Adjoint-based sensitivity analysis of steady char burnout

Simulations of pulverised coal combustion rely on various models, required in order to correctly approximate the flow, chemical reactions, and behaviour of solid particles. These models, in turn, rely on multiple model parameters, which are determined through experiments or small-scale simulations and contain a certain level of uncertainty. The competing effects of transport, particle physics, and chemistry give rise to various scales and disparate dynamics, making it a very challenging problem to analyse. Therefore, the steady combustion process of a single solid particle is considered as a starting point for this study. As an added complication, the large number of parameters present in such simulations makes a purely forward approach to sensitivity analysis very expensive and almost infeasible. Therefore, the use of adjoint-based algorithms, to identify and quantify the underlying sensitivities and uncertainties, is proposed. This adjoint framework bears a great advantage in this case, where a large input space is analysed, since a single forward and backward sweep provides sensitivity information with respect to all parameters of interest. In order to investigate the applicability of such methods, both discrete and continuous adjoints are considered, and compared to the conventional approaches, such as finite differences, and forward sensitivity analysis. Various quantities of interest are considered, and sensitivities with respect to the relevant combustion parameters are reported for two different free-stream compositions, describing air and oxy atmospheres. This study serves as a benchmark for future research, where unsteady and finally turbulent cases will be considered.