Question: A mixture of water and water vapor having a temperature T = 68◦F is heated at constant pressure until all the water evaporates. What is the final density of the water vapor in lb/ft3?

1. (36 points) Conceptual Questions (Cite all sources used in answering these questions, e.g. lecture 21, Moran page 158, proper citation of an IEEE Journal article, Table A22, ...)

 

1. 1. (5 points) A mixture of water and water vapor having a temperature T = 68^◦F is heated at constant pressure until all the water evaporates. What is the final density of the water vapor in lb/ft³?

 

1. 2. (5 points) A Rankine cycle has been designed for use on the space station. Should it include a radiator or a condenser to reject heat? Explain.

 

 

1. 3. (6 points) Identify the law of thermodynamics (zeroth, first, second) that is most appli- cable to the following:
      1. Heat always flows from a hotter body to a colder body. [ 0 1 2 ]
      2. Plants convert electromagnetic radiation from the sun into chemical energy. [ 0 1 2 ]
      3. A mercury thermometer can be used to measure temperature. [ 0 1 2 ]

 

1. 1. 4.  

(5 points) In an Lox/LH2 rocket engine, the reaction H₂ + ¹ O₂ → H₂O releases massive amounts of energy plus water vapor, which expands and exits the engine nozzles providing the thrust for a rocket to launch. The fuel is stored as a liquid at temperature T₀, and the steam exits the combustion chamber at temperature T . In your analysis of the reactor, you determine that the enthalpy of the steam leaving the combustion chamber/entering the nozzle is:

 

h¯H₂O

 

(T ) = h¯

 

1

¯

H2 (T₀) + 2 h_O2

(T₀)

from which you can determine the exit velocity (neglecting the enthalpy of the water vapor as it exits the nozzle because it is at much lower pressure and temperature)

 

V 2

2 ≈ h_H2O(T )

Is your analysis correct or have you missed something? Explain.

1. 1. 5. (5 points) What is the efficiency of an Otto cycle with a compression ratio r = 16 using a cold-air standard basis?

 

 

1. 1. 6. (10 points) Both fuel supply and thermal pollution considerations strongly favor the de- velopment of high temperature, high efficiency power plants. One option that has been explored by the Department of Energy uses a potassium Rankine vapor cycle that operates at a higher temperature than the water vapor cycle. The heat rejected by the potassium topping cycle is used as the heat source for the water vapor bottoming cycle. Assuming that the thermal efficiency of the water cycle is η_w = 40% and the thermal efficiency of the  potassium  cycle  is  η_K  = 22%.  The  efficiency  of  the  combined  cycle  can  be  shown  to be (extra credit if you show it):

 

η = η_K + η_w − η_Kη_w

Assuming the amount of fuel required is proportional to the heat input into the cycle determine (a) what percentage of fuel is saved by adding the topping potassium vapor cycle and (b) by what precentage is the thermal pollution reduced?

2. (24 points) Wind Generation

Iowa is a national leader in wind energy and is the first state to generate over 30% of its electricity from wind. Wind energy also significantly benefits the economy of Iowa as manu- facturing, operations and maintenance of wind farms provides at least 8000 jobs in the state, while landowners in rural Iowa receive approximately $25 million dollars per year in land lease payments. The figure shows the typical size of wind turbines used in farms throughout the state. The minimum wind speed required for power generation is called the cut-in speed, which is around 9 mph and the optimum power is achieved with a wind speed around 30 mph.

1. 1. (12 points) Use control volume analysis to estimate the ratio of the power generated at 9 mph and 30 mph assuming conditions having the same temperature and air pressure. For an estimate of the power generated, you may assume that roughly the same fraction of kinetic energy of the wind is converted into work and you should list any additional model assumptions.

 

 

 

1. 2.  

(12 points)  During the winter, the air temperature at night in Iowa can drop to   15^◦C, while in the summer the high temperature can be around 30^◦C. Determine the ratio of power generation on a hot summer day compared with a cold winter night assuming that the wind speed and air pressure are the same. (It should be noted that the coldest temperatures typically occur when there is less wind, so additional factors would need to be included when analyzing the seasonal dependence of wind energy generation).

3. (35 points) Concentrated Solar Power (CSP) Plant

CSP is a proven means of solar power generation and new technologies are lowering its cost curve, but a common characteristic of current CSP technologies is the use of steam turbines for power generation. Steam turbines, although well understood, consume large amounts of water and require extensive balance-of-plant equipment. CSP works best in regions with a lot of sun year-round, and these tend to be desert areas where water is in short supply and permission to use water may be difficult or impossible to obtain.

The Brayton cycle provides an attractive alternative because it only utilizes air. Consider the following Brayton cycle. Air enters the compressor at 100 kPa and 300K and is compressed to  1.67  MPa.  As  the  air  passes  through  the  solar  receiver  device  it  is  heated  at  a  rate  Q˙ in  =

2525kW. The heated air then expands through the turbine and is exhausted. The isentropic efficiency of the compressor is 87% and the isentropic efficiency of the turbine is 89%.  The

mass flow rate through the cycle is m˙   = 5kg/s.

1. 1. (5 points) Describe your model assumptions

 

1. 2. (5 points) Provide an accurate sketch of the cycle on a T-s diagram and the process flow diagram (label all states that you will use in your analysis, e.g. 1, 2s, 2, ...)

1. 3. (20 points) Determine the electrical power output (it is not necessary to interpolate unless the table value of a reference state is different by more than 1 percent)

1. 4. (5 points) Determine the overall efficiency. If the efficiency is less than the typical Rankine efficiency of 42%, how could the cycle be improved?