For the alpha prototype, the team decided to design, construct, and test a single induction system. The team chose this particular subsystem to focus on because it is one of the most vital components in regards to the entire system since it enables the conversion of mechanical energy into useful electrical energy. Previously in Phase 3, an analytical model of an induction system was made using Excel to realize the production of alternating current from the motion of the drivers in a 1 m/s current. This model allowed for the optimization of the induction system design. 

Prior to setting up the optimization solver, a few assumptions had to be made. It was generally known that the power output could be increased with a greater number of turns of the coil,  a stronger magnet, and multiple overlaid coils. With this being known, the team assumed that a very thin wire should be used since the number of turns would be limited by height constraints of the coil. For the analysis, the team used a standard gauge of 28 copper magnet wire, which is the thinnest standard wire. The team also assumed that the magnet being used would be made of neodymium, a material renowned for its magnetic strength, with a remanence strength of 1.45 T, which is one of the stronger but affordable types. The team also assumed that the model would analyze a system with one coil, since it is known that the more additional coils would just increase the power from an already optimized value. After these assumptions were made, there was enough information to carry out optimization.

To carry out the optimization, the parameters which could be manipulated were set as design variables. These variables included the radius of the magnet (Rm), the height of the magnet (H), the number of turns in the coil (N), and the radius of the coil (Rc). For the optimization to run properly, limits were set on certain variables that would allow the optimized design to meet the design criteria. A table giving a breakdown of these limits can be seen below. 

 

Table 1: Induction Optimization Constraints

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The limits set on the magnet dimensions were meant to keep the weight and size of the magnet down since portability is one of the main constraints. Additionally, these components would be in the top portion of the device, so space is very limited. The same goes for the coil dimensions, which could not be too long or wide due to space, especially since the team desired to overlap additional coils on the coil designed through Excel optimization. Next, the objective function was chosen to be maximized. The objective function here was the flux at the point where z = 0 which was known to be the moment for the largest possible flux value. After solving, the optimized design for a single coil induction system was found as seen in Table 2 below.

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Table 2: Induction Optimization Results

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The resulting power from this design comes out to be .64 W, which is low but was to be expected. By adding additional coils around the optimized single coil, the power output was increased. With these additional coils, the number of turns would remain constant, but the cross sectional area would increase with each additional coil. As a result the length of wire used would increase as well as the resistance. The iterations to show the increase in power output with the addition of coils can be seen in Table 3 and Figure 1 below.

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Table 3: Additional Coils

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Figure 1: Power Output with Added Coils

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So in conclusion, it can be seen that a total of 9 overlapping coils could ideally produce around 6.4 W per induction system. Given that the team planned on designing each driver to have an induction system on each side and a total of two drivers in the device, the overall power output in this ideal scenario would be 25.6 W, which compared to the power input from the fluid is 51% efficient. While this sounds great, this analytical model assumes that the reactive motion of the drivers will be ideal harmonic motion and that there will be no losses from other areas such as friction and conversions between AC and DC. So moving forward, it has to be expected that the final power output will not be as efficient as calculated.

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