Three-dimensional direct numerical simulations of V-flames interacting with chemically inert walls in a fully developed turbulent channel flow have been performed under adiabatic and isothermal wall ...boundary conditions using single-step chemistry. These simulations are representative of stoichiometric methane-air mixture at unity Lewis number under atmospheric conditions. The turbulence in the non-reacting channel is representative of the friction velocity based Reynolds number
R
e
τ
=
110
. Differences in the statistical behaviours of the mean values of progress variable, temperature, and density have been reported for different wall boundary conditions. It is found that the mean location of the oblique flame interacting with the wall is affected by the choice of the wall boundary condition used. The influence of these differences on the flame dynamics is investigated by analysing the statistical behaviours of the surface density function (SDF) and the strain rates, which govern the evolution of the SDF. The mean variation of the SDF and the flame displacement speed are strongly affected by the wall boundary condition within the viscous sub-layer region of the boundary layer. The behaviours of the normal and tangential strain rates are found to be influenced by not only the differences in the wall boundary conditions, but also by the distance from the wall. The differences in the displacement speed statistics for different wall boundary conditions and wall distance affect the behaviours of the normal strain rate arising due to flame propagation and curvature stretch. The changes in the SDF behaviour in the near wall region have been explained in terms of the statistics of effective normal strain rate experienced by the progress variable iso-surfaces under different wall boundary conditions and wall normal distances.
The influence of flow configuration on flame-wall interaction (FWI) of premixed flames within turbulent boundary layers has been investigated. Direct numerical simulations (DNS) of two different flow ...configurations for flames interacting with chemically inert isothermal and adiabatic walls in fully developed turbulent boundary layers have been performed. The first configuration is an oblique wall interaction (OWI) of a V-flame in a turbulent channel flow and the second configuration is a head-on interaction (HOI) of a planar flame in a turbulent boundary layer. These simulations are representative of stoichiometric methane-air mixture under atmospheric conditions and the non-reacting turbulence for these simulations corresponds to the friction velocity based Reynolds number of
R
e
τ
=
110
. It is found that the mean wall shear stress, mean wall friction velocity and the mean velocity statistics are affected during FWI and the behaviour for these quantities varies under the different flow configurations as well as for the different thermal wall boundary conditions. The behaviour of the quenching distance and mean wall heat flux under isothermal wall conditions is found to be significantly different between the two flow configurations. The variation of the non-dimensional temperature in wall units for cases with isothermal walls suggests that the temperature in the log-layer region is significantly altered by the evolving wall heat flux in both flow configurations. Statistics of the mean Reynolds stresses and turbulence dissipation rate show that the flame significantly alters the behaviour of turbulence due to thermal expansion effects and flow configuration plays an important role.
Three-dimensional direct numerical simulations (DNS) of two different flow configurations have been performed for premixed flames interacting with chemically inert isothermal walls at the unburned ...gas temperature in fully developed turbulent boundary layers. The first configuration is an oblique flame-wall interaction (FWI) of a V-flame in a turbulent channel flow and the second configuration is a head-on quenching planar flame in a turbulent boundary layer. These simulations are representative of stoichiometric methane-air mixture at unity Lewis number under atmospheric conditions. The turbulence in the non-reacting conditions for these simulations is representative of the friction velocity based Reynolds number of Reτ=110. Differences in the statistical behaviours of the mean values of progress variable, temperature, and density during the FWI process have been reported for the two configurations. It is found that the mean flame brush thickens in the near wall region leading to significant departures from the strict Bray Moss Libby (BML) formulation limit during the FWI process and that is reflected in the probability density function (PDF) distributions of c for both flame configurations. The closures from the BML formulation for Reynolds averaged progress variable c¯ and the Favre averaged variance of the progress variable c′′2˜ have also been investigated and it is found that these closures need to be modified to account for the FWI process even when the flame away from the wall represents high Damköhler number premixed turbulent combustion. Furthermore, the statistical behaviours of the quantities required for Flame Surface Density (FSD) based mean reaction rate closure including the flame orientation factor σy, the flamelet length scale Ly and the flame stretch factor I0 have been interrogated from the DNS data for the two flame configurations. The flamelet length scale and the stretch factor extracted from the DNS data are compared with the closures for these quantities proposed in the literature. It is found that σy exhibits significant spatial variation for both cases. The existing closures for Ly and I0 which exhibit the best quantitative agreement with DNS data have been identified. It has been found that the models for Ly and I0 have scopes for further improvement to enable satisfactory predictions of these quantities during the FWI process within turbulent boundary layers.
The interaction of large and small scale structures is fundamental to the energy cascade in turbulent flows. The correct representation of this interaction becomes important in the context of large ...eddy simulation (LES), where the response of small-scale structures to the resolved quantities, or large-scale structures, must be parametrised. This challenging task becomes more demanding when LES of premixed flames are considered, as heat release affects the interaction of turbulence and chemistry occurring at the unresolved scales. In this work, the influence of sub-grid scale (SGS) stresses on the kinetic energy budget of the resolved velocity field in turbulent premixed flames is investigated. In this spirit, the alignment between the SGS stresses and the resolved strain rate has been analysed by interrogating a direct numerical simulation (DNS) database of statistically planar premixed flames subjected to forced isotropic turbulence. It has been found that the alignment between the eigenvectors of the SGS stresses and the resolved strain rate changes across the flame brush and this change is dependent on the level of turbulence experienced by the flame. The influence of different turbulence intensities and different filter widths along with the implications of this misalignment on the SGS modelling are discussed in detail in the paper.
The influence of mixture stratification on the development of turbulent flames in a slot-jet configuration has been analysed using Direct Numerical Simulation data. Mixture stratification was imposed ...at the inlet by varying the equivalence ratio between 0.6 and 1.0 with different alignments to the reaction progress variable gradient: aligned gradients (back-supported), opposed gradients (front-supported) and misaligned gradients. An additional premixed case with a global equivalence ratio of 0.8 was simulated for comparison. The flame is shortest for the front-supported case, followed by the premixed flame, with the back-supported and misaligned gradient flames being the tallest and of comparable size. This behaviour has been explained in terms of the variations of the mean equivalence ratio within the flame and the volume-integrated reaction rate in the streamwise direction. The difference in mixture composition for these cases results in significant variations in the burning rate, flame area, flame wrinkling and flame brush thickness in the streamwise direction. The globally front-supported case has the highest volume-integrated burning rate and flame area, while the back-supported case has the lowest. The misaligned scalar gradient case exhibits qualitatively similar behaviour to that of the globally back-supported case. The burning intensity is unity for a major part of the flame length but assumes values greater than unity towards the flame tip where the effects of flame curvature become strong. All cases predominantly exhibit the premixed mode of combustion within the flamelet regime, so flamelet assumption-based reaction rate closures, originally proposed for premixed combustion, were evaluated using a priori analysis. The terms which require improved closures have been identified and existing closures have been improved where necessary. It was found that the global nature of mixture stratification does not influence the performance of the mean reaction rate closures or the parameterisation of marginal probability density functions of scalars in turbulent stratified mixture combustion.
The cross-scalar dissipation rate of reaction progress variable and mixture fraction
ε
c
ξ
~
plays an important role in the modelling of stratified combustion. The evolution and statistical behaviour ...of
ε
c
ξ
~
have been analysed using a direct numerical simulation (DNS) database of statistically planar turbulent stratified flames with a globally stochiometric mixture. A parametric analysis has been conducted by considering a number of DNS cases with a varying initial root-mean-square velocity fluctuation
u
′
and initial scalar integral length scale
ℓ
ϕ
. The explicitly Reynolds averaged DNS data suggests that the linear relaxation model for
ε
c
ξ
~
is inadequate for most cases, but its performance appears to improve with increasing initial
ℓ
ϕ
and
u
′
values. An exact transport equation for
ε
c
ξ
~
has been derived from the first principle, and the budget of the unclosed terms of the
ε
c
ξ
~
transport equation has been analysed in detail. It has been found that the terms arising from the density variation, scalar-turbulence interaction, chemical reaction rate and molecular dissipation rate play leading order roles in the
ε
c
ξ
~
transport. These observations have been justified by a scaling analysis, which has been utilised to identify the dominant components of the leading order terms to aid model development for the unclosed terms of the
ε
c
ξ
~
transport equation. The performances of newly proposed models for the unclosed terms have been assessed with respect to the corresponding terms extracted from DNS data, and the newly proposed closures yield satisfactory predictions of the unclosed terms in the
ε
c
ξ
~
transport equation.
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