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After completing necessary analysis of the theory and constructing an analytical model in Excel, the team decided to utilize Excel optimization tools in order to find appropriate designs for a variety of flow speed scenarios. To carry out this optimization, the variables within the governing equations that could be manipulated in any given design were set as “design variables”. These variables included the driver dimensions (diameter and length), the mass added to the driver, and the stiffness of the springs. Constraints were set on certain variables so that the optimization solver could complete multiple iterations within a range that would produce designs acceptable for our criteria. These limits can be seen in the table below (See Table 3). 

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Table 3: Driver Optimization Constraints

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The limits set on the driver dimensions were meant to ensure portability and ability for storage. The upper limits were set at 0.05 m for the diameter and 0.5 m for the length, which corresponds to the typical dimensions of portable generators and accounts for the use of multiple drivers within one device. Portability also associates weight, and since the device will already incorporate heavy components such as the battery pack, the upper limit of added mass in the driver was set to 5 kg. Additional mass in the driver was necessary for neutral buoyancy since the drivers are hollow and displace water when submerged. To ensure neutral buoyancy, the mass of water displaced, which is a function of the driver dimensions, and the mass of the driver, which is also a function of driver dimensions and additional mass, were constrained to be equal. Finally, the spring constant was constrained to a maximum of 3000 N/m after finding through previous trials that the optimized design for high flow speeds required much higher spring constant values which yielded oscillation frequencies that the team deemed unsafe.  After all of the constraints were set in place, the objective function that was chosen to be maximized was the amplitude of the power function as seen highlighted in red in the figure to the left (Figure 5).

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Multiple iterations were run to find optimized designs in a series of flow speed scenarios. These scenarios focused on the average flow speeds of typical bodies of water around the world including 0.35 m/s (small creek), 0.5 m/s (small river), 1 m/s (ocean tide change or average river flow), and 3 m/s (high speed river flow). The results of these iterations can be seen in Figure 6 below.   

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As seen in the results (Figure 7), the driver diameter and length reached their maximum values and remained constant throughout each iteration. This occurred because these variables were directly proportional with the power. As a result of these dimensions being constant, the additional mass reached a constant value of 0.52 kg to ensure neutral buoyancy. The one design variable that change through each iteration was the spring constant. This value changed to allow for resonance to occur, where the frequency of vortex shedding closely matches the natural frequency of the design which is governed by the springs. These optimized spring constant values fell within the acceptable range except for the 3 m/s flow speed scenario, which reached the maximum allowable value. A fully optimized spring constant for the 3 m/s flow would be around 10,000 N/m and result in very high oscillation frequency, which was deemed unsafe for durability purposes. By comparing the power output found in each optimized design scenario to the ideal power of the fluid, the team was able to determine the efficiency of each design (See Figure 7).  Just based on the optimization of driver design and disregarding how the electrical design will affect power output, the most efficient design was determined to be the design for 1 m/s flow. This design was found to be 76% efficient and a viable option due to the prevalence of waterways that tend to flow at this speed. To provide a frame of reference, the Hudson river and coastal inlets tend to flow at 1 m/s. Due to its viability and efficiency, the team chose to apply this design moving forward in the analysis of electrical design. Although this design was chosen for further analysis, it is important to note that this decision is not binding in regards to alpha prototyping and testing since the only variance between designs would be the springs.

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