Analysis of Relationship between Entropy Generation and Soot

Subscriber access provided by Nottingham Trent University

Combustion

Analysis of Relationship between Entropy Generation and Soot Formation in Turbulent Kerosene/Air Jet Diffusion Flames Farzad Bazdidi-Tehrani, Mohammad Sadegh Abedinejad, and Milad Mohammadi Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.9b01671 • Publication Date (Web): 08 Aug 2019 Downloaded from pubs.acs.org on August 17, 2019

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 36 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

Energy & Fuels

Analysis of Relationship between Entropy Generation and Soot Formation in Turbulent Kerosene/Air Jet Diffusion Flames

Farzad Bazdidi–Tehrani*, Mohammad Sadegh Abedinejad, Milad Mohammadi,

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

1 ACS Paragon Plus Environment

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

Abstract A comprehensive study of turbulent combustion is carried out to analyze the relationship between entropy generation and soot formation in turbulent vaporized kerosene/air jet diffusion flames. Dealing with the laminar flamelet combustion model for predicting the temperature distribution, the Moss-Brookes-Hall model is applied for estimating the soot formation. The radiation heat transfer and turbulent flow are simulated employing the discrete ordinates model and the realizable 𝑘 ― 𝜀 turbulence model, respectively. There are credible agreements between the present results of mean temperature, soot volume fraction and mean mixture fraction, and the available experimental data. Results show that the chemical reaction process has the biggest role in the computation of entropy generation while the other processes including viscous dissipation, mass diffusion and heat conduction can be neglected. The main region of soot formation can directly be predicted by the entropy generation with an acceptable deviation. Also, the surface growth has the major role in the soot formation among the various processes.

Keywords: Entropy generation, Soot formation, Turbulent combustion, Chemical reaction


Page 2 of 36

Page 3 of 36 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

Energy & Fuels

1. Introduction Analysis of the entropy generation in the gas turbine combustion chambers has been one of the most interesting issues in the recent years. It is aimed to improve the performance of combustors or the other energy systems based on the second law of thermodynamics. There are numerous irreversible processes in the gas turbine combustors that result in the loss of exergy. Thus, in order to improve the performance, it is essential to identify the causes of irreversibility and entropy generation. The major reasons are heat conduction, viscous dissipation, mass diffusion and chemical reaction 1. Jejurkar and Mishra 2 have numerically investigated the entropy generation in an annular micro combustor by utilizing multi-step kinetics for hydrogen-air mixture. They have studied the influence of chemical kinetics and transport processes on entropy generation and predicted the amount of heat losses. Their analysis show that the reactions supply most of the generated entropy. Furthermore, they have noticed that the overall combustion entropy generation rates do not follow the trend of flame temperature on the rich side. Because, heat and mass transfer play an important role in decreasing the entropy generation and balancing the combustion irreversibility for the rich flame. Chen 3 has investigated the effects of the inlet Reynolds number and equivalence ratio on the entropy generation in a hydrogen–air combustion. The results indicate that the relative total entropy generation rate is nearly insensitive to the change of equivalence ratio. In return, the order of the relative total entropy generation rate depends meaningfully on the inlet Reynolds number. Som and datta 4 have reported that the exergy destruction by chemical reaction can be reduced by keeping the flame temperature high and decreasing the temperature gradient in the combustion. 3 ACS Paragon Plus Environment

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

Wenming et al. 5 have investigated the entropy generation in a micro-combustor that involves a block insert. They have found that a block insert can make a more uniform wall temperature and less entropy generation. Safari et al. 6 have investigated local entropy generation using large eddy simulation in turbulent methane/air combustion. They have analyzed the sources of irreversibility comprising heat conduction, viscous dissipation, mass diffusion and chemical reaction. Their study has shown that the heat conduction is the main source of entropy production and occurs mostly in regions with large temperature gradient. In another work, Safari 7 has studied local entropy generation in a turbulent reacting flow. He has employed the stochastic model to calculate entropy generation and a GRI3.0 mechanism for simulating the reactive flow. The results have demonstrated that the stochastic model provides enough accuracy for evaluating the local entropy. Dunbar and Lior 8 have reported the sources of irreversibility in combustion. Their study on the entropy generation includes three parts, namely, combined diffusion/fuel oxidation, heat transfer and product constituent mixing process. They have used two fuels for their investigation which are hydrogen and methane. Their results have indicated that the internal thermal energy exchange (heat transfer) is the major reason for the exergy destruction. The irreversibility of chemical reaction is the most significant factor in the entropy generation. Several combustion reactions, including soot and NOx formation, are irreversible. Soot emission is one of the main output pollutants of the combustors. Watanabe et al. 9 have performed a simulation of the spray combustion to investigate the soot and NO formation. They have employed a transport equation for calculating the soot mass fraction. Thermal and prompt NO formation have been modeled in a post-processing model. They have noticed that taking into account the soot radiation has a great effect on the temperature distribution. It is such that 4 ACS Paragon Plus Environment

Page 4 of 36

Page 5 of 36 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

Energy & Fuels

without the soot radiation, the temperature is predicted higher. Saqr et al. 10 have investigated the influence of free stream turbulence on soot and NO formation in CH4-air flames. Their results display that an increase in the turbulence intensity causes a considerable reduction in the soot and NO formation. Guo and Smallwood 11 have studied the effects of NO and soot formation on each other in the ethylene-air diffusion flame. They have reported that the NO formation has a small effect on the soot formation. Young 12 has investigated soot formation in vaporized kerosene/air jet diffusion flames. He has performed both theoretical and experimental studies. His goal has been to develop a soot formation model which can be employed for the simulation of combustion. In the recent years, Li 13, Liu et al. 14, Yen et al. 15, Fu et al. 16, Huang and Vander Wal 17, Sirignano et al. 18, Sarlak et al. 19 and Wang et al. 20 have all investigated the effects of various characteristics on soot formation in a combustion chamber. However, none of these works has been devoted to the investigation of the relationship between entropy generation rate and soot formation. The main objective of the present paper is to make clear the ways to control the soot formation. For this purpose, the soot formation processes encompassing nucleation, coagulation, surface growth and oxidation, and entropy generation processes comprising viscous dissipation, heat conduction, mass diffusion and chemical reaction are discussed. The laminar flamelet and the Moss-Brookes-Hall (MBH) models are applied for simulating the combustion and soot formation in vaporized kerosene/air jet diffusion flames, respectively. Also, the radiation heat transfer and turbulent flow are simulated employing the discrete ordinates model (DOM) and the realizable 𝑘 ― 𝜀 turbulence model, consecutively. Validation of the present results is performed by comparisons between the temperature, mixture fraction and soot volume fraction and the available experimental data of Young 12. 5 ACS Paragon Plus Environment

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

Page 6 of 36

3. Numerical Models and Equations 3.1 General Equations and Models The governing equations of turbulent reactive gas flow comprise mass, energy, momentum and chemical species mass conservation. The general form of these transport equations is defined as in equations (1) 21.

(

)

∂Ψ𝑘 ∂ ∂ ∂ (𝜌Ψ𝑘) + (𝜌𝑢𝑗Ψ𝑘) = + 𝑆Ψ𝑘 ΓΨ ∂𝑡 ∂𝑥𝑗 ∂𝑥𝑗 ∂𝑥𝑗

(1)

where, Ψ denotes dependent variables including mass, velocity components, temperature, and mass fraction of species. ΓΨ is an effective diffusion coefficient of the parameter Ψ and 𝑆Ψ indicates the source term. Some supplementary terms, similar to the Reynolds stresses tensors, are appeared by the Favre averaging of the governing equations. On the basis of the previously reported studies 22-28, the realizable 𝑘 ― 𝜀 model 29 is employed presently to model the Reynolds viscous stresses in a combustor. The realizable 𝑘 ― 𝜀 transport equations are defined, as follows:

[( ) ]

𝜇𝑡 ∂𝑘 ∂ ∂ ∂ (𝜌𝑢𝑗𝑘) = (𝜌𝑘) + 𝜇+ + 𝐺𝑘 + 𝐺𝑏 ― 𝜌𝜀 ― 𝑌𝑀 ∂𝑡 ∂𝑥𝑗 ∂𝑥𝑗 𝜎𝑘 ∂𝑥𝑗

[( ) ]

𝜇𝑡 ∂𝜀 ∂ ∂ ∂ (𝜌𝑢𝑗𝜀) = + 𝜌𝐶1𝑆𝜀 ― 𝜌𝐶2 𝜇+ (𝜌𝜀) + ∂𝑥𝑗 𝜎𝜀 ∂𝑥𝑗 ∂𝑡 ∂𝑥𝑗

𝜀2

𝑘+

(2)

𝜀 + 𝐶1𝜀 𝐶3𝜀𝐺𝑏 𝑘 𝜇𝜀

(3)

𝜌

where, 𝑘 and 𝜀 signify kinetic energy and dissipation rate, successively. 𝐺𝑘 and 𝐺𝑏 specifies the turbulence kinetic energy generation and 𝑆 is the mean strain tensor. 𝑌𝑀 denotes the fluctuating dilatation contribution to the total dissipation rate. 𝐶1 is not a constant and it depends on the ratio of turbulence characteristic time to flow field characteristic time. The chemical reactions in the combustor are modeled employing the laminar flamelet model 30, which is also applied recently by the authors

28, 31

and some other researchers


6, 15, 32.

The non-

Page 7 of 36 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

Energy & Fuels

premixed combustion and turbulent flows are correlated via the 𝛽𝑃𝐷𝐹 33. The flamelet equations are formulated as: 1 ∂2𝑌𝑖 = 𝜌𝜒 + 𝜔𝑖 + 𝑆𝑖 ∂𝑡 2 ∂𝑓2

∂𝑌𝑖

∂𝑇 1 ∂2𝑇 1 𝜌 = 𝜌𝜒 2 ― ∂𝑡 2 ∂𝑓 𝑐𝑝

∑

(4)

𝐻𝑖𝑆𝑖 +

𝑖

[

∂𝑐𝑝 1 + 𝜌𝜒 2𝑐𝑝 ∂𝑓

∑ 𝑖

]

∂𝑌𝑖 ∂𝑇 𝑐𝑝,𝑖 + 𝑆𝑟 ∂𝑓 ∂𝑓

(5)

where, 𝜔𝑖, 𝑆𝑖, 𝐻𝑖, 𝐶p,i, 𝐶p, 𝑌𝑖 and 𝜒 are the production rate from chemical reaction, the source term of reaction rate, the specific enthalpy of species 𝑖, the specific heat of species 𝑖, the mixture mean specific heat, the mass ratio of species 𝑖 and the scalar dissipation rate, respectively. In the present work, the vaporized kerosene fuel with a chemical formula of C10H22 is considered as the fuel. The flamelet database is produced on the basis of JetSurf 1.0 reaction mechanism

34

which

includes 194 species and 1459 reduced chemical reactions of kerosene. Further descriptions of the flamelet model are available in references 28, 30-31, 35. In a combustor simulation, because of the existence of a high temperature zone, the modeling of the radiation heat transfer is necessary (DOM)

36

19.

In the present work, the discrete ordinates model

is applied for modeling the radiation heat transfer. The weighted sum of gray gases

model (WSGGM)

37

is implemented for gaining the non-constant absorption coefficient of

combustion gases due to the continuous variations of the combustion characteristics (i.e., temperature and species concentration) during the combustion process

28, 38.

More information

about the WSGGM and DOM is available in the references 31, 39-41. 3.2 Entropy Generation The local entropy generation rate due to the different processes (i.e., viscous dissipation, heat conduction, mass diffusion and chemical reaction) is obtained from the following two equations 1, 42:


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

𝑆ʼʼʼ𝑡𝑜𝑡𝑎𝑙 = 𝑆ʼʼʼ 𝑣𝑖𝑠𝑐𝑜𝑢𝑠 + 𝑆ʼʼʼ 𝑑𝑖𝑠𝑠𝑖𝑝𝑎𝑡𝑖𝑜𝑛

𝑆ʼʼʼ𝑡𝑜𝑡𝑎𝑙 =

ℎ𝑒𝑎𝑡 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑜𝑛

𝜏:∇𝑢 𝑘𝑒𝑓𝑓∇𝑇 ∙ ∇𝑇 ― +𝑅 𝑇 𝑇2

+ 𝑆ʼʼʼ

𝑚𝑎𝑠𝑠 𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑜𝑛

∑ 𝑖

𝜌𝐷𝑖 ― 𝑚𝑖𝑥 𝑋𝑖

Page 8 of 36

+ 𝑆ʼʼʼ𝑐ℎ𝑒𝑚𝑖𝑐𝑎𝑙

(6-a)

𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛

∇𝑌𝑖 ∙ ∇𝑋𝑖 ―

∑ 𝑖

𝜔𝑖.𝛾𝑖 𝑇

(6-b)

where, 𝜏 is the viscous stress and 𝐷𝑖 ― 𝑚𝑖𝑥 represents the mass diffusivity of species 𝑖 in the mixture. 𝜔𝑖 and 𝛾𝑖 are the chemical reaction rate of species 𝑖 and chemical potential of species 𝑖, respectively. 𝑌𝑖 and 𝑋𝑖 denote the mass fraction and mole fraction of species i in the mixture, consecutively. 3.3 Soot modeling The soot is formed by the four main processes including nucleation, coagulation, surface growth and oxidation. The processes start after the production of soot precursors (i.e., C2H2, C2H4, C6H6, C6H5). In the nucleation process, a coagulation between the two soot precursor species occurs and soot particles are formed. These soot particles are practically very small. In the coagulation process, these formed particles have collisions with each other which change the size of soot particles 43-44. After these processes, concentration of carbon on the surface of soot particles gets high. Therefore, the surface of soot particles grows which makes an increase in the soot mass. In the oxidation process, the soot particles surface oxidizes by oxygen, hydroxyl radical or any other oxidation species and, therefore, the mass of these particles is reduced. According to the previous works 45-47, the Moss-Brookes-Hall 48 model is applied for modeling the soot formation. It is a developed version of the Moss-Brookes model 49 which is useful for the higher hydrocarbon fuels such as kerosene. Equations (7) and (8) represent the transport equations for the normalized radical nuclei concentration and soot mass fraction47:

[( ) ]

𝜇𝑡 ∂𝑌𝑠𝑜𝑜𝑡 ∂ ∂ ∂ 𝑑𝑀 (𝜌𝑌𝑠𝑜𝑜𝑡) + (𝜌𝑢𝑗𝑌𝑠𝑜𝑜𝑡) = + ∂𝑡 𝑑𝑡 ∂𝑥𝑗 ∂𝑥𝑗 𝜎𝑠𝑜𝑜𝑡 ∂𝑥𝑗


(7)

Page 9 of 36 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

Energy & Fuels

[( ) ]

∗ 𝜇𝑡 ∂𝑏𝑛𝑢𝑐 ∂ ∂ ∂ 1 𝑑𝑁 ∗ ∗ (𝜌𝑏𝑛𝑢𝑐) + (𝜌𝑢𝑗𝑏𝑛𝑢𝑐) = + ∂𝑡 𝑁𝑛𝑜𝑟𝑚 𝑑𝑡 ∂𝑥𝑗 ∂𝑥𝑗 𝜎𝑛𝑢𝑐 ∂𝑥𝑗

(8)

∗ where, 𝑌𝑠𝑜𝑜𝑡 and 𝑏𝑛𝑢𝑐 indicate the soot mass fraction and normalized radical nuclei concentration,

respectively. 𝑀 and 𝑁 represent the soot mass concentration and soot particle number density and their rates are estimated, as follows 48, 50:

( ) ( ) 𝑑𝑁 𝑑𝑁 = 𝑑𝑡 𝑑𝑡

Nucleation

( ) 𝑑𝑁 𝑑𝑡

+

= 8𝐶𝛼1


𝑁𝐴

[( ) 𝜌2

𝑀𝑝

Nucleation

(9)

Coagulation

]

𝑌𝐶2𝐻2 2𝑌𝐶6𝐻5𝑊𝐻2

𝑊𝐶2𝐻2 𝑊𝐶6𝐻5𝑌𝐻2

( 𝑒

―

𝑇𝛼1 𝑇

) (10-a)

𝑌𝐶2𝐻2 𝑌𝐶6𝐻6𝑌𝐶6𝐻5𝑊𝐻2 𝑁𝐴 𝑒 𝜌2 + 8𝐶𝛼2 𝑀𝑝 𝑊𝐶2𝐻2𝑊𝐶6𝐻6𝑊𝐶6𝐻5𝑌𝐻2

[

]

(

24𝑅 =― 𝜌𝑠𝑜𝑜𝑡𝑁𝐴 Coagulation


(𝑑𝑀𝑑𝑡) = (𝑑𝑀𝑑𝑡) ( )

Nucleation

( ) 𝑑𝑀 𝑑𝑡

Surface growth

( ) 𝑑𝑀 𝑑𝑡

=

―

𝑇

)

12

+

Surface growth

𝑀𝑃 𝑑𝑁 𝑁𝐴 𝑑𝑡

𝑇

16

)( ) 6 𝜋𝜌𝑠𝑜𝑜𝑡

(𝑑𝑀𝑑𝑡)

+

Nucleation

𝑑𝑀 𝑑𝑡

12

(

𝑇𝛼2

𝑀

16

𝑁

11 6

(10-b)

(𝑑𝑀𝑑𝑡)

(11)

Oxidation

( )

(

(11-a)

Nucleation

= 𝐶𝑔𝑟𝑜 𝜌

𝑌𝐶2𝐻2

― 𝑇𝑎𝑐𝑡𝑖𝑣𝑒

)

𝑊𝐶2𝐻2

𝑇

𝑒

2 3

( )[

1 3

6𝑀 = ― 𝑇(𝜋𝑁) 𝜌𝑠𝑜𝑜𝑡 Oxidation

[

23

( )

13

(𝜋𝑁)

6𝑀 𝜌𝑠𝑜𝑜𝑡

𝑋𝑂𝐻𝑃

( )

𝐶𝑜𝑥𝑖𝑑𝐶𝜔1𝜂𝑐𝑜𝑙𝑙

𝑅𝑇

]

(11-b)

𝑋𝑂2𝑃

( 𝑒

( )

+𝐶𝑜𝑥𝑖𝑑𝐶𝜔2

𝑅𝑇

―

𝑇𝜔2 𝑇

)

]

(11-c)

where, 𝑁𝐴 and 𝑀𝑝 represent the Avogadro number and the mass of an incipient soot particle, respectively. 4. Computational Details 9 ACS Paragon Plus Environment

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

A three-dimensional finite volume method (FVM) 51 is implemented for solving the set of mass, momentum, energy and species conservation equations plus the realizable 𝑘 ― 𝜀 model, DOM and laminar flamelet combustion model in an Eulerian approach. The equations are implicitly linearized and the second order scheme is used for discretization. The diffusion and advection terms of the equations are discretized employing the central difference and second order upwind schemes, respectively. The SIMPLE C algorithm

52

is applied for connecting the pressure and

velocity terms. 200 angular directions over the solid angle, 4𝜋, is considered for the DOM radiation computation by assuming five divisions in both the azimuthal and polar directions of every octant around the control volume. Simulations are carried out using a convergence criterion of 10 ―5 for the continuity equation and 10 ―6 for the momentum, species, energy, thermal radiation and combustion equations. In the solution procedure, first of all, the partial differential equations for the conservation equations are solved. Then, the transport equation for the soot species is solved to provide soot distributions. 2. Flow Geometry and Boundary Conditions The present investigation of the entropy generation and soot formation is carried out on a combustion chamber geometry provided by Young 12. As illustrated in Figure 1, the combustor comprises a cylindrical tube of 155 mm inside diameter and 600 mm long. 0.0013 kg/s of vaporized kerosene at a temperature of 598 K is injected through a cylindrical fuel nozzle positioned in the center of the chamber with 1.5 mm diameter. The incoming air to the cylindrical tube is of 0.0054 kg/s at pressure and temperature of and 1.0 atm and 288 K, respectively. [Insert Figure 1.] Figure 1. Schematic view of combustion chamber 12.


Page 10 of 36

Page 11 of 36 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

Energy & Fuels

The combustion chamber is made of borosilicate glass-tube which has been surrounded by a polished aluminum tube. The velocity inlet and pressure outlet boundary conditions are considered as the inlet and outlet of the flow simulation computational domain, respectively. The no-slip and adiabatic conditions

12

are assumed as the wall velocity and thermal boundary

conditions, successively. The emissivity of the wall is assumed to be 0.05 for the radiation heat transfer. A summary of the geometrical and incoming information is listed in Table 1. [Insert Table 1.] Table 1. Boundary conditions and geometry specifications. 12

In order to perform the computations, the geometry is discretized by the structured grids which are generated finer at the fuel entry to the combustor and adjacent to the walls, due to the pressure gradients. The grid independence test is executed by evaluating four different grid sizes, in the range of 2.5 × 105 to 1.5 × 106 cells (see Table 2). [Insert Table 2.] Table 2. Different grid size.

Figure 2 illustrates the grid independence regarding the profiles of mean temperature and soot volume fraction along the center-line. Grid C with 1 × 106 cells provides an acceptable accuracy along with a lower cost in comparison with the other three grids and it is, thus, employed throughout the present work. Maximum deviations of Grid C from Grid D, based on the profiles of mean temperature and soot volume fraction, are almost 1.6 % and 1.83 %, respectively. It is shown that the accuracy of soot volume fraction prediction is more dependent on the mesh resolution. The maximum deviation of Grid A from Grid D, based on the profiles of mean


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

Page 12 of 36

temperature and soot volume fraction, are nearly 22.7 % and 75.34%, successively. It is due to the soot's dependence on temperature distribution.

[Insert Figure 2.] Figure 2. Grid independence test: (a) mean temperature, (b) soot volume fraction along the center-line.

Figure 3 displays the final structured grid for the present flow simulations. Grids are considered to be finer at the entrance to the combustor and next to the walls, owing to the presence of combustion phenomenon. The standard wall functions are employed by considering the Y + in the range 30−40 for modeling the turbulent flow using the realizable 𝑘 ― 𝜀 turbulence model 53. [Insert Figure 3.] Figure 3. Structured grid on combustor geometry.

5. Results and discussion The present results concerning temperature, mixture fraction and soot volume fraction are discussed and also compared with the available experimental data of Young

12

. Further, the

mechanisms of soot formation and entropy generation are discussed. In order to evaluate the accuracy of the present numerical procedure and simulations, the mean deviation (MD) parameter is defined and employed, as follows:

𝑀𝐷 =

|𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑑𝑎𝑡𝑎 ― 𝑁𝑢𝑚𝑒𝑟𝑖𝑐𝑎𝑙 𝑟𝑒𝑠𝑢𝑙𝑡𝑠| × 100 𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑑𝑎𝑡𝑎

(12)

Figure 4 depicts the profiles of mean temperature, soot volume fraction and mean mixture fraction along the center-line of the combustor. Relatively credible agreements with the


Page 13 of 36 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

Energy & Fuels

deviations of less than 15.3%, 6.1% and 3.1%, on average, exist between the present results of mean temperature, soot volume fraction and mean mixture fraction and the available experimental data 12, respectively. The numerical mean temperature is slightly over-predicted, as compared with the available experimental data 12. This can be because of disregarding the liquid fuel spray and the incoming pre-vaporized kerosene fuel to the combustor. The mean temperature rises up from X = 0.0 m till X = 0.4 m due to the occurrence of combustion phenomenon and then it cools down. It can be seen that the maximum soot volume fraction is observed before the highest value of temperature where most of the fuel is consumed (i.e., low amount of mean mixture fraction). After that, the soot volume fraction decreases in the downstream of the combustor due to the oxidation of soot and more complete combustion. The deviation of the numerical soot volume fraction from experiment may also be due to disregarding the liquid fuel spray and, therefore, a more complete combustion occurs in comparison with the experimental test conditions. Figure 4 (c) shows that the mean mixture fraction has the highest value where the fuel is injected to the combustor. Then, due to the mixing of fuel with the air flow and its consumption, the mean mixture fraction begins to decrease along the center-line. [Insert Figure 4.] Figure 4. Comparison of present profiles and experiment 12 along the center-line (Y=0, Z=0): (a) mean temperature, (b) soot volume fraction and (c) mean mixture fraction.

The mean mixture fraction profiles at four different axial positions are illustrated in Figure 5. The maximum mean deviation between the present results of the mean mixture fraction and the experimental data

12

is almost 6.1%, at X = 0.1 m. This can be because of being near the fuel

nozzle. As discussed before in Figure 4 (c), the mean mixture fraction is reduced by moving


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

Page 14 of 36

away from the fuel nozzle. Also, the mean deviation decreases from 6.1% to 2.7%, as the axial position increases. [Insert Figure 5.] Figure 5. Comparison of present lateral profiles of mean mixture fraction and experiment 12.

The mean temperature profiles at four axial positions are depicted in Figure 6. Similar to the mean mixture fraction profiles, the maximum mean deviation (nearly 10.2%) between the present temperature profiles and those of the experiment

12

is at X = 0.1 m. As discussed before

in Figures 4 and 5, this discrepancy can be because of disregarding the liquid fuel spray due to the lack of sufficient information about the fuel atomizer. The highest mean temperature is shown at X = 0.1 m and R≅0.01 m. Near the fuel nozzle (X = 0.1 m and 0.205 m), the combustion zone is limited and the mean temperature drops with a sharp slope after the peak point. By getting distant from the fuel nozzle (X = 0.3 m and 0.406 m), the combustion is radially developed and the mean temperature is increased towards the walls. [Insert Figure 6.] Figure 6. Comparison of present lateral profiles of mean temperature and experiment 12.

Four main processes of soot formation in a pre-vaporized kerosene combustion are shown in Figure 7 comprising nucleation, coagulation, surface growth and oxidation. Soot is mostly produced in the beginning of the combustion zone and after that, due to oxidation, a part of soot is consumed. The surface growth process has a major role in the soot formation. Next, the soot is produced by the nucleation and coagulation processes in nearly the same rates. The soot oxidation process begins with its formation and the mass of soot is reduced. It is observed that the maximum rate of oxidation is at X = 0.07 m up to X = 0.2 m. 14 ACS Paragon Plus Environment

Page 15 of 36 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

Energy & Fuels

[Insert Figure 7.] Figure 7. Four main processes of soot formation in a model combustor (mid-plane, Y=0)

Figure 8 demonstrates a comparison of the present lateral profiles of soot volume fraction and the existing experimental data

12,

at four axial positions. All of the presently predicted profiles

are slightly higher than those of the experiment. In accordance with the discussion of Figure 4, this can be due to the relatively higher mean temperature predicted by the present simulation. The minimum mean deviation of the present soot volume fraction profiles from those of the experimental data

12

is 6.2%, at X = 0.406 m where the combustion reactions are almost

completed (see Figure 10). [Insert Figure 8.] Figure 8. Comparison of present lateral profiles of soot volume fraction and experiment 12.

Figure 9 illustrates the entropy generation rate due to the viscous dissipation, mass diffusion, heat conduction and chemical reaction processes. All the four mentioned processes have an irreversible nature. Chemical reaction has the biggest role in the generation of entropy. Entropy generation due to the chemical reaction process is based on the behavior of each species. After the chemical reaction, the entropy is shown to be generated in a descending order by heat conduction, mass diffusion and viscous dissipation. The maximum entropy generation rate by the chemical reaction is observed at X = 0.05 m up to X = 0.2 m where the main reactions occur. It can be seen that the contributions toward the entropy generation by the viscous dissipation, mass diffusion and heat conduction are sparse and can, thus, be neglected in a turbulent reactive flow modeling. [Insert Figure 9.]


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

Figure 9. Entropy generation rate due to viscous dissipation, mass diffusion, heat conduction and chemical reaction along mid-plane (Y=0).

Figure 10 compares the contours of the total entropy generation rate, soot volume fraction and mean temperature along the mid-plane of the combustor. The main region of soot formation is near the center-line at 0.05 m < X < 0.3 m, where, the minimum total entropy generation rate and mean temperature are observed. By moving away from the combustion zone and getting closer to the outlet of the combustor (0.4 m < X < 0.6 m), due to the oxidation process, the soot volume fraction is decreased. Also, the total entropy generation rate is reduced because of a drop in the mean temperature (i.e., lack of chemical reactions). It is observed that, in a reactive flow, the chemical reaction process practically defines the temperature and entropy generation distributions. Where the combustion reactions occur, the entropy generation rate and temperature are high. Therefore, the distribution of the entropy generation can be an indicator for predicting the combustion zone in a reactive flow. Furthermore, the soot formation rate is inversely related to the mean temperature and entropy generation rate in the combustion zone. [Insert Figure 10.] Figure 10. Contours of total entropy generation rate, rate of soot formation, soot volume fraction and mean temperature.

Figure 11 (a) shows the normalized soot formation rate and total entropy generation rate along the center-line. The normalized variable is defined as the variable divided by its greatest value. The total entropy generation rate starts to grow simultaneously with completing the combustion process by an almost 0.2 m local delay in comparison with soot formation. The peak value of soot formation rate is observed near the axial position of X = 0.16 m where the minimum


Page 16 of 36

Page 17 of 36 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

Energy & Fuels

entropy is generated. On the other hand, the maximum entropy is produced where the soot formation processes are finished (X = 0.38 m). Figure 11 (b) demonstrates the normalized soot formation rate and total entropy generation rate concerning the mean temperature along the mid-plane. It can be seen that the entropy generation is more dependent on the temperature than soot formation rate. Near T = 1250 K, the rate of entropy generation grows with a steeper slope at a small temperature gradient. However, the rate of soot formation rises with a gentler slope at a lesser temperature (T = 1000 K) in comparison with the entropy generation rate. According to Figures 9 and 10, at the locations with the lower entropy generation rates due to chemical reactions, the combustion process is not complete and, hence, more soot is formed. Thus, the main region of soot formation can directly be predicted by the entropy generation rate with an acceptable deviation. This may be applied to the analysis of the reduction of the soot formation in a combustor. By implementing the activities that increase the chemical reaction rate and entropy generation, the mean temperature can be increased and, consequently, a reduction in the soot formation occurs. For instance, both the mixing and reaction processes are examples of the mutual causes of the entropy generation in a turbulent reactive flow. Hence, optimizing the mixing (a desirable mixture fraction) and reaction (a complete combustion) processes leads to the less soot precursors. The less soot precursors result in a reduction in the soot formation and entropy generation (less species). This matter may be of more significance and benefit when the heavy fuels such as kerosene, which have added potential for creating more soot precursors, are employed. [Insert Figure 11.]


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

Figure 11. Normalized variable of soot formation rate and total entropy generation rate: a) along centerline (Y=0, Z=0) and b) mean temperature.

6. Conclusions In the present article, the relations between entropy generation rate and soot formation in vaporized kerosene/air jet diffusion flames is investigated by employing the laminar flamelet and the Moss-Brookes-Hall models for simulating the combustion and soot formation. In order to confirm the validity of the simulation, various present numerical results are compared with the available experimental data

12.

The processes of soot formation (i.e., nucleation, coagulation,

surface growth and oxidation) and those of entropy generation (i.e., viscous dissipation, heat conduction, mass diffusion and chemical reaction) are discussed. The main conclusions may be drawn, as follows: I.

In the center-line (Z=0,Y=0), there are credible agreements with deviations of less than 15.3%, 6.1%, 3.1% between the present results of mean temperature, soot volume fraction and mean mixture fraction and the available experimental data 12, respectively.

II.

Soot is mostly produced in the beginning of the combustion zone and after that, due to oxidation, a part of it is consumed. The maximum soot volume fraction is observed before the highest value of the temperature, where most of the fuel is consumed (i.e., low amount of mean mixture fraction).

III.

The surface growth is the most important process in the soot formation. Rates of the nucleation and coagulation processes are nearly the same. The soot oxidation process begins with soot formation.


Page 18 of 36

Page 19 of 36 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

Energy & Fuels

IV.

The chemical reaction process has the biggest role in entropy generation regarding a turbulent reactive flow modeling. Entropy generation due to the other processes of viscous dissipation, mass diffusion and heat conduction can be neglected.

V.

Near the outlet of the combustor (0.4 m < X < 0.6 m), due to the oxidation process, the soot volume fraction decreases. Also, the total entropy generation rate is reduced due to the lack of chemical reactions and temperature gradient.

VI.

The chemical reaction process practically defines the temperature and entropy generation distributions in a reactive flow. The distribution of entropy generation is an indicator for predicting the combustion zone in a reactive flow.

VII.

The entropy generation is more dependent on the temperature than soot formation rate. The rate of entropy generation grows with a steeper slope at a small temperature gradient.

VIII.

the soot formation rate is inversely related to the mean temperature and entropy generation rate in the combustion zone. The main region of soot formation can directly be predicted by entropy generation with an acceptable deviation.


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

References 1. Briones, A. M.; Mukhopadhyay, A.; Aggarwal, S. K., Analysis of entropy generation in hydrogen-enriched methane–air propagating triple flames. international journal of hydrogen energy 2009, 34 (2), 1074-1083. 2. Jejurkar, S. Y.; Mishra, D. P., Numerical analysis of entropy generation in an annular microcombustor using multistep kinetics. Applied Thermal Engineering 2013, 52 (2), 394-401. 3. Chen, S., Analysis of entropy generation in counter-flow premixed hydrogen–air combustion. international journal of hydrogen energy 2010, 35 (3), 1401-1411. 4. Som, S.; Datta, A., Thermodynamic irreversibilities and exergy balance in combustion processes. Progress in energy and combustion science 2008, 34 (3), 351-376. 5. Wenming, Y.; Dongyue, J.; Kenny, C. K. Y.; Dan, Z.; Jianfeng, P., Combustion process and entropy generation in a novel microcombustor with a block insert. Chemical Engineering Journal 2015, 274, 231-237. 6. Safari, M.; Sheikhi, M. R. H., Large eddy simulation for prediction of entropy generation in a nonpremixed turbulent jet flame. Journal of Energy Resources Technology 2014, 136 (2), 022002. 7. Safari, M. In Local Entropy Generation in Large Eddy Simulation of Turbulent Reacting Flows, ASME 2017 International Mechanical Engineering Congress and Exposition, American Society of Mechanical Engineers: 2017; pp V006T08A079-V006T08A079. 8. Dunbar, W. R.; Lior, N., Sources of combustion irreversibility. Combustion Science and Technology 1994, 103 (1-6), 41-61. 9. Watanabe, H.; Suwa, Y.; Matsushita, Y.; Morozumi, Y.; Aoki, H.; Tanno, S.; Miura, T., Spray combustion simulation including soot and NO formation. Energy Conversion and Management 2007, 48 (7), 2077-2089. 10. Saqr, K. M.; Aly, H. S.; Sies, M. M.; Wahid, M. A., Effect of free stream turbulence on NOx and soot formation in turbulent diffusion CH4-air flames. International Communications in Heat and Mass Transfer 2010, 37 (6), 611-617. 11. Guo, H.; Smallwood, G. J., The interaction between soot and NO formation in a laminar axisymmetric coflow ethylene/air diffusion flame. Combustion and flame 2007, 149 (1-2), 225-233. 12. Young, K., Soot formation in turbulent vaporised kerosine/air jet flames at elevated pressure. P.h.D. Thesis, Cranfield Institute of Technology, School of Mechanical Engineering 1993. 13. Li, S., Modeling of pressure effects on flame structure and soot formation of n-heptane/air coflow laminar flames by skeletal reaction mechanism. Applied Thermal Engineering 2016, 106, 14581465. 14. Liu, F.; Gao, Y.; Wu, H.; Zhang, Z.; He, X.; Li, X., Investigation on Soot Characteristics of Gasoline/Diesel Blends in a Laminar Coflow Diffusion Flame. Energy & Fuels 2018, 32 (7), 7841-7850.


Page 20 of 36

Page 21 of 36 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

Energy & Fuels

15. Yen, M.; Magi, V.; Abraham, J., Modeling Soot Formation in Turbulent Jet Flames at Atmospheric and High-Pressure Conditions. Energy & Fuels 2018, 32 (8), 8857-8867. 16. Fu, X.; Han, X.; Brezinsky, K.; Aggarwal, S., Effect of Fuel Molecular Structure and Premixing on Soot Emissions from n-Heptane and 1-Heptene Flames. Energy & Fuels 2013, 27 (10), 6262-6272. 17. Huang, C.-H.; Vander Wal, R. L., Effect of Soot Structure Evolution from Commercial Jet Engine Burning Petroleum Based JP-8 and Synthetic HRJ and FT Fuels. Energy & Fuels 2013, 27 (8), 4946-4958. 18. Sirignano, M.; Kent, J.; D’Anna, A., Modeling Formation and Oxidation of Soot in Nonpremixed Flames. Energy & Fuels 2013, 27 (4), 2303-2315. 19. Sarlak, R.; Shams, M.; Ebrahimi, R., Numerical simulation of soot formation in a turbulent diffusion flame: comparison among three soot formation models. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 2012, 226 (5), 1290-1301. 20. Wang, W.; Liu, J.; Zuo, Z.; Yang, W., Entropy generation analysis of unsteady premixed methane/air flames in a narrow channel. Applied Thermal Engineering 2017, 126, 929-938. 21. Bazdidi-Tehrani, F.; Abedinejad, M. S., Influence of incoming air conditions on fuel spray evaporation in an evaporating chamber. Chemical Engineering Science 2018, 189, 233-244. 22. 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. 23. Zeinivand, H.; Bazdidi-Tehrani, F., Influence of stabilizer jets on combustion characteristics and NOx emission in a jet-stabilized combustor. Applied energy 2012, 92, 348-360. 24. Alemi, E.; Zargarabadi, M. R., Effects of jet characteristics on NO formation in a jet-stabilized combustor. International Journal of Thermal Sciences 2017, 112, 55-67. 25. Ganji, H. B.; Ebrahimi, R., Numerical estimation of blowout, flashback, and flame position in MIT micro gas-turbine chamber. Chemical Engineering Science 2013, 104, 857-867. 26. Song, M.; Zeng, L.; Li, X.; Chen, Z.; Li, Z., Effect of Stoichiometric Ratio of Fuel-Rich Flow on Combustion Characteristics in a Down-Fired Boiler. Journal of Energy Engineering 2016, 04016058. 27. 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. 28. Bazdidi-Tehrani, F.; Mirzaei, S.; Abedinejad, M. S., Influence of Chemical Mechanisms on Spray Combustion Characteristics of Turbulent Flow in a Wall Jet Can Combustor. Energy & Fuels 2017, 31 (7), 7523-7539. 29. Shih, T.-H.; Liou, W. W.; Shabbir, A.; Yang, Z.; Zhu, J., A new k-ϵ eddy viscosity model for high reynolds number turbulent flows. Computers & Fluids 1995, 24 (3), 227-238. 30. Pitsch, H.; Peters, N., A consistent flamelet formulation for non-premixed combustion considering differential diffusion effects. Combustion and Flame 1998, 114 (1), 26-40. 31. Bazdidi-Tehrani, F.; Abedinejad, M. S.; Yazdani-Ahmadabadi, H., Influence of Variable Air Distribution on Pollutants Emission in a Model Wall Jet Can Combustor. Heat Transfer Research 2018, 49, 1667-1688. 32. Zettervall, N.; Fureby, C.; Nilsson, E., Small skeletal kinetic mechanism for kerosene combustion. Energy & Fuels 2016, 30 (11), 9801-9813. 33. 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. 34. Sirjean, B.; Dames, E.; Sheen, D.; You, X.; Sung, C.; Holley, A.; Egolfopoulos, F.; Wang, H.; Vasu, S.; Davidson, D., A high-temperature chemical kinetic model of n-alkane oxidation. JetSurF version 2009, 1, 2009. 35. Peters, N., Turbulent combustion. Cambridge university press: 2000. 36. Fiveland, W., Discrete-ordinates solutions of the radiative transport equation for rectangular enclosures. Journal of Heat Transfer 1984, 106 (4), 699-706. 21 ACS Paragon Plus Environment

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

37. 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. 38. Chu, H.; Consalvi, J.-L.; Gu, M.; Liu, F., Calculations of radiative heat transfer in an axisymmetric jet diffusion flame at elevated pressures using different gas radiation models. Journal of Quantitative Spectroscopy and Radiative Transfer 2017, 197, 12-25. 39. Viskanta, R.; Mengüç, M., Radiation heat transfer in combustion systems. Progress in Energy and Combustion Science 1987, 13 (2), 97-160. 40. Rahmanpour, M.; Ebrahimi, R.; Shams, M., Numerically gas radiation heat transfer modeling in chemically nonequilibrium reactive flow. Heat and mass transfer 2011, 47 (12), 1659-1670. 41. Howell, J. R.; Menguc, M. P.; Siegel, R., Thermal radiation heat transfer. CRC press: 2010. 42. Hirschfelder, J. O.; Curtiss, C. F.; Bird, R. B.; Mayer, M. G., Molecular theory of gases and liquids. Wiley New York: 1954; Vol. 26. 43. Dizaji, F. F.; Marshall, J. S., On the significance of two-way coupling in simulation of turbulent particle agglomeration. Powder technology 2017, 318, 83-94. 44. Dizaji, F. F.; Marshall, J. S.; Grant, J. R., Collision and breakup of fractal particle agglomerates in a shear flow. Journal of Fluid Mechanics 2019, 862, 592-623. 45. Mazzei, L.; Puggelli, S.; Bertini, D.; Pampaloni, D.; Andreini, A., Modelling soot production and thermal radiation for turbulent diffusion flames. Energy Procedia 2017, 126, 826-833. 46. Yuen, A.; Yeoh, G.; Timchenko, V.; Chen, T.; Chan, Q.; Wang, C.; Li, D., Comparison of detailed soot formation models for sooty and non-sooty flames in an under-ventilated ISO room. International Journal of Heat and Mass Transfer 2017, 115, 717-729. 47. Rajeshirke, P.; Nakod, P.; Yadav, R.; Orsino, S. In Parametric study of Moss-Brookes (MB) and Moss-Brookes-Hall (MBH) model constants for prediction of soot formation in a turbulent Hydrocarbon flames, ASME 2013 Gas Turbine India Conference, American Society of Mechanical Engineers: 2013; pp V001T03A009-V001T03A009. 48. Hall, R.; Smooke, M.; Colket, M., Physical and chemical aspects of combustion. Gordon and Breach 1997. 49. Brookes, S.; Moss, J., Predictions of soot and thermal radiation properties in confined turbulent jet diffusion flames. Combustion and Flame 1999, 116 (4), 486-503. 50. Wen, Z.; Yun, S.; Thomson, M.; Lightstone, M., Modeling soot formation in turbulent kerosene/air jet diffusion flames. Combustion and Flame 2003, 135 (3), 323-340. 51. Patankar, S., Numerical heat transfer and fluid flow. CRC press: 1980. 52. Ashgriz, N.; Mostaghimi, J., An introduction to computational fluid dynamics. Fluid flow handbook. McGraw-Hill Professional 2002. 53. Davidson, L., Fluid mechanics, turbulent flow and turbulence modeling. Chalmers University of Technology, Goteborg, Sweden (Nov 2011) 2011.


Page 22 of 36

Page 23 of 36 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

Energy & Fuels

NOMENCLATURE ∗ 𝑏𝑛𝑢𝑐

Normalized radical nuclei concentration

𝐶𝑔𝑟𝑜 𝐶𝑜𝑥𝑖𝑑 𝑐𝑝

Model constant in equation 11-b Oxidation rate scaling parameter Specific heat capacity at constant pressure (J/kg K) Model constant in equation 11-c Coefficient in realizable 𝑘 ― 𝜀 equation Constant number in realizable 𝑘 ― 𝜀 equation Model constant in equation 10-a Mass diffusivity of species i in mixture (m2/s) Mixture fraction

𝐶𝜔1,𝐶𝜔2 𝐶1 𝐶2, 𝐶1𝜀, 𝐶3𝜀 𝐶𝛼1,𝐶𝛼2 𝐷𝑖 ― 𝑚𝑖𝑥 𝑓 𝐺𝑘, 𝐺𝑏 𝐻𝑖 𝑘 𝑘𝑒𝑓𝑓 𝑀 𝑀𝑝 𝑀𝐷 𝑁 𝑁𝐴 𝑁𝑛𝑜𝑟𝑚 𝑃𝐷𝐹

𝑇𝛼1,𝑇𝛼2, Activation temperature of soot nucleus 𝑇𝑎𝑐𝑡𝑖𝑣𝑒 𝑢𝑗 Velocity component (m s) Velocity vector 𝑢 𝑊𝑖 Molecular weight of species i (kg/kmol) 𝑋𝑖 𝑥𝑗 𝑋,𝑌,𝑍

Mole fraction of species i Cartesian coordinates Cartesian coordinates

𝑌+ 𝑌𝑖

Non-dimensional distance Mass fraction of species i

𝑌𝑀

Fluctuating dilatation contribution to the total dissipation rate.

Source for generation of turbulence kinetic energy Specific enthalpy of species Turbulence kinetic energy Effective thermal conductivity (W/m.K) Soot mass density(𝑘𝑔/𝑚3)

𝑌𝑠𝑜𝑜𝑡

Molar mass of a soot nucleus (kg/kmol) Mean deviation Soot particle number density (particles/m3) Avogadro number [ = 1015 particles] Presumed density function

𝜂𝑐𝑜𝑙𝑙 𝜇 𝜌

𝛾𝑖 Γ 𝜀

𝜎 𝜏 𝜒

Soot mass fraction Greek symbols Chemical potential of species 𝑖 (J/kg K) Diffusion coefficient Dissipation rate of turbulence kinetic energy Collisional efficiency parameter Dynamic viscosity (N s m2) Density (kg m3) Turbulent Prandtl number Viscous stress (N/m2) Scalar dissipation rate (1/s)


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

𝑅 𝑅,𝜃,𝑍 𝑆 𝑆_𝑖 𝑆Ψ 𝑆ʼʼʼ 𝑆𝑟 𝑡 𝑇 𝑇𝜔2

Gas constant, (J/kg K) Cylindrical system of coordinates Mean strain tensor Source term of reaction rate Source terms Volumetric entropy generation rate, (W/m3K) Source term in equation 5 Time (s) Temperature (K) Model constant in equation 11-c

Page 24 of 36

𝛹 𝜔𝑖

Dependent variables Production rate from chemical reaction Subscripts

𝑡 𝑛𝑢𝑐 𝑒𝑓𝑓

. : ∇

Turbulent Nucleation Effective

Dot product (Multiplication) Double dot product (Multiplication) Vector differential operator

Table 1. Boundary conditions and geometry specifications. 12

Name

Value

Fuel inlet diameter (𝐦𝐦)

1.5

Outlet diameter (𝐦𝐦)

155 Kerosene

Fuel

1

Operating pressure (𝐚𝐭𝐦) Air flow rate (𝐤𝐠/𝐬)

0.0054

Fuel flow rate (𝐤𝐠/𝐬)

0.0013

Air inlet temperature (𝐊)

288

Fuel inlet temperature (𝐊)

598 No-slip, adiabatic

Wall conditions

1.0

Outlet pressure (𝐚𝐭𝐦)


Page 25 of 36 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

Energy & Fuels

Table 2. Different grid size

Name Grid A Grid B Grid C Grid D

Size 2.5 × 105 5 × 105 1 × 106 1.5 × 106


𝐗×𝐑×𝛉

174 × 27 × 53 238 × 35 × 60 319 × 42 × 74 350 × 50 × 85

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

Figure 1. Schematic view of combustion chamber 12.


Page 26 of 36

Page 27 of 36 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

Energy & Fuels

Figure 2. Grid independence test: (a) mean temperature, (b) soot volume fraction along the center-line.


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

Figure 3. Structured grid on combustor geometry.


Page 28 of 36

Page 29 of 36 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

Energy & Fuels

Figure 4. Comparison of present profiles and experiment 12 along the center-line (Y=0, Z=0): (a) mean temperature, (b) soot volume fraction and (c) mean mixture fraction. 29 ACS Paragon Plus Environment

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

Figure 5. Comparison of present lateral profiles of mean mixture fraction and experiment 12.


Page 30 of 36

Page 31 of 36 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

Energy & Fuels

Figure 6. Comparison of present lateral profiles of mean temperature and experiment 12.


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

Figure 7. Four main processes of soot formation in a model combustor (mid-plane, Y=0)


Page 32 of 36

Page 33 of 36 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

Energy & Fuels

Figure 8. Comparison of present lateral profiles of soot volume fraction and experiment 12.


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

Figure 9. Entropy generation rate due to viscous dissipation, mass diffusion, heat conduction and chemical reaction along mid-plane (Y=0).


Page 34 of 36

Page 35 of 36 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

Energy & Fuels

Figure 10. Contours of total entropy generation rate, rate of soot formation, soot volume fraction and mean temperature.


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

Figure 11. Normalized variable of soot formation rate and total entropy generation rate: a) along center-line (Y=0, Z=0) and b) mean temperature.


Page 36 of 36

Analysis of Relationship between Entropy Generation and Soot

Recommend Documents