# ME 410 Day 25 • Example Problem and Exercise - Rose ```ME 410
Day 25
• Example Problem and Exercise:
Turbocharged Limited Pressure “Air” Engine
PV Diagram -- Not to Scale
P
3a
3b
4
2
Pi
8
Pe
7
1
b
a
6
5
V
V2
V1
• Solid lines indicate processes in the cylinder
• Dashed lines indicate other processes of interest.
Note how Pi > Pe. This is the effect of turbocharging the engine with
a compressor which is driven by the hot exhaust gases.
There is an intercooler which removes heat from the air after
compression.
Exercise:
Predict the performance of this engine.
• Indicated Fuel Conversion Efficiency (Gross & Net)
• Indicated Power at 4000 rpm (Gross & Net)
• Imep at 4000 rpm (Gross and Net)
• Estimated Brake Power at 4000 rpm. ηm = 0.70
• Estimated Brake Torque at 4000 rpm
Engine Data
Specification
Max cylinder volume (liters)
Min cylinder volume (liters)
Displacement (liters)
Compression ratio
AF
Fuel Heating Value (kJ/kg)
3.687
0.410
3.277
9
15
44,300
Cycle / Process Data
Point
a
Description
Air at intake
b
After
turbocharging
Property
T (K)
P (kPa)
v (m3/kg)
h (kJ/kg)
u (kJ/kg)
s (kJ/ kg-K)
T (K)
P
v
h
u
s
(kPa)
(m3/kg)
(kJ/kg)
(kJ/kg)
(kJ/ kg-K)
Value
333
103.4
0.9244
333.7
238.1
5.797
361.5
137.9
0.7524
362.3
258.6
5.797
Point
1
2
3a
3b
4
Description
Start of
compression
End of
compression
End of cv
combustion
End of cp
combustion
End of
expansion
Property
T (K)
Value
333
P
v
h
u
s
T
(kPa)
(m3/kg)
(kJ/kg)
(kJ/kg)
(kJ/ kg-K)
(K)
137.9
0.6931
333.7
238.1
5.714
772.5
P
v
h
u
s
T
(kPa)
(m3/kg)
(kJ/kg)
(kJ/kg)
(kJ/ kg-K)
(K)
2879
P
v
h
u
s
T
(kPa)
(m3/kg)
(kJ/kg)
(kJ/kg)
(kJ/ kg-K)
(K)
2569
1923
6.676
3307
P
v
h
u
s
T
(kPa)
(m3/kg)
(kJ/kg)
(kJ/kg)
(kJ/ kg-K)
(K)
0.1130
3922
2972
7.168
1952
P
v
h
u
s
(kPa)
(m3/kg)
(kJ/kg)
(kJ/kg)
(kJ/ kg-K)
791.9
570.2
2253
808.5
2192
1631
Point
5
6
Description
Expanded
exhaust 7
residue
In cylinder
after
blowdown
Property
T (K)
P
v
h
u
s
T
(kPa)
(m3/kg)
(kJ/kg)
(kJ/kg)
(kJ/ kg-K)
(K)
P
v
h
u
s
(kPa)
(m3/kg)
(kJ/kg)
(kJ/kg)
(kJ/ kg-K)
Value
1200
103.4
3.33
1277
932.7
7.168
1. Begin by filling in all blanks in this table based on your
knowledge of the engine processes.
2. Calculate the masses:
• mass of charge filling cylinder at 1
• residual fraction
• mass of residual in the charge
• mass of fuel in the charge
• mass of air in the charge
3. Calculate the total heat in (kJ) added at constant volume. Do
the same for the total heat added at constant pressure.
4. Calculate the works:
• Work done on the gas in compression stroke
• Work done by the gas during expansion 3a to 3b
• Work done by the gas during expansion 3b to 4
• Work done by the gas during intake stroke
• Gross and net work per cycle
5. Calculate the fuel conversion efficiencies:
• Net based on net work per cycle
• Gross based on gross work per cycle
• Which is greatest?
6. Calculate the powers:
• Net based on net work per cycle
• Gross based on gross work per cycle
• Which is greatest?
• Base the brake power estimate on gross work/cycle
7. Calculate the imeps
• Net based on net work / cycle
• Gross based on gross work / cycle
8. Calculate the torque estimate based on brake power.
Complete this as hw by Thursday, October 24.
There are a couple of other interesting things that we will go over
together.
• heat removal in intercooler
• energy available to run turbo
There will be a question similar to this one on the next test.
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