Engineering Homework Help. SUNY at Stony Brook Internal Combustions Thermodynamic Review Questions
1. A famous inventor proposes a new engine concept to control engine load without throttling. To achieve efficient operation at part load, the concept uses late intake valve closing which effectively creates an expansion ratio larger than the compression ratio. The engine is four-stroke, spark ignition and operates unthrottled. The engine has a clearance volume of 300 cm3 and a displaced volume of 2700 cm3 per cylinder. The fresh working fluid is a lean mixture of methane (CH4) and air at an equivalent ratio = 0.8. The lower heating value of methane is 50 MJ/kg.The cylinder contents behave as an ideal gas with constant specific heats (y = 1.25, 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 top dead center (TDC) to bottom dead center (BDC). For the second part of the process (6-1), the piston moves up to half-way into the compression stroke while the intake valve is still open. Throughout the intake process (5-6-
1), the fresh fuel air mixture is inducted into the cylinder and mixed with residual gas, while the cylinder pressure remains constant at 100 kPa. When the intake valve is closed (State 1), the temperature of the cylinder contents is 440K.
Compression Process 1-2
Compression is reversible and adiabatic. The gas pressure rises as the piston moves towards
TDC. The “compression” rc is defined as the ratio of the cylinder volume at the 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 TDC 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 TDC to BDC,
until the cylinder pressure drops to the exhaust pressure (100 kPa) and the gas temperature drops to 800K. 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 BDC to TDC while the exhaust gas is displaced out of the cylinder at 100 kPa. The exhaust valve closes at State 5.
(1.1) Draw the cycle on a p -V diagram, clearly showing all relevant states and processes.
(1.2) Determine the residual fraction when the exhaust 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 compression ratio, rc, and the expansion ratio, re.
(1.5) Determine the magnitudes of the peak temperature and pressure in the cylinder.
(1.6) Calculate the gross heat released by the fuel during 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 four-cylinder engine at 7200 RPM.
(1.10) The inventor claims that the timing of the closing of the intake valve can be
varied to control engine power output without throttling. When should the intake
valve be closed for a maximum output equivalent to wide open throttle (WOT) in
a conventional design? State physical arguments, but do not repeat any of the
calculations! Briefly comment on the potential of the concept.
2. It has been shown that blending hydrogen (H2) and carbon monoxide (CO) with
hydrocarbon fuels, n-Octane (C8H18) in this case, can improve the lean limit of spark ignited
engines. Assuming that the fuels are all in the gaseous phase, the Lower Heating Value of n-
Octane (C8H18) is 44,788 kJ/kg, the Lower Heating Value of CO is 10,100 kJ/kg, while the Lower
Heating Value of hydrogen (H2) is 119,953 kJ/kg. On a volume basis the fuel mixture consists
of:
25% n-Octane (C8H18), 25% carbon monoxide (CO) and 50% hydrogen (H2)
Fuel and air enter the engine at standard state conditions (1 atm, 25?C). The mass flow rate of air
into the engine is 200 g/sec, while the equivalence ratio is 0.5. The heat losses from the
working fluid to the engine coolant and the environment are 50 kW. The temperature of the
combustion products in the exhaust manifold is 900 K.
(2.1) Determine the overall combustion reaction for this engine’s fuel mixture using
atmospheric air (O2 + 3.76 N2). Normalize to a per mole fuel basis.
(2.2) The molecular weight of the fuel mixture.
(2.3) Calculate the air-to-fuel ratio (mass based) at which this engine is operating.
(2.4) Calculate the fuel mass flow rate.
(2.5) Calculate the lower heating value per kg of fuel.
(2.6) Calculate the higher heating value per kg of fuel, where hfg, H2O = 2442 kJ/kg
(2.7) Determine the net indicated power output of this engine in kW
(2.8) Determine the fuel conversion efficiency of this engine.
