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Modeling and control of the wakes in rigid and flexible canopies


In this thesis, we introduced a model based on momentum entrainment to investigate the interaction of fluid flow with canopies of solid elements. We have used this model for different canopy types and flow situations to control the wakes and optimize the design factors and energy efficiency for a variety of applications.

In the first section, the model is used to introduce a new design for cost reduction of CO2 direct air capture systems. Although Direct Air Capture of CO2 has the potential to be a large source of negative carbon emissions, the design still needs to be much more cost effective and energy efficient to be economically viable. The land required for DAC systems is considerably less than other carbon renewal methods like biomass and reforestation; and currently the high cost is the most limiting factor for wide usage of DAC. Fair amount of work has been done to explore and optimize the internal system and chemical reactions, whereas the fluid mechanics and external design have been neglected. We developed a model to explore flow and carbon mass field for optimal design and cost reduction of DAC systems. Using this model, we have explored a new design based on thinner absorbers spread in a larger land area which can be effectively operated by wind flow if placed in regions with sufficient wind potential.

In the second section, a more generalized form of the model is developed to estimate the flow power loss through flexible vegetation canopies. Performing accurate estimates of bottom friction in tidal channels is essential to obtain precise assessments of the fluid power available for extraction by arrays of turbines. The presence of vegetation canopies can increase the bottom drag coefficient and change the velocity profile considerably. In order to improve available estimations of drag coefficients, we developed a model that is applicable to rigid and flexible canopies in both fully developed and developing flow regions. The results were validated by performing new experiments and setting up comparisons with past theories and experimental data. We found that the total drag force is highly affected by the flexibility of the vegetation. The pattern and length of the canopy can also increase the drag force by changing the length of developing flow through the canopy. Based on our results, the drag force is highly underestimated in the regions where vegetation canopies tend to grow.

Lastly, the third section addresses the characterization and control of vortical flows, which are primarily responsible for momentum entrainment into the canopies. We apply the Koopman mode representation (through an SVD-enhanced DMD algorithm) to co-rotating, patch-like vortices in inviscid and viscous flows. We recover the linear stability eigenvalues and eigenmodes. We show that Koopman mode analysis can detect qualitatively distinct stages of vortex merger. By applying Koopman mode decomposition to symmetric and asymmetric vortices, we quantitatively characterize the dynamics of each instability, and propose a criterion for symmetry-breaking. These results suggest a path forward towards using KMD for data-driven modeling of vortex flows.

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