Estimates of the three-dimensional flame surface density and every term in its transport equation from two-dimensional measurements

2011 ◽  
Vol 33 (1) ◽  
pp. 1447-1454 ◽  
Author(s):  
Evatt R. Hawkes ◽  
Ramanan Sankaran ◽  
Jacqueline H. Chen
Keyword(s):  
Transport Equation ◽  
Surface Density ◽  
Three Dimensional ◽  
Flame Surface ◽  
Two Dimensional ◽  
Flame Surface Density ◽  
Dimensional Measurements

scholarly journals A PrioriDirect Numerical Simulation Modelling of the Curvature Term of the Flame Surface Density Transport Equation for Nonunity Lewis Number Flames in the Context of Large Eddy Simulations

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Mohit Katragadda ◽  
Nilanjan Chakraborty
Keyword(s):  
Numerical Simulation ◽  
Transport Equation ◽  
Surface Density ◽  
Lewis Number ◽  
Simulation Modelling ◽  
Flame Surface ◽  
Flame Surface Density ◽  
Curvature Term ◽  
Wide Range ◽  
Large Eddy

A Direct Numerical Simulation (DNS) database of freely propagating statistically planar turbulent premixed flames with Lewis numbersLeranging from 0.34 to 1.2 has been used to analyse the statistical behaviours of the curvature term of the generalised Flame surface Density (FSD) transport equation, in the context of the Large Eddy Simulation (LES). Lewis number is shown to have significant influences on the statistical behaviours of the resolved and sub-grid parts of the FSD curvature term. It has been found that the existing models for the sub-grid curvature termCsgdo not capture the qualitative behaviour of this term extracted from the DNS database for flames withLe<<1. The existing models ofCsgonly predict negative values, whereas the sub-grid curvature term is shown to assume positive values within the flame brush for theLe=0.34and 0.6 flames. Here the sub-grid curvature terms arising from combined reaction and normal diffusion and tangential diffusion components of displacement speed are individually modelled, and the new model of the sub-grid curvature term has been found to captureCsgextracted from DNS data satisfactorily for all the different Lewis number flames considered here for a wide range of filter widths.

A posteriori testing of the flame surface density transport equation for LES

2013 ◽  
Vol 18 (1) ◽  
pp. 32-64 ◽  
Author(s):  
T. Ma ◽  
O.T. Stein ◽  
N. Chakraborty ◽  
A.M. Kempf
Keyword(s):  
Transport Equation ◽  
Surface Density ◽  
Flame Surface ◽  
A Posteriori ◽  
Flame Surface Density

scholarly journals Effects of Body Forces on the Statistics of Flame Surface Density and Its Evolution in Statistically Planar Turbulent Premixed Flames

2021 ◽  
Author(s):  
Arun Ravi Varma ◽  
Umair Ahmed ◽  
Nilanjan Chakraborty
Keyword(s):  
Transport Equation ◽  
Surface Density ◽  
Body Force ◽  
Density Stratification ◽  
Flame Surface ◽  
Turbulent Premixed Flames ◽  
Flame Surface Density ◽  
Body Forces ◽  
Gradient Type ◽  
Turbulent Premixed

AbstractBody forces such as buoyancy and externally imposed pressure gradients are expected to have a strong influence on turbulent premixed combustion due to the considerable changes in density between the unburned and fully burned gases. The present work utilises Direct Numerical Simulation data of three-dimensional statistically planar turbulent premixed flames to study the influence of body forces on the statistical behaviour of the flame surface density (FSD) and its evolution within the flame brush. The analysis has been carried out for different turbulence intensities and normalised body force values (i.e., Froude numbers). A positive value of the body force signifies an unstable density stratification (i.e., body force is directed from the heavier unburned gas to the lighter burned gas) and vice versa. It is found that for a given set of turbulence parameters, flame wrinkling increases with an increase in body force magnitude in the unstable configuration. Furthermore, higher magnitudes of body force in the unstable density stratification configuration promote a gradient type transport of turbulent scalar and FSD fluxes, and this tendency weakens in the stable density stratification configuration where a counter-gradient type transport is promoted. The statistical behaviours of the different terms in the FSD transport equation and their closures in the context of Reynolds Averaged Navier–Stokes simulations have been analysed in detail. It has been demonstrated that the effects of body force on the FSD and the terms of its transport equation weakens with increasing turbulence intensity as a result of the diminishing relative strength of body force in comparison to the inertial force. The predictions of the existing models have been assessed with respect to the corresponding terms extracted from the explicitly averaged DNS data, and based on this evaluation, suitable modifications have been made to the existing models to incorporate the effects of body force (or Froude number).

scholarly journals Modelling of the Curvature Term of the Flame Surface Density Transport Equation for Large Eddy Simulations

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Mohit Katragadda ◽  
Nilanjan Chakraborty
Keyword(s):  
Transport Equation ◽  
Surface Density ◽  
Flame Surface ◽  
Flame Surface Density ◽  
New Model ◽  
Curvature Term ◽  
Large Eddy ◽  
Diffusion Component ◽  
Normal Diffusion ◽  
Displacement Speed

A simplified chemistry based three-dimensional Direct Numerical Simulation (DNS) database of freely propagating statistically planar turbulent premixed flames with a range of different values of turbulent Reynolds number has been used for the a priori modelling of the curvature term of the generalised Flame Surface Density (FSD) transport equation in the context of Large Eddy Simulation (LES). The curvature term has been split into the contributions arising due to the reaction and normal diffusion components of displacement speed and the term originating from the tangential diffusion component of displacement speed. Subsequently, these contributions of the curvature term have been split into the resolved and subgrid contributions. New models have been proposed for the subgrid curvature terms arising from the combined reaction and normal diffusion components and the tangential diffusion component of displacement speed. The performances of the new model and the existing models for the subgrid curvature term have been compared with the corresponding quantity extracted from the explicitly filtered DNS data. The new model for the subgrid curvature term is shown to perform satisfactorily in all cases considered in the current study, accounting for wide variations in LES filter size.

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