Parametric uncertainty and sensitivity methods for reacting flows
A Bayesian framework for quantification of uncertainties has been used to quantify the uncertainty introduced by chemistry models. This framework adopts a probabilistic view to describe the state of knowledge of the chemistry model parameters and simulation results. Given experimental data, this method updates the model parameters' values and uncertainties and propagates that parametric uncertainty into simulations. This study focuses on syngas, a combination in various ratios of H2 and CO, which is the product of coal gasification. Coal gasification promises to reduce emissions by replacing the burning of coal with the less polluting burning of syngas. Despite the simplicity of syngas chemistry models, they nonetheless fail to accurately predict burning rates at high pressure. Three syngas models have been calibrated using laminar flame speed measurements. After calibration the resulting uncertainty in the parameters is propagated forward into the simulation of laminar flame speeds. The model evidence is then used to compare candidate models.
Sensitivity studies, in addition to Bayesian methods, can be used to assess chemistry models. Sensitivity studies provide a measure of how responsive target quantities of interest (QoIs) are to changes in the parameters. The adjoint equations have been derived for laminar, incompressible, variable density reacting flow and applied to hydrogen flame simulations. From the adjoint solution, the sensitivity of the QoI to the chemistry model parameters has been calculated. The results indicate the most sensitive parameters for flame tip temperature and NOx emission. Such information can be used in the development of new experiments by pointing out which are the critical chemistry model parameters.
Finally, a broader goal for chemistry model development is set through the adjoint methodology. A new quantity, termed field sensitivity, is introduced to guide chemistry model development. Field sensitivity describes how information of perturbations in flowfields propagates to specified QoIs. The field sensitivity, mathematically shown as equivalent to finding the adjoint of the primal governing equations, is obtained for laminar hydrogen flame simulations using three different chemistry models. Results show that even when the primal solution is sufficiently close for the three mechanisms, the field sensitivity can vary.