A six-cylinder SI engine with a total displacement of 1.86 liters operates at 24
ID: 2073245 • Letter: A
Question
A six-cylinder SI engine with a total displacement of 1.86 liters operates at 2400 RPM using gasoline direct injection (GDI) with two injections per cycle in each cylinder. The spark plug is fired at 19 degree bTDC, and there is an ignition dealy 0.0015 seconds before combustion is established.
During combustion, there is a rich air fuel mixture around the spark plug of AF=11.1 and a lean mixture in the rest of the combustion chamber of AF=20.1.
The rich zone can be modeled as a 2cm diameter hemisphere around the spark plug with flame speed of 32 m/s. The lean zone then fills the rest of the combustion chamber to the outer edge of the bore and a flame speed of 19 m/s. The engine has a compression ratio of 9.8 a stroke of 7.2 cm and a connecting rod length of 13.3 cm with the spark plug at the center of the combustion chamber. calculate :
a) Crank angle position at the end of combustion.
b) Piston speed at the end combustion.
c) volume in combustion chamber of one cylinder at end of combustion.
Explanation / Answer
a) Crank angle position at the end of combustion = ?
I2 = r2 + X2 - 2 .r. X . Cos(A)
where,
l = rod length (distance between piston pin and crank pin)
r = crank radius (distance between crank pin and crank center, i.e. half stroke)
A = crank angle (from cylinder bore centerline at TDC)
x = piston pin position (upward from crank center along cylinder bore centerline)
Now, I = 13.3 cm r = 7.2 / 2 = 3.6cm x = 2cm
13.32 = 3.62 + 22 - 2 X 3.6 X 2 Cos (A)
From this Cos A = -11.1 / 100
A = 83.460
b) Piston speed at end of combustion =?
x = r cos B + I cos A
= 3.6 Cos ( 19 ) + 13.3 Cos ( 83.34 )
= 4.94 cm/s
C) Volume in combustion chamber of one cylinder at end of combustion = ?
Compression ratio = Swept volume + Combustion chamber volume / combustion chamber volume
9.8 = swept volume + 1.86 / 1.86
swept volume = 16.36 cm3