Investigation of the effect of correlated uncertain rate parameters on a model of hydrogen combustion using a generalized HDMR method

The High Dimensional Model Representation (HDMR) method has been applied in several previous studies to obtain global sensitivity indices of uncorrelated model parameters in combustion systems. However, the rate parameters of combustion models are intrinsically correlated and therefore uncertainty analysis methods are needed that can handle such parameters. A generalized HDMR method is presented here, which uses the Rosenblatt transformation on a correlated model parameter sample to obtain a sample of independent parameters. The method provides a full set of both correlated and marginal sensitivity indices. Ignition delay times predicted by an optimized hydrogen-air combustion model in stoichiometric mixtures near the three explosion limits are investigated with this new global sensitivity analysis tool. The sensitivity indices which account for all the correlated effects of the rate parameters are shown to dominate uncertainties in the model output. However, these correlated indices mask the individual influence of parameters. The final marginal uncorrelated sensitivity indices for individual parameters better indicate the change of importance of homogeneous gas phase and species wall-loss reactions as the pressure is increased from above the first explosion limit to above the third limit. However, these uncorrelated indices are small and whilst they provide insights into the dominant chemical and physical processes of the model over the range of conditions studied, the correlations between parameters have a very significant effect. The implications of this result on model tuning will be discussed.