calculate the aerodynamic efficiency of the wind turbine

Take-Home Exam Part Of The Second Midterm Exam Due Thursday, May 16, 2024, 11:00 PM Important: This part will be considered as HW2 as well. Background The following equation is used to calculate the aerodynamic efficiency of the wind turbine: Equ.1 𝜆 = 𝑅𝑢 𝜔 Equ.2 ℎ𝑢𝑏 𝛼 ℎ 𝑢ℎ𝑢𝑏 = 𝑢𝑟𝑒𝑓 ( ℎℎ𝑢𝑏 ) 𝑟𝑒𝑓 Equ.3 FIGURE 1: the values of each constant in Equ.1 It is important to ensure that each quantity should be in the “SI” unit for obtaining correct results. In reality, this value is typically calculated for each wind turbine; then, the end user can benefit from the obtained results the best operating conditions to achieve the highest 𝐶𝑝 . In particular, a graph of 𝐶𝑝 vs. the tip speed ratio (might be named: 𝜆 or X) is provided as a summarized results in a graphical form. Problem For unknown wind turbine, use Equ 1-3, to obtain a full graph that shows the bell shape of the 𝐶𝑝 vs. 𝜆 or X. follow the given, per name, condition in the table below: Table 1per-student’s-name condition to follow to obtain the targeted results. 2 2.01 2.1 2.2 2.3 2.35 2.4 2.5 2.6 2.44 2.7 2.68 2.46 u_ref [m/s] 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.1 1.11 1.12 1.13 h_hub [m] 30 40 45 50 55 60 70 75 78 79 80 85 100 2.02 1.14 115 No. Name length of the blade (R) [m] α h_ref [m] 1 ‫ابراهيم العقالن‬ 15 2 ‫تركي المطرودي‬ 15.1 3 ‫تقي الحارثي‬ 15.2 4 ‫خالد المحيميد‬ 20 5 ‫زياد السالمه‬ 25 6 ‫سلمان المحسن‬ 25 7 ‫عبداالله الفائز‬ 23 8 ‫عبدهللا صالح‬ 24 1.4 1.45 1.5 1.55 1.56 1.57 1.58 1.59 1.6 1.62 1.63 1.65 1.67 1.7 9 ‫مجدي ابو شقفه‬ 17 10 ‫محمد الطناني‬ 16 11 ‫محمد الحربي‬ 18 12 ‫معاذ الناصر‬ 19 13 ‫نواف الحربي‬ 20 14 ‫وليد الرشيدي‬ 14 (hint: you should start by a random value of angular velocity (𝜔), then move-on accordingly) Report First: equation, inputs/outputs, values/units You are required to show your work of full details; you can provide it in whatever form you may want to use; for example, either of the following: 1. 2. 3. 4. your entire MATLAB code or OR Excel sheet (show the used formula in each cell) OR your handwriting calculations or Or your word file that has the equations and their results (i.e., full definition of inputs/outputs and their values/units) Second: plot 1. The 𝐶𝑝 vs. 𝜆 curve 2. Label each axis 3. Show the best 𝐶𝑝 and 𝑋𝑜𝑝𝑡 or 𝜆𝑜𝑝𝑡