Open AccessRigorous Derivation of an Unclosed Mean G-Equation for Statistically 1D Premixed Turbulent Flames
Author(s) -
Vladimir Sabelnikov,
Andrei Lipatnikov
Publication year - 2010
Publication title -
international journal of spray and combustion dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.614
H-Index - 16
eISSN - 1756-8285
pISSN - 1756-8277
DOI - 10.1260/1756-8277.2.4.301
Subject(s) - mechanics , turbulence , flame speed , mean flow , premixed flame , physics , laminar flame speed , kinematics , combustion , classical mechanics , thermodynamics , chemistry , combustor , organic chemistry
A promising approach to simulating premixed turbulent combustion in gas turbine and spark ignition engines consists of tracking an average flame surface in an average velocity field. Although such an approach is widely used both within RANS and LES framework, the basic substantiation of the corresponding kinematic (or level set, or mean Gt) equation has not yet been elaborated well. The goal of the present paper is to derive such an equation in a straight forward manner from the well-known G-equation for tracking an infinitely thin flame sheet (flamelet) in a turbulent flow in the simplest case of a statistically one-dimensional premixed turbulent flame. The derived equation clarifies the physical meaning of (i) the speed of the self-propagation of the mean flame surface and (ii) the mean flow velocity used to track the surface. In order for the mean flame speed to be equal to the turbulent burning velocity, the velocity used to track the mean flame should differ from the mean flow velocity at the flame surface. In the simplest case of a statistically one-dimensional (planar or spherical) premixed turbulent flame, the former velocity is equal to the extrapolation of the mean velocity profile in the fresh gas to the mean flame surface. An extension of the aforementioned kinematic equation to a general three-dimensional case is discussed