1 Midterm Exam, ENERGY/EE 293B (Winter 2021) Name: __________________________________ Honor Code observed: ___________________________ • On the first page of your solution, please write “I observed the Honor Code” and sign your name. • 110 minute open book exam. You have 10 minutes to assemble your exam, scan it, and submit on Canvas. Exams must be submitted on Canvas no later than 8 February at 4:30 PM. • Show your work for full credit. • No collaboration on exam problems is permitted • This is an open book and open note exam. The Board on Judicial affairs has outlined the following policy positions on remote exams. o Permitted informational resources only includes material a reasonable student would have found to be helpful when trying to understand class material or preparing for an assignment or exam. o This does not include material that becomes useful once the assignment or exam begins and questions are known. o In all cases, it is not permissible for students to enter exam questions into any software, apps, or websites. 1. Living off the land … on the moon [65 pts] NASA has a policy to develop technology to leverage extraterrestrial resources for space exploration and for the necessities of life off of earth including oxygen and water. The moon appears to have an abundant store of oxygen present in minerals such as ilmenite (FeTiO3) that can be released by processing with heat. One of the technologies recently selected by NASA for development uses concentrated solar power and a chemical reactor to process the mineral ilmenite (FeTiO3)1. The lunar south pole may be an especially good place for a solar-powered lunar base because it receives constant sunlight year round. The chemical reactions for releasing oxygen from ilmenite are as follows FeTiO3 (+ heat) → Fe + TiO2 + H20 H20 (+ electricity) → H2 +0.502 where the H2 is recycled in the process. (a) 5 points. Recall that the moon orbits the earth. What value do you expect for the minimum acceptance angle (max) on the moon? No calculations. Explain your answer briefly in a few sentences. (b) 10 points. Assume that sunlight is concentrated using a parabolic dish with a spherical receiver. Heat losses are only by radiation. Derive an expression for the receiver 1 NASA Selects 10 Small Business Proposals For Lunar ISRU, http://www.parabolicarc.com/2020/07/09/nasa-selects-10-small-business-proposals-for-lunar-isru/ 2 efficiency. This expression should be as general as possible. That is, parameters such as and so on should appear in your formula. (c) 10 points. The parabolic dish has a rim angle of (2=) 110 ° (=55 °) and an acceptance angle of 1°. The reactor to generate O2 has a semi-spherical window that is 0.15 m in diameter. Assume that this is the receiver and that its area is 0.035m2. What is the diameter of the dish? (d) 15 points. The first reaction needs temperatures of roughly 1000 °C to proceed. Can the system that you designed in parts (b) and (c) reach this temperature? That is, what is the maximum temperature that you expect? You may assume the following: • the system is at the south pole of the moon where the average ambient temperature is about 260 K (-13 °C), • = = = • the insolation is 1350 W/m2 (because the moon has no atmosphere), • the concentration ratio is 500 (this is not the answer to part (c)) • the Stefan Boltzmann constant is 5.67x10-8 W/m2K4 Make clear the numerical values any additional parameters that you may need to complete your calculation. (e) 10 points. The hot (1000 °C) and cold (-13 °C) temperatures in part (d) look interesting in the context of a heat engine. Assume that we use a Stirling engine that has a regenerator with an effectiveness of 1 and hydrogen is the working fluid. The Stirling engine is connected to a generator with an efficiency of 85%. What is the overall efficiency of the Stirling engine and generator to electricity? List any additional assumptions made. (f) 15 points. Another base is to be located in the equatorial region of the moon. There, sunlight is continuous for 14 days and is followed by continuous dark of 14 days. In this case, oxygen needs to be stored sufficient for the 14 days of lunar night with no sun. A person needs 550 liters of oxygen per day (at standard conditions) or 15,400 liters over 28 days. Develop an equation for the volume (V) of oxygen in storage per person where • t=0 is sunup, • oxygen generation rate (qgen) follows a sinusoidal function similar to energy delivery ( = ), • sunset is at t=14 days, • night lasts for 14 days, • the initial volume in storage at sunup is V0=0, • the O2 demand (qdemand) is constant at 550 l/d, and • there are no losses. 3 If the maximum production rate of oxygen is 1600 l/d per person, will there be enough O2 in storage for the 14 days of night when the sun sets? To be clear, will there be at least 7,700 liters of O2 per person in storage on day 14? 2. Hyper-local energy independence for Stanford? [35 pts] Can the Stanford campus be “energy independent” by harvesting only renewable exergy fluxes? One challenge is that the central Stanford campus is somewhat dense, and contains energy-intensive lab facilities. An advantage is that Stanford contains a lot of land that is currently lightly used and could be used to harvest energy. Stanford’s total campus area is 33.05 x106 m2. Counting students, staff, and faculty, the campus headcount in 2018 was about 32,400 people. Electric power use at Stanford was 36.6 MW averaged over the year in 2018. Which of these exergy resources are larger than the electricity demand at Stanford? a. Thermal exergy from Earth’s crust under Stanford [assume fluid at T = 120 °C @ 3 km deep] b. Solar exergy hitting the campus area c. Kinetic exergy contained in rain falling on the campus Use material from class and from your own knowledge of the world to help solve the problems. You must make some assumptions: justify any estimates with a reasonable argument. Show your work so that partial credit can be given.
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