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Continuum Mechanics and Thermodynamics
Published in: Continuum Mechanics and Thermodynamics 5/2022

25-06-2022 | Original Article

Modeling of combustion and turbulent jet diffusion flames in fractal dimensions

Authors: Rami Ahmad El-Nabulsi, Waranont Anukool

Published in: Continuum Mechanics and Thermodynamics | Issue 5/2022

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Abstract

Turbulent diffusion flames are considered an active field of research used in many engineering applications of combustion theory. The basic properties of jet diffusion flames were obtained in the literature, and their confrontation with observations and experiments support the mathematical aspects of combustion theory founded by famous researchers throughout dozen of years. From the other side, fractal analysis was undertaken effectively in the literature based on recent experimental studies and observations supporting the idea that flame instability results in growth of fractal structures at a flame front. Besides, fractals were used successfully to model the effects of turbulence on flame propagation in heat engines and turbulent flows. In this study, we used the new concept of “product-like fractal measure” introduced recently in the literature by Li and Ostoja-Starzewski in their formulation of anisotropic continuum media to model combustion and turbulent jet diffusion flames in fractal dimensions. The basic equations for flames in fractal dimensions have been derived and applied to study laminar and turbulent non-premixed flame besides flame extinction due to heat volumetric heat loss. Several features have been obtained and discussed in particular the application of the theory at small combustion scales.
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Literature
1.
2.
Varga, B.E., Gao, W., Laurik, K.L., Tatrai, E., Simo, M., Somfai, G.M., Cabrera DeBuc, D.: Investigating tissue optical properties and texture descriptors of the retina in patients with multiple sclerosis. PLoS ONE 10(11), e0143711 (2015)CrossRef
3.
Ivanova, V.S., Bunin, I.J., Nosenko, V.I.: Fractal material science: a new direction in materials science, JOM50, 52–54 (1998)
4.
Carpinteri, A.: Fractal nature of material microstructure and size effects on apparent mechanical properties. Mech. Mater. 18, 89–101 (1994)CrossRef
5.
Agrisuelas, J., García-Jareño, J.J., Gimenez-Romero, D., Negrete, F., Vicente, F.: The fractal dimension as estimator of the fractional content of metal matrix composite materials. J. Solid State Electrochem. 13, 1599–1603 (2009)CrossRef
6.
Balankin, A.S., Bugrimov, A.L.: A fractal theory of polymer plasticity. Polym. Sci. USSR 34, 246 (1992)
7.
Balankin, A.S., Bugrimov, A.L.: Fractal theory of elasticity and rubber-like state of polymers. Polym. Sci. 34, 889 (1992)
8.
Balankin, A.S., Tamayo, P.: Fractal solid mechanics. Rev. Mex. Phys. 40, 506 (1994)
9.
Balankin, A.S.: Elastic behavior of materials with multifractal structure. Phys. Rev. B 53, 5438 (1996)CrossRefADS
10.
Balankin, A.S.: The theory of multifractal elasticity: basic laws and constitutive equations. Rev. Mex. Phys. 42, 343 (1996)MathSciNetMATH
11.
El-Nabulsi, R.A.: Path integral formulation of fractionally perturbed Lagrangian oscillators on fractal. J. Stat. Phys. 172, 1617–1640 (2018)MathSciNetMATHCrossRefADS
12.
El-Nabulsi, R.A.: Emergence of quasiperiodic quantum wave functions in Hausdorff dimensional crystals and improved intrinsic Carrier concentrations. J. Phys. Chem. Sol. 127, 224–230 (2019)CrossRefADS
13.
El-Nabulsi, R.A.: On a new fractional uncertainty relation and its implications in quantum mechanics and molecular physics. Proc. Roy. Soc. A476, 20190729 (2020)MathSciNetMATHCrossRefADS
14.
El-Nabulsi, R.A.: Inverse-power potentials with positive-bound energy spectrum from fractal, extended uncertainty principle and position-dependent mass arguments. Eur. Phys. J. P135, 683 (2020)
15.
El-Nabulsi, R.A.: Dirac equation with position-dependent mass and Coulomb-like field in Hausdorff dimension. Few Body Syst. 61, 10 (2020)CrossRefADS
16.
El-Nabulsi, R.A.: On generalized fractional spin, fractional angular momentum, fractional momentum operators and noncommutativity in quantum mechanics. Few Body Syst. 61, 1–13 (2020)CrossRefADS
17.
18.
Lindner, J.F., Kohar, V., Kia, B., Hippke, M., Learned, J.G., Ditto, W.L.: Strange nonchaotic stars. Phys. Rev. Lett. 114(5), 054101 (2015)CrossRefADS
19.
Sanchez, N., Alfaro, E.J., Perez, E.: The fractal dimension of projected clouds. Astrophys. J. 625, 849–856 (2005)CrossRefADS
20.
Federrath, C., Klessen, R.S., Schmidt, W.: The fractal density structure in supersonic isothermal turbulence: solenoidal versus compressive energy injection. Astrophys. J. 692, 364–374 (2009)CrossRefADS
21.
Beattie, J.R., Federrath, C.C., Klessen, R.S.: The relation between the true and observed fractal dimensions of turbulent clouds. Month. Not. R. Astron. Soc. 487, 2070–2081 (2019)CrossRefADS
22.
Falconer, K.J.: Fractal Geometry-Mathematical Foundations and Applications. Wiley, New York (2003)MATHCrossRef
23.
Mandelbrot, B.B.: The Fractal Geometry of Nature. W. H. Freeman and Company, New York (1983)CrossRef
24.
Mandelbrot, B.B.: Fractals: Form, Chance, and Dimension, San Francisco. W. H. Freeman, CA (1977)MATH
25.
26.
Schonwetter, M.: Fractal Dimensions in Classical and Quantum Mechanical Open Chaotic Systems, PhD Thesis, Angefertigt in der Arbeitsgruppe Dynamical Systems and Social Dynamics am Max-Planck-Institut fur Physik komplexer Systeme in Dresden, (2016)
27.
28.
Davey, K., Prosser, R.: Analytical solutions for heat transfer on fractal and pre-fractal domains. Appl. Math. Mod. 37, 554–569 (2013)MathSciNetMATHCrossRef
29.
30.
31.
32.
33.
34.
Ostoja-Starzewski, M.: Towards thermoelasticity of fractal media. J. Therm. Stress 30, 889 (2007)MATHCrossRef
35.
Ostoja-Starzewski, M., Li, J.: Towards thermoelasticity of fractal media. Z. Angew. Math. Phys. 60, 1 (2009)MathSciNet
36.
37.
Ostoja-Starzewski, M.: Extremum and variational principles for elastic and inelastic media with fractal geometries. Acta Mech. 205, 161–170 (2009)MATHCrossRef
38.
39.
Li, J., Ostoja-Starzewski, M.: Fractal materials, beams and fracture mechanics. Z. Angew. Math. Phys. 60, 1–12 (2009)MathSciNetMATH
40.
Ignaczak, J., Ostoja-Starzewski, M.: Thermoelasticity with Finite Wave Speeds. Oxford University Press, London (2009)MATHCrossRef
41.
42.
43.
44.
Prasad, R.R., Sreenivasan, K.R.: The measurement and interpretation of fractal dimensions of the scalar interface in turbulent flows. Phys. Fluids A2, 792 (1990)CrossRefADS
45.
Flohr, P., Olivari, D.: Fractal and multifractal characteristics of a scalar dispersed in a turbulent jet. Phys. D 76, 278–290 (1994)CrossRef
46.
Vorobieff, P., Rightley, P.M., Benjamin, R.F.: Shock-driven gas curtain: fractal dimension evolution in transition to turbulence. Phys. D 133, 469–476 (1999)MATHCrossRef
47.
Beattie, J.R., Federrath, C., Klessen, R.S.: The relation between the true and observed fractal dimensions of turbulent clouds. Month. Not. Roy. Astron. Soc. 487, 2070–2081 (2019)CrossRefADS
48.
Chester, S., Meneveau, C., Parlange, M.B.: Modeling turbulent flow over fractal trees with renormalized numerical simulation. J. Comp. Phys. 225, 427–448 (2007)MathSciNetMATHCrossRefADS
49.
Yakhot, A., Orszag, S., Yakhot, V., Israeli, M.: Renormalization group formulation of large-eddy simulations. J. Sci. Comput. 4, 139–158 (1989)MathSciNetMATHCrossRef
50.
51.
Vassilicos, J.C., Hunt, J.C.R.: Fractal dimensions and spectra of interfaces with application to turbulence. J. Roy. Soc. London A 435, 505–534 (1991)MathSciNetMATHADS
52.
53.
Chin, Y.-W., Matthews, R.D., Nichols, S.P., Kiehne, T.M.: Use of fractal geometry to model turbulent combustion in SI engines. Combust. Sci. Tech. 86, 1–30 (1992)CrossRef
54.
Mora, D.O., Bourgoin, M., Mininni, P.D., Obligado, M.: Clustering of vector nulls in homogeneous isotropic turbulence. Phys. Rev. Fluids 6, 024609 (2021)CrossRefADS
55.
Takeno, T., Murayama, M., Tanida, Y.: Fractal analysis of turbulent premixed flame surface. Exp. Fluids 10, 61–70 (1990)CrossRef
56.
Roy, A., Sujith, R.I.: Fractal dimension of premixed flames in intermittent turbulence. Combust. Flame 226, 412–418 (2021)CrossRef
57.
Majda, A.J., Souganidis, P.: Flame fronts in a turbulent combustion model with fractal velocity fields. Commun. Pure Appl. Math. 51, 1337–1348 (1998)MathSciNetMATHCrossRef
58.
Verbeek, A.A., Bouten, T.W.F.M., Stoffels, G.G.M., Geurts, B.J., van der Meer, T.H.: Fractal turbulence enhancing low-swirl combustion. Combust. Flame 162, 129–143 (2015)CrossRef
59.
Chatakonda, O., Hawkes, E.R., Aspden, A.J., Kerstein, A.R., Kolla, H., Chen, J.H.: On the fractal characteristics of low Damkohler number flames. Combust. Flame 160, 2422–2433 (2013)CrossRef
60.
Gulder, O., Smallwood, G.J., Wong, R., Snelling, D.R., Smith, R., Deschamps, B., Sautet, J.-C.: Flame front surface characteristics in turbulent premixed propane/air combustion. Combust. Flame 120, 407–416 (2000)CrossRef
61.
Chen, Y.-C., Mansour, M.S.: Geometric interpretation of fractal parameters measured in turbulent premixed Bunsen flames. Exp. Therm. Fluid Sci. 27, 409–416 (2003)CrossRef
62.
Roy, A., Sujith, R.I.: Fractal dimensions of premixed flames in intermittent turbulence. Combust. Flame 226, 412–418 (2021)CrossRef
63.
64.
Ostoja-Starzewski, M., Li, J., Joumaa, H., Demmie, P.N.: From fractal media to continuum mechanics. Z. Angew. Math. Mech. 93, 1 (2013)MATH
65.
Li, J., Ostoja-Starzewski, M.: Fractal solids, product measures and continuum mechanics. In: Maugin, G.A., Metrikine, A.V. (eds.) Mechanics of Generalized Continua: One Hundred Years after the Cosserats, pp. 315–323. Springer, Berlin. Chap. 33 (2010)
66.
El-Nabulsi, R.A.: Thermal transport equations in porous media from product-like fractal measure. J. Therm. Stress. 44, 899–912 (2021)CrossRef
67.
El-Nabulsi, R.A.: Superconductivity and nucleation from fractal anisotropy and product-like fractal measure. Proc. Roy. Soc. A477, 20210065 (2021)MathSciNetCrossRefADS
68.
El-Nabulsi, R.A.: Quantum dynamics in low-dimensional systems with position-dependent mass and product-like fractal geometry. Phys. E: Low Dim. Syst. Nanostruct. 134, 114827 (2021)CrossRef
69.
El-Nabulsi, R.A.: On a new fractional uncertainty relation and its implications in quantum mechanics and molecular physics. Proc. R. Soc. A476, 20190729 (2020)MathSciNetMATHCrossRefADS
70.
El-Nabulsi, R.A.: Quantization of Foster mesoscopic circuit and DC-pumped Josephson parametric amplifier from fractal measure arguments. Phys. E: Low Dim. Syst. Nanostruct. 133, 114845 (2021)CrossRef
71.
El-Nabulsi, R.A.: Position-dependent mass fractal Schrodinger equation from fractal anisotropy and product-like fractal measure and its implications in quantum dots and nanocrystals. Opt. Quant. Elect. 53, 503 (2021)CrossRef
72.
El-Nabulsi, R.A.: Fractal neutrons diffusion equation: uniformization of heat and fuel burn-up in nuclear reactor. Nucl. Eng. Des. 380, 111312 (2021)CrossRef
73.
74.
Malyarenko, A., Ostoja-Starzewski, M.: Fractal planetary rings: energy inequalities and random field model. Int. J. Mod. Phys. B 31, 1750236 (2017)MathSciNetMATHCrossRefADS
75.
Mashayekhi, S., Miles, P., Hussaini, M.Y., Oates, W.S.: Fractional viscoelasticity in fractal and non-fractal media: theory, experimental validation, and uncertainty analysis. J. Mech. Phys. Solids 111, 134–156 (2018)MathSciNetMATHCrossRefADS
76.
Mashayekhi, S., Hussaini, M.Y., Oates, W.S.: A physical interpretation of fractional viscoelasticity based on the fractal structure of media: theory and experimental validation. J. Mech. Phys. Solids 128, 137–150 (2019)MathSciNetCrossRefADS
77.
Mashayekhi, S., Beerli, P.: Fractional coalescent. Proc. Nat. Acad. Sci. 116, 6244–6249 (2019)CrossRef
78.
79.
Oates, W., Stanisaukis, E., Pahari, B.R., Mashayekhi, S.: Entropy dynamics approach to fractional order mechanics with applications to elastomers. Behav. Mech. Multifunct. Mater. XV 15, 1158905 (2021)
80.
El-Nabulsi, R.A.: Some geometrical aspects of nonconservative autonomous Hamiltonian dynamical systems. Int. J. Appl. Math. Stat. 5, 50–61 (2006)MathSciNetMATH
81.
El-Nabulsi, R.A.: Some implications of position-dependent mass quantum fractional Hamiltonian in quantum mechanics. Eur. Phys. J. P134, 192 (2019)
82.
El-Nabulsi, R.A.: Fractional action-like variational problems in holonomic, non-holonomic and semi-holonomic constrained and dissipative dynamical systems. Chaos Solitons Fractals 42, 52–61 (2009)MathSciNetMATHCrossRefADS
83.
El-Nabulsi, R.A., Wu, G.-C.: Fractional complexified field theory from Saxena-Kumbhat fractional integral, fractional derivative of order (\(\alpha,\beta \)) and dynamical fractional integral exponent. Afr. Diasp. J. Math. 13, 56–61 (2012)MathSciNetMATH
84.
85.
You, J., Lu, Z., Yang, Y.: Anisotropic velocity statistics and vortex surfaces in turbulent premixed combustion. Acta Aerodyn. Sinica 38, 603–610 (2020)
86.
Belmont, M.R., Haviland, J.S., Thomas, J., Hacohen, J., Thurley, R.: Methods for examining anisotropies in early combustion, Part I: Multi-scale experimental determinations. Combust. Sci. Tech. 108, 149–173 (1995)CrossRef
87.
Ijioma, E.R., Munteam, A., Ogawa, T.: Effect of material anisotropy on the fingering instability in reverse smoldering combustion. Int. J. Heat Mass Transf. 81, 924–938 (2015)CrossRef
88.
Poludnenko, A.Y.: Pulsating instability and self-acceleration of fast turbulent flames. Phys. Fluids 27, 014106 (2015)CrossRefADS
89.
Tori, S.: Thermal transport phenomena of turbulent jet diffusion flames by means of anisotropic \(k\)-\(\epsilon \)-\(t^{2}\)-\(\epsilon _{t}\) model. Int. J. Energy Res. 23, 989–998 (1999)CrossRef
90.
Treurniet, T.C., Nieuwstadt, F.T.M., Boersma, B.J.: Direct numerical simulation of homogeneous turbulence in combination with premixed combustion at low Mach number modelled by the G-equation. J. Fluid Mech. 565, 25–62 (2006)MathSciNetMATHCrossRefADS
91.
Najm, H.N., Wyckoff, P.S., Knio, O.M.A.: A semi-implicit numerical scheme for reacting flow: I. Stiff chemistry. J. Comput. Phys. 143, 381–402 (1998)MathSciNetMATHCrossRefADS
92.
Savard, B.: Characterization and modeling of premixed turbulent n-heptane flames in the thin reaction zone regime, PhD thesis, California Institute of Technology, Pasadena, California, (2015)
93.
Williams, F. A.: Combustion Theory, 2\(^{nd}\) Edition. Addison-Wesley, (1985)
94.
Xuan, Y., Blanquart, G.: Numerical modeling of sooting tendencies in a laminar co-flow diffusion flame. Combust. Flame 160, 1657–1666 (2013)CrossRef
95.
Chen, C., Riley, J.J., McMurtry, P.A.: A study of Favre averaging in turbulent flows with chemical reaction. Combust. Flame 87, 257–277 (1991)CrossRefADS
96.
Altimira, K. C.: Numerical simulation of non-premixed laminar and turbulent flames by means of flamelet modeling approaches, PhD thesis, Universitat Politecnica de Catalunya, (2005)
97.
Abdel-Gayed, R., Bradley, D.: Combustion regimes and the straining of turbulent premixed flames. Combust. Flame 76, 213–218 (1989)CrossRef
98.
Altantzis, C., Frouzakis, C., Tomboulides, A., Matalon, M., Boulouchos, K.: Hydrodynamic and thermodiffusive instability effects on the evolution of laminar planar lean premixed hydrogen flames. J. Fluid Mech. 700, 329–361 (2012)MATHCrossRefADS
99.
Chakraborty, N., Cant, R.: Unsteady effects of strain rate and curvature on turbulent premixed flames in an inflow-outflow configuration. Combust. Flame 137, 129–147 (2004)CrossRef
100.
Chen, Z., Burke, M.P., Ju, Y.: Effects of Lewis number and ignition energy on the determination of laminar flame speed using propagating spherical flames. Proc. Comb. Inst. 32, 1253–1260 (2009)CrossRef
101.
Daniele, S., Mantzaras, J., Jansohn, P., Denisov, A., Boulouchos, K.: Flame front/turbulence interaction for syngas fuels in the thin reaction zones regime: turbulent and stretched laminar flame speeds at elevated pressures and temperatures. J. Fluid Mech. 724, 36–68 (2013)MATHCrossRefADS
102.
Peters, N.: Combustion Theory, Lectures given at CEFRC Summer School at Princeton University, June 28\(^{th}\)-July 2\(^{nd}\), (2010)
103.
Popkov, A.N., Chapman-Rubesin method in boundary layer theory, Aviatsionnaia Tekhnika 18. 90–93. Soviet Aeronautics 8(1975), 72–75 (1975)
104.
Gavish, B.: Position-dependent viscosity effects on rate coefficients. Phys. Rev. Lett. 44, 1160 (1980)CrossRefADS
105.
Zhang, J., Todd, B.D., Travis, K.P.: Viscosity of confined inhomogeneous nonequilibrium fluids. J. Chem. Phys. 121, 10778 (2004)CrossRefADS
106.
Xi, Z., Fu, Z., Hu, X., Sabir, S.W., Jiang, Y.: An investigation on flame shape and size for a high-pressure turbulent non-premixed swirl combustion. Energies 11, 930 (2018)CrossRef
107.
Kang, S.H., Im, H.G., Baek, W.W.: A computational study of Saffman-Taylor instability in premixed flames. Combust. Theor. Model. 7, 343–363 (2003)CrossRefADS
108.
109.
Han, Y., Modestov, M., Valiev, D.M.: Effect of momentum and heat losses on the hydrodynamic instability of a premixed equidiffusive flame in a Hele-Shaw cell. Phys. Fluids 33, 103608 (2021)CrossRefADS
110.
Anjali Devi, S.P., Prakash, M.: Temperature dependent viscosity and thermal conductivity effects on hydromagnetic flow over a slendering stretching sheet. J. Nigerian Math. Soc. 34, 318–330 (2015)MathSciNetMATHCrossRef
111.
Hassanien, I., Essawy, A., Moursy, N.: Variable viscosity and thermal conductivity effects on combined heat and mass transfer in mixed convection over a UHF/UMF wedge in porous media: the entire regime. Appl. Math. Comput. 145, 667–682 (2003)MathSciNetMATH
112.
Khan, Y., Wu, Q., Faraz, N., Yildirim, A.: The effects of variable viscosity and thermal conductivity on a thin film flow over a shrinking/stretching sheet. Comput. Math. Appl. 61, 3391–3399 (2011)MathSciNetMATHCrossRef
113.
Lotfizadeh Dehkordi, B., Shiller, P.J., Doll, G.L.: Pressure- and temperature-dependent viscosity measurements of lubricants with polymeric viscosity modifiers. Front. Mech. Eng. 5, 18 (2019)CrossRef
114.
Griffiths, R.W.: Thermals in extremely viscous fluids, including the effects of temperature-dependent viscosity. J. Fluid Mech. 166, 115–138 (1986)CrossRefADS
115.
Garby, R., Selle, L., Poinsot, T.: Large-Eddy Simulation of combustion instabilities in a variable-length combustor. Compt. Rend. Mec. 341, 220–229 (2013)ADS
116.
Schildmacher, K.-U., Hoffman, A., Selle, L., Koch, R., Schulz, C., Bauer, H.-J., Poinsot, T.: Unsteady flame and flow field interaction of a premixed model gas turbine burner. Proc. Combust. Inst. 31, 3197–3205 (2007)CrossRef
117.
Kang, Y., Lu, T., Lu, X., Gou, X., Huang, X., Peng, S., Ji, X., Zhou, Y., Song, Y.: On predicting the length, width, and volume of the jet diffusion flame. Appl. Therm. Eng. 94, 799–812 (2016)CrossRef
118.
Pitsch, H.: Turbulent Non-Premixed Combustion, Lectures given at CEFRC Combustion Summer School. RWTH Aachen University (Rheinisch-Westfälische Technische Hochschule Aachen), Inst. Tech. Verbrennung (2014)
119.
Adams, B.R., Smith, P.J.: Modeling effects of soot and radiative transfer in turbulent gaseous combustion. Combust. Sci. Tech. 109, 121–140 (1995)CrossRef
120.
Peters, N.: Laminar and Turbulent Combustion, Lectures given at Ercoftac Summer School September 14–28. Aachen, Germany (1992)
121.
Ajibade, A.O., Tafida, M.K.: The combined effect of variable viscosity and variable thermal conductivity on natural convection couette flow. Int. J. Thermofluids 5–6, 100036 (2020)CrossRef
122.
Tam, K.K.: Criticality dependence on data and parameters for a problem in combustion theory, with temperature-dependent conductivity. ANZIAM J. 31, 76–80 (1989)MathSciNetMATH
123.
Peters, N., Williams, F.A.: Asymptotic structure of stoichiometric methane-air flames. Combust. Flame 68, 185–207 (1987)CrossRef
124.
Gottgens, J., Terhoeven, P., Peters, N.: Calculation of lean flammability limits based on analytical approximations of burning velocities. Bull. Soc. Chim. Belg. 101, 885–891 (1992)
125.
Abramowitz, M., Stegun, I. A.: (Eds.), Exponential Integral and Related Functions, Ch. 6.5 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, (1972)
126.
Peters, N.: Numerical and asymptotic analysis of systematically reduced reaction schemes for hydrocarbon flames. Lect. Notes Phys. 241, 90–109 (1985)CrossRefADS
127.
Noguchi, Y., Nakamura, K., Hagiwara, Y., Hitomi, S., Kuwana, K.: Flame propagation and fractal dimension in a concentric double cylinder apparatus. J. JSEM 14, s101–s104 (2014)
128.
Kulkami, T., Bisetti, F.: Surface morphology and inner fractal cutoff scale of spherical turbulent premixed fames in decaying isotropic turbulence. Proc. Combust. Inst. 38, 2861–2868 (2021)CrossRef
129.
Cintosum, E., Smallwood, G.J., Gulder, O.L.: Flame surface fractal characteristics in premixed turbulence combustion at high turbulence intensities. AIAA J. 45, 2785–2789 (2007)CrossRefADS
130.
Cheng, T.S., Chen, C.-P., Chen, C.-S., Li, Y.-H., Wu, C.-Y., Chao, Y.-C.: Characteristics of microjet methane diffusion flames. Combust. Theor. Model. 10, 861–881 (2006)MATHCrossRefADS
131.
Hiraoka, K., Minamoto, Y., Shimura, M., Naka, Y., Fukushima, N., Tanahashi, M.: A fractal dynamics SGS combustion model for large Eddy simulation of turbulent premixed flame. Combust. Sci. Tech. 188, 1472–1495 (2016)CrossRef
132.
Kertstein, A.R.: Fractal dimension of turbulent premixed flames. Combust. Sci. Tech. 60, 441–445 (1988)CrossRef
133.
Bychkov, V.: Flame front instabilities and development of fractal flames, in Emergent Nature: Patterns, Growth and Scaling in the Life Sciences, 247-254, (2002), World Scientific, Editor M. M. Novak, Singapore
134.
Golub, V. V., Volodin, V. V.: On the description of the turbulent flame acceleration with Kolmogorov law, J. Phys.: Conf. Ser. 946, 012065 (2018)
135.
Searby, G.: Acoustic instability in premixed flames. Combust. Sci. Technol. 81, 221–231 (1992)CrossRef
136.
Searby, G., Rochwerger, D.: A parametric acoustic instability in premixed flame. J. Fluid Mech. 231, 529–543 (1991)MATHCrossRefADS
137.
Quinard, J., Searby, G., Denet, B., Grana-Otero, J.: Self-turbulent flame speeds. Flow Turbul. Combust. 89, 231–247 (2012)MATHCrossRef
138.
Cambray, P., Joulin, G.: On a scaling law for coarsening cells of premixed flames: an approach to fractalization. Combust. Sci. Technol. 161, 139–164 (2000)CrossRef
139.
Travnikov, O.Y., Bychkov, V.V., Liberman, M.A.: Numerical studies of flames in wide tubes: Stability limits of curved stationary flames. Phys. Rev. E 61, 468–474 (2000)CrossRefADS
140.
Kaisare, N.S., Vlachos, D.G.: A review on microcombustion: Fundamentals, devices and applications. Prog. Energy Combust. Sci. 38, 321–259 (2012)CrossRef
141.
Ju, Y., Maruta, K.: Microscale combustion: technology development and fundamental research. Prog. Energy Combust. Sci. 37, 669–715 (2011)CrossRef
142.
Cova, A., Resende, P.R., Cuoci, A., Ayoobi, M., Afonso, A.M., Pinho, C.T.: Numerical studies of premixed and diffusion meso/micro-scale flames. Energy Proc. 120(6), 73–680 (2017)
143.
Conforto, F., Monaco, R., Ricciardello, A.: Analysis of steady combustion processes in a recombination reaction. Cont. Mech. Therm. 26, 503–619 (2014)MathSciNetMATHCrossRef
144.
145.
Conforto, F., Groppi, M., Monaco, R., Spiga, G.: Steady detonation waves for gases undergoing dissociation/recombination and bimolecular reactions. Cont. Mech. Therm. 16, 149–161 (2004)MathSciNetMATHCrossRef
146.
Chen, F., Chien, S.-W., Lang, H.-M., Chang, W.-J.: Stack effects on smoke propagation in subway stations. Cont. Mech. Therm. 15, 425–440 (2003)MATHCrossRef
Metadata
Title
Modeling of combustion and turbulent jet diffusion flames in fractal dimensions
Authors
Rami Ahmad El-Nabulsi
Waranont Anukool
Publication date
25-06-2022
Publisher
Springer Berlin Heidelberg
Published in
Continuum Mechanics and Thermodynamics / Issue 5/2022
Print ISSN: 0935-1175
Electronic ISSN: 1432-0959
DOI
https://doi.org/10.1007/s00161-022-01116-5

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