46 research outputs found
Controlling the onset of turbulence by streamwise traveling waves. Part 2. Direct numerical simulations
This work builds on and confirms the theoretical findings of Part 1 of this
paper, Moarref & Jovanovi\'c (2010). We use direct numerical simulations of the
Navier-Stokes equations to assess the efficacy of blowing and suction in the
form of streamwise traveling waves for controlling the onset of turbulence in a
channel flow. We highlight the effects of the modified base flow on the
dynamics of velocity fluctuations and net power balance. Our simulations verify
the theoretical predictions of Part 1 that the upstream traveling waves promote
turbulence even when the uncontrolled flow stays laminar. On the other hand,
the downstream traveling waves with parameters selected in Part 1 are capable
of reducing the fluctuations' kinetic energy, thereby maintaining the laminar
flow. In flows driven by a fixed pressure gradient, a positive net efficiency
as large as 25 % relative to the uncontrolled turbulent flow can be achieved
with downstream waves. Furthermore, we show that these waves can also
relaminarize fully developed turbulent flows at low Reynolds numbers. We
conclude that the theory developed in Part 1 for the linearized flow equations
with uncertainty has considerable ability to predict full-scale phenomena.Comment: To appear in J. Fluid Mec
Design of Optimal Sparse Feedback Gains via the Alternating Direction Method of Multipliers
We design sparse and block sparse feedback gains that minimize the variance
amplification (i.e., the norm) of distributed systems. Our approach
consists of two steps. First, we identify sparsity patterns of feedback gains
by incorporating sparsity-promoting penalty functions into the optimal control
problem, where the added terms penalize the number of communication links in
the distributed controller. Second, we optimize feedback gains subject to
structural constraints determined by the identified sparsity patterns. In the
first step, the sparsity structure of feedback gains is identified using the
alternating direction method of multipliers, which is a powerful algorithm
well-suited to large optimization problems. This method alternates between
promoting the sparsity of the controller and optimizing the closed-loop
performance, which allows us to exploit the structure of the corresponding
objective functions. In particular, we take advantage of the separability of
the sparsity-promoting penalty functions to decompose the minimization problem
into sub-problems that can be solved analytically. Several examples are
provided to illustrate the effectiveness of the developed approach.Comment: To appear in IEEE Trans. Automat. Contro