Answer Happy

An inventor has proposed a modern manifestation of an Atkinson cycle engine concept to control engine load without throttling and thus achieve efficient operation at part load. The concept uses late intake valve closing which effectively creates an expansion ratio larger than the effective compression ratio. The engine is four-stroke, spark-ignition, and operates unthrottled. Each cylinder has a clearance volume of 300 cm³ and a displaced volume of 2700 cm³. The fresh working fluid is a lean mixture of methane (CH₂) and air at an equivalence ratio=0.75. The lower heating value of methane is 50 MJ/kg. The cylinder contents behave as an ideal gas with constant specific heats (y= 1.3, R = .300 kJ/kg-K). The cycle processes are described below: Intake Process(5-6) and Constant Pressure Work Process (6-1) For the first part of the process (5-6), the piston moves from TC to BC. For the second part of the process (6-1), the piston moves up to half-way into the geometric compression stroke while the intake valve is still open. Throughout the intake process (5-6), fresh fuel-air mixture is inducted into the cylinder and mixed with the residual gas, while from (6-1) mixture is displaced from the cylinder; the cylinder pressure remains constant at 100 kPa from (5-6-1). When the intake valve is closed (state 1), the temperature of the cylinder contents is 440 K. Compression Process 1-2 Compression is reversible and adiabatic. The gas pressure rises as the piston moves towards TC. The "compression ratio" re is defined as the ratio of cylinder volume at intake valve closing to clearance volume.
Combustion process 2-3 The mixture is ignited with a spark and releases the fuel chemical energy at the TC position. The "gross" heat released by the fuel during the constant volume combustion process is accompanied by considerable heat loss to the engine walls. The "net" heat release raises the temperature and pressure of the working fluid. Expansion Process 3-4 The combustion gases follow a reversible and adiabatic expansion process from TC to BC, until the cylinder pressure drops to the exhaust pressure (100 KPa) and the gas temperature drops to 800 K. The "expansion ratio" re is defined as the ratio of cylinder volume at exhaust valve opening (state 4) to clearance volume. Exhaust Displacement Process 4-5 With the exhaust valve open, the piston moves from BC to TC while exhaust gas is displaced out of the cylinder at 100 kPa. The exhaust valve is closed at state 5. (1.1) Draw the cycle on a p-V diagram, clearly showing all relevant states. (1.2) Determine the residual fraction when the intake valve is closed. (1.3) Determine the total mass of the cylinder contents and the mass of fuel when the valves are closed. (1.4) Determine the effective compression ratio re and the expansion ratio re (1.5) Determine the magnitudes of the peak temperature and pressure in the cylinder. (1.6) Determine the gross heat released by the fuel during the combustion process and the heat losses to the walls. (1.7) Calculate the gross-indicated, pumping, and net indicated work transfers of this cycle. (1.8) Calculate the gross-indicated and net indicated fuel conversion efficiencies of this cycle. (1.9) Calculate the net indicated power of a six-cylinder engine at 5500 rpm.