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Modeling and Simulation of Turbulent Combustion pp 3–43Cite as

Mechanics and Modelling of Turbulence–Combustion Interaction

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

Abstract

Engineering applications of combustion for aviation, automotive and power generation invariably encounter an underlying turbulent flow field. A proper understanding of the complex turbulence–combustion interactions, flame structure and dynamics is indispensable towards the optimal design and systematic evolution of these applications. A predictive solution of turbulent combustion phenomenon in a practical combustion system where all scales of turbulence are fully resolved is extremely difficult with currently available computational facilities. The urgent requirement for the solution of fluid engineering problems has led to the emergence of turbulence models. The turbulence models could be systematically derived based on the Navier–Stokes equations up to a certain point; however, they require closure hypotheses that depend on dimensional arguments and empirical input. Over the past several decades, turbulence models based on Reynolds-averaged Navier–Stokes (RANS) and large eddy simulation (LES) framework have been developed and used for engineering applications. The success of turbulence models for non-reactive flows has encouraged similar approaches for turbulent reactive flows which consequently led to the development of turbulent combustion models. Modelling of the chemical source term remains the central issue of turbulent combustion simulations. In this introductory chapter, we will review the basics of turbulent flows and multiscale interactions between turbulence and combustion, and proceed towards a brief discussion on the state-of-the-art turbulent combustion models.

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Abbreviations

ρ :

Density

u :

Velocity

R u :

Universal gas constant

p :

Pressure

\( \tau_{ij} \) :

Viscous stress tensor

\( \mu \) :

Dynamic viscosity

\( \upsilon \) :

Kinematic viscosity

Y :

Mass fraction

D :

Mass diffusivity

Sc :

Schmidt number

Pr :

Prandtl number

Le :

Lewis number

Re:

Reynold’s number

\( \lambda \) :

Thermal conductivity

\( \alpha \) :

Thermal diffusivity

X :

Mole fraction

W :

Molecular weight

E a :

Activation energy

T :

Temperature

h :

Enthalpy

\( \overrightarrow {{\dot{q}}} \) :

Heat flux

Q :

Conditional mean

C χ :

Scalar dissipation constant

Z:

Mixture fraction

J :

Flux

\( \tau_{L} \) :

Mixing timescale

Δ:

Filter width

T a :

Activation temperature

k (f), k (r) :

Forward and reverse reaction rates

n r :

Number of reactions

n s :

Number of species

\( \chi \) :

Scalar dissipation

\( {\varepsilon } \) :

Dissipation rate

\( {k} \) :

Turbulent kinetic energy

\( \mathop \omega \limits^{ \cdot } \) :

Chemical source term

η :

Sample space

P :

Probability density function

C s :

Smagorinsky model constant

\( {\mathcal{T}}_{ij} \) :

Residual stress tensor

\( {\mathcal{L}}_{ij} \) :

Leonard term

\( {\mathcal{M}}_{ij} \) :

Modelled term

\(\eta\) :

Kolmogorov length scale

–:

Average, ensemble or time average depending on context

~:

Favre average

″:

Fluctuations with respect to conditional mean

′:

Fluctuations with respect to unconditional mean

J:

Reaction number

I:

Species

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Authors and Affiliations

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

    Santanu De

  2. Department of Aerospace Engineering, Indian Institute of Science, Bangalore, India

    Swetaprovo Chaudhuri

Authors
  1. Santanu De
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  2. Swetaprovo Chaudhuri
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Correspondence to Santanu De .

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Editors and Affiliations

  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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Santanu De, Chaudhuri, S. (2018). Mechanics and Modelling of Turbulence–Combustion Interaction. 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_1

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  • DOI: https://doi.org/10.1007/978-981-10-7410-3_1

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