| Popis: |
The experimental data from the Cambridge-Sandia 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 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 reactive scalars in addition to the joint PDF of the conditioning variables, the manifold is applied to calculate the unconditional averages for each of the scalars. The mean values are also obtained by ensemble averaging all 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 decrease when using the third condition. Moreover, the experimental data are employed to obtain the marginal PDFs for the conditioning variables at various points in the reacting domain. The measurements are then combined from all positions in space to form conditional PDFs of the normalized total enthalpy for various values of the other two variables. The correlation coefficients between the conditioning variables are also investigated. Next, to consider the association between the conditioning variables for modeling, the copula concept is introduced, and the performance of three different copulas are tested. Furthermore, the statistical moments of the conditioning variables are computed from the experimental data at different points and are utilized for modeling the joint PDF of the conditioning variables from two different approaches which are compared. |
