Direct numerical simulations (DNS) and optimal control theory are used in a predictive
control setting to determine controls that effectively reduce the turbulent kinetic
energy and drag of a turbulent flow in a plane channel at
Reτ = 100 and Reτ = 180.
Wall transpiration (unsteady blowing/suction) with zero net mass flux is used as the
control. The algorithm used for the control optimization is based solely on the control
objective and the nonlinear partial differential equation governing the flow, with no
ad hoc assumptions other than the finite prediction horizon, T, over which the control
is optimized.Flow relaminarization, accompanied by a drag reduction of over 50%, is obtained
in some of the control cases with the predictive control approach in direct numerical
simulations of subcritical turbulent channel flows. Such performance far exceeds what
has been obtained to date in similar flows (using this type of actuation) via adaptive
strategies such as neural networks, intuition-based strategies such as opposition
control, and the so-called ‘suboptimal’ strategies, which involve optimizations over a
vanishingly small prediction horizon T+ → 0. To achieve flow relaminarization in the
predictive control approach, it is shown that it is necessary to optimize the controls
over a sufficiently long prediction horizon T+ [gsim ] 25. Implications of this result are
discussed.The predictive control algorithm requires full flow field information and is computationally
expensive, involving iterative direct numerical simulations. It is, therefore,
impossible to implement this algorithm directly in a practical setting. However, these
calculations allow us to quantify the best possible system performance given a certain
class of flow actuation and to qualify how optimized controls correlate with the
near-wall coherent structures believed to dominate the process of turbulence production
in wall-bounded flows. Further, various approaches have been proposed to
distil practical feedback schemes from the predictive control approach without the
suboptimal approximation, which is shown in the present work to restrict severely
the effectiveness of the resulting control algorithm. The present work thus represents
a further step towards the determination of optimally effective yet implementable
control strategies for the mitigation or enhancement of the consequential effects of
turbulence.
Review of Control and Energy Management Approaches in Micro-Grid Systems