A simple, yet powerful model for spark ignition engines is the Otto cycle. In the ideal...

 

 

Transcribed Image Text:

A simple, yet powerful model for spark ignition engines is the Otto cycle. In the ideal Otto Cycle, the spark, the fuel and the intake/exhaust stages are replaced with simpler stages. There are 4 processes that occur over 2 strokes in the ideal Otto Cycle. Also, a closed system of air is the center analysis. ALSO, the ideal Otto Cycle is often analyzed under COLD AIR STANDARD ASSUMPTIONS meaning heat capacities are constant and ideal gas. b. The first process is an adiabatic compression of air starting at the BDC cylinder volume under STP conditions and ending at a higher energy state at the TDC volume. For now, all we need to know is adiabatic compression under cold air assumptions means we can use these equations: p vk = constant or p v = P2 vk or T V1= T Vk1; k = 1.4 (cold air) What is the pressure and temperature after the compression stroke, P2 & V ? c. What is the work involved per cylinder in this isentropic compression stage? d. This BMW engine is designed as a cycle reaching a maximum pressure of 90 atm (P3) in the cylinder. The ideal Otto Cycle replaces the fuel combustion stage with a process where a close piston of air gets heated from the surroundings in an isochoric process. What is the temperature at the end of this isochoric process (T3)? e. What is the heat transfer per cylinder at this isochoric heating stage if there is 0.724 grams of air in each cylinder and assuming the cold air standard (ideal gas air only, constant heat capacity)? Pin TDC ideal gas air Isentropic Isentropic BDC Yout V stroke Air Isentropic compression (2) (1) TDC wait Air Fin V= const heat addition (2)-(3) stroke Air Isentropic expansion | (4) BDC wait Air out V=const. heat rejection f. The power stroke in combustion engines occurs when the high temperature gas in the cylinder expands to transfer work to the drivetrain. In the Ideal Otto Cycle, the power stroke is modeled as a closed cylinder of air undergoing an isentropic expansion from TDC volume to BDC volume. What is the pressure and temperature after the power stroke, P4 & T4 ? g. What is the work involved per cylinder during the power stoke of this engine? h. What is the net work per cylinder per cycle for this engine? i. The ideal Otto Cycle is 2 strokes because the ideal cycle ignores intake and exhaust strokes. There is no additional net work in or out for intake - exhaust strokes but these strokes do take time. We can account for this time in a more realistic 4 stroke engine by saying that there are 4 strokes per cycle (4 strokes / cycle) in this engine without changing the net work involved. Also, per cycle, there is 1 amount of net work or (1 Wnet /cycle ). Also, this engine crankshaft operates such that there are 2 revolutions per cycle or (2 rev / cycle). What is the power (in kW) of this BMW M5 Sedan if the engine is running at 6500 RPM on all cylinders? j. What is the internal energy change of the system over the whole cycle, Ufinal - Uinitial ? A simple, yet powerful model for spark ignition engines is the Otto cycle. In the ideal Otto Cycle, the spark, the fuel and the intake/exhaust stages are replaced with simpler stages. There are 4 processes that occur over 2 strokes in the ideal Otto Cycle. Also, a closed system of air is the center analysis. ALSO, the ideal Otto Cycle is often analyzed under COLD AIR STANDARD ASSUMPTIONS meaning heat capacities are constant and ideal gas. b. The first process is an adiabatic compression of air starting at the BDC cylinder volume under STP conditions and ending at a higher energy state at the TDC volume. For now, all we need to know is adiabatic compression under cold air assumptions means we can use these equations: p vk = constant or p v = P2 vk or T V1= T Vk1; k = 1.4 (cold air) What is the pressure and temperature after the compression stroke, P2 & V ? c. What is the work involved per cylinder in this isentropic compression stage? d. This BMW engine is designed as a cycle reaching a maximum pressure of 90 atm (P3) in the cylinder. The ideal Otto Cycle replaces the fuel combustion stage with a process where a close piston of air gets heated from the surroundings in an isochoric process. What is the temperature at the end of this isochoric process (T3)? e. What is the heat transfer per cylinder at this isochoric heating stage if there is 0.724 grams of air in each cylinder and assuming the cold air standard (ideal gas air only, constant heat capacity)? Pin TDC ideal gas air Isentropic Isentropic BDC Yout V stroke Air Isentropic compression (2) (1) TDC wait Air Fin V= const heat addition (2)-(3) stroke Air Isentropic expansion | (4) BDC wait Air out V=const. heat rejection f. The power stroke in combustion engines occurs when the high temperature gas in the cylinder expands to transfer work to the drivetrain. In the Ideal Otto Cycle, the power stroke is modeled as a closed cylinder of air undergoing an isentropic expansion from TDC volume to BDC volume. What is the pressure and temperature after the power stroke, P4 & T4 ? g. What is the work involved per cylinder during the power stoke of this engine? h. What is the net work per cylinder per cycle for this engine? i. The ideal Otto Cycle is 2 strokes because the ideal cycle ignores intake and exhaust strokes. There is no additional net work in or out for intake - exhaust strokes but these strokes do take time. We can account for this time in a more realistic 4 stroke engine by saying that there are 4 strokes per cycle (4 strokes / cycle) in this engine without changing the net work involved. Also, per cycle, there is 1 amount of net work or (1 Wnet /cycle ). Also, this engine crankshaft operates such that there are 2 revolutions per cycle or (2 rev / cycle). What is the power (in kW) of this BMW M5 Sedan if the engine is running at 6500 RPM on all cylinders? j. What is the internal energy change of the system over the whole cycle, Ufinal - Uinitial ?