Sensitivity calculations in PDF particle methods

In combustion modeling, it is desirable to know how sensitive the predictions are to certain parameters in the model formulation. In this study, we develop a method for accurate and efficient sensitivity calculation in PDF modeling of turbulent combustion. This method enables the calculation of the sensitivities for each particle in PDF particle methods. These particle-level sensitivities are very revealing. They allow one to examine the particles with the largest sensitivities, and the corresponding compositions reveal the sensitive region of composition space. By ensemble averaging the particle sensitivities, sensitivities of mean (and conditional mean) quantities can be extracted. The method is applied to the PDF calculations of the oxidation of diluted hydrogen in a partially stirred reactor (PaSR) using three different mixing models. It is demonstrated that the method is capable of accurately calculating the sensitivities at the particle level. The study also illustrates the qualitatively different behavior of the three mixing models as revealed by both the particle composition and the particle sensitivities. The sensitivities of mean (and conditional mean) quantities reveal the controlling processes in a PaSR. They confirm that when combustion is controlled by mixing, the combustion is insensitive to chemistry; when the system is close to global extinction, the combustion is extremely sensitive both to mixing and to chemistry.