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1 UNIVERSITY OF TORONTO FACULTY OF APPLIED SCIENCE AND ENGINEERING FINAL EXAMINATION, DECEMBER 2008 MIE 411H1 F - THERMAL ENERGY CONVERSION Exam Type: X Examiner: J.S. Wallace You may use your copy of the textbook by Cengal and Boles or Moran and Shapiro, your lab manual, your class notes, returned problems sets, and any other material distributed in class or via the course web site. Calculators will be non-printing, noncommunicating, silent & self-powered. Show your work on your exam booklet. 1. (21%) The Detroit Diesel engine is our laboratory is a three-cylinder 2-stroke direct injection diesel engine having a bore of 108 mm and a stroke of 127 mm for a total displacement of litres. The nominal (geometric) compression ratio is 17:1. Intake air conditions are 100 kpa and 27 o C. The engine operates on a cycle that can be approximated by an air-standard limited pressure cycle where P max = 11 MPa. The total heat input to a cycle is 1100 kj/kg. Due to the large temperature range involved, the variation of specific heat with temperature cannot be neglected so the Air Tables must be used. Determine: (a) the clearance volume in one cylinder (b) the temperature and pressure at the end of each process (c) the net work output and the thermal efficiency for the cycle (d) the mean effective pressure for the cycle (e) Estimate the power produced by the engine at 1800 rpm. 2. (21%) A vapor compression cycle heat pump having refrigerant R-134a as the working fluid is used to heat a commercial building. The mass flow rate of refrigerant is 0.24 kg/s, while the condenser and evaporator pressures are 900 kpa and 240 kpa respectively. The compressor has an isentropic efficiency of 75%. (a) Show the process on a T-s diagram (b) Determine the rate at which heat is supplied to the building (kw) (c) Determine the volume flow rate of refrigerant at the compressor inlet. (d) Determine the power required to drive the compressor (kw) (e) Determine the COP of this heat pump. (f) What is the ambient temperature supplying heat to the evaporator of this heat pump? Page 1 of 4

2 3. (21%) As energy costs increase, there is much greater interest in recovering energy from waste heat. Simple Rankine cycle systems often using organic working fluids instead of the more conventional steam are used for producing power. The figure below shows a simple organic Rankine cycle system (N.B.: Thermodynamically a turbine and expander are equivalent - an expander could be a turbine, but in a smaller system it could also be a reciprocating expander). Cooling water is available at 20 o C. Waste heat is available at 100 o C. The working fluid is HCFC-124 a Pressure-Enthalpy diagram for HCFC-124 is attached at the back of the exam. Assume that the heat exchanger terminal temperature differences are such that the condenser operates at 0.4 MPa pressure and the evaporator (boiler) operates at 2 MPa pressure. Saturated vapor at 2 MPa leaves the boiler. Saturated liquid at 0.4 MPa leaves the condenser. Neglect any pressure drop in the recuperator. State 6 is saturated vapor at 0.4 MPa. (a) If the pump efficiency is 60%, calculate the pump work required per unit mass of HCFC-124 (the pump is the object just below state 1). (b) If the expander efficiency is 80%, calculate the expander work output per unit mass of HCFC-124 (c) The waste heat input rate to the organic Rankine cycle system is 45 kw. What is the HCFC-124 flow rate (kg/s) and the net power output (kw) of the system? (d) What is the overall efficiency of this Rankine system? Page 2 of 4

3 4. (16%) A fuel gas mixture of 15% hydrogen and 85% methane (by volume) at 27 o C is compressed from 100 kpa to 383 kpa in a steady-flow process. You may assume that both gases behave as ideal gases under these conditions. Thermodynamic data for both gases at 300 K is provided in the table below. Gas Molecular weight C p (kj/kg-k) C v (kj/kg-k) Hydrogen Methane (a) If the compressor has an efficiency of 80%, how much energy per unit mass of mixture (kj/kg) is required to drive the compressor. (b) What is the mixture temperature at the outlet of the compressor? 5. (21%) A solar-powered device that could be used to remove the salt from sea water to make fresh water is shown in the figure below. Also shown are typical operating conditions. The device makes use of two characteristics of air-water vapor mixtures: 1) only pure H 2 0 vapor mixes with the air (all the salt stays in the liquid) and 2) the amount of water vapor that air can contain varies with temperature. How it works: Sea water is heated inside tubes in the condenser where it acts as the energy sink for the energy released in the condensation process. Because air cannot contain as much water at low temperatures, the cooling of the air in the condenser causes a condensation process in which fresh water is released. The now warm salt Page 3 of 4

4 water is further heated in solar collectors and pumped into a packed column evaporator. The air from the condenser is forced up from the evaporator and becomes saturated with water vapor at a high temperature. In effect the air acts as a transfer medium for water vapor. Assumptions for analysis: The air side of the condenser is at 14.7 psia. For the purpose of this problem, the properties of salt water can be considered to be those of saturated liquid water at the same temperature. Salt water states are identified on the figure with letters, while air-water vapor mixtures and pure liquid water states are identified with numbers. (a) Determine the fresh-water production (lbm) per lbm of dry air circulated in the system (Hint: analyze the condenser). (b) If the device is to produce 1,250 US gallons per hour, what (dry) air flow rate must be maintained through the condenser? (1 US gallon = 8.33 lb m liquid water) (c) For the conditions of part (b), what is the water flow rate on the water side of the condenser? (d) What is the heat input (from the solar collector) per lbm of water produced? Page 4 of 4

5 HCFC-124 Pressure-Enthalpy Diagram Pressure-Enthalpy Diagram (SI (SI Units) Units)