ME 576 COMBUSTION THEORY H.W.
SET #1 FALL 2014
ASSIGNED THURS. 9/25/14, DUE THURS. 10/2/14 AT START OF CLASS, NO LATE HOMEWORK ACCEPTED
NAME:_______________________________
(attach this cover sheet to your analysis)
1. A high-performance four-stroke SI engine has a swept volume of 875 cm
3
and a compression ratio of 10:1. The
indicated efficiency is 55% of the corresponding ideal air standard Otto Cycle efficiency. At 8000 rpm, the
mechanical efficiency is 85%, and the volumetric efficiency is 90%. The Air/Fuel ratio by mass is 13:1 and the
heating value of the fuel is 44 MJ/kg. The inlet air is at 20 C and 1 bar. Determine:
a. The overall efficiency (%)
b. Specific Fuel Consumption (kg/MJ)
c. Air mass flow rate (kg/sec)
d. Output power (kW)
e. MEP (bar)
2. For the ideal air standard Diesel cycle with a volumetric compression ratio of 17:1 calculate the efficiencies for cut-off
ratios of o= 1, 2, 4, 9. Take =k = 1.4. Verify your answers can be checked with the figure shown below.
3. The Lenoir engine operates without compression before ignition, and it can be modeled by the following processes in an
air standard cycle:
12 heat addition at constant volume, to increase the temperature to T
1
23 reversible and adiabatic expansion through a volumetric expansion ratio, re
34 heat rejection at constant volume, to decrease the pressure to p
1
41 heat rejection at constant pressure, to decrease the temperature to T
1
a) Draw the processes on a p-V diagram
b) Show that the air standard cycle efficiency is given by
( )
( )
1
1
1
1
1
+
=
k
e
k
e
k
e
r
kr r k
q where re= volumetric expansion
ratio, and =temperature ratio during constant-volume heat addition
c) Show that the Atkinson cycle efficiency reduces to the result of b) when the compression ratio is set to unity, recall
the Atkinson cycle efficiency is given by
( ) ( )
1
1
1
1
+ +
=
k
e c
k
c
k
e c
k
e
A
r r
r kr r r k
u
u
q where u=-1 & r
c
=r
v
= compression ratio.
4. Many diesel engines can be approximated by a limited-pressure cycle. In a limited-pressure cycle, a fraction of
the fuel is burnt at constant volume and the remaining fuel is burnt at constant pressure.
Use the limited-pressure cycle with specific heat ratio = k = 1.3 to analyze the following problem:
Inlet conditions: p
1
= 1.0 bar, T
1
= 289 K
Compression ratio: 15:1
Heat added during combustion: 43,000 kJ/kg of fuel
Overall fuel/air ratio: 0.045 kg fuel/kg air
(a) label the above p-V diagram with numerical values
(b) compute the fuel conversion efficiency of the cycle
( )
a
b
a
b a a
k
k
c
T
T
V
V
T
T
p
p
k
r
3
3
3
3
2
3
2
3
1
, ;
1 1
1 1
1 = = = =
(
(
+
=
| o
o | o
o|
q
(c) Compare the efficiency and peak pressure of the cycle with the efficiency and peak pressure that would be
obtained if all of the fuel were burnt at i. Constant pressure, ii. Constant volume
4
4
4*
1
3*
3a 3b
2 3
V
p
5. A diesel engine is fitted with a turbocharger which is comprised of a radial compressor driven by a radial
exhaust gas turbine. The air is drawn into the compressor at a pressure of 0.95 bar and at a temperature of 15
C, and is delivered to the engine at a pressure of 2 bar. The engine is operating on a gravimetric (mass based)
air/fuel ratio of 18:1, and the exhaust leaves the engine at a temperature of 600 C and at a pressure of 1.8
bar. The turbine exhausts at 1.05 bar. The isentropic efficiencies of the compressor and turbine are 70% and
80%, respectively. Using the following parameter values: C
p,air
=1.01kJ/kg-K, k
air
=1.4, C
p,ex
= 1.15 kJ/kg-K, k
ex
=
1.33. Referring to the T-s diagram shown below
Compute:
a) The temperature of the air leaving the compressor, T
2
(C)
b) The temperature of the gases leaving the turbine, T
4
(C)
c) The mechanical power loss in the turbocharger expressed as a percentage of the power generated by the
turbine.
6. A turbocharged six-cylinder Diesel engine has a swept volume of 39 liters. The inlet manifold conditions are 2.0 bar and
53 C. The volumetric efficiency of the engine is 95 per cent, and it is operating at a load of 16.1 bar bmep, at 1200 rpm
with an air/fuel ratio of 21.4. The power delivered to the compressor is 100 kW, with entry conditions of 25 C and 0.95
bar. The fuel has a calorific value of 42 MJ/kg. Stating any assumptions, calculate/address the following :
a. the power output of the engine
b. the brake efficiency of the engine
c. the compressor isentropic efficiency
d. the effectiveness of the inter-cooler
e. estimate the effect of removing the inter-cooler on the power output and emissions of the engine, and the
operating point of the turbocharger
