A discrete-adjoint framework for optimizing high-fidelity simulations of turbulent reacting flows

Abstract

An adjoint-based framework is presented that measures exact sensitivity from high-fidelity simulations of turbulent reacting flows. The framework leverages and extends state-of-the-art numerical methods in a manner that is compatible with a discrete adjoint solver. To ensure energy stability and accuracy, high-order narrow-stencil finite-difference operators satisfying the summation-by-parts (SBP) property are combined with simultaneous-approximation-term boundary treatment. An adaptive SBP dissipation operator and its corresponding adjoint are formulated in a way to dampen unresolved modes and preserve scalar boundedness. A flamelet/progress variable approach is employed to handle chemical reactions using tabulated chemistry. The utility of using pre-computed lookup tables is that discrete adjoint sensitivity can be computed efficiently for arbitrary chemical mechanisms. Gradient-based optimization utilizing the sensitivity obtained from the adjoint solution is demonstrated on two configurations. First, momentum actuation is applied upstream in a spatial mixing layer to control the evolution of a passive scalar in a target region downstream. Then, the framework is used to optimize an acoustic actuator in a three-dimensional turbulent jet with the aim of anchoring an H2 lifted flame at a target location. Both cases involve manipulating discrete space-time fields with O(108)−O(109) degrees of freedom, which would not be possible via a brute-force trial-and-error approach.