Optimization of a Vortex Induced Vibrations Energy Harvester

Machine Learning (ML), data driven modeling and optimization have extensive use in the technology industry with applications ranging anywhere from fraud detection to image recognition to self-driving vehicles. One field for these techniques to grow is the field of fluid mechanics where the advancements of more powerful computers allows for the processing of large datasets into knowledge about optimization and flow control of systems in fluids. Our project focuses on using a multiobjective evolutionary algorithm in conjunction with computational fluid dynamics using OpenFOAM as compared to more traditional methods to analysis. Using optimization methods such as NSGA-II allows us to explore a large parameter space that would otherwise be restricted to a couple of cases. Using the NSGA-II algorithm as the optimization method, we were able to explore a large parameter space across two optimization methods to develop an optimal mechanical system.

WHAT MAKES OUR DESIGN INNOVATIVE

WHAT MAKES OUR DESIGN SOLUTION EFFECTIVE

The NSGA-II algorithm used for the optimization method allows for us to efficiently explore the parameter space of mass, stiffness and damping across two objective functions. Having the ability to analyze a two-objective problem, we can confidently address the effect different physical parameters have on the amplitude, velocity, and power generation of the cylinder. Additionally, NSGA-II is a fast sorting and an elite multi-objective evolutionary algorithm commonly used for similar optimization problems. As a validated and common model, we are confident in its ability to sort, rank and create parameters that consistently explore new parameters spaces which improve the results of the objective functions evaluated.

Additionally, the parameter space we explored is purely non-dimensional. This allows the group to easily scale the results to different scenarios and flow environments. Different flow conditions create different flow physics, and the fluid structure interactions can become highly complex and unpredictable. Non-dimensional mechanical parameters allow us to easily adapt the mechanical system to different flow fields that our system can be used in. For example, scaling from a river flowing at 1 knot requires different dimensional quantities for mass, stiffness and damping compared to a flow speed of 2 knots. This method ultimately allows us to generate a universal solution to the optimization problem that is easily scalable.

To ensure a realistic, and scalable outcome from the optimization process our group undertook, the decision was made to non-dimensionalize the complete parameter space. This decision is made because it allows for easy validation of our results with those obtained through research by other academic scholars studying the field. The three parameters that make up our space are:

Our results were validated by comparing the optimized parameters with literature reference values for the same non-dimensional parameters. P.W. Bearman’s research paper on flow-induced vibrations at low Reynolds number is used as an initial baseline to compare how our reduced velocity parameter converged compared to the results provided in this research paper. What we find is that the range for reduced velocity converged to the “lock-in” range as defined by P.W. Bearman.

Lastly, we compared the results of our optimization with the work conducted by the Marine Renewable Energy Laboratory (MRELab) at the University of Michigan. We compared our maximum power coefficient of approximately 0.2 to their 0.22, however, we believe our optimization process and methods would generate a greater power coefficient and a better-optimized system when a greater number of generations can be run for the problem. The team at MRELab hypothesized a maximum coefficient of power being 0.37 and this value would serve as the goal for our algorithm.

HOW WE VALIDATED OUR DESIGN SOLUTION

FEASIBILITY OF OUR DESIGN SOLUTION

By formatting our project results into non-dimensional parameters and variables, we are able to scale our results to real-world applications. For instance, the maximum power coefficient found from the optimization process can be applied to a hypothetical system in the Bow River. The flow of the river is around 3 knots or 1.5m/s. For a cylinder diameter of half a meter, the power output of one cylinder per unit length is around 170 W/m.

Under the Electric Utilities Act and the microgeneration regulation, where small-scale micro-generators are less than 150 kW in capacity, this energy generation system would require a maximum of 880 cylinders in an array to be classified as a small scale micro-generator. Since the harvester uses simple and cheap cylinders, the cost of operating and maintaining this system would be much less than even other sources of renewable energy. The cylinder dimensions are easily scalable to the point where you could have a large array of large cylinders or a small array of small cylinders. This source of cheap mechanical to electric energy would be ideal in the rural communities in Canada or in communities in developing countries as around 66% of the world’s population is at least near a small river.