scholarly journals Modelling of the Tangential Strain Rate Term in the Flame Surface Density Transport Equation in the Context of Reynolds Averaged Navier Stokes Simulations: A Direct Numerical Simulation Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Mohit Katragadda ◽  
Sean P. Malkeson ◽  
Nilanjan Chakraborty
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Strain Rate ◽  
Transport Equation ◽  
Surface Density ◽  
Navier Stokes ◽  
Flame Surface ◽  
Normal Strain ◽  
Tangential Strain ◽  
Dilatation Rate

A direct numerical simulation (DNS) database of freely propagating statistically planar turbulent premixed flames with a range of different values of Karlovitz number Ka, turbulent Reynolds numberRet, heat release parameterτ, and global Lewis number Le has been used to assess the models of the tangential strain rate term in the generalised flame surface density (FSD) transport equation in the context of Reynolds averaged Navier Stokes (RANS) simulations. The tangential strain rate term has been split into contributions arising due to dilatation rateTDand flame normal strain rate (-TN). Subsequently,TDand (-TN) were split into their resolved (i.e.,TD1and (-TN1)) and unresolved (TD2and (-TN2)) components. Detailed physical explanations have been provided for the observed behaviours of the components of the tangential strain rate term. This analysis gave way to the modelling of the unresolved dilatation rate and flame normal strain rate contributions. Models have been identified forTD2and (-TN2) for RANS simulations, which are shown to perform satisfactorily in all cases considered, accounting for the variations in Ka,Ret,τand Le. The performance of the newly proposed models for the FSD strain rate term have been found to be either comparable to or better than the existing models.

scholarly journals Effects of Turbulent Reynolds Number on the Performance of Algebraic Flame Surface Density Models for Large Eddy Simulation in the Thin Reaction Zones Regime: A Direct Numerical Simulation Analysis

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Mohit Katragadda ◽  
Nilanjan Chakraborty ◽  
R. S. Cant
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Fractal Dimension ◽  
Direct Numerical Simulation ◽  
Surface Density ◽  
Flame Surface ◽  
Algebraic Models ◽  
Flame Surface Density ◽  
Turbulent Reynolds Number ◽  
Reaction Zones

A direct numerical simulation (DNS) database of freely propagating statistically planar turbulent premixed flames with a range of different turbulent Reynolds numbers has been used to assess the performance of algebraic flame surface density (FSD) models based on a fractal representation of the flame wrinkling factor. The turbulent Reynolds number Rethas been varied by modifying the Karlovitz number Ka and the Damköhler number Da independently of each other in such a way that the flames remain within the thin reaction zones regime. It has been found that the turbulent Reynolds number and the Karlovitz number both have a significant influence on the fractal dimension, which is found to increase with increasing Retand Ka before reaching an asymptotic value for large values of Retand Ka. A parameterisation of the fractal dimension is presented in which the effects of the Reynolds and the Karlovitz numbers are explicitly taken into account. By contrast, the inner cut-off scale normalised by the Zel’dovich flame thicknessηi/δzdoes not exhibit any significant dependence on Retfor the cases considered here. The performance of several algebraic FSD models has been assessed based on various criteria. Most of the algebraic models show a deterioration in performance with increasing the LES filter width.

scholarly journals Effects of Turbulent Reynolds Number on the Displacement Speed Statistics in the Thin Reaction Zones Regime of Turbulent Premixed Combustion

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Nilanjan Chakraborty ◽  
Markus Klein ◽  
R. S. Cant
Keyword(s):  
Reynolds Number ◽  
Strain Rate ◽  
Surface Density ◽  
Three Dimensional ◽  
Flame Surface ◽  
Tangential Strain ◽  
Turbulent Reynolds Number ◽  
Qualitative Nature ◽  
Displacement Speed ◽  
Turbulent Premixed

The effects of turbulent Reynolds number on the statistical behaviour of the displacement speed have been studied using three-dimensional Direct Numerical Simulation of statistically planar turbulent premixed flames. The probability of finding negative values of the displacement speed is found to increase with increasing turbulent Reynolds number when the Damköhler number is held constant. It has been shown that the statistical behaviour of the Surface Density Function, and its strain rate and curvature dependence, plays a key role in determining the response of the different components of displacement speed. Increasing the turbulent Reynolds number is shown to reduce the strength of the correlations between tangential strain rate and dilatation rate with curvature, although the qualitative nature of the correlations remains unaffected. The dependence of displacement speed on strain rate and curvature is found to weaken with increasing turbulent Reynolds number when either Damköhler or Karlovitz number is held constant, but the qualitative nature of the correlation remains unaltered. The implications of turbulent Reynolds number effects in the context of Flame Surface Density (FSD) modelling have also been addressed, with emphasis on the influence of displacement speed on the curvature and propagation terms in the FSD balance equation.

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.

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