Approximate models for optimal control of turbulent channel flow

Abstract

Advances in high-performance computing and Large-Eddy Simulation (LES) have made it possible to obtain accurate solutions of complex, turbulent flows at moderate Reynolds numbers. With these advances, computational modeling of turbulent flows in order to develop, evaluate, and optimize active control strategies is feasible. In this thesis, we present approaches to numerical modeling of opposition control and optimal control of turbulent flows with attention to algorithms that utilize the dynamic subgrid-scale LES model. Approximately 25% drag reduction is achieved by opposition control using LES, which is in good agreement with previous DNS results at a low Reynolds number of Retau = 180. Based on this success, we have used our LES approach to extend opposition control to a high Reynolds number flow of Retau = 590. With the sensing location at y+ ≈ 15, which is the best sensing plane for Retau = 180, only 21% drag reduction can be achieved, suggesting that opposition control is less effective at higher Reynolds numbers. An optimal control scheme based on LES has been implemented successfully using an instantaneous control approach with a nonlinear conjugate gradient algorithm used to update the control. The flow sensitivity is computed from the adjoint LES equations which are presented herein, and LES results are compared to prior DNS results for optimal control under similar conditions at Retau = 100. These comparisons indicate that optimal control based on LES can relaminarize low Reynolds number turbulent channel flow similar to results obtained using DNS but with significantly lower computational expense. Optimal control is also explored for turbulent channel flow at Retau = 180. At this Reynolds number, our optimal control approach is not as effective as the results at Retau = 100, the flow eventually enters a statistically stable state with approximately 40% drag reduction. Some possible ways to improve the control effectiveness are discussed, including the use of the discrete adjoint equations. Results are also presented for a novel hybrid LES/DNS scheme in which the optimization iterations are performed using LES while the flow is advanced in time using DNS for flow at Retau = 100. These hybrid simulations retain the computational efficiency of LES and the accuracy of DNS. Results from hybrid simulations clearly demonstrate that the controls computed based on LES optimization are also viable in the context of DNS. In all cases, the agreement between LES, DNS, and hybrid LES/DNS indicates that reliable turbulence control strategies can be efficiently developed based on LES models. We conclude that LES can be used as a reduced order model for optimal control of turbulence and this conclusions is shown to hold for even low resolution LES. The control mechanisms for drag reduction using opposition control and optimal control are discussed. Opposition control creates a virtual wall that affects all scales of turbulent motions near the physical wall. In contrast, optimal control creates a virtual wall for the large scale roll mode of the turbulent flow. Since this virtual wall affects directly the scales of motion responsible for increased drag in a turbulent flow, the optimal control is able to achieve larger drag reductions