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Modeling and Simulation of Turbulent Combustion pp 181–240Cite as

RANS Simulations of Premixed Turbulent Flames

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Part of the book series: Energy, Environment, and Sustainability ((ENENSU))

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. 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. 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. 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. 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. 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. 6.

    Curvature is considered to be positive or negative if the curvature center is in burned or unburned gas, respectively.

  7. 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. 8.

    There is the same function in Table 6.1 also.

  9. 9.

    This feature of premixed turbulent burning will be discussed in Sect. 6.4.4.

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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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  1. Chalmers University of Technology, 41296, Gothenburg, Sweden

    Andrei N. Lipatnikov

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  1. Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India

    Santanu De

  2. Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India

    Avinash Kumar Agarwal

  3. Department of Aerospace Engineering, Indian Institute of Science, Bangalore, Karnataka, India

    Swetaprovo Chaudhuri

  4. Department of Mechanical Engineering, Jadavpur University, Kolkata, West Bengal, India

    Swarnendu Sen

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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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