Internal combustion engine and reciprocating machine
AAiT, Mechanical engineering Department
Exercise on chapter 5 and 6
Atomic weights for H: 1 g/mol, C: 12 g/mol, O: 16 g/mol, N: 14 g/mol
Heat of formation for CO2: -393,546 kJ/kmol, H2O(g): -241,847 kJ/kmol, C10H22(g): -249,659
kJ/kmol
Average specific heat (cp) for CO2: 49 kJ/kmol-K, H2O: 42.5 kJ/kmol-K, N2: 32.5 kJ/kmol-K.
The enthalpy of vaporization at 298K of water is 44,010 kJ/kmol.
I.
Workout problems
1. A spark ignition engine with a displaced volume of 2.2 litres has a volumetric efficiency
of 0.85 at a speed of 4000 rpm. The volumetric efficiency is based on the conditions in
the inlet manifold (In this case 40oC and 1 bar). The engine is operating with a fuel/air
equivalence ratio of 0.9 using propane C3H8 as fuel and the fuel (in gas form) is mixed
with the air before the inlet manifold.
Tasks:
a. Calculate the exhaust gas flow in kg/s
b. Calculate the volume fraction of CO2 in dry exhaust gas. (Assume complete
combustion and no dissociation of combustion products)
c. In reality, there is always some CO in the exhaust from a spark ignition engine
also when the engine is operated with an equivalence ratio Φ<1.0. Identify at least
two reasons for this.
Molecular weights for C and H are about 12 and 1 kg/kmol respectively. Consider
both air and propane as ideal gases. The volume of 1 kmol of ideal gas at 0oC and
1 bar is 22.7 m3.
2. A passenger car with a spark ignition engine is driving at constant speed 90 km/h in a
slight up-hill with a slope of 2o. The performance map for the 2 litre engine is shown in
the attached diagram.
Data for the car are as follows:
Frontal area
2 m2
Weight
1700 kg
Wheel diameter
0.62 m
st
Gear ratios: 1 : 4.03:1 2nd : 2.16:1 3rd 1.37:1 4th :1.00:1 5th : 0.82:1
A further speed reduction by a factor of 4 is obtained at the back shaft gear
The aerodynamic drag coefficient of the car is 0.29 and the rolling resistance
coefficient is 0.015. Ambient conditions are 15oC and 1 bar.
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Internal combustion engine and reciprocating machine
AAiT, Mechanical engineering Department
Tasks:
a. Determine the brake specific fuel consumption for driving on the most
fuel efficient gear under these conditions.
b. Find the most fuel efficient speed for driving on flat ground on the 4th gear
3. One of the operating parameters that can relatively easily be changed for a spark ignition
engine is the spark timing. Assume that the spark timing is initially set at the time when
the piston is in the top position (TDC) and that the spark timing is gradually advanced to
40 crank angle degrees before TDC.
Tasks:
a) Discuss how the efficiency of the engine will vary as the spark advance is increased
in this range and explain the reasons for this variation
b) Discuss how NOx emissions will vary as the spark advance is increased in this range
and explain the reasons for this variation
c) Discuss how the tendency for knocking will change as the spark advance is increased
in this range
4. A car with a spark ignition engine is equipped with a three-way catalyst exhaust gas
cleaner with performance according to the diagram shown below.
The emissions from the engine (upstream of the exhaust gas cleaner) are:
NOx
CO
HC
1 g/km
13 g/km
1.3 g/km
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Internal combustion engine and reciprocating machine
AAiT, Mechanical engineering Department
For 10% of the driving time the catalyst is cold and ineffective and for the rest of the time
the catalyst performs according to the diagram shown above.
The average fuel consumption is 75 g of gasoline (C10H19) per km and the fuel air
mixture is stoichiometric (Φ =1.0).
Task:
a. Estimate the average emissions in g/km and compare with the emission standard
Euro 4.
b. Calculate the volume fractions of the pollutants in the dry exhaust gases.
5. A four cylinder four stroke turbocharged diesel engine with displaced volume 4.8 liter
operates at an inlet pressure of 1.8 bar and an inlet temperature of 325 K after the
aftercooler at a speed of 2000 rpm with a volumetric efficiency of 0.9 (based on the inlet
conditions) and a fuel/air equivalence ratio of 0.5.
The compressor characteristics are those shown in figure below. The exhaust gas
temperature is 650oC. Ambient conditions are 1 bar, 15oC.
Tasks:
a. Calculate the speed of the turbocharger rotor.
b. Calculate the required pressure at the turbine inlet if the isentropic efficiency of
the turbine is 0.65
The isentropic exponent for compression of air in the compressor can be assumed to be
1.4 and that for expansion in the turbine to 1.33.
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Internal combustion engine and reciprocating machine
AAiT, Mechanical engineering Department
The specific heats for air and combustion gases can be assumed to be 1005 and 1130
kJ/kg K respectively.
The compressor power can be obtained from:
 1






p
T

 m
 air c p , air in  out 
W
 1
c
c  p in 



And the turbine power from:
 1 

  
 p
 m
 exh cp,exh T  Tin 1   out 
W
T

  p in 



6. Calculate the volume fraction of CO and H2 in the combustion products after the
combustion of Methanol (CH3OH) in an Otto cycle with air factor of γ = 0.9. Use the
assumption that in fuel rich mixture combustion, equilibrium between the compounds,
CO, H2, CO2 and H2O determine the composition of the combustion products. Assume
equilibrium at 1300K and 1 bar is assumed.
7. In the combustion of Methanol (CH3OH) in an Otto engine the air fuel mixture is ignited
at the pressure of 20bar. The local temperature where the spark from the spark plug has
passed is 2500K.
a. Assume that the reaction rate can be estimated from global single stage reaction
relationship and use this to estimate the initial rate of consumption of the fuel in (Kg
Methanol/s.m3) if the air fuel mixture is stoichiometric
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Internal combustion engine and reciprocating machine
AAiT, Mechanical engineering Department
b. Calculate the initial rate of energy released (MJ/s.m3). The lower heating value of
Methanol is 19Mj/Kg
Where A = 3.2 *1011
E = 30 kcal/gmole
n = 0.25, m = 1.5 and l = 0
̅
𝑅 = 8.314 𝐾𝐽/𝐾𝑚𝑜𝑙𝑒. 𝐾
8. Methyl alcohol (CH3OH) burns with excess air at an air-fuel ratio (mass) of 8.0.
Determine the equivalence ratio and the mole fraction of CO2 in the product mixture
assuming complete combustion.
9. Determine the enthalpy of formation in kJ/kmol for methane, given the lower heating
value of 50,016 kJ/kg at 298 K.
10. If a lean ( = 0.8) mixture of methane is burned at a temperature of 1500K and pressure
of 500 kPa producing CO2, H2O, O2, N2. Calculate by hand the mole fraction of the
products, then use the applet to calculate the equilibrium mole fractions, comment on the
difference if any between the two sets of values
11. A mixture of ethane (C2H6) and air with an equivalence ratio of 1.1 is burned at constant
pressure. The products of combustion include CO2, H2O, CO, H2 and N2. Gas
chromatograph measurements indicate that for every mole of CO in the products there are
3 moles of CO2.
a) Determine the air to fuel ratio for the reactant mixture.
b) Determine the mole fractions of the species in the product mixture.
12.
a. A. Determine the upper and lower heating values at 298K of gaseous n-decane
(C10H22) per kilomol of fuel, and per kilogram of fuel.
b. If the enthalpy of vaporization of n-decane at 298K is 359 kJ/kgfuel, what are the
upper and lower heating values?
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Internal combustion engine and reciprocating machine
AAiT, Mechanical engineering Department
c.
Calculate the adiabatic flame temperature for a stoichiometric gaseous mixture of ndecane and air at 298K and 1 atm assuming complete combustion. Calculate to within
50K. Assume constant specific heats, use average values provided above.
13. Calculate the adiabatic temperature of Stoichiometric Methane-Air. Assume that cp
=1005J/Kg.K. The properties of the combustion products are given in the table below
14. Using the same data as above, recalculate the flame temperature if the fuel is burned with
10% excess air.
II.
Theoretical questions
1. In a spark ignition engine if the knock sensor picks up knock, the ECU immediately
retards ignition. Explain why this alleviates knock.
a. Explain why a high octane gasoline would make a terrible fuel for a
compression ignition engine
b. As far as emissions go, explain why a lean mixture is burned in a CI engine.
What affect does that have on power and the emission after-treatment that can
be implemented.
c. Ethanol is considered a “green” fuel yet when it is burned in an IC engine it
produces the greenhouse gas CO2. Explain why it is considered “green”.
d. What type of fuel when burned does not produce CO2?
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