Adjoint-Based Sensitivity and Optimization of Turbulent Reacting Flows

Abstract

Turbulent reacting flows drive many energy conversion devices and play crucial roles in the power generation and transportation sectors. Due to their chaotic and multi-scale nature, predicting and optimizing such systems is challenging. Over the past several decades, direct numerical simulation (DNS) and large-eddy simulation (LES) have gained in popularity within the scientific and engineering community for simulating this class of flows. However, owing to their high computational cost, they have primarily been used to investigate micro-scale physics or develop sub-grid scale models. Meanwhile, optimizing new engineering systems or improving existing devices requires iterating upon many design/input parameters. A brute-force trial-and-error approach involves performing many simulations and is thus not practical even with modern computational resources. Current approaches typically reduce the complexity of the model, which compromises its fidelity and decreases dimensionality of the physical system.

Discrete adjoint-based methods provide exact sensitivity of a quantity of interest (QoI) to many input parameters with a tractable computational cost. The sensitivity gradient obtained from an adjoint solution provides a direction to adjust parameters for minimizing (i.e., improving) the QoI. However, computing discrete adjoint sensitivity from high-fidelity numerical simulations like DNS or LES is challenging. Modern numerical methods are typically developed for solving the original governing equations and are not necessarily consistent with the discrete adjoint formulation.

The objective of this dissertation is to develop a high-fidelity numerical framework that provides exact sensitivity of a QoI for turbulent reacting flows. This builds off state-of-the-art numerical discretization methods and extends them to be compatible with a discrete adjoint solver. The adjoint sensitivity is combined with gradient-based optimization techniques to find optimal parameters. The numerical framework solves the multi-component compressible Navier--Stokes equations using high-order narrow-stencil finite difference operators that satisfy the summation-by-parts (SBP) property. Simultaneous-approximation-term boundary treatment is used to enforce the boundary conditions. A SBP adaptive artificial dissipation scheme with a compatible adjoint solver is introduced to minimize boundedness errors in the scalars and retain high-order accuracy of the solution. In addition, a flamelet/progress variable approach is employed for combustion modeling, and its adjoint is formulated. This approach avoids transporting many chemical species and makes the adjoint solver flexible with respect to the choice of chemical reactions. The adjoint solver makes use of an efficient check-pointing scheme, and it computes analytic Jacobians of the Navier--Stokes equations instead of automatically differentiating them. The cost of the combined forward-adjoint simulation is about 3--3.5 times the cost of the forward run.

The framework is applied to several challenging cases to assess its performance and demonstrate its efficacy in optimizing various QoIs. The methodology is used to enhance and suppress mixing and growth of high-resolution multi-mode Rayleigh--Taylor instabilities by strategically manipulating the interfacial perturbations. This example demonstrates the utility of the adjoint framework on chaotic variable-density flows before introducing complexities associated with chemical reactions and unboundedness of the mass fraction. Next, a momentum actuator is optimized to control the temporal evolution of scalar mixing in a shear layer, where more than one hundred million parameters are manipulated simultaneously by the adjoint solver. Using a coarse grid necessitates the adaptive dissipation scheme to preserve scalar boundedness. Finally, the adjoint solver is used to identify optimal forcing to control flame position in a non-premixed turbulent round jet.