If the instantaneous chemistry reaction rate is taken as ws = Bρ2Y1Y2 exp(−E/RT) = ρ2Y1Y2K, here K is a contraction for the exponential term. Then, ignoring the three order fluctuation correlation term, the average reaction rate could be ws = ρ2(Y1Y2K + Y1′Y2′K + Y1K′Y2′ + Y2K′Y1′). The authors have simulated jet combustion and swirl combustion using this kind of second order moment (SOM) turbulent combustion model. The predictions are close to experimental data in most regions. In order to improve the SOM turbulent combustion model, the effect of various correlation moments in the simulation of turbulent swirl combustion and NO formation is studied by comparing different SOM turbulence-chemistry models, including the unified second-order moment (USM) model, the model accounting for only the time-averaged reaction-rate coefficient, the model accounting for only the concentration fluctuation and the model accounting for both the time-averaged reaction-rate coefficient and the concentration fluctuation. These models are incorporated into the FLUENT code for a methane-air swirling combustion and NO formation under various swirl numbers. The magnitude of various correlations and their effect on the time-averaged reaction rate are analyzed, and the simulation results are compared with the corresponding measurement results. The results showed that the USM model gives the best agreement with the experimental results and among various correlation moments the correlation of reaction-rate coefficient fluctuation with the concentration fluctuation is most important. Additionally, a direct numerical simulation (DNS) of three-dimensional channel turbulent reacting flows with consideration of buoyancy effect using a spectral method was carried out. The statistical results are shown that K′Y′ are larger than Y1′Y2′.
Method for Measuring the Second-Order Moment of Atmospheric Turbulence
