Abstract
While Reynolds-Averaged Navier-Stokes (RANS) simulations are widely used in applied research into premixed turbulent burning in spark ignition piston engines and gas-turbine combustors, fundamental challenges associated with modeling various unclosed terms in the RANS transport equations that describe premixed flames have not yet been solved. These challenges stem from two kinds of phenomena. First, thermal expansion due to heat release in combustion reactions affects turbulent flow and turbulent transport. Such effects manifest themselves in the so-called counter gradient turbulent transport, flame-generated turbulence, hydrodynamic instability of premixed combustion, etc. Second, turbulent eddies wrinkle and stretch reaction zones, thus, increasing their surface area and changing their local structure. Both the former effects, i.e. the influence of combustion on turbulence, and the latter effects, i.e. the influence of turbulence on combustion, are localized to small scales unresolved in RANS simulations and, therefore, require modeling. In the present chapter, the former effects, their physical mechanisms and manifestations, and approaches to modeling them are briefly overviewed, while discussion of the latter effects is more detailed. More specifically, the state-of-the-art of RANS modeling of the influence of turbulence on premixed combustion is considered, including widely used approaches such as models that deal with a transport equation for the mean Flame Surface Density or the mean Scalar Dissipation Rate. Subsequently, the focus of discussion is placed on phenomenological foundations, closed equations, qualitative features, quantitative validation, and applications of the so-called Turbulent Flame Closure (TFC) model and its extension known as Flame Speed Closure (FSC) model.
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Notes
- 1.
It is worth remembering that the pressure in a turbulent flow always fluctuates with time, but the magnitude of such fluctuations is much smaller than the mean pressure if the Mach number is low. Here, term “iso-baric case” means that the mean pressure does not depend on time.
- 2.
Premixed turbulent flame brush is a spatial volume where the probabilities of finding \(c=0\) and \(c=1\) are both less than unity.
- 3.
If the curl operator is applied to the Navier–Stokes equations, then, the pressure gradient term vanishes, because \(\nabla \times \nabla q \equiv 0\) for any scalar quantity q.
- 4.
In the case of a single-step chemistry, the local burning rate in an adiabatic laminar premixed flame is not affected by the flame curvature or the local strain rate if (i) the activation temperature of the combustion reaction is asymptotically high, i.e., \(\varTheta /T_b \gg 1\), and (ii) the mixture is equidiffusive, i.e., \(D_F=D_O=\kappa \), e.g., see a review paper by Clavin (1985).
- 5.
Within the framework of the classical thermal theory of laminar premixed combustion (Zel’dovich et al. 1985), a laminar flame consists of a preheat zone, where the reaction rate vanishes, and a significantly thinner reaction zone which heat release is localized to.
- 6.
Curvature is considered to be positive or negative if the curvature center is in burned or unburned gas, respectively.
- 7.
A product of \(\rho |\nabla c|\) is mathematically meaningless in the case of an infinitely thin flame front, because both \(\rho \) and \(|\nabla c|\) are discontinuous at the front.
- 8.
There is the same function in Table 6.1 also.
- 9.
This feature of premixed turbulent burning will be discussed in Sect. 6.4.4.
References
Abdel-Gayed RG, Al-Khishali KJ, Bradley D (1984) Turbulent burning velocities and flame straining in explosions. Proc R Soc Lond A 391:391–414
Atashkari K, Lawes M, Sheppard CGW, Woolley R (1999) Towards a general correlation of turbulent premixed flame wrinkling. In: Rodi W, Laurence D (eds) Engineering turbulence modelling and measurements 4. In: Proceedings of 4th International Symposium on Engineering Turbulence Modelling and Measurements, Ajaccio, Corsica, France, 24–26 May, 1999, pp 805–814
Bailly P, Champion M, Garreton D (1997) Counter-gradient diffusion in a confined turbulent premixed flame. Phys Fluids 9:766–775
Bilger RW, Pope SB, Bray KNC, Driscoll JF (2005) Paradigms in turbulent combustion research. Proc Combust Inst 30:21–42
Borghi R (1990) Turbulent premixed combustion: further discussions of the scales of fluctuations. Combust Flame 80:304–312
Boudier P, Henriot S, Poinsot T, Baritaud T (1992) A model for turbulent flame ignition and propagation in spark ignition engines. Proc Combust Inst 24:503–510
Boughanem H, Trouvé A (1998) The domain of influence of flame instabilities in turbulent premixed combustion. Proc Combust Inst 27:971–978
Bradley D (1992) How fast can we burn? Proc Combust Inst 24:247–262
Bradley D (2002) Problems of predicting turbulent burning rates. Combust Theory Model 6:361–382
Bradley D, Lau AKC, Lawes M (1992) Flame stretch rate as a determinant of turbulent burning velocity. Philos Trans R Soc Lond A 338:359–387
Bradley D, Lawes M, Sheppard CGW (1994a) Study of turbulence and combustion interaction: measurement and prediction of the rate of turbulent burning. Report, University of Leeds
Bradley D, Lawes M, Scott MJ, Mushi EMJ (1994b) Afterburning in spherical premixed turbulent explosions. Combust Flame 99:581–590
Bradley D, Gaskell PH, Gu XJ, Sedaghat A (2005) Premixed flamelet modelling: factors influencing the turbulent heat release rate source term and the turbulent burning velocity. Combust Flame 143:227–245
Bray KNC (1979) The interaction between turbulence and combustion. Proc Combust Inst 17:223–233
Bray KNC (1980) Turbulent flows with premixed reactants. In: Libby PA, Williams FA (eds) Turbulent reacting flows. Springer, Berlin
Bray KNC (1987) Methods of including realistic chemical reaction mechanisms in turbulent combustion models. In: Warnatz J, Jager W (ed) Complex chemical reaction systems. Mathematical modelling and simulation. Springer, Heidelberg
Bray KNC (1990) Studies of the turbulent burning velocity. Proc R Soc Lond A 431:315–335
Bray KNC (1995) Turbulent transport in flames. Proc R Soc Lond A 451:231–256
Bray KNC (1996) The challenge of turbulent combustion. Proc Combust Inst 26:1–26
Bray KNC, Moss JB (1977) A unified statistical model for the premixed turbulent flame. Acta Astronaut 4:291–319
Bray KNC, Cant RS (1991) Some applications of Kolmogorov’s turbulence research in the field of combustion. Proc R Soc Lond A 434:217–240
Bray KNC, Libby PA, Moss JB (1985) Unified modeling approach for premixed turbulent combustion—Part I: General formulation. Combust Flame 61:87–102
Bray KNC, Champion M, Libby PA, Swaminathan N (2006) Finite rate chemistry and presumed PDF models for premixed turbulent combustion. Combust Flame 146:665–667
Brodkey RS (1967) The phenomena of fluid motions. Addison-Wesley Publishing Company, London
Burluka AA, Griffiths JF, Liu K, Orms M (2009) Experimental studies of the role of chemical kinetics in turbulent flames. Combust Explos Shock Waves 45:383–391
Candel S, Poinsot T (1990) Flame stretch and the balance equation for the flame area. Combust Sci Technol 170:1–15
Candel S, Veynante D, Lacas F, Maistret E, Darabiha N, Poinsot T (1990) Coherent flame model: applications and recent extensions. In: Larrouturou BE (ed) Advances in combustion modeling. World Scientific, Singapore
Cant RS, Pope SB, Bray KNC (1990) Modelling of flamelet surface-to-volume ratio in turbulent premixed combustion. Proc Combust Inst 23:809–815
Chakraborty N, Champion M, Mura A, Swaminathan N (2011) Scalar-dissipation-rate approach. In: Swaminathan N, Bray KNC (eds) Turbulent premixed flames. Cambridge University Press, Cambridge
Chaudhuri S, Akkerman V, Law CK (2011) Spectral formulation of turbulent flame speed with consideration of hydrodynamic instability. Phys Rev E 84:026322
Cheng RK, Shepherd IG (1991) The influence of burner geometry on premixed turbulent flame propagation. Combust Flame 85:7–26
Cheng WK, Diringer JA (1991) Numerical modelling of SI engine combustion with a flame sheet model. SAE Paper 910268
Cho P, Law CK, Cheng RK, Shepherd IG (1988) Velocity and scalar fields of turbulent premixed flames in stagnation flow. Proc Combust Inst 22:739–745
Choi CR, Huh KY (1998) Development of a coherent flamelet model for spark-ignited turbulent premixed flame in a closed vessel. Combust Flame 114:336–348
Chowdhury BR, Cetegen BM (2017) Experimental study of the effects of free stream turbulence on characteristics and flame structure of bluff-body stabilized conical lean premixed flames. Combust Flame 178:311–328
Clavin P (1985) Dynamical behavior of premixed flame fronts in laminar and turbulent flows. Prog Energy Combust Sci 11:1–59
Clavin P, Williams FA (1979) Theory of premixed-flame propagation in large-scale turbulence. J Fluid Mech 90:589–604
Cohé C, Chauveau C, Gökalp I, Kurtuluş DF (2009) CO\(_2\) addition and pressure effects on laminar and turbulent lean premixed CH\(_4\) air flames. Proc Combust Inst 32:1803–1810
Damköhler G (1940) Der einfuss der turbulenz auf die flammengeschwindigkeit in gasgemischen. Z Electrochem 46:601–652
Darrieus G (1938) Propagation d’un front de flamme. Presented at La Technique Moderne (Paris) and in 1945 at Congrés de Mećanique Appliqueé (Paris)
Dasgupta D, Sun W, Day M, Lieuwen T (2017) Effect of turbulence-chemistry interactions on chemical pathways for turbulent hydrogen-air premixed flames. Combust Flame 176:191–201
Dinkelacker F (2002) Numerical calculation of turbulent premixed flames with an efficient turbulent flame speed closure model. In: Breuer M, Durst F, Zenger C (eds) High-performance scientific and engineering computing. Lecture notes in computational science and engineering, vol 21, pp 81–88
Dinkelacker F, Hölzler S (2000) Investigation of a turbulent flame speed closure approach for premixed flame calculations. Combust Sci Technol 158:321–340
Duclos JM, Veynante D, Poinsot T (1993) A comparison of flamelet models for premixed turbulent combustion. Combust Flame 95:101–117
Fichot F, Lacas F, Veynante D, Candel S (1993) One-dimensional propagation of a premixed turbulent flame with a balance equation for the flame surface density. Combust Sci Technol 90:35–60
Fogla N, Creta F, Matalon M (2017) The turbulent flame speed for low-to-moderate turbulence intensities: Hydrodynamic theory vs. experiments. Combust Flame 175:155–169
Frank JH, Kalt PAM, Bilger RW (1999) Measurements of conditional velocities in turbulent premixed flames by simultaneous OH PLIF and PIV. Combust Flame 116:220–232
Ghirelli F (2011) Turbulent premixed flame model based on a recent dispersion model. Comput Fluids 44:369–376
Giovangigli V (1999) Multicomponent flow modeling. Springer, Berlin
Goix P, Paranthoen P, Trinité M (1990) A tomographic study of measurements in a V-shaped H\(_2\)-air flame and a Lagrangian interpretation of the turbulent flame brush thickness. Combust Flame 81:229–241
Gouldin FC, Miles PC (1995) Chemical closure and burning rates in premixed turbulent flames. Combust Flame 100:202–210
Goulier J, Comandini A, Halter F, Chaumeix N (2017) Experimental study on turbulent expanding flames of lean hydrogen/air mixtures. Proc Combust Inst 36:2823–2832
Griebel P, Siewert P, Jansohn P (2007) Flame characteristics of turbulent lean premixed methane/air flames at high-pressure: turbulent flame speed and flame brush thickness. Proc Combust Inst 31:3083–3090
Hinze JO (1975) Turbulence, 2nd edn. McGraw Hill, New York
Hirschfelder JO, Curtiss CF, Bird RB (1954) Molecular theory of gases and liquids. Wiley, New York
Huang C, Yasari E, Johansen LCR, Hemdal S, Lipatnikov AN (2016) Application of flame speed closure model to RANS simulations of stratified turbulent combustion in a gasoline direct-injection spark-ignition engine. Combust Sci Technol 188:98–131
Karlovitz B, Denniston DW, Wells FE (1951) Investigation of turbulent flames. J Chem Phys 19:541–547
Karpov VP, Severin ES (1980) Effects of molecular-transport coefficients on the rate of turbulent combustion. Combust Explos Shock Waves 16:41–46
Karpov VP, Lipatnikov AN (1995) An effect of molecular thermal conductivity and diffusion on premixed combustion. Doklady Phys Chemistry 341:83–85
Karpov VP, Lipatnikov AN, Zimont, (1996) A test of an engineering model of premixed turbulent combustion. Proc Combust Inst 26:249–257
Karpov VP, Lipatnikov AN, Zimont (1997) Flame curvature as a determinant of preferential diffusion effects in premixed turbulent combustion. In: Sirignano WA, Merzhanov AG, De Luca L (eds) Advances in combustion science: In honor of Ya.B. Zel’dovich. Prog Astronaut Aeronaut 173:235-250
Kha KQN, Robin V, Mura A, Champion M (2016) Implications of laminar flame finite thickness on the structure of turbulent premixed flames. J Fluid Mech 787:116–147
Kheirkhah S, Gülder ÖL (2013) Turbulent premixed combustion in V-shaped flames: characteristics of flame front. Phys Fluids 25:055107
Kheirkhah S, Gülder ÖL (2014) Influence of edge velocity on flame front position and displacement speed in turbulent premixed combustion. Combust Flame 161:2614–2626
Kheirkhah S, Gülder ÖL (2015) Consumption speed and burning velocity in counter-gradient and gradient diffusion regimes of turbulent premixed combustion. Combust Flame 162:1422–1439
Kim SH (2017) Leading points and heat release effects in turbulent premixed flames. Proc Combust Inst 36:2017–2024
Kobayashi H, Tamura T, Maruta K, Niioka T, Williams FA (1996) Burning velocity of turbulent premixed flames in a high-pressure environment. Proc Combust Inst 26:389–396
Kuznetsov VR (1975) Certain peculiarities of movement of a flame front in a turbulent flow of homogeneous fuel mixtures. Combust Explos Shock Waves 11:487–493
Kuznetsov VR, Sabelnikov VA (1990) Turbulence and combustion. Hemisphere Publ Corp, New York
Landau LD (1944) On the theory of slow combustion. Acta Psysicochim USSR 19:77–85
Lapointe S, Blanquart G (2016) Fuel and chemistry effects in high Karlovitz premixed turbulent flames. Combust Flame 167:294–307
Launder BE, Spalding DB (1972) Mathematical models of turbulence. Academic Press, London
Law CK (2006) Combustion physics. Cambridge University Press, Cambridge
Lee B, Choi CR, Huh KY (1998) Application of the coherent flamelet model to counterflow turbulent premixed combustion and extinction. Combust Sci Technol 138:1–25
Li SC, Libby PA, Williams FA (1994) Experimental investigation of a premixed flame in an impinging turbulent stream. Proc Combust Inst 25:1207–1214
Libby PA (1975) On the prediction of intermittent turbulent flows. J Fluid Mech 68:273–295
Libby PA, Bray KNC (1977) Variable density effects in premixed turbulent flames. AIAA J 15:1186–1193
Libby PA, Bray KNC (1981) Countergradient diffusion in premixed turbulent flames. AIAA J 19:205–213
Libby PA, Williams FA (1994) Fundamental aspects and a review. In: Libby PA, Williams FA (eds) Turbulent reactive flows. Academic Press, London
Lindstedt RP, Váos EM (1999) Modeling of premixed turbulent flames with second moment methods. Combust Flame 116:461–485
Lipatnikov AN (2009a) Can we characterize turbulence in premixed flames? Combust Flame 156:1242–1247
Lipatnikov AN (2009b) Testing premixed turbulent combustion models by studying flame dynamics. Int J Spray Combust Dyn 1:39–66
Lipatnikov AN (2011a) Conditioned moments in premixed turbulent reacting flows. Proc Combust Inst 33:1489–1496
Lipatnikov AN (2011b) Transient behavior of turbulent scalar transport in premixed flames. Flow Turbul Combust 86:609–637
Lipatnikov AN (2012) Fundamentals of premixed turbulent combustion. CRC Press, Boca-Raton, Florida
Lipatnikov AN, Chomiak J (1997) A simple model of unsteady turbulent flame propagation. SAE Paper 972993
Lipatnikov AN, Chomiak J (2000a) Transient and geometrical effects in expanding turbulent flames. Combust Sci Technol 154:75–117
Lipatnikov AN, Chomiak J (2000b) Dependence of heat release on the progress variable in premixed turbulent combustion. Proc Combust Inst 28:227–234
Lipatnikov AN, Chomiak J (2001) Developing premixed turbulent flames: Part I. A self-similar regime of flame propagation. Combust Sci Technol 162:85–112
Lipatnikov AN, Chomiak J (2002) Turbulent flame speed and thickness: phenomenology, evaluation, and application in multi-dimensional simulations. Prog Energy Combust Sci 28:1–74
Lipatnikov AN, Chomiak J (2004) Comment on “Turbulent burning velocity, burned gas distribution, and associated flame surface definition” Bradley D, Haq MZ, Hicks RA, Kitagawa T, Lawes M, Sheppard CGW, Woolley R, Combust Flame, 133:415 (2003). Combust Flame 137:261–263
Lipatnikov AN, Chomiak J (2005a) A theoretical study of premixed turbulent flame development. Proc Combust Inst 30:843–850
Lipatnikov AN, Chomiak J (2005b) Self-similarly developing, premixed, turbulent flames: a theoretical study. Phys Fluids 17:065105
Lipatnikov AN, Chomiak J (2005c) Molecular transport effects on turbulent flame propagation and structure. Prog Energy Combust Sci 31:1–73
Lipatnikov AN, Sathiah P (2005) Effects of turbulent flame development on thermoacoustic oscillations. Combust Flame 142:130–139
Lipatnikov AN, Chomiak J (2010) Effects of premixed flames on turbulence and turbulent scalar transport. Prog Energy Combust Sci 36:1–102
Lipatnikov AN, Wallesten J, Nisbet J (1998) Testing of a model for multi-dimensional computations of turbulent combustion in spark ignition engines. In: Proc Fourth Int Symp Diagnostics and modeling of combustion in internal combustion engines—COMODIA98. JSME, Kyoto, pp 239–44
Lipatnikov AN, Nishiki S, Hasegawa T (2015a) DNS assessment of relation between mean reaction and scalar dissipation rates in the flamelet regime of premixed turbulent combustion. Combust Theory Model 19:309–328
Lipatnikov AN, Chomiak J, Sabelnikov VA, Nishiki S, Hasegawa T (2015b) Unburned mixture fingers in premixed turbulent flames. Proc Combust Inst 35:1401–1408
Lipatnikov AN, Sabelnikov VA, Nishiki S, Hasegawa T, Chakraborty N (2015c) DNS assessment of a simple model for evaluating velocity conditioned to unburned gas in premixed turbulent flames. Flow Turbul Combust 94:513–526
Lipatnikov AN, Sabelnikov VA, Nishiki S, Hasegawa T (2017) Flamelet perturbations and flame surface density transport in weakly turbulent premixed combustion. Combust Theory Model 21:205–227
Majda A, Sethian J (1985) The derivation and numerical solution of the equations for zero Mach number combustion. Combust Sci Technol 42:185–205
Meneveau C, Poinsot T (1991) Stretching and quenching of flamelets in premixed turbulent combustion. Combust Flame 86:311–332
Moreau P (1977) Turbulent flame development in a high velocity premixed flow. AIAA paper 77/49
Moreau V (2009) A self-similar premixed turbulent flame model. Appl Math Model 33:835–851
Moss JB (1980) Simultaneous measurements of concentration and velocity in an open premixed turbulent flame. Combust Sci Technol 22:119–129
Mouqallid M, Lecordier B, Trinité M (1994) High speed laser tomography analysis of flame propagation in a simulated internal combustion engine—applications to nonuniform mixture. SAE paper 941990
Muppala SRP, Dinkelacker F (2004) Numerical modelling of the pressure dependent reaction source term for turbulent premixed methane-air flames. Prog Comp Fluid Dyn 4:328–336
Namazian M, Shepherd IG, Talbot L (1986) Characterization of the density fluctuations in turbulent V-shaped premixed flames. Combust Flame 64:299–308
van Oijen JA, Donini A, Bastiaans RJM, ten Thije Boonkkamp JHM, de Goey LPH (2016) State-of-the-art in premixed combustion modeling using flamelet generated manifolds. Prog Energy Combust Sci 57:30–74
Peters N (2000) Turbulent combustion. The University Press, Cambridge
Pfadler S, Leipertz A, Dinkelacker F (2008) Systematic experiments on turbulent premixed Bunsen flames including turbulent flux measurements. Combust Flame 152:616–631
Poinsot T, Veynante D (2005) Theoretical and numerical combustion, 2nd edn. Edwards, Philadelphia
Poinsot T, Veynante D, Candel S (1991) Quenching processes and premixed turbulent combustion diagrams. J Fluid Mech 228:561–606
Polifke W, Flohr P, Brandt M (2002) Modeling of inhomogeneously premixed combustion with an extended TFC model. ASME J Eng Gas Turbines Power 124:58–65
Poludnenko AY, Oran ES (2011) The interaction of high-speed turbulence with flames: turbulent flame speed. Combust Flame 158:301–326
Pope SB (1988) The evolution of surface in turbulence. Int J Eng Sci 26:445–469
Pope SB (2000) Turbulent flows. The University Press, Cambridge
Prudnikov AG (1960) Hydrodynamics equations in turbulent flames. In: Prudnikov AG (ed) Combustion in a turbulent flow. Oborongiz, Moscow (in Russian)
Prudnikov AG (1964) Burning of homogeneous fuel-air mixtures in a turbulent flow. In: Raushenbakh BV (ed) Physical principles of the working process in combustion chambers of jet engines. Mashinostroenie, Moscow (in Russian; translated from Russian by the Translation Division, Foreign and Technology Division, Wright Patterson AFB, Clearing House for Federal Scientific & Technical Information, Ohio, 1967, pp 244–336)
Renou B, Mura A, Samson E, Boukhalfa A (2002) Characterization of the local flame structure and flame surface density for freely-propagating premixed flames at various Lewis numbers. Combust Sci Technol 174:143–179
Roberts WL, Driscoll JF, Drake MC, Goss LP (1993) Images of the quenching of a flame by a vortex—to quantify regimes of turbulent combustion. Combust Flame 94:58–69
Sabelnikov VA, Lipatnikov AN (2011) A simple model for evaluating conditioned velocities in premixed turbulent flames. Combust Sci Technol 183:588–613
Sabelnikov VA, Lipatnikov AN (2013) Transition from pulled to pushed premixed turbulent flames due to countergradient transport. Combust Theory Model 17:1154–1175
Sabelnikov VA, Lipatnikov AN (2015) Transition from pulled to pushed fronts in premixed turbulent combustion: theoretical and numerical study. Combust Flame 162:2893–2903
Sabelnikov VA, Lipatnikov AN (2017) Recent advances in understanding of thermal expansion effects in premixed turbulent flames. Annu Rev Fluid Mech 49:91–117
Sabelnikov VA, Lipatnikov AN, Chakraborty N, Nishiki S, Hasegawa T (2016) A transport equation for reaction rate in turbulent flows. Phys Fluids 28:081701
Sabelnikov VA, Lipatnikov AN, Chakraborty N, Nishiki S, Hasegawa T (2017) A balance equation for the mean rate of product creation in premixed turbulent flames. Proc Combust Inst 36:1893–1901
Sathiah P, Lipatnikov AN (2007) Effects of flame development on stationary premixed turbulent combustion. Proc Combust Inst 31:3115–3122
Schmidt HP, Habisreuther P, Leuckel W (1998) A model for calculating heat release in premixed turbulent flames. Combust Flame 113:79–91
Scurlock AC, Grover JH (1953) Propagation of turbulent flames. Proc Combust Inst 4:645–658
Shelkin KI (1943) On combustion in a turbulent flow. J Tech Phys 13:520–530. Transl NACA, 1967, in NACA TM 1110:1–18 (from Russian)
Siewert P (2006) Flame front characteristics of turbulent lean premixed methane/air flames at high-pressure. PhD thesis, ETHZ Zürich
Sjunnesson A, Henrikson, Löfström C (1992) CARS measurements and visualization of reacting flows in a bluff body stabilized flame. AIAA paper 92/3650
Sponfeldner T, Soulopoulos N, Beyrau F, Hardalupas Y, Taylor AMKP, Vassilicos JC (2015) The structure of turbulent flames in fractal- and regular-grid-generated turbulence. Combust Flame 162:3379–3393
Stevens EJ, Bray KNC, Lecordier B (1998) Velocity and scalar statistics for premixed turbulent stagnation flames using PIV. Proc Combust Inst 27:949–955
Swaminathan N, Bray KNC (2005) Effect of dilatation on scalar dissipation in turbulent premixed flames. Combust Flame 143:549–565
Taylor GI (1935) Statistical theory of turbulence. IV. Diffusion in a turbulent air stream. Proc R Soc Lond A 151:465–478
Tamadonfar P, Gülder ÖL (2014) Flame brush characteristics and burning velocities of premixed turbulent methane/air Bunsen flames. Combust Flame 161:3154–3165
Tamadonfar P, Gülder ÖL (2015) Effects of mixture composition and turbulence intensity on flame front structure and burning velocities of premixed turbulent hydrocarbon/air Bunsen flames. Combust Flame 162:4417–4441
Townsend AA (1976) The structure of turbulent shear flow, 2nd edn. Cambridge University Press, Cambridge
Trouvé A, Poinsot T (1994) Evolution equation for flame surface density in turbulent premixed combustion. J Fluid Mech 278:1–31
Venkateswaran P, Marshall A, Shin DH, Noble D, Seitzman J, Lieuwen T (2011) Measurements and analysis of turbulent consumption speeds of H\(_2\)/CO mixtures. Combust Flame 158:1602–1614
Venkateswaran P, Marshall A, Seitzman J, Lieuwen T (2013) Pressure and fuel effects on turbulent consumption speeds of H\(_2\)/CO blends. Proc Combust Inst 34:1527–1535
Venkateswaran P, Marshall A, Seitzman J, Lieuwen T (2015) Scaling turbulent flame speeds of negative Markstein length fuel blends using leading points concepts. Combust Flame 162:375–387
Verma S, Lipatnikov AN (2016) Does sensitivity of measured scaling exponents for turbulent burning velocity to flame configuration prove lack of generality of notion of turbulent burning velocity? Combust Flame 173:77–88
Vervisch L, Bidaux E, Bray KNC, Kollmann W (1995) Surface densiuty function in premixed turbulent combustion modeling, similarities between probability density function and flame surface approaches. Phys Fluids 7:2496–2503
Veynante D, Vervisch L (2002) Turbulent combustion modeling. Prog Energy Combust Sci 28:193–266
Wallesten J, Lipatnikov AN, Chomiak J (2002) Modeling of stratified combustion in a DI SI engine using detailed chemistry pre-processing. Proc Combust Inst 29:703–709
Wang Z, Magi V, Abraham J (2017) Turbulent flame speed dependencies of lean methane-air mixtures under engine relevant conditions. Combust Flame 180:53–62
Williams FA (1985) Combustion theory, 2nd edn. Benjamin/Cummings, Menlo Park, California
Wu MS, Kwon A, Driscoll G, Faeth GM (1990) Turbulent premixed hydrogen/air flames at high Reynolds numbers. Combust Sci Technol 73:327–350
Yanagi T, Mimura Y (1981) Velocity-temperature correlation in premixed flame. Proc Combust Inst 18:1031–1039
Yasari E, Lipatnikov AN (2015) Assessment of a recent model of turbulent scalar flux in RANS simulations of premixed Bunsen flames. In: Hanjalic K, Miyauchi T, Borello D, Had\(\breve{\rm z}\)iabdi\(\acute{\rm c}\) M, Venturini P (eds) THMT15, Proceedings of the International Symposium Turbulence, Heat and Mass Transfer 8, Sarajevo, Bosnia and Herzegovina, September 15–18, 2015. ICHMT
Yasari E, Verma S, Lipatnikov AN (2015) RANS simulations of statistically stationary premixed turbulent combustion using flame speed closure model. Flow Turbul Combust 94:381–414
Yu R, Lipatnikov AN (2017a) A direct numerical simulation study of statistically stationary propagation of reaction wave in homogeneous turbulence. Phys Rev E 95:063101
Yu R, Lipatnikov AN (2017b) DNS study of dependence of bulk consumption velocity in a constant-density reacting flow on turbulence and mixture characteristics. Phys Fluids 29:065116
Yu R, Lipatnikov AN, Bay XS (2014) Three-dimensional direct numerical simulation study of conditioned moments associated with front propagation in turbulent flows. Phys Fluids 26:085104
Yu R, Bay XS, Lipatnikov AN (2015) A direct numerical simulation study of interface propagation in homogeneous turbulence. J Fluid Mech 772:127–164
Zel’dovich YaB, Barenblatt GI, Librovich VB, Makhviladze GM (1985) The mathematical theory of combustion and explosions. Consultants Bureau, New York
Zimont VL (1979) Theory of turbulent combustion of a homogeneous fuel mixture at high Reynolds number. Combust Explos Shock Waves 15:305–311
Zimont VL (2000) Gas premixed combustion at high turbulence. Turbulent flame closure combustion model. Exp Thermal Fluid Sci 21:179–186
Zimont VL (2015) Unclosed Favre-averaged equation for the chemical source and an analytical formulation of the problem of turbulent premixed combustion in the flamelet regime. Combust Flame 162:874–875
Zimont VL, Lipatnikov AN (1993) Calculation of the rate of heat release in a turbulent flame. Doklady Phys Chem 332:440–443
Zimont VL, Lipatnikov AN (1995) A numerical model of premixed turbulent combustion. Chem Phys Rep 14:993–1025
Zimont VL, Biagioli F, Syed K (2001) Modelling turbulent premixed combustion in the intermediate steady propagation regime. Prog Comput Fluid Dyn 1:14–28
Zimont VL, Polifke W, Bettelini M, Weisenstein W (1998) An efficient computational model for premixed turbulent combustion at high Reynolds number based on a turbulent flame speed closure. J Eng Gas Turbines Power 120:526–532
Acknowledgements
This work was supported by Swedish Research Council (VR), Swedish Energy Agency (EM), Swedish Gas Turbine Center (GTC), Chalmers Areas of Advance Transport and Energy, and Combustion Engine Research Center (CERC). The author is grateful to Profs. Chomiak, Karpov, Sabelnikov, and Zimont for valuable discussions.
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Lipatnikov, A.N. (2018). RANS Simulations of Premixed Turbulent Flames. In: De, S., Agarwal, A., Chaudhuri, S., Sen, S. (eds) Modeling and Simulation of Turbulent Combustion. Energy, Environment, and Sustainability. Springer, Singapore. https://doi.org/10.1007/978-981-10-7410-3_6
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