Displacement Speed Statistics for Stratified Mixture Combustion in an Igniting Turbulent Planar Jet

The statistics of the density-weighted displacement speed of the reaction progress variable c isosurfaces for stratified mixture combustion arising from localized ignition in a turbulent planar coflowing jet have been studied based on 3D Direct Numerical Simulation data where the jet is considered to be fuel-rich and the coflow is taken to be fuel-lean. The resulting flame following successful ignition shows the premixed mode of combustion in fuel-rich and fuel-lean zones although an additional diffusion flame branch was also observed on the stoichiometric mixture isosurface at early times of flame evolution. The flame propagation characteristics have been analyzed in terms of the reaction, normal diffusion and tangential diffusion components of the density-weighted displacement speed for different values of reaction progress variables across the flame brush. It has been found that the reaction, normal diffusion and tangential diffusion components of density-weighted displacement speed, remain the major contributors to the density-weighted displacement speed at all stages of flame evolution as the magnitude of the component which originates due to mixture inhomogeneity remains negligible in comparison to the magnitudes of other components in accordance with previous experimental studies. It has been demonstrated that curvature and tangential strain rate dependences of the reaction progress variable gradient play key roles in determining strain rate dependences of the reaction and normal diffusion components of the density-weighted displacement speed. It has been shown that the interrelation between tangential strain rate and curvature affects the strain rate dependence of tangential diffusion component of the density-weighted displacement speed. The density-weighted displacement speed and curvature are found to be predominantly negatively correlated throughout the flame brush at all stages of the flame evolution. The relative strengths of the tangential strain rate dependence of the reaction, normal diffusion and tangential diffusion components of the density-weighted displacement speed ultimately determine the nature of correlation between the density-weighted displacement speed and the tangential strain rate. The strain rate and curvature dependences of the density-weighted displacement speed in stratified mixtures are found to be qualitatively similar to the statistics previously obtained for turbulent premixed flames.

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Comparison of Flame Propagation Statistics Based on Direct Numerical Simulation of Simple and Detailed Chemistry. Part 2: Influence of Choice of Reaction Progress Variable

Energies ◽

10.3390/en14185695 ◽

2021 ◽

Vol 14 (18) ◽

pp. 5695

Author(s):

Felix B. Keil ◽

Marvin Amzehnhoff ◽

Umair Ahmed ◽

Nilanjan Chakraborty ◽

Markus Klein

Keyword(s):

Numerical Simulation ◽

Direct Numerical Simulation ◽

Flame Propagation ◽

Flame Structure ◽

Tangential Strain ◽

Detailed Chemistry ◽

Reaction Progress ◽

Considerable Uncertainty ◽

Progress Variable ◽

Displacement Speed

Flame propagation statistics for turbulent, statistically planar premixed flames obtained from 3D Direct Numerical Simulations using both simple and detailed chemistry have been evaluated and compared to each other. To achieve this, a new database has been established encompassing five different conditions on the turbulent combustion regime diagram, using nearly identical numerical methods and the same initial and boundary conditions. The discussion includes interdependencies of displacement speed and its individual components as well as surface density function (i.e., magnitude of the reaction progress variable) with tangential strain rate and curvature. For the analysis of detailed chemistry Direct Numerical Simulation data, three different definitions of reaction progress variable, based on CH4,H2O and O2 mass fractions will be used. While the displacement speed statistics remain qualitatively and to a large extent quantitatively similar for simple chemistry and detailed chemistry, there are pronounced differences for its individual contributions which to a large extent depend on the definition of reaction progress variable as well as on the chosen isosurface level. It is concluded that, while detailed chemistry simulations provide more detailed information about the flame structure, the choice of the reaction progress variable definition and the choice of the resulting isosurface give rise to considerable uncertainty in the interpretation of displacement speed statistics, sometimes even showing opposing trends. Simple chemistry simulations are shown to provide (a) the global flame propagation statistics which are qualitatively similar to the corresponding results from detailed chemistry simulations, (b) remove the uncertainties with respect to the choice of reaction progress variable, and (c) are more straightforward to compare with theoretical analysis or model assumptions that are mostly based on simple chemistry assumptions.

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Strain rate dependence of strength-differential effect in two steels

Journal de Physique IV (Proceedings) ◽

10.1051/jp4:2000911 ◽

2000 ◽

Vol 10 (PR9) ◽

pp. Pr9-63-Pr9-68 ◽

Cited By ~ 5

Author(s):

L. W. Meyer ◽

S. Abdel-Malek

Keyword(s):

Strain Rate ◽

Differential Effect ◽

Rate Dependence ◽

Strain Rate Dependence ◽

Strength Differential Effect ◽

Strength Differential

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Assessment of Extrapolation Relations of Displacement Speed for Detailed Chemistry Direct Numerical Simulation Database of Statistically Planar Turbulent Premixed Flames

Flow Turbulence and Combustion ◽

10.1007/s10494-021-00283-w ◽

2021 ◽

Author(s):

Nilanjan Chakraborty ◽

Alexander Herbert ◽

Umair Ahmed ◽

Hong G. Im ◽

Markus Klein

Keyword(s):

Numerical Simulation ◽

Direct Numerical Simulation ◽

Premixed Flames ◽

Turbulent Premixed Flames ◽

Reaction Progress ◽

Progress Variable ◽

Stretch Rate ◽

Non Linear ◽

Displacement Speed ◽

Curvature Dependence

AbstractA three-dimensional Direct Numerical Simulation (DNS) database of statistically planar $$H_{2} -$$ H 2 - air turbulent premixed flames with an equivalence ratio of 0.7 spanning a large range of Karlovitz number has been utilised to assess the performances of the extrapolation relations, which approximate the stretch rate and curvature dependences of density-weighted displacement speed $$S_{d}^{*}$$ S d ∗ . It has been found that the correlation between $$S_{d}^{*}$$ S d ∗ and curvature remains negative and a significantly non-linear interrelation between $$S_{d}^{*}$$ S d ∗ and stretch rate has been observed for all cases considered here. Thus, an extrapolation relation, which assumes a linear stretch rate dependence of density-weighted displacement speed has been found to be inadequate. However, an alternative extrapolation relation, which assumes a linear curvature dependence of $$S_{d}^{*}$$ S d ∗ but allows for a non-linear stretch rate dependence of $$S_{d}^{*}$$ S d ∗ , has been found to be more successful in capturing local behaviour of the density-weighted displacement speed. The extrapolation relations, which express $$S_{d}^{*}$$ S d ∗ as non-linear functions of either curvature or stretch rate, have been found to capture qualitatively the non-linear curvature and stretch rate dependences of $$S_{d}^{*}$$ S d ∗ more satisfactorily than the linear extrapolation relations. However, the improvement comes at the cost of additional tuning parameter. The Markstein lengths LM for all the extrapolation relations show dependence on the choice of reaction progress variable definition and for some extrapolation relations LM also varies with the value of reaction progress variable. The predictions of an extrapolation relation which involve solving a non-linear equation in terms of stretch rate have been found to be sensitive to the initial guess value, whereas a high order polynomial-based extrapolation relation may lead to overshoots and undershoots. Thus, a recently proposed extrapolation relation based on the analysis of simple chemistry DNS data, which explicitly accounts for the non-linear curvature dependence of the combined reaction and normal diffusion components of $$S_{d}^{*}$$ S d ∗ , has been shown to exhibit promising predictions of $$S_{d}^{*}$$ S d ∗ for all cases considered here.

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