This homework set allows you to evaluate an open system analysis of an idealized engine.

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 makes the expansion ratio larger than the effective compression ratio. The engine is four$-$stroke, spark$-$ignition, and operates unthrottled. The engine has a clearance volume of $200$ cm$3$ and a displaced volume of $2500$ cm$3$ per cylinder. The fresh working fluid is a lean mixture of gasoline and air at an equivalence ratio $=0\mathrm{.}9.$ The lower heating value of gasoline is $43$ MJ$/$kg$.$ The cylinder contents behave as an ideal gas with constant specific heats $(=1\mathrm{.}3,$ R $=300$ J$/$kg$-$K$).$ The cycle processes are described below:

Intake Process $5-6-1$

For the first part of the process $(5-6),$ the piston moves from TC to BC$.$ During this part, fresh fuel$-$ air mixture is inducted into the cylinder and mixes with residual gas. The temperature at State $6$ is $440$ K$.$ 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. During this part, some mass of the mixture exits the cylinder until the intake valve closes at State $1.$ During the entire process, the pressure of the cylinder remains constant at $100$ kPa. When the intake valve is closed $($state $1),$ the temperature of the cylinder contents is $400$ K$.$

Compression Process $1-2$

Compression is reversible and adiabatic. The gas pressure rises as the piston moves towards TC$.$ The $$compression ratio$$ rc 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 mixture follows a reversible and adiabatic expansion process from TC to BC$,$ until the cylinder pressure drops to the exhaust pressure $(120$ KPa$)$ and the gas temperature drops to $750$ 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 $120$ kPa. The exhaust valve is closed at state $5.$

$1.$ Draw the cycle on a p$-$V diagram, clearly showing all relevant states.

$2.$ Determine the residual fraction when the exhaust valve is closed.

$3.$ Determine the total mass of the cylinder contents and the mass of fuel when the valves are closed.

$4.$ Determine the effective compression ratio rc and the expansion ratio re $.$

$5.$ Determine the magnitudes of the peak temperature and pressure in the cylinder.

$6.$ Determine the gross heat released by the fuel during the combustion process and the heat losses to the walls.

$7.$ Calculate the gross$-$indicated, pumping, and net indicated work transfers of this cycle.

$8.$ Calculate the gross$-$indicated and net indicated fuel conversion efficiencies of this cycle.

$9.$ Calculate the net indicated power of a six$-$cylinder engine at $5000$ rpm$.$

$10.$ This process is more typically called the Miller Cycle. Investigate the differences in the mechanical design of the engine to enable the Atkinson Cycle and compare it to the Miller Cycle.