"Fluid-structure interaction arises in a wide array of technological applications including naval and marine hydrodynamics, civil and wind engineering and flight vehicle aerodynamics. When a fluid flows over a bluff body such as a circular cylinder, the periodic vortex shedding in the wake causes fluctuating lift and drag forces on the body. This phenomenon can lead to fatigue damage of the structure due to large amplitude vibration. It is widely believed that the wake structures behind the structure determine the hydrodynamic forces acting on the structure and control of wake structures can lead to vibration control of the structure. Modeling this complex non-linear interaction requires coupling of the dynamics of the fluid and the structure. In this thesis, however, the vibration of the flexible cylinder is prescribed, and the focus is on modeling the fluid dynamics in its wake. Low-dimensional iterative circle maps have been found to predict the universal dynamics of a two-oscillator system such as the rigid cylinder wake. Coupled map lattice (CML)models that combine a series of low-dimensional circle maps with a diffusion model have previously predicted qualitative features of wake patterns behind freely vibrating cables at low Reynolds number. However, the simple nature of the CML models implies that there will always be unmodelled wake dynamics if a detailed, quantitative comparison is made with laboratory or simulated wake flows. Motivated by a desire to develop an improved CML model, we incorporate self-learning features into a new CML that is trained to precisely estimate wake patterns from target numerical simulations and experimental wake flows. The eventual goal is to have the CML learn from a laboratory flow in real time. A real-time self-learning CML capable of estimating experimental wake patterns could serve as a wake model in a future anticipated feedback control system designed to produce desired wake patterns. A new convective-diffusive map that includes additional wake dynamics is developed. Two different self-learning CML models, each capable of precisely estimating complex wake patterns, have been developed by considering additional dynamics from the convective-diffusive map. The new self-learning CML models use adaptive estimation schemes which seek to precisely estimate target wake patterns from numerical simulations and experiments. In the first self-learning CML, the estimator scheme uses a multi-variable least-squares algorithm to adaptively vary the spanwise velocity distribution in order to minimize the state error (difference between modeled and target wake patterns). The second self-learning model uses radial basis function neural networks as online approximators of the unmodelled dynamics. Additional unmodelled dynamics not present in the first self-learning CML model are considered here. The estimator model uses a combination of a multi-variable normalized least squares scheme and a projection algorithm to adaptively vary the neural network weights. Studies of this approach are conducted using wake patterns from spectral element based NEKTAR simulations of freely vibrating cable wakes at low Reynolds numbers on the order of 100. It is shown that the self-learning models accurately and efficiently estimate the simulated wake patterns within several shedding cycles. Next, experimental wake patterns behind different configurations of rigid cylinders were obtained. The self-learning CML models were then used for off-line estimation of the stored wake patterns. With the eventual goal of incorporating low-order CML models into a wake pattern control system in mind, in a related study control terms were added to the simple CML model in order to drive the wake to the desired target pattern of shedding. Proportional, adaptive proportional and non-linear control techniques were developed and their control efficiencies compared."
Worcester Polytechnic Institute
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Balasubramanian, G. (2003). Low-order coupled map lattices for estimation of wake patterns behind vibrating flexible cables. Retrieved from https://digitalcommons.wpi.edu/etd-dissertations/378
fluid-structure interaction, low dimensional models, coupled map lattices, vortex shedding, cylinder wake patterns, flow control, multi-variable least squares algorithm, neural networks, adaptive estimation, Fluid dynamics, Wakes (Fluid dynamics), Vibration