c) To examine the behavior of turbocharging, we shall consider the following example of a four stroke 2.0 L displacement passenger car diesel engine turbocharged with a single stage centrifugal compressor, and a single stage turbine. For simplicity, there is no waste-gate and no inter-cooler. You may assume the following: 1. The ambient conditions are Ti=300K and Pi=1 bar. The working fluid may be assumed to have constant properties of y = 1.35 and molecular weight of 29. 2. The turbine and compressor have constant efficiencies: ni= 0.85 and ne= 0.65. You may also assume that the Mach no. is small so that the kinetic energy of the fluid is negligible. 3. The compressor and turbine maps are shown in the accompanied figures. (For this simplified example, ignore the actual values of the ŋe contours on the compressor map and assume ne to be constant.) 4. The reference conditions of these maps are the same as the ambient conditions: Tref= T1; PreF Pi. 5. The engine volumetric efficiency based on the intake manifold condition is constant: ŋv= 0.8. 6. The heating value of the diesel fuel is 43 MJ/kg. 7. Assume that 30% of the fuel energy is lost as heat transfer in the engine 8. The engine indicated net fuel conversion efficiency is nr= 0.33 We shall look at the engine operating at 3000 rpm with A/F ratio = 22, and compressor pressure ratio (tc) of 1.5. i. What is the compressor outlet temperatures (T2) at compressor pressure ratios nc= 1.5? ii. What is the engine intake air mass flow rate at this value of rc? iii. What is the compressor speed at this value of rc? iv. Draw on the compressor map the operating point corresponding to your answers of (ii). V. What is the corresponding turbine inlet temperature? vi. What is the turbine pressure ratio (1.) that is required to power the compressor? (Assume that all mechanical losses are already incorporated into the definition of the compressor/turbine efficiencies.) vii. The turbine and compressor run at the same speed. From the turbine map, using the result of (vi), determine the mass flow rate required by the turbine to power the compressor. viii. Put this point also on the compressor map; plot the mass flow rate required by the turbine versus the compressor pressure ratio (1.). Does this point match up to the point plotted in part (iv)?