1 Midterm Exam, ENERGY/EE 293B (Winter 2020) 90 minute open book exam. Computers are allowed for notes, Xsteam, and so on, but not for internet use. Show your work for full credit. Name: __________________________________ Honor code observed: ___________________________ 1. Shining some light on Heliogen [45 pts] During lecture we discussed Heliogen who are marketing a new power tower design. There is little technical information available about Heliogen and this problem takes a deeper look. Recall that the Stefan-Boltzmann constant is 5.67x10-8 Wm-2K-4. (a) 15 points. The Heliogen website describes the system as “Captured sunlight equivalent to 1200 suns …” and it also claims that they can achieve temperatures up to 1500 °C. Heliogen documents that their system attained 1000 °C but there is no proof that 1500 °C has been achieved or is possible. Use this limited information, reasonable assumptions, and your own calculations to support or refute the claim of 1500 °C. (b) 10 points. At the Heliogen test site, there are about 380 heliostats with an area of 1.5 m2. The receiver appears to be a circular surface of about 0.5 m in diameter. Use this limited information, reasonable assumptions, and your own calculations to support or refute the claim of “captured sunlight equivalent to 1200 suns”. (c) 10 points. An article in Popular Mechanics (19 Nov 2019) discusses Heliogen’s heliostat mirrors in some detail as well as the maximum temperature that glass can withstand. The reporter writes: “Most consumer glass melts at or below that temperature (1500 °C), but pure silica glass doesn’t melt until 2000 degrees Celsius. Solar mirrors can also hypothetically be made with materials other than glass.” Do you expect the heliostat mirrors to become especially hot in a typical power tower design? Explain. No calculations needed here. (d) 10 points. What elevation angle and surface azimuth of a heliostat maximize the solar insolation incident on the heliostat today (February 3) at 2:24 pm local solar time. The Heliogen test site is located at latitude = 34.69°N and longitude =118.15°W. 2. Ocean thermal energy [55 pts] Although we have not discussed ocean thermal energy conversion (OTEC) in detail, we have developed sufficient background to take a first look at it. Figure 1 is a schematic of the temperature profile found in the tropical oceans. Note that the well-mixed shallow ocean is substantially warmer than the deep ocean. OTEC exploits these temperature differences using a heat engine. 2 Figure 1. Temperature profile of tropical ocean (source: DaRosa). (a) 10 points. Take the surface water as 26.5°C and the deep ocean as 8.0°C. For the purposes of this problem, assume that the earth’s oceans are semi-infinite reservoirs that retain 3x1023 J/yr (1016 W) of solar insolation. Estimate the total (thermal) exergy flow of the oceans in units of Watts. What is your value of T0? (Note that your answer will not match Hermann’s). (b) 15 points. Figure 2 shows the primary input and output flows of energy, water, and electricity produced for a binary OTEC system. Note that the system boundary for part (b) is indicated by a dashed line. Conduct an energy balance and compute the electrical power and energy efficiency of generation for the system. 3 Figure 2. Schematic of temperatures in an OTEC. The control volume for part (b)is indicated by a dashed line. (c) 15 points. Now, conduct the exergy balance and compute the exergy efficiency of electricity generation for the system in Fig. 2. Why is the exergetic efficiency in part (c) greater than the efficiency in part (b)? (d) 15 points. The Rankine cycle turbine in Fig. 2 uses ammonia as a working fluid. Compute the Rankine cycle efficiency where the turbine operates between temperatures of 23.4 and 11.1 °C. The input to the turbine is (saturated) vapor. The properties of ammonia are given in Table 1. Assume that the turbine and pump achieve 100% of their theoretical efficiency and include the pump in your efficiency calculation. List any other assumptions that you make. Note that the answers for efficiency in parts (d) and (b) are not the same. Table 1. Properties of ammonia for part (d) of problem 2. T (°C) P (kPa) vliq (m3/kg) hliq(kJ/kg) hvap (kJ/kg) sliq(kJ/kgK) svap (kJ/kgK) 11.1 6.389 0.1984 233.0 1455.3 0.8992 5.200 23.4 9.457 0.1359 289.8 1464.6 1.094 5.059 turbine pump 25.1 °C 26.5 °C 9.0 °C 8.0 °C We heat exchange heat exchange condenser boiler Warm water: 1000.0 kg/s Cold water: 1325.7 kg/s Cp,warm=Cp,cold = 4.18 kJ/kg-K
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