGGM is provided in the references33, 36. 2.7. Computational Techniques A three-dimensional (3-D) finite volume method (FVM)37 is employed for solving the set of continuity, momentum and energy conservation equations, flamelet combustion model and DOM equations. The flow governing equations are implicitly linearized and discretized of the second order. The diffusive terms of the equations are discretized employing the central difference scheme and the advection terms are discretized using the second order upwind scheme. The SIMPLEC algorithm38 relating the velocity and pressure variables is adopted. For predicting the dynamic characteristics of droplets and gas, an Eulerian approach is applied for the continuous (gas) phase, while a Lagrangian approach is adopted for tracking the motion and thermodynamic behavior of the discrete (droplets) phase. Coupling between the gas flow and liquid phase is achieved by a two-way approach and the effect of droplets on the base fluid is also considered. Polynomial temperature dependent functions are used for the calculation of species specific heat. In the solution procedure, first of all, the partial differential equations for the conservation equations are solved. Then, the transport equation for 𝑁𝑂 species is solved to provide the 𝑁𝑂 distributions. In this paper, two thermal and prompt 𝑁𝑂 formations are presently addressed and computed by the finite-rate chemistry. The thermal 𝑁𝑂 formation rate is estimated employing the extended Zeldovich mechanism39 and for calculating the concentration of 𝑂 and 𝑂𝐻 radicals, the partial equilibrium approach is used40. The prompt 𝑁𝑂 formation rate is acquired employing the De Soete equation41. The 𝛽𝑃𝐷𝐹 of the normalized temperature, 𝑓 = (𝑇 − 𝑇𝑚𝑖𝑛 )⁄(𝑇𝑚𝑎𝑥 − 𝑇𝑚𝑖𝑛 ), is utilized for evaluating the influence of turbulent mixing on the 𝑁𝑂 formation computed in a laminar field. For further information on the methods of


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estimation of 𝑁𝑂 concentration, references4-5, 40 may be referred to. Simulations are conducted by employing a convergence criterion of 10−5 for the continuity equation and 10−6 for the other equations. 3. Geometry and Boundary Conditions According to Figure 1, the geometry of the model can-type combustor presented by Cameron et al.14 is presently implemented for the investigation of the reactive spraying flow characteristics. [Insert Figure 1.] Figure 1. A schematic view of model combustion chamber14 and boundary conditions (dimensions in 𝑚𝑚). This particular wall jet can combustor (WJCC) consists of a 320 mm long and 80 mm diameter octagon. Four 7 mm diameter primary jets and four 9.5 mm diameter dilution holes are located peripherally at distances of 80 𝑚𝑚 and 160 𝑚𝑚 from the combustor’s inlet plane, respectively. The swirler adopted in the WJCC is of an axial type. 25% of the incoming air goes to the swirler. The remainder is allocated such that 35% is for the primary jets and 40% for the dilution jets. A summary of the relevant geometrical and flow information concerning the WJCC is listed in Table 7. [Insert Table 7.] Table 7. Geometrical and flow specifications of WJCC The present boundary conditions at the inlet and outlet of the computational domain are assumed as inlet mass flow and pressure outlet, successively. Due to the sensitivity of the numerical computations to the initial values of turbulence vanishing rate, equations (16) and (17) are employed for the primary evaluation of 𝑘 and 𝜀 5, 42. Furthermore, the thermal and 17 ACS Paragon Plus Environment

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velocity boundary conditions at all of the walls are assumed as adiabatic and no-slip, consecutively. For radiation modeling, the emissivity of the walls is considered equal to 0.7.

𝑘𝑖𝑛𝑙𝑒𝑡 =

3 (|𝑈𝑖𝑛𝑙𝑒𝑡 |𝐼𝑡 )2 2

𝜀𝑖𝑛𝑙𝑒𝑡 =

3⁄ 𝐶𝜇 4

(16)

3⁄

(17)

2 𝑘𝑖𝑛𝑙𝑒𝑡 0.07𝐷ℎ

A structured grid is generated for discretizing the geometry of WJCC. Grids are considered finer adjacent to the walls (particularly near the jet holes) and at the combustor entry, due to the presence of pressure gradients and combustion phenomenon. A grid independence test is carried out by examining four different mesh sizes, within the range 2.5 × 105 − 1.3 × 106 cells (see Table 8). [Insert Table 8.] Table 8. Different mesh size Figure 2 illustrates the results of the grid independence test in the form of the profiles of mean axial velocity at the centerline and concentration of 𝐶𝑂2 species at 𝑋 = 0.1 𝑚. Grid C provides a reasonably acceptable accuracy along with a lower computational effort in comparison with the other three grids and it is hence taken on throughout the present work. Maximum deviations of Grid C from Grid D, based on the profiles of 𝐶𝑂2 concentration and mean axial velocity, are nearly 2.05% and 3.45%, successively. [Insert Figure 2.]


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Figure 2. Grid independence test: (a) mean axial velocity at centerline and (b) 𝐶𝑂2 concentration at 𝑋 = 0.1 𝑚 along Y direction Figure 3 displays the ultimate structured grid for the present modeling. Since the realizable 𝑘 − 𝜀 turbulence model is adopted for the turbulent flow simulation, the cells density close to the wall and the first cell distance relative to the wall unit are selected such that 𝑌 + lies in the range of 30 to 40 for employing the standard wall functions42. [Insert Figure 3.] Figure 3. Structured mesh on the model combustor geometry 4. Results and Discussion In this section, the results obtained for some physical quantities such as velocity, temperature, flame’s scalar dissipation rate, mixture fraction and concentration of combustion species, are discussed for the three cases (cases A to C - Tables 3 to 6) of kerosene fuel combustion mechanisms. Also, production and consumption rates of species and decomposition process of the kerosene fuel with 𝐶12 𝐻23 chemical formula (as the initial fuel) are presented for the three cases by solving the governing equations in a laminar flame calculation domain without an influence of turbulent flow. In order to evaluate the accuracy of the present simulations and numerical procedure, several comparisons are made between the present results and the available experimental data of Cameron et al.14. The mean axial velocity and mean temperature parameters are considered for this purpose. The deviations of present results from experimental data are estimated according to equation (18):

𝑀𝐷 =

|𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑑𝑎𝑡𝑎 − 𝑁𝑢𝑚𝑒𝑟𝑖𝑐𝑎𝑙 𝑟𝑒𝑠𝑢𝑙𝑡𝑠| × 100 𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑑𝑎𝑡𝑎


(18)

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Figure 4 depicts the present mean axial velocity for cases A to C across the model combustor’s radius (Y direction), at three longitudinal cross-sections. A lower velocity is observed close to the central axis of the model combustion chamber, at 𝑋 = 0.04 𝑚. It is due to the recirculation zone formation at the primary zone, as a result of the collisions and mixing of fuel, swirl air and primary jets altogether. At 𝑋 = 0.1 𝑚, between the primary jets and dilution jets, the flow velocity is increased. At 𝑋 = 0.18 𝑚, the flow is not affected by the fuel nozzle, swirler and primary jets and the axial velocity profile tends to become a uniform one. Different fuel chemical reaction mechanisms (cases A to C) lead to different distributions of flow velocities. For case A, the acquired velocity distribution is closer to the available experimental data14, as compared with the other two cases (𝑀𝐷 = 15%). For case B, more flow recirculation is observed. At 𝑋 = 0.1 𝑚, the difference among the velocity profiles of the three cases becomes negligible due to the lower effects of flame and fuel breaking mechanisms in that region. However, For case B the velocity profile is yet predicted with a higher deviation (𝑀𝐷 = 21%). At 𝑋 = 0.18 𝑚, very similar velocity profiles are predicted for cases A and C. This is in line with the corresponding predictions of temperature distributions for cases A and C (see Figure 5-c). However, the predicted velocity profiles by case B shows the higher percentages of deviations in comparison with the experimental data14 (𝑀𝐷 = 25%). The maximum deviation concerning the mean axial velocities among the three cases of chemical reaction mechanisms is about 61%, which is related to case B at 𝑋 = 0.04 𝑚. [Insert Figure 4.] Figure 4. Comparison of present profiles of mean axial velocity (cases A to C) and experiment14; (a) 𝑋 = 0.04 𝑚, (b) 𝑋 = 0.1 𝑚 and (c) 𝑋 = 0.18 𝑚 (Y direction) The radial profiles of mean temperature for cases A to C, at three axial locations, are demonstrated in Figure 5. The maximum effect of fuel breaking mechanisms on the mean


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temperature prediction is observed at 𝑋 = 0.03 𝑚 where the flame is formed. By moving away from the primary zone (0 < 𝑋 < 0.08 𝑚), as the flame is stretched and gradually extinguished, the temperature distribution trends become similar for all the three cases. According to Figures 4 and 5, the minimum deviations concerning the mean axial velocities and mean temperatures are related to case A. Nevertheless, there is an almost 13% deviation on average between the present results of case A and available experimental data14. [Insert Figure 5.] Figure 5. Comparison of present profiles of mean temperature (cases A to C) and experiment14; (a) 𝑋 = 0.03 𝑚, (b) 𝑋 = 0.1 𝑚 and (c) 𝑋 = 0.18 𝑚 (Y direction) Figure 6-a demonstrates the distributions of mean temperatures in the axial direction and across the mid-plane (𝑍 = 0) for cases A to C. Accumulation regions of the hot combustion products, cold liquid fuel injection from the fuel nozzle, and cold entering air from the swirler are observed. Figure 6-b depicts the mean temperature at the centerline (𝑌 = 𝑍 = 0) of the model combustor. The maximum temperature is seen at the flame formation region where a higher energy is released by the vaporized fuel reacting with air. Further distance from the injector (𝑋 > 0.05 𝑚 and −0.02 < 𝑌 < 0.02 𝑚), the mean temperature is reduced under the influence of cold air entering through the primary jets. As the primary air diffuses into the combustion products, combustion and chemical reactions are more developed and the temperature is again increased. The mean temperature is reduced by injection of the cold air through the dilution holes. Finally, the dilution air temperature and the combustion products temperature come into equilibrium with each other. The predicted temperature for case B is remarkably lower as compared with the other two cases. [Insert Figure 6.] 21 ACS Paragon Plus Environment

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Figure 6. Distributions of mean temperature in axial direction: a) across mid-plane and b) centerline Figure 7 displays the decomposition process of the initial fuel (kerosene) until reaching the ultimate combustion products for the three mechanisms (cases A to C). Subsidiary reactions are neglected and the vector lines thicknesses denote the progress level of each reaction. During the first mechanism (case A), 𝐶12 𝐻23 is decomposed only to 𝐶𝐻 while it is decomposed to 𝐶2 𝐻3 and 𝐶2 𝐻4 through the second mechanism (case B) and to 𝐶𝐻 and 𝐶2 𝐻2 in the third mechanism (case C). Figure 8 shows the decomposition rate of 𝐶12 𝐻23 for the three mentioned mechanisms. The reaction development and energy release rates are slower in the third mechanism (case C), as compared with the other two. It is because of a higher required activation energy for case C relative to the other two cases. As the distance from the flame region is increased (𝑋 direction), the required steps activation energy is reduced. Therefore, the energy release rate and temperature growth are decreased for the third mechanism, as compared with the other two. [Insert Figure 7.] Figure 7. Process of decomposition of initial fuel to ultimate products for cases A to C [Insert Figure 8.] Figure 8. Decomposition rate of 𝐶12 𝐻23 for three chemical reaction mechanisms Figure 9 illustrates the mean mixture fraction of liquid fuel and air along the centerline of model combustor. Considering that the mixture fraction completely depends on the fuel mass, it possesses a certain value until the entire fuel is consumed. By getting farther from the flame region, the mixture fraction reaches its minimum. Due to the difference in the development rate of 𝐶12 𝐻23 decomposition reactions and 𝑂2 consumption rate, the mean mixture fraction is


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predicted differently for the three different chemical mechanisms. A higher value of 𝐶12 𝐻23 concentration and also lower value of 𝑂2 concentration result in a greater value of mixture fraction. The maximum mixture fraction is detected for case B due to a higher value of 𝐶12 𝐻23 concentration for case B as compared with the other two cases (see Figure 12). This maximum takes place at 𝑋 = 0.025 𝑚 where the rich flame is present. Figures 8 and 10 demonstrate the decomposition rate of 𝐶12 𝐻23 and 𝑂2

production and consumption rates for the three

mentioned mechanisms, respectively. According to Figure 10, case A has the maximum value (2.88𝐸 − 04) and case C has the minimum value (2.09𝐸 − 04) of 𝑂2 consumption rate, whilst cases A and B represent the maximum and minimum values of 𝑂2 production rate during the reactions development, successively (1.54𝐸 − 04 and 2.76𝐸 − 05, respectively). High values of 𝐶12 𝐻23 consumption rate lead to fast reduction of mixture fraction (see case B in Figures 8 and 9). Whereas, high values of 𝑂2 consumption rate delay the mixture fraction reduction (see cases A in Figures 9 and 10). [Insert Figure 9.] Figure 9. Mean mixture fraction at centerline of model combustion chamber [Insert Figure 10.] Figure 10. Production and consumption rates of oxygen for three chemical mechanisms (production: 𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑟𝑎𝑡𝑒 > 0.0 and consumption: 𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑟𝑎𝑡𝑒 < 0.0) Figure 11-a shows the axial variations of the flame scalar dissipation rate along the centerline of model combustor for cases A to C. This Variable is zero everywhere except in the flame region. Its value reaches maximum for all the three chemical mechanisms at the flame front where the maximum development rate of chemical reactions takes place. Because the flow turbulence and flame strain effects simultaneously dominate the flame front. The position of


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maximum scalar dissipation rate value is also similar to the positions of maximum mean mixture fraction and 𝐶12 𝐻23 concentration (see Figures 9 and 12-a). According to Figure 11-a, the scalar dissipation rate for case B is 46% greater than that for case A and, in turn, its value for case A is 22% higher than that for case C. This can be explained by the definition of scalar dissipation rate (equation 13). The scalar dissipation rate is in direct relation with the mixture fraction variance (𝑓́) and the 𝜀⁄𝑘 ratio. As shown in Figure 11-b, the influence of application of different fuel mechanisms on the turbulence parameters (𝜀⁄𝑘 ratio) is negligible. Figure 11c indicates that the distributions of mixture fraction variance at the centerline of model combustor are different for the three cases. It can then be concluded that the maximum value of the scalar dissipation rate for case B is because of its highest mixture fraction variance. [Insert Figure 11.] Figure 11. Influence of chemical reaction mechanism on axial distribution of a) scalar dissipation rate, b) ratio of turbulence dissipation rate to kinetic energy, and c) mixture fraction variance at centerline Figure 12-a illustrates the mole fraction of 𝐶12 𝐻23 along the centerline of model combustion chamber for cases A to C. It should be noted that only the 𝐶12 𝐻23 mole fraction in the gas phase is displayed. Therefore, an increasing slope of the mole fraction from zero to its maximum value indicates a higher evaporation rate of liquid fuel droplets and their transformation to fuel vapor. The initial fuel (kerosene) with the 𝐶12 𝐻23 chemical formula only exists in the beginning region of the flame. Since 𝐶12 𝐻23 is decomposed to secondary species by getting close to the combustion region where it absorbs enough activation energy. Its decomposition rate depends on the local temperature and pressure inside the combustor. As shown earlier in Figure 6, the increasing and decreasing slopes of the mean temperature distribution as well as the maximum temperature value strongly differ for the three cases. Due to the higher decomposition rate of 24 ACS Paragon Plus Environment

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𝐶12 𝐻23 to the secondary species for case B, in comparison with the other two cases (see also Figures 9 and 10), the mole fraction of this species is reduced faster than the others. This is revealed at 𝑋 = 0.04 𝑚 in Figure 12-a. In the primary zone, the fuel evaporation rate is remarkably increased for case B due to a higher released heat values, as compared with the other two cases. However, the majority of the initially produced fuel vapor is decomposed to the secondary species in a very short time. Due to the existence of a higher equilibrium between the evaporation and decomposition rates for case C, the maximum mole fraction value of 𝐶12 𝐻23 for case C is lower than those for cases A and B. Figure 12-b displays the mole fraction of 𝑂2 at the centerline. Two maxima and minima are observed. The initial decrease of the 𝑂2 mole fraction reaching its minimum value is due to the combustion process to take place in that region accompanied by oxygen consumption during the reactions. By injecting air through the primary jets, the 𝑂2 amount increases and it again decreases before reaching the dilution jets as the combustion process is developed and 𝑂2 is further consumed. By adding the dilution air, the 𝑂2 amount grows and after that it reaches an equilibrium and steady-state condition until the end of the combustor. As revealed earlier in Figure 10 (𝑂2 consumption and production rates during the three mechanisms), the 𝑂2 consumption rate is higher for case B in comparison with the other two cases. According to Figure 12-b, the 𝑂2 mole fraction value for case B is almost lower than those for the other two. The reason for more oxygen consumption during case B lies in the more equilibrium nature of its reaction mechanism relative to the other two cases. Since, in an equilibrium flame the entire fuel and oxygen are consumed. In case B, the fuel is firstly decomposed into more diverse species and the same trend of gradual decomposition of combustible species continues until they are turned into the final combustion products. Consequently, a more complete combustion process takes place. [Insert Figure 12.] 25 ACS Paragon Plus Environment

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Figure 12. Influence of chemical reaction mechanism on axial distribution of a) Mole fraction of 𝐶12 𝐻23 and b) Mole fraction of 𝑂2 at centerline Figure 13 depicts the 𝐻 mole fraction against the 𝐻2 𝑂 mole fraction for three cases A to C, along the centerline of model combustion chamber. The numerical data have not been plotted in the order of zero to the highest value of the longitudinal central axis. The data have been arranged toward an increase of the mole fraction of oxygen in the non-consecutive axial coordinates. The vertical straight lines in parts of the curves, represent the points on the centerline where there are the same 𝐻2 𝑂 mole fractions with various 𝐻 concentrations. The main importance of this set of results lies in determining the amount of 𝐻 production based on the 𝐻2 𝑂 production. Since, the 𝐻2 𝑂 molecules are decomposed into the 𝐻 atoms under the influence of temperature conditions. An inverse reaction (i.e., composition of the 𝐻 atoms and formation of water vapor) also takes place commonly. It can be seen that the amount of 𝐻 per unit amount of 𝐻2 𝑂 is negligible for case B. This is due to the effects of the reaction numbers (6) and (7) in the second chemical mechanism (case B, Table 4), which lead to a high transformation rate of 𝐻 to 𝐻2 𝑂 species. Whereas, for cases A and C the amounts of hydrogen atom and water vapor are very close to one another, because of the effects of the reaction numbers (3) and (1) in the first and third chemical mechanisms, respectively (case A and case C, Tables 3 and 5). However, a significant difference is still detected between the mole fraction results of cases A and C. This deviation is caused by the existing differences in the values of the activation energy (𝐸) and pre-exponential factor (𝐴) for the two mechanisms, as represented in Tables 3 and 5. In the other words, reducing the activation energy results in a further increase of the reaction development, as is the situation for case A (see Figure 13). [Insert Figure 13.] Figure 13. 𝐻 mole fraction against 𝐻2 𝑂 mole fraction for three cases at centerline 26 ACS Paragon Plus Environment

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Figure 14 demonstrates the mole fractions of 𝐶𝑂2 and 𝑂2 species against the mixture fraction at the last laminar scalar dissipation rate. The present data are extracted from an extinguished flame front (i.e., flame front with a maximum laminar dissipation rate) for each of the three cases. The 𝐶𝑂2 concentration is in direct relation to the mean temperature distribution (see Figure 15-a). Hence, a more produced 𝐶𝑂2 concentration implies a higher mean temperature and a more complete fuel combustion. On the other hand, the 𝑂2 concentration is inversely related to the mean temperature and combustion development. The 𝐶𝑂2 concentration is significantly higher for case B in comparison with the other two cases at various mixture fraction. However, moderately higher amounts of 𝐶𝑂2 for case A relative to case C is only observed in the mixture fractions lower than 0.15 value. Figure 15-a shows the mean temperature versus mixture fraction at the last laminar scalar dissipation rate for all the three cases. The maximum mean temperature is observed for case B and, in turn, the mean temperature is higher for case A relative to case C. Because, according to Table 6, due to the lowest last laminar scalar dissipation rate for case B, the reactions are more similar to the stoichiometric and equilibrium combustion. Also, case C has the least similarity to the equilibrium combustion (lowest mean temperature is observed for case C (Figure 15-a)) owing to its highest last laminar scalar dissipation rate (Table 6). From Figure 14, when the mixture fraction exceeds from the stoichiometric amount of every chemical mechanism, the flame is exposed to an air shortage and incomplete combustion due to a higher ratio of fuel to air and, consequently, the 𝐶𝑂2 amount is decreased for all the three cases. For each mixture fraction and independent of its stoichiometric value, 𝑂2 amount is lower for case B, as compared with the other two. This indicates a higher consumption of oxygen during the second chemical mechanism. It is also because of the lowest dissipation rates for case B (Table 6).The same relation exists between the scalar dissipation rate and lower 𝑂2 concentration for case A relative to case C. 27 ACS Paragon Plus Environment

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[Insert Figure 14.] Figure 14. Mole fractions of 𝐶𝑂2and 𝑂2 species versus mixture fraction at last laminar scalar dissipation rate Figure 15-b represents the mean temperature versus mixture fraction specifically at the laminar scalar dissipation rate of 0.01 for all the three cases. It should be mentioned that the reported temperature values are those before exerting the turbulence effects over the flame and are only useful for comparing the flame front among the three cases. The temperature distributions based on the various values of mixture fraction are significantly different for cases A to C. Different acquired temperature distributions in Figures 15-a and 15-b indicate the major and mutual relations between the scalar dissipation rate and the mean temperature. By enhancing the laminar scalar dissipation rate, the mean temperature is reduced against the mixture fraction (see cases A and B in Table 6 and Figures 15-a and 15-b). [Insert Figure 15.] Figure 15. Mean temperature against mixture fraction for all three cases a) at last laminar scalar dissipation rate, and b) at laminar scalar dissipation rate of 0.01 Figure 16 displays the thermal and prompt 𝑁𝑂 formation rates as well as 𝑁𝑂 concentration in the axial direction and across the mid-plane (𝑍 = 0) for cases A to C. It is revealed that the order magnitude of formation rate of thermal 𝑁𝑂 is approximately 10-100 times larger than that of the prompt 𝑁𝑂 for all the three cases. Considering the absolute dependence of thermal 𝑁𝑂 formation rate on the mean temperature distribution (presented earlier in Figure 6), thermal 𝑁𝑂 formation rate is higher for case A than that for case C and also it is higher for case C than that for case B. The prompt 𝑁𝑂 for the three cases is only formed at the flame front and the existing differences have a similar trend to the thermal 𝑁𝑂. It is illustrated that the produced


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𝑁𝑂 concentration within the region of hot gases is larger for cases A, C and B, respectively. Considering the important role of back reactions within the hot regions, the 𝑁𝑂 concentration values for cases A and C get closer to one another at the end of the model combustor. In addition to the influence of temperature distribution (Figure 6) on the produced 𝑁𝑂 concentration, the significant difference between the produced 𝑁𝑂 concentration for case B and the other two cases, could be due to the major differences between the chemical mechanisms, especially in the reactions including 𝑁 species. For example, two intermediate species of 𝑁2 𝑂 and 𝑁𝐻 are among the differences that are not utilized in case B. [Insert Figure 16.] Figure 16. Formation rate of thermal 𝑁𝑂, prompt 𝑁𝑂 and 𝑁𝑂 concentration for three chemical mechanisms in the axial direction and across the mid-plane (𝑍 = 0) 5. Conclusions In the present work, an inclusive numerical model is developed to study the influence of different chemical reaction mechanisms of kerosene fuel on the reactive flow characteristics in a model combustor. An Eulerian-Lagrangian approach along with the realizable 𝑘 − 𝜀 turbulence model and laminar flamelet model are implemented for modeling the spray combustion of liquid fuel. Various present results are validated by comparing directly with the available experimental data14. The main conclusions may be drawn as follows: At farther distances from the fuel nozzle, the effect of chemical reaction mechanism of fuel on distribution of mean velocity and temperature is reduced. Minimum deviations concerning the mean axial velocities and mean temperatures are related to case A which consists of 17 species and 26 reactions steps. Nevertheless, there is an almost 13% deviation on average between the present results of case A and available experimental data14.


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The maximum mixture fraction is detected for case B due to a higher value of 𝐶12 𝐻23 concentration for case B. High values of 𝑂2 consumption rate delay the mixture fraction reduction. The position of maximum scalar dissipation rate value is similar to the positions of maximum mean mixture fraction and 𝐶12 𝐻23 concentration. The maximum value of the mixture fraction variance is revealed for case B which causes the highest scalar dissipation rate for this case. The 𝐶𝑂2 concentration and mean temperature is significantly higher for case B in comparison with the other two cases at various mixture fraction. By enhancing the laminar scalar dissipation rate, the mean temperature is reduced against the mixture fraction. The order magnitude of formation rate of thermal 𝑁𝑂 is approximately 10-100 times larger than that of the prompt 𝑁𝑂 formation rate for all three cases. Thermal 𝑁𝑂 formation rate is higher for case A than that for case C and also it is higher for case C than that for case B. In addition to the influence of temperature distribution on the produced 𝑁𝑂 concentration, the significant difference between the produced 𝑁𝑂 concentration for case B and the other two cases, could be due to the major differences between the chemical mechanisms, especially in the reactions including 𝑁 species. [Insert Nomenclature] References

1. Yan, Y.; Liu, Y.; Di, D.; Dai, C.; Li, J., Simplified Chemical Reaction Mechanism for Surrogate Fuel of Aviation Kerosene and Its Verification. Energy & Fuels 2016. 2. Zettervall, N.; Fureby, C.; Nilsson, E. J. K., Small Skeletal Kinetic Mechanism for Kerosene Combustion. Energy & Fuels 2016, 30 (11), 9801-9813. 3. Mardani, A.; Fazlollahi-Ghomshi, A., Numerical Investigation of a Double-Swirled Gas Turbine Model Combustor Using a RANS Approach with Different Turbulence– Chemistry Interaction Models. Energy & Fuels 2016, 30 (8), 6764-6776.


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4. Zeinivand, H.; Bazdidi-Tehrani, F., Influence of stabilizer jets on combustion characteristics and NOx emission in a jet-stabilized combustor. Applied energy 2012, 92, 348360. 5. Bazdidi-Tehrani, F.; Zeinivand, H., Presumed PDF modeling of reactive two-phase flow in a three dimensional jet-stabilized model combustor. Energy Conversion and Management 2010, 51 (1), 225-234. 6. Apte, S.; Moin, P., Spray Modeling and Predictive Simulations in Realistic GasTurbine Engines. In Handbook of Atomization and Sprays, Springer: 2011; pp 811-835. 7. Torkzadeh, M.; Bolourchifard, F.; Amani, E., An investigation of air-swirl design criteria for gas turbine combustors through a multi-objective CFD optimization. Fuel 2016, 186, 734-749. 8. Ge, H.-W.; Gutheil, E., Simulation of a turbulent spray flame using coupled PDF gas phase and spray flamelet modeling. Combustion and Flame 2008, 153 (1), 173-185. 9. Niu, J.; Piao, Y. In Numerical Simulation of Liquid Kerosene Combustion in a DualMode Scramjet Combustor Using Flamelet/Progress Variable Approach, 46th AIAA Fluid Dynamics Conference, 2016; p 3959. 10. Dagaut, P.; l, S. G. ï., Chemical kinetic study of the effect of a biofuel additive on JetA1 combustion. The Journal of Physical Chemistry A 2007, 111 (19), 3992-4000. 11. Molnar, M.; Marek, C. J., Reduced equations for calculating the combustion rates of jet-A and methane fuel. 2003. 12. Kundu, K.; Penko, P.; Yang, S. In Simplified Jet-A/air combustion mechanisms for calculation of NO (x) emissions, AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, 34 th, Cleveland, OH, 1998. 13. Richards, C.; Samuelsen, G. In The role of primary jets in the dome region aerodynamics of a model can combustor, ASME 1990 International Gas Turbine and Aeroengine Congress and Exposition, American Society of Mechanical Engineers: 1990; pp V003T06A028-V003T06A028. 14. Cameron, C.; Brouwer, J.; Wood, C.; Samuelsen, G., A detailed characterization of the velocity and thermal fields in a model can combustor with wall jet injection. Journal of Engineering for Gas Turbines and Power 1989, 111 (1), 31-35. 15. Cameron, C.; Brouwer, J.; Samuelsen, G. In A model gas turbine combustor with wall jets and optical access for turbulent mixing, fuel effects, and spray studies, Symposium (International) on Combustion, Elsevier: 1989; pp 465-474. 16. Kohnen, G.; Rüger, M.; Sommerfeld, M., Convergence behaviour for numerical calculations by the Euler/Lagrange method for strongly coupled phases. ASMEPUBLICATIONS-FED 1994, 185, 191-191. 17. Berlemont, A.; Grancher, M.; Gouesbet, G., Heat and mass transfer coupling between vaporizing droplets and turbulence using a Lagrangian approach. International journal of heat and mass transfer 1995, 38 (16), 3023-3034. 18. Sazhin, S. S., Advanced models of fuel droplet heating and evaporation. Progress in energy and combustion science 2006, 32 (2), 162-214. 19. Faeth, G., Evaporation and combustion of sprays. Progress in Energy and Combustion Science 1983, 9 (1), 1-76. 20. Flows, S. I. A. f. M.; Sommerfeld, M., Best Practice Guidelines for Computational Fluid Dynamics of Dispersed Multi-Phase Flows. European Research Community on Flow, Turbulence and Combustion (ERCOFTAC): 2008. 21. Park, J.-H.; Yoon, Y.; Hwang, S.-S., Improved TAB model for prediction of spray droplet deformation and breakup. Atomization and Sprays 2002, 12 (4).


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22. Ghose, P.; Patra, J.; Datta, A.; Mukhopadhyay, A., Prediction of soot and thermal radiation in a model gas turbine combustor burning kerosene fuel spray at different swirl levels. Combustion Theory and Modelling 2016, 1-29. 23. Ghose, P.; Patra, J.; Datta, A.; Mukhopadhyay, A., Effect of air flow distribution on soot formation and radiative heat transfer in a model liquid fuel spray combustor firing kerosene. International Journal of Heat and Mass Transfer 2014, 74, 143-155. 24. Shih, T.-H.; Liou, W.; Shabbir, A.; Yang, Z.; Zhu, J., A new k-epsilon eddy viscosity model for high Reynolds number turbulent flows: Model development and validation. 1994. 25. Pitsch, H.; Peters, N., A consistent flamelet formulation for non-premixed combustion considering differential diffusion effects. Combustion and Flame 1998, 114 (1), 26-40. 26. Hjertager, L. K.; Hjertager, B. H.; Solberg, T., CFD modelling of fast chemical reactions in turbulent liquid flows. Computers & Chemical Engineering 2002, 26 (4), 507-515. 27. Veynante, D.; Vervisch, L., Turbulent combustion modeling. Progress in energy and combustion science 2002, 28 (3), 193-266. 28. Claramunt, K., Numerical Simulation of Non-premixed Laminar and Turbulent Flames by means of Flamelet Modelling Approaches. 2005. 29. Peters, N., Turbulent combustion. Cambridge university press: 2000. 30. Lower, S., Chem1 virtual textbook. http://www.chem1.com/acad/webtext/virtualtextbook.html, 2016. 31. Mattingly, J. D., Aircraft engine design. Aiaa: 2002. 32. Ghose, P.; Datta, A.; Mukhopadhyay, A., Modeling Nonequilibrium Combustion Chemistry Using Constrained Equilibrium Flamelet Model for Kerosene Spray Flame. Journal of Thermal Science and Engineering Applications 2016, 8 (1), 011004. 33. Modest, M. F., Radiative heat transfer. Academic press: 2013. 34. Moss, J.; Perera, S.; Stewart, C.; Makida, M. In Radiation heat transfer in gas turbine combustors, Proc. 16th (Int’l.) Symp. on Airbreathing Engines, Cleveland, OH, 2003. 35. Fiveland, W., Discrete-ordinates solutions of the radiative transport equation for rectangular enclosures. Journal of Heat Transfer 1984, 106 (4), 699-706. 36. Smith, T.; Shen, Z.; Friedman, J., Evaluation of coefficients for the weighted sum of gray gases model. Journal of Heat Transfer 1982, 104 (4), 602-608. 37. Patankar, S., Numerical heat transfer and fluid flow. CRC press: 1980. 38. Van Doormaal, J.; Raithby, G., Enhancements of the SIMPLE method for predicting incompressible fluid flows. Numerical heat transfer 1984, 7 (2), 147-163. 39. Zel'dovich, Y. B.; Sadovnikov, P. Y.; Frank-Kamenetskii, D., Nitrogen oxidation in combustion. Izd. Akad. Nauk SSSR, Moscow 1947. 40. Westbrook, C. K.; Dryer, F. L., Chemical kinetic modeling of hydrocarbon combustion. Progress in Energy and Combustion Science 1984, 10 (1), 1-57. 41. De Soete, G. G. In Overall reaction rates of NO and N 2 formation from fuel nitrogen, Symposium (international) on combustion, Elsevier: 1975; pp 1093-1102. 42. Davidson, L., Fluid mechanics, turbulent flow and turbulence modeling. Chalmers University of Technology, Goteborg, Sweden (Nov 2011) 2011.


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Energy & Fuels

NOMENCLATURE 𝐴 𝐴𝑝

𝑟 𝑆

Position vector Mean strain tensor

𝑠

Direction vector

𝑆ℎ𝐴𝐵

Shroud number

𝑆Ψ1

source terms for gas phase

𝑆Ψ2

sink terms droplets phase

𝑠́

Scattering direction vector

𝑇

Temperature (𝐾)

𝑡

Time (𝑠)

𝑈, 𝑉, 𝑊

Velocity Component (𝑚⁄𝑠)

𝐶𝜒

Pre-exponential factor Droplet surface area Coefficient in reaction equation Spalding mass number Coefficient in reaction equation Coefficient in realizable 𝑘 − 𝜀 equation model Constant number in realizable 𝑘 − 𝜀 equation model Coefficient in flamelet equation Coefficient in realizable 𝑘 − 𝜀 equation model Coefficient in flamelet equation

𝑐𝑝

Specific heat capacity at constant pressure (𝐽/𝑘𝑔 𝐾)

𝑢 ⃗

Velocity vector

𝐷ℎ 𝐷𝑖,𝑚 𝑑𝑝

WJCC 𝑋, 𝑌, 𝑍 𝑌𝑖

Wall jet can combustor Cartesian system of coordinates Mass fraction of species

𝐹𝐷 𝑓

Hydraulic diameter Constant in discrete phase Diameter of droplet Activation energy for the reaction Inverse of complementary error function Drag force Mixture fraction

𝑓́

Mixture fraction variance

𝜀

𝐺𝑘

Source for generation of turbulence kinetic energy

𝜂

𝐻

Enthalpy Heat transfer coefficient of convection (𝑊 ⁄𝑚2 𝑘) Latent heat of vaporization Radiation intensity Turbulence intensity Kinetic energy

𝑎 𝐵𝑚 𝑏 𝐶1 𝐶2 𝐶𝑔 𝐶𝜇

𝐸 𝑒𝑟𝑓𝑐 −1

ℎ ℎ𝑓𝑔 𝐼 𝐼𝑡 𝑘

Greek Symbols 𝛼

Absorption coefficient

𝛼𝑠 Γ

𝜄𝑡

Rate of deformation characteristics Diffusion coefficient Dissipation rate of turbulence kinetic energy Ratio of characteristic time of turbulence to characteristic time of flow field Turbulent Schmidt number

𝜆

Conduction heat transfer coefficient

𝜇𝑡 𝜌 𝜎 𝜎𝑠

Turbulent dynamic viscosity (𝑁𝑠⁄𝑚2 ) Density (𝑘𝑔⁄𝑚3) Turbulent Prandtl number Scattering coefficient


Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

𝐾 𝑀 𝑀𝐷 𝑚 𝑛 𝑅 RANS 𝑅, 𝜃, 𝑍

Chemical reaction rate Third-body reactant and product Mean deviation Mass Refractive index Universal gas constant Reynolds averaged Navier Stokes Cylindrical system of coordinates

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𝜒

Scalar dissipation rate

𝜒̅

Mean scalar dissipation rate

𝛹 Ώ 𝑝

dependent variables Solid angle Subscripts Particle (droplet)

𝑠𝑡

Stoichiometric condition

∞

Gas phase


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Table 1. Chemical mechanism of decomposition of nitrogen dioxide into nitric oxide and oxygen30 Reactions

Steps

2𝑁𝑂2 → 𝑁𝑂3 + 𝑁𝑂

First elementary step

𝑁𝑂3 → 𝑁𝑂 + 𝑂2

Second elementary step

2𝑁𝑂2 → 2𝑁𝑂 + 𝑂2

Net reaction


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Table 2. Chemical mechanism of oxidation of hydrogen gas30 1 𝐻2 + 𝑂2 → 𝐻2 𝑂 2

𝛥𝐻 𝑜 = −242 𝑘𝑗/𝑚𝑜𝑙

1) 𝐻2 + 𝑂2 → 𝐻𝑂2 ⋅ +𝐻 ⋅

Chain initiation

2) 𝐻2 + 𝐻𝑂2 ⋅→ 𝐻𝑂 ⋅ +𝐻2 𝑂

Chain propagation

3) 𝐻 ⋅ +𝑂2 → 𝐻𝑂 ⋅ +𝑂 ⋅

Chain propagation + Branching

4) 𝑂 ⋅ +𝐻2 → 𝐻𝑂 ⋅ +𝐻 ⋅

Chain propagation + Branching

5) 𝐻𝑂 ⋅ +𝐻2 → 𝐻2 𝑂 + 𝐻 ⋅

Chain propagation


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Table 3. First chemical reaction mechanism12 (case A) Number 1

K = A𝑇 𝑏 exp(−E/RT)

A

𝑁2 + 𝐶12 𝐻23 → 12𝐶𝐻 + 11𝐻 + 𝑁2 4.35𝐸 + 09

b

E

0.0

30000

2𝑓

𝐶𝐻 + 𝐻2 + 𝑁2 → 2𝑁𝐻 + 𝐶𝐻

1.00𝐸 + 15

0.0

78000

2𝑏

𝐶𝐻 + 2𝑁𝐻 → 𝐶𝐻 + 𝐻2 + 𝑁2

1.95𝐸 + 15

0.0

0

3

𝐻2 + 𝑂𝐻 ↔ 𝐻 + 𝐻2 𝑂

2.16𝐸 + 08

1.5

3430

4

𝐻2 + 𝑂 ↔ 𝐻 + 𝑂𝐻

3.87𝐸 + 04

2.7

6260

5

𝐻 + 𝑂2 ↔ 𝑂 + 𝑂𝐻

2.65𝐸 + 16

−0.7

17041

6𝑓

𝑁2 + 𝑂2 → 2O + 𝑁2

1.00𝐸 + 18

0.0

122239

6𝑏

𝐻2 + 2𝑂 → 𝑂2 𝐻2

1.00𝐸 + 18

0.0

0

7

𝐻2 + 2𝐻 ↔ 2𝐻2

9.00𝐸 + 16

−0.6

0

8

𝐻 + 𝑂2 ↔ 𝐻𝑂2

1.00𝐸 + 15 −1.01

0

9

𝐻 + 𝐻𝑂2 ↔ 𝐻2 + 𝑂2

4.48𝐸 + 13

0.0

1068

10

𝑂 + 𝐻𝑂2 ↔ 𝑂𝐻 + 𝑂2

2.00𝐸 + 13

0.0

0

11

𝐶𝑂 + 𝐻𝑂2 ↔ 𝐶𝑂2 + 𝑂𝐻

1.50𝐸 + 14

0.0

23600

12

𝐶𝑂 + 𝑂𝐻 ↔ 𝐶𝑂2 + 𝐻

4.76𝐸 + 07

1.2

70

13

𝐶𝐻 + 𝑂 ↔ 𝐶𝑂 + 𝐻

5.70𝐸 + 13

0.0

0

14

𝐶𝐻 + 𝑂𝐻 ↔ 𝐶𝑂 + 𝐻2

3.00𝐸 + 13

0.0

0

15

𝐶𝐻 + 𝑁𝑂 ↔ 𝑁𝐻 + 𝐶𝑂

1.00𝐸 + 11

0.0

0

16

𝑁2 + 2𝐶𝐻 ↔ 𝐶2 𝐻2 + 𝑁2

1.00𝐸 + 14

0.0

0

17

𝐶2 𝐻2 + 𝑂2 ↔ 2𝐶𝑂 + 𝐻2

3.00𝐸 + 16

0.0

19000

18

𝑁2 + 𝑂 ↔ 𝑁 + 𝑁𝑂

6.50𝐸 + 13

0.0

75000

19

𝑁 + 𝑂2 ↔ 𝑁𝑂 + 𝑂

9.00𝐸 + 09

1.0

6500

20

𝑁 + 𝑂𝐻 ↔ 𝑁𝑂 + 𝐻

3.36𝐸 + 13

0.0

385


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21

𝑁𝐻 + 𝑁𝑂 ↔ 𝑁2 𝑂 + 𝐻

3.65𝐸 + 14

−0.5

0

22

𝑁2 𝑂 + 𝑂𝐻 ↔ 𝑁2 + 𝐻𝑂2

2.00𝐸 + 12

0.0

21060

23

𝑁2 𝑂 + 𝑂 ↔ 2𝑁𝑂

2.90𝐸 + 13

0.0

23150

24

𝑁2 𝑂 + 𝑂 ↔ 𝑁2 + 𝑂2

1.40𝐸 + 12

0.0

10810

25

𝑁2 𝑂 + 𝐻 ↔ 𝑁2 + 𝑂𝐻

3.87𝐸 + 14

0.0

18880

26

𝑁𝐻 + 𝑂 ↔ 𝑁𝑂 + 𝐻

4.00𝐸 + 13

0.0

0


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Table 4. Second chemical mechanism31 (case B) Number


A

b

E

1

𝐶12 𝐻23 + 𝑂2 → 5𝐶2 𝐻4 + 𝐶2 𝐻3

30199.52

1.5

15698

+ 𝑂2 2

𝐶12 𝐻23 + 𝑂𝐻 → 6𝐶2 𝐻4 + 𝑂

19952623.15

1.0

8942

3

𝐶2 𝐻4 + 𝐻 → 𝐶2 𝐻3 + 𝐻2

30199517204.02

0.0

18878

4

𝐻 + 𝐻 + 𝑀 → 𝐻2 + 𝑀

5

𝑂 + 𝑂 + 𝑀 → 𝑂2 + 𝑀

6

𝐻 + 𝑂𝐻 + 𝑀 → 𝐻2 𝑂 + 𝑀

7

𝐻 + 𝑂2 → 𝑂𝐻 + 𝑂

223872113856.84

0.0

16692

8

𝑂 + 𝐻2 → 𝑂𝐻 + 𝐻

17378008287.5

0.0

9400

9

𝐶𝑂 + 𝑂𝐻 → 𝐶𝑂2 + 𝐻

1.78𝐸 − 15

7.0

−13910

10

𝐻 + 𝐻2 𝑂 → 𝑂𝐻 + 𝐻2

83176377110.27

0.0

19971

11

𝐶𝐻3 + 𝑂2 → 𝐶𝐻2 𝑂 + 𝑂𝐻

1000000000

0.0

7948

12

𝐻𝑂2 + 𝑀 → 𝐻 + 𝑂2 + 𝑀

2089296130854.04

0.0

45705

13

𝐻𝑂2 + 𝐻 → 𝑂𝐻 + 𝑂𝐻

7762471166.29

0.0

1888

14

𝐶𝐻2 𝑂 + 𝑂𝐻 → 𝐻2 𝑂 + 𝐻𝐶𝑂

79432823472.4

0.0

4213

15

𝑂 + 𝐻2 𝑂 → 𝑂𝐻 + 𝑂𝐻

57543993733.71

0.0

17884

16

𝑁2 + 𝑂 → 𝑁𝑂 + 𝑁

1000000000

0.0

49680

17

𝑁 + 𝑂2 → 𝑁𝑂 + 𝑂

100000

1.0

3974

18

𝑁 + 𝑂𝐻 → 𝑁𝑂 + 𝐻

1000000000

0.0

0.0

19

𝐻𝐶𝑂 + 𝑂2 → 𝐻𝑂2 + 𝐶𝑂

30199517204.02

0.0

13910

20

𝐻𝐶𝑂 + 𝑂𝐻 → 𝐻2 𝑂 + 𝐶𝑂

19952623149.69

0.0

0.0

21

𝐶2 𝐻4 + 𝑂𝐻 → 𝐶2 𝐻3 + 𝐻2 𝑂

6025595860.743

0.0

3478

1995262314968.88 −1.0 100000000000

0.0

−1.0

0.0

70794578438413.8 −1.0

0.0


Energy & Fuels

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22

𝐶𝐻2 𝑂 + 𝐻𝑂2 → 𝐻𝐶𝑂 + 𝑂𝐻 + 𝑂𝐻

1000000000

0.0

8942

23

𝐶2 𝐻2 + 𝐻𝑂2 → 𝐻𝐶𝑂 + 𝐶𝐻2 𝑂

1995262314.97

0.0

10930

24

𝐶2 𝐻3 + 𝑂2 → 𝐶2 𝐻2 + 𝐻𝑂2

1698243652.46

0.0

9936

25

𝑁𝑂 + 𝐻𝑂2 → 𝑁𝑂2 + 𝑂𝐻

1000

1.0

0.0

26

𝐶2 𝐻4 + 𝑂 → 𝐶𝐻3 + 𝐻𝐶𝑂

8511380382.024

0.0

2980

27

𝐶2 𝐻4 + 𝐻𝑂2 → 𝐶𝐻3 + 𝐻𝐶𝑂 + 𝑂𝐻

7943282347.243

0.0

9936

28

𝐻2 + 𝐶𝐻3 → 𝐶𝐻4 + 𝐻

10000000

−1.5

14190

29

𝐶2 𝐻2 + 𝑂𝐻 → 𝐶𝐻3 + 𝐶𝑂

158489319.25

0.0

4968

30

𝐶𝐻3 + 𝑂 → 𝐶𝐻2 𝑂 + 𝐻

128824955169.31

0.0

1987


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Energy & Fuels

Table 5. Third chemical mechanism11 (case C) Number


A

b

E

1

𝐻2 + 𝑂𝐻 ↔ 𝐻 + 𝐻2 𝑂

1.17𝐸 + 11

1.1

3626

2

𝐻2 + 𝑂 ↔ 𝐻 + 𝑂𝐻

2.50𝐸 + 15

0

6000

3

𝐻 + 𝑂2 ↔ 𝑂 + 𝑂𝐻

4.00𝐸 + 14

0

18000

4𝑓

𝑁2 + 𝑂2 → 2O + 𝑁2

1.00𝐸 + 18

0

122239

4𝑏

𝐻2 + 2𝑂 → 𝑂2 + 𝐻2

5.00𝐸 + 17

0.5

0

5

𝐻2 + 2𝐻 ↔ 2𝐻2

4.00𝐸 + 20

−1

0

6

𝐻 + 𝑂2 ↔ 𝐻𝑂2

1.00𝐸 + 15 −1.1

0

7

𝑂 + 𝐻𝑂2 ↔ 𝑂𝐻 + 𝑂2

1.50𝐸 + 13

0

0

8

𝐻 + 𝐻𝑂2 ↔ 𝐻2 + 𝑂2

1.50𝐸 + 13

0

0

9

𝐶𝑂 + 𝑂𝐻 ↔ 𝐶𝑂2 + 𝐻

4.17𝐸 + 11

0

1000

10

𝐶𝑂 + 𝐻𝑂2 ↔ 𝐶𝑂2 + 𝑂𝐻

5.80𝐸 + 13

0

22934

11

𝐶𝐻 + 𝑂 ↔ 𝐶𝑂 + 𝐻

1.00𝐸 + 10

0.5

0

12

𝐶𝐻 + 𝑁𝑂 ↔ 𝑁𝐻 + 𝐶𝑂

1.00𝐸 + 11

0

0

13

𝐶𝐻 + 𝑂2 ↔ 𝐶𝑂 + 𝑂𝐻

3.00𝐸 + 10

0

0

14

𝐶2 𝐻2 + 𝑂2 ↔ 2𝐶𝑂 + 2𝐻

3.00𝐸 + 12

0

49000

15

𝑁2 + 2𝑁 ↔ 𝑁2 + 𝑁2

1.00𝐸 + 15

0

0

16

𝑁 + 𝑂2 ↔ 𝑁𝑂 + 𝑂

6.30𝐸 + 09

1.0

6300

17

𝑁 + 𝑂𝐻 ↔ 𝑁𝑂 + 𝐻

3.00𝐸 + 13

0

0

18

𝑁𝐻 + 𝑂 ↔ 𝑁𝑂 + 𝐻

1.50𝐸 + 13

0

0

20

𝑁𝐻 + 𝑁𝑂 ↔ 𝑁2 + 𝑂𝐻

21

𝑂 + 𝑁2 + 𝐻𝑂2 → 2𝑁𝑂 + 𝑂 + 𝐻

1.50𝐸 + 07

1.0

45900

22

2𝑁𝑂 + 𝐻 ↔ 𝑁2 + 𝐻𝑂2

2.50𝐸 + 10

0.16

8000

2.00𝐸 + 15 −0.8


0

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23𝑓

𝑁2 + 𝑂 ↔ 𝑁𝑂 + 𝑁

4.75𝐸 + 10

0.29

75010

23𝑏

𝑁 + 𝑁𝑂 ↔ 𝑁2 + 𝑂

3.00𝐸 + 12

0.2

0

24𝑓

𝑁2 + 𝐻2 + 2𝐶𝐻 → 2𝐶𝐻 + 2𝑁𝐻

1.00𝐸 + 16

0

78000

24𝑏

2𝐶𝐻 + 2𝑁𝐻 → 𝑁2 + 𝐻2 + 2𝐶𝐻

1.95𝐸 + 15

0

0

25

𝐶12 𝐻23 + 𝑁2 → 11𝐻 + 6𝐶2 𝐻2 + 𝑁2 2.50𝐸 + 09

0

30000

26

𝐶12 𝐻23 + 𝑁2 → 12𝐶𝐻 + 11𝐻 + 𝑁2

0

30000

2.50𝐸 + 10


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Energy & Fuels

Table 6. Specifications of three different modeling cases Last scalar Chemical

Number of

Number of

Number of

mechanism

species

reactions

flamelets

Cases

dissipation rate 1

(𝑠 ) case A

Table (4)

17

26

28

13

case B

Table (5)

21

30

3

0.01

case C

Table (6)

16

26

11

19.1


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Page 44 of 61

Table 7. Geometrical and flow specifications of WJCC Parameter

Value

Combustor’s diameter (𝑚)

0.08

Combustor’s length (𝑚)

0.32

Type of fuel

kerosene

Operating pressure (𝑎𝑡𝑚)

1 inside: 0.019

Swirler diameter (𝑚)

outside: 0.057 Swirl number

1.4

Spray angle (degree)

60

Air mass flow rate

𝟏𝟔𝟑 𝒌𝒈⁄𝒉

Fuel mass flow rate

𝟑. 𝟐𝟕 𝒌𝒈⁄𝒉


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Energy & Fuels

Table 8. Different mesh size Name

Mesh size

Grid points 𝑋 × 𝑅 × 𝜃

Grid A

2.5 × 105

60 × 37 × 113

Grid B

5 × 105

75 × 47 × 142

Grid C

8.7 × 105

90 × 56 × 170

Grid D

1.3 × 106

102 × 64 × 196


Energy & Fuels

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Figure 1. A schematic view of model combustion chamber14 and boundary conditions (dimensions in 𝑚𝑚).


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Figure 2. Grid independence test: (a) mean axial velocity at centerline and (b) 𝐶𝑂2 concentration at 𝑋 = 0.1 𝑚 along Y direction


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Figure 3. Structured mesh on the model combustor geometry


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Figure 4. Comparison of present profiles of mean axial velocity (cases A to C) and experiment14; (a) 𝑋 = 0.04 𝑚, (b) 𝑋 = 0.1 𝑚 and (c) 𝑋 = 0.18 𝑚 (Y direction) 49 ACS Paragon Plus Environment

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Figure 5. Comparison of present profiles of mean temperature (cases A to C) and experiment14; (a) 𝑋 = 0.03 𝑚, (b) 𝑋 = 0.1 𝑚 and (c) 𝑋 = 0.18 𝑚 (Y direction) 50 ACS Paragon Plus Environment

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Energy & Fuels

Figure 6. Distributions of mean temperature in axial direction: a) across mid-plane and b) centerline


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Figure 7. Process of decomposition of initial fuel to ultimate products for cases A to C


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Figure 8. Decomposition rate of 𝐶12 𝐻23 for three chemical reaction mechanisms


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Figure 9. Mean mixture fraction at centerline of model combustion chamber


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Figure 10. Production and consumption rates of oxygen for three chemical mechanisms (production: 𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑟𝑎𝑡𝑒 > 0.0 and consumption: 𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑟𝑎𝑡𝑒 < 0.0)


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Figure 11. Influence of chemical reaction mechanism on axial distribution of a) scalar dissipation rate, b) ratio of turbulence dissipation rate to kinetic energy, and c) mixture fraction variance at centerline


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Figure 12. Influence of chemical reaction mechanism on axial distribution of a) Mole fraction of 𝐶12 𝐻23 and b) Mole fraction of 𝑂2 at centerline


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Figure 13. 𝐻 mole fraction against 𝐻2 𝑂 mole fraction for three cases at centerline


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Figure 14. Mole fractions of 𝐶𝑂2and 𝑂2 species versus mixture fraction at last laminar scalar dissipation rate


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Figure 15. Mean temperature against mixture fraction for all three cases a) at last laminar scalar dissipation rate, and b) at laminar scalar dissipation rate of 0.01


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Figure 16. Formation rate of thermal 𝑁𝑂, prompt 𝑁𝑂 and 𝑁𝑂 concentration for three chemical mechanisms in the axial direction and across the mid-plane (𝑍 = 0)


Influence of Chemical Mechanisms on Spray Combustion

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