Sensitivity calculations in PDF modelling of turbulent flames

In modelling turbulent combustion, it is desirable to know the sensitivities of the predictions to certain parameters. Recently, a method for calculating particle-level sensitivities in PDF modelling of turbulent combustion has been described by Ren and Pope [1]. In this work, we develop a methodology for the efficient calculation of these particle-level sensitivities using in situ adaptive tabulation. In addition, PDF calculations with sensitivities of the Cabra H2/N2 jet flame are performed to investigate the sensitivities of the predictions to certain important parameters. The accuracy of the proposed methodology is demonstrated by comparing its prediction of sensitivities with those obtained by divided difference. For the Cabra flame, the sensitivities confirm that the predictions are extremely sensitive to the coflow temperature: the sensitivities to coflow temperature are about 10 times larger than those to chemistry, and about 100 times larger than those to the mixing model constant. The particle-level sensitivities show that, at the flame base, strong chemical reactions start at in very fuel-lean region, which indicates that this region is important to the stabilization of the flame. The sensitivities also indicate the physical regions where the effects of different parameters are significant. Further insights are obtained by investigating the compositions and the sensitivity vectors in the composition space. The most sensitive particles are found to lie close to a saddle-shaped two-dimensional manifold, and the sensitivity vectors are generally tangential to the manifold. The singular value decomposition of the sensitivity matrices reveals that there is only one significant singular value and hence there is a dominant direction of the response to a change in the sensitivity parameters considered. Similarities in particle sensitivities are also illustrated. Similar PDF calculations (with sensitivities) of the Barlow and Frank flame F are reported in the Supplementary material. 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved.