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The statistics of mean fluid velocity components conditional in unburned reactants and fully burned products in the context of Reynolds Averaged Navier Stokes (RANS) simulations have been studied using a Direct Numerical Simulation database of statistically planar turbulent premixed flame representing the corrugated flamelets regime combustion. Expressions for conditional mean velocity and conditional velocity correlations which are derived based on a presumed bimodal probability density function of reaction progress variable for unity Lewis number flames are assessed in this study with respect to the corresponding quantities extracted from DNS data. In particular, conditional surface averaged velocities

Mean fluid velocities conditional in reactants, products, and instantaneous flame surface often play a key role in the theoretical analysis and modelling of turbulent premixed combustion [

In the case of an asymptotically high Damköhler number

However, in spite of the key importance of conditional velocities in turbulent premixed combustion modelling, there is yet to be a detailed Direct Numerical Simulation (DNS) based assessment of the validity of the expressions of the mean conditional velocities, which can be derived based on a presumed bi-modal pdf of

In this respect the main objectives of this study are as follows.

To analyse the statistical behaviours of the conditional mean velocity and their relation to the Favre mean velocity in the context of RANS for the corrugated flamelets regime combustion.

To analyse the statistical behaviours of the conditional surface averaged velocities and their relation to the conditional mean velocities for the corrugated flamelets regime combustion.

The rest of the paper will be organised as follows. The necessary mathematical background will be provided in the next section of the paper. This will be followed by a brief discussion on numerical implementation. Following this, results will be presented and subsequently discussed. Finally the main findings will be summarised and conclusions will be drawn.

DNS of turbulent combustion should account for both three-dimensionality of turbulence and detailed chemical mechanism. However, the limitation of computer storage capacity until recently restricted DNS either to two dimensions with detailed chemistry or to three dimensions with simplified chemistry. As turbulent velocity field is inherently three-dimensional in nature and vortex stretching mechanism is absent in two dimensions, the second approach takes precedence in the present study, which is based on a single-step irreversible Arrhenius-type chemistry.

In premixed combustion the species field is often represented in terms of a reaction progress variable

The simplest possible model for the conditional surface-weighted mean of the correlation between velocity components (i.e.,

For the present study, a decaying turbulence DNS database of statistically planar freely propagating turbulent premixed flame representing the corrugated flamelets regime combustion has been considered. The initial values of normalised root-mean-square value of turbulent velocity fluctuation

List of initial values of turbulence and combustion parameters for the present DNS database.

Grid size | |||||||
---|---|---|---|---|---|---|---|

2.3 | 1.0 | 1.41 | 9.64 | 56.4 | 6.84 | 0.54 |

The DNS database considered here is taken from [

A sixth-order finite difference scheme is used for evaluating spatial derivatives in the direction of flame propagation. The spatial derivatives in the transverse direction are evaluated using a pseudospectral method. The density change is accounted for by the relation between density and reaction progress variable according to the BML formulation for the unity Lewis number flames [

In this case, flame-turbulence interaction takes place under decaying turbulence. The simulation in this case was run for about 4 initial eddy turn over times

For the purpose of postprocessing DNS data, the mean quantities are assumed to be a function of the coordinate in the direction of mean flame propagation (

In the present study the conditional mean quantities are evaluated using (

The contours of the reaction progress variable for the flame considered here are plotted in Figure

(a) Contours of reaction progress variable

The nature of pdf of

The variation of

(a) Variations

The variation of

Comparing Figures

The variations of

(a) Variations of

The evolution of

It is surprising that poor agreement (at

The variations of

(a) Variations of

Figures

The variations of

(a) Variations of

Lee and Huh [

The variations of

The variations of

(a) Variations of

It is evident from Figure

The variations of

(a) Variations of

It is worth noting that the above analysis is carried out using a simplified chemistry-based DNS database representing the corrugated flamelets regime combustion for a moderate value of turbulent Reynolds number following several previous studies [

The statistics of mean fluid velocities conditional in reactants and products in the context of Reynolds Averaged Navier Stokes simulations are analysed in detail using a DNS database of statistically planar turbulent premixed flame representing the corrugated flamelets regime of premixed turbulent combustion. It has been found that the conditional mean velocities

While the conditional velocities

As the present analysis has been carried out for moderate value of turbulent Reynolds number

N. Chakraborty gratefully acknowledges the financial support provided by EPSRC, UK. A. N. Lipatnikov gratefully acknowledges the financial support provided by Swedish Energy Agency and by the Chalmers Combustion Engine Research Centre (CERC).