Large eddy simulation and turbulence control

Abstract

This paper reviews LES methods, based on the dynamic subgrid-scale model, that greatly improve the efficiency of turbulence control simulations in the context of drag reduction for plane turbulent channel flow. We begin by performing simulations of opposition control at Reynolds numbers in the range Re τ = 100 to 590 which demonstrate a decrease in effectiveness of this control strategy with increased Reynolds number. We then review techniques for optimal control of turbulent flows and discuss our implementation using an instantaneous control framework where the flow sensitivity is computed from the adjoint LES equations. Detailed optimal control results are presented that demonstrate excellent agreement with available DNS at a fraction of the computational expense. Given the added efficiency of LES, a receding horizon control framework is also explored that results in increased drag reduction along with improved control distributions. Results are also presented for a hybrid LES/DNS method where optimization is performed using LES but the flow is advanced using DNS. This approach demonstrates that even coarse grid LES can serve as a viable reduced order model for DNS. In our ongoing efforts to seek greater model reductions for predictive control, we also explore the influence of control on the basis functions obtained from proper orthogonal decomposition.

DNS and LES of estimation and control of transition in boundary layers subject to free-stream turbulence

“…An example of a robust controller that addresses that problem is described by Bewley et al (2000). Other examples of application of nonlinear controllers are Berggren (1998), Bewley et al (2001) and Collis et al (2000).…”

Investigation of a continuous adjoint-based optimization procedure for aeroacoustic control of plane jets

“…For each time window, however, a longer control interval T c > T p is chosen. This procedure reduces errors associated with the gradient direction and could be shown by Collis et al (2000) to improve results in channel flow simulations in some circumstances considerably. The applicability of this approach is furthermore investigated in this paper, too, since the possibility to control flows over long time intervals is of practical relevance.…”

“…Recently, there have been several successful attempts using the adjoint equations in shape optimization (Kuruvila et al, 1994;Anderson and Venkatakrishnan, 1999;Giles and Pierce, 2000;Jameson, 2001;Brezillon and Gauger, 2004;Giering et al, 2005;Carpentieri et al, 2007;Zymaris et al, 2009;Peter and Dwight, 2010;Srinath and Mittal, 2010;Zymaris et al, 2010;Jameson and Ou, 2011), optimal boundary control (Bewley et al, 2001;Collis et al, 2000;Collis et al, 2004) and optimal noise control (Cerviño and Bewley, 2002;Joslin et al, 2005;Wei and Freund, 2006;Spagnoli and Airiau, 2008;Babucke et al, 2009;Kim et al, 2010;Rumpfkeil and Zingg, 2010;Schulze et al, 2011). However, because of the expensive iterative optimization procedure, which involves solving the adjoint equations backward in time and which necessitates the storage of the flow fields obtained during the solution of the Navier-Stokes equations, calculations for the purpose of noise reduction have been carried out almost exclusively for 2D-DNS only and recently for 3D-LES in Kim et al (2010).…”

“…The influence of the length of the control interval was investigated for example for channel flow drag reduction by Collis et al (2000) and Bewley et al (2001). They both showed that intervals larger than a certain threshold were required for full laminarization of the flow.…”

Numerical Solution of Optimal Control Problems Governed by the Compressible Navier-Stokes Equations

“…Optimal control problems have been studied mathematically and numerically for steady and unsteady incompressible Navier-Stokes flow. The references [1,2,5,11,12] present a small sample of the work in this area. Compressible steady state Euler equations and Navier-Stokes equations have been used in the context of optimal design, see, e.g., [3,14,15,16,21].…”