Evaluation of manifold representations of chemistry in stratified, swirl-stabilized flames

Abstract

The validity of assuming that a simple, low-dimensional manifold can sufficiently accurately represent the chemical state in a turbulent flame is investigated. The experimental data from the Cambridge/Sandia stratified swirl burner working in nine different configurations are post-processed to explore the effects of coordinate, swirl flow ratio, and stratification factor on the conditionally-averaged reactive scalars. First, the mixture fraction and thermal progress variable are employed to construct a two-dimensional conditional manifold by using all of the data – regardless of the coordinate in the physical domain, swirl ratio, and stratification factor. Moreover, one-point, one-time measurements are utilized to compute the exact joint Probability Density Function (PDF) of the conditioning variables at each point. Having the conditional averages of temperature and mass fractions of CO2, CO, CH4, H2, and H2O in addition to the joint PDF of the conditioning variables, the low-dimensional manifold is applied to calculate the unconditional averages for each of the scalars. The mean values are also obtained by ensemble averaging all of the data available for each of the measuring points, and the discrepancies between the values calculated from the two approaches are reported in order to assess the validity of the assumptions underlying the low-dimensional chemistry representations. The results suggest that the two chosen conditioning variables are not sufficient to make the manifold independent of the real domain, so, the normalized total enthalpy is introduced as the third conditioning variable and the process repeated. Results obtained from the three-condition manifold demonstrate that the discrepancies for prediction of the reactive scalars, more significantly for CO2 and CO mass fractions, decrease when using the third condition. The discrepancies with three conditions show that a three-dimensional manifold is sufficient to assume the conditional averages are independent of swirl and stratification. A normalized accumulated discrepancy is used as a metric for each of the cases so one can see the overall effect of each assumption that is made for constructing the conditional manifold. Decoupling the manifold from the coordinate, swirl ratio, and stratification level makes it possible to obtain the filtered chemical source-terms from a static lookup table for many flames which will considerably reduce the computational cost for simulating turbulent reacting flows.