Article

A low-dimensional model of separation bubbles

Department of Mechanical Engineering, University of California at Santa Barbara, Santa Barbara, United States; Control & Dynamical Systems, California Institute of Technology, Pasadena, United States; Mechanical, Materials, and Aerospace Engineering Department, Illinois Institute of Technology, Chicago, United States
Physica D Nonlinear Phenomena (Impact Factor: 1.67). 07/2009; DOI: 10.1016/j.physd.2009.03.017
Source: OAI

ABSTRACT In this work, motivated by the problem of model-based predictive control of separated flows, we identify the key variables and the requirements on a model-based observer and construct a prototype low-dimensional model to be embedded in control applications.Namely, using a phenomenological physics-based approach and dynamical systems and singularity theories, we uncover the low-dimensional nature of the complex dynamics of actuated separated flows and capture the crucial bifurcation and hysteresis inherent in separation phenomena. This new look at the problem naturally leads to several important implications, such as, firstly, uncovering the physical mechanisms for hysteresis, secondly, predicting a finite amplitude instability of the bubble, and, thirdly, to new issues to be studied theoretically and tested experimentally.

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    ABSTRACT: A low-order point vortex model for the two-dimensional unsteady aerodynamics of a flat plate wing section is developed. A vortex is released from both the trailing and leading edges of the flat plate, and the strength of each is determined by enforcing the Kutta condition at the edges. The strength of a vortex is frozen when it reaches an extremum, and a new vortex is released from the corresponding edge. The motion of variable-strength vortices is computed in one of two ways. In the first approach, the Brown–Michael equation is used in order to ensure that no spurious force is generated by the branch cut associated with each vortex. In the second approach, we propose a new evolution equation for a vortex by equating the rate of change of its impulse with that of an equivalent surrogate vortex with identical properties but constant strength. This impulse matching approach leads to a model that admits more general criteria for shedding, since the variable-strength vortex can be exchanged for its constant-strength surrogate at any instant. We show that the results of the new model, when applied to a pitching or perching plate, agree better with experiments and high-fidelity simulations than the Brown–Michael model, using fewer than ten degrees of freedom. We also assess the model performance on the impulsive start of a flat plate at various angles of attack. Current limitations of the model and extensions to more general unsteady aerodynamic problems are discussed.
    Theoretical and Computational Fluid Dynamics 27(5). · 0.88 Impact Factor

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