Reduced-Order Modelling for Flow Control

Abstract

All contributions have been typeset by the authors. ,6%1 6SULQJHU:LHQ1HZ<RUN FOREWORD Practical interests in flow control have no longer to be demonstrated. Flow control has motivated rapid developments in the past two decades in experiments, flow stability theory and computational fluid dynamics (CFD). Recent advances in experimental studies include applications of more and more sophisticated actuators and sensors. However, up to now, most of the results are predominantly related to open loop, at most, adaptive approaches. Early closed-loop applications of control methods were in noise control based on antinoise concepts. These studies established the pioneering link between fluid mechanics and control theory. However, in most aerodynamic applications, turbulent flows are encountered. Due to the intrinsic nonlinearities, turbulence gives rise to a large variety of temporal and spatial scales of more or less organized nature. Turbulence has remained one of the last not satisfactorily resolved physical phenomenon of practical importance in engineering sciences. It is obvious that the complexity of these flows is so pronounced that simpler -if this term can be used for turbulent flows -descriptions need to be derived.The encountered complexity is observed at three levels. First, the characterization of the flow itself is complex and depends on the type of available information (e.g. sensors). Any state information is by nature incomplete or of excessive extent for turbulent flows. Second, the effect of any actuator is by nature 3D and unsteady, thus difficult to characterize. Third, the complete modelling of the flow (CFD), its sensitivity to perturbations, etc. exceeds available computer power by many orders of magnitudes, particularly for online capability in experiment. In the same vein, the predominantly (locally) linear approaches of control theory need to be adapted to the reality of the complex, turbulent flow characteristics. This leads to different levels of fluid mechanics one has to take into account. These levels can start from a detailed fluid mechanics characterization, including the more or less organized nature of the turbulent flows, the so called white-box model and end with entirely black and eventually 'empty-box' models.The communities of flow control, applied mathematics and turbulence in fluids have then to work altogether in a close manner. Each domain enriches the other for the dedicated goal of controlling different types of flows. No currently available approach can be re-tained, due to the variability of the physics to be controlled (e.g. flow separation, drag, lift, mixing, noise generation and fluid structure interactions). The present volume is written by leading experts of flow control and represents the state of the art of the different approaches whose complementarity will open new areas by mutual fertilization.Abstract Constrained optimization is presented as a key enabler for answering numerous important questions in the heart of flow control. These problems range from the extrac...

A nonmonotone line search for the LBFGS method in parabolic optimal control problems

“…Also, t f denotes the final time. The control problem (8) -(11) is a nonlinear parabolic optimal control problem and is widely applied in flow control [23]. Recently, many efforts have been devoted to the development of the optimal control techniques for the Burgers equation [18,26,31,36].…”

“…This example is an optimal flow control problem and corresponds to a target optimal control problem. ( [23], section 7.2). Two targets z(x, t) and f (x) are generally determined based on physical arguments such as laminar flow and solutions of minimum drag.…”

Reduced-Order Model Approaches for Predicting Airfoil Performance

“…As a matter of fact, when employing reduced-order models one encounters several drawbacks, for instance, the introduction of unphysical artifacts and instabilities (Noack et al [19]), the loss of fidelity at fine temporal and spatial scales (Taira et al [20]), and the inability to accurately predict rare or extreme events due to nonlinear interactions (Racca and Magri [21]). Cluster-based network modeling (CNM) stands as a robust approach for investigating complex nonlinear dynamics using data (Fernex et al [22]).…”

A simple trick to improve the accuracy of PIV/PTV data

“…In fluid mechanics, for example, the extension of PCA onto POD aimed at using such dimensionality reduction methods to identify coherent structures in turbulent flows [1,9,17]. In computational physics, the Galerkin projection of a PDE onto these modes is the cornerstone to reduce the computational cost of large simulations [18], to build a reduced order model that enables model-based control [19,20] and to derive more efficient Large Eddy Simulation formulations [21]. In climatology, the EOF [2,22,23] has been developed to identify and analyze dominant patterns of variability in climate data and to reduce the dimensionality of large climate datasets.…”