Scaling of reaction progress variable variance in highly turbulent reaction waves

2021 ◽  
Vol 33 (8) ◽  
pp. 085103
Author(s):  
V. A. Sabelnikov ◽  
A. N. Lipatnikov
Keyword(s):  
Reaction Progress ◽  
Progress Variable

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

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.

A Generalized FGM Progress Variable Weight Optimization Using HEEDS

2017 ◽  
Author(s):  
Graham Goldin ◽  
Yongzhe Zhang
Keyword(s):  
Constant Pressure ◽  
Operating Conditions ◽  
Weighted Sum ◽  
Weight Optimization ◽  
Reaction Progress ◽  
Optimization Software ◽  
Progress Variable ◽  
Flamelet Generated Manifold ◽  
Variable Weight ◽  
Mass Fractions

The Flamelet Generated Manifold (FGM) model requires a reaction progress variable which is usually defined as a weighted sum of species mass fractions. This progress variable should increase monotonically as flamelet states progress from unburnt to chemical equilibrium. A favorable attribute of the progress variable is that the flamelet species should change gradually with the progress variable, which reduces sensitivity of these species to any predicted errors in the progress variable. Previous publications have presented optimization algorithms for specific flamelet operating conditions, including fuel and oxidizer compositions and temperatures, and pressures. This work applies the HEEDS optimization software to find optimal species weights for a range of fuels and operating conditions. The fuels included are methane, methane-hydrogen, n-dodecane and n-heptane, at fuel-oxidizer temperatures of 293K and 1000K, and pressures of 1 and 30 atmospheres. For manifolds modeled by constant pressure ignition reactors, the optimal progress variable weights using four species weights are {αCO2 = 1, αCO = 0.91, αH2O = 0.52, αH2 = 1}, and for eight species weights are {αCO2 = 1, αCO = 0.91, αH2O = 0.51, αH2 = 1, αC2H2 = 0.16, αOH = −0.66, αH = −0.38, αO = 0.4}.

scholarly journals Effects of Lewis number on the statistics of the invariants of the velocity gradient tensor and local flow topologies in turbulent premixed flames

2018 ◽  
Vol 474 (2212) ◽  
pp. 20170706 ◽  
Author(s):  
Daniel Wacks ◽  
Ilias Konstantinou ◽  
Nilanjan Chakraborty
Keyword(s):  
Velocity Gradient ◽  
Joint Probability ◽  
Lewis Number ◽  
Gradient Tensor ◽  
Local Flow ◽  
Reaction Progress ◽  
Velocity Gradient Tensor ◽  
Progress Variable ◽  
Joint Probability Density ◽  
Turbulent Premixed

The behaviours of the three invariants of the velocity gradient tensor and the resultant local flow topologies in turbulent premixed flames have been analysed using three-dimensional direct numerical simulation data for different values of the characteristic Lewis number ranging from 0.34 to 1.2. The results have been analysed to reveal the statistical behaviours of the invariants and the flow topologies conditional upon the reaction progress variable. The behaviours of the invariants have been explained in terms of the relative strengths of the thermal and mass diffusions, embodied by the influence of the Lewis number on turbulent premixed combustion. Similarly, the behaviours of the flow topologies have been explained in terms not only of the Lewis number but also of the likelihood of the occurrence of individual flow topologies in the different flame regions. Furthermore, the sensitivity of the joint probability density function of the second and third invariants and the joint probability density functions of the mean and Gaussian curvatures to the variation in Lewis number have similarly been examined. Finally, the dependences of the scalar--turbulence interaction term on augmented heat release and of the vortex-stretching term on flame-induced turbulence have been explained in terms of the Lewis number, flow topology and reaction progress variable.

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