1. Problem 1
Diesel fuel (C12H26) at 25 ºC is burned in a steady flow combustion chamber with 20% excess air which also enters at 25 ºC. The products leave the combustion chamber at 500 K. Assuming complete combustion, determine the required mass flow rate of the diesel fuel to supply heat at a rate of 1500 KJ/s.
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C12H *( /4) (O N2) 
12 CO2 + (26/2) H2O + 0.2*12*O *( /4) *3.76 N2
Introduction
Combustion

2. Problem 1 Introduction Enthalpies of formation are taken from tables:
Sensible enthalpies are tabulated: (
(KJ/Kmol)
CO2
H2O O2 N2
8301
6947
6097
5920
(this enthalpy refers to the combustion of 1 kmol of C12H16)
Introduction
Combustion

3. Themochemical properties of CO2
T (K)
(kJ/kmol K)
(kJ/kmol)
298
37.198
300
37.280 69
400
41.276
4 003
500
44.569
8 301
600
47.313
12 899
700
49.617
17 749
800
51.550
22 810
900
53.136
28 047
1000
54.360
33 425
Introduction
Combustion

4. Problem 2
Determine the temperature at which 10% of H2 dissociates into H at 10 atm.
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2 H  H (equilibrium reaction)
Composition of the mixture: H2  0.9 H H
Linear interpolation from the table of equilibrium constants yields T = 3537 K.
Introduction
Combustion

5. Equilibrium constants
T (K)
log10 Kp
298
71,232
2600
2,836
300
70,762
2800
2,178
400
51,758
3000
1,608
600
32,676
3200
1,108
800
23,082
3400
0,664
1000
17,294
3600
0,270
1200
13,416
3800
-0,082
1400
10,632
4000
-0,400
1600
8,534
4500
-1,072
1800
6,896
5000
-1,612
2000
5,582
5500
-2,054
2200
4,504
6000
-2,422
2400
3,602
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Combustion

6. H2O + 2 O2  x H2O + y H2 + z O2 + w OH (equilibrium reaction)
Problem 3
A mixture of 1 Kmol of H2O and 2 Kmol of O2 is heated to 4000 K at a pressure of 1 atm. Determine the equilibrium composition of the mixture, assuming that only H2O, OH, O2 and H2 are present.
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H2O + 2 O2  x H2O + y H2 + z O2 + w OH (equilibrium reaction)
Mass balance for H: 2 = 2x + 2y + w
Mass balance for O: 5 = x + 2z + w
H2 and O2 are taken as independent species; H2O and OH may be formed from those two species as follows:
H2 + ½ O2  H2O log10 Kp (4000 K) = 0.238
½ H2 + ½ O2  OH Kp (4000 K)= (from the book by Kuo, 1986) .
Introduction
Combustion

7. Problem 3 Introduction (noting that p=po=1atm)
The solution of the system of 4 simultaneous equations yields the equilibrium composition:
x = 0.271, y = 0.213, z =1.849, w = 1.032
Introduction
Combustion

8. Problem 4
A closed chamber initially contains 1000 ppm of CO, 3% O2, and the remainder N2 at 1500K and 1 atm pressure. Determine the time for 90% of the CO to react assuming only the elementary reaction
CO + O2  CO2 + O
with k=2.5×106 exp(24060/T) [mol-1.m-3.s-1]
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The initial concentrations of CO and O2 are given by:
The reaction rate of CO is given by
Introduction
Combustion

9. Problem 4
Since [O2] >> [CO], it can be assumed that [O2] is essentially constant. Then, Integration in time is carried out as follows:
and
yielding t=34.9 s
Introduction
Combustion

10. Problem 5 Introduction Consider the following reaction mechanism:
2 NO  N2O2 (R1)
N2O2  2 NO (R2)
N2O2 + O2 2 NO2 (R3)
Determine the reaction rate of NO2 using the steady state assumption for N2O2
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The reaction rates of NO2 and N2O2 are given by:
The steady state assumption for N2O2 implies that
Introduction
Combustion

11. Problem 5
Therefore,
and
Introduction
Combustion

12. Problem 6
Calculate the stoichiometric mixture fraction for combustion of diesel fuel, approximated as C12H26, in (i) air; (ii) air diluted with recirculated gas products such that the mass fraction of air in the oxidizer is 80%.
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(i)
(ii)
C12H26 + ( /4) (O N2) 
12 CO2 + (26/2) H2O + ( /4) *3.76 N2
Introduction
Combustion

13. Problem 7
Compare the auto-ignition time of a fuel at 500 K and 520 K for two cases:
Fuel with Ea/Ro  = 3800 K; (ii) Fuel with Ea/Ro  = 20 000 K.
Assume that the reactive system is homogeneous and adiabatic.
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Assuming that the volume is constant, then B is approximately constant and
(i)
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Combustion

14. Problem 7
(ii)
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Combustion

15. Problem 8
Natural gas with a kJ/m3 higher heating value and a specific gravity of is to be replaced with a propane-air mixture. The higher heating value of propane is kJ/m3 and its specific gravity is
What is the volume fraction of propane for identical thermal output and upstream pressure?
What will be the ratio of volume flow rate of the replacement gas to that of the original gas?
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(a) The Wobbe index must be same for the two fuels. Hence,
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Combustion

16. Problem 8
(b)
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Combustion

17. Problem 9
A circular burner with an area of 0,80 cm2 has a uniform velocity profile (the boundary layer is neglected) at its exit. The mixture is air/propane, the temperature is 25 ºC and the pressure is 1 bar.
What is the height of the flame when  = 1.1 and the flow velocity at the exit of the burner is u = 1.2 ms-1 ?
To keep the same flame height, what should the velocity be if the mixture changes to  = 1.3 ?
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From the figure we obtain SL=0.39 for f=1.1. Since,
then
Moreover, r/h = tg a leading to
Introduction
Combustion

18. Problem 9
From the figure we obtain SL=0.32 for f =1.3. Since, the height of the flame remains constant, so does a. Therefore, from
we obtain
Introduction
Combustion

19. Problem 10
A certain Standard for testing the fire resistance of cloths requires that cloth samples should be burned in controlled conditions. One of those conditions states that the sample should be burned by a premixed laminar flame of 25 mm in height. Some (few) conditions for the fuel to be used are also imposed. One laboratory has a fuel made out of a mixture of light hydrocarbons that complies with the requirements imposed by the Standard. It has also a burner carefully designed, containing a very short tube of inner diameter equal to 12.0 mm and preceded by a contraction. The known properties of the fuel are as follows: M=28.5 kg/kmol, C/H=5.33, /cp=1.61x10‑5 kg/(ms) and = 6.2 moles/dm3s.
a)  Calculate the volumetric flow rates of air and of fuel to obtain the flame with the specified height, using a stoichiometric mixture.
b)  If the air flow rate is kept and the one of fuel is reduced, what will happen to the flame height ? And if the fuel flow rate increases rather than decrease ? Explain. Can you draw any conclusions from the behaviour of the flame ?
c)  Indicate which were the simplifying assumptions used in the resolution of a). The result obtained in a) is obtained by excess, by default, or you cannot know?
Introduction
Combustion

20. Problem 10 Introduction Calculation of the fuel composition (CxHy):
This yields x=2, y=4.5
CxHy + (x + y/4) (O N2)  x CO2 + (y/2) H2O (x + y/4) N2
Introduction
Combustion

21. Problem 10
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Combustion

22. Problem 11
Consider a spherical perfectly stirred reactor with an internal volume of 50.0 cm3 burning a mixture of methane and air with an equivalence ratio of The data presented below concerns the maximum possible flow of mixture fed to the reactor. From these data and making assumptions you feel are necessary or appropriate answer the following questions:
(a)  What is the mass flow rate of the mixture ?
(b)  What is the thermal power released in the reactor ?
(c)  What is the reaction rate in this situation ? How much could the maximum rate of reaction be ?
(d)  What are the molar fractions of oxygen and nitrogen inside the reactor ?
(e)  What is the concentration of NO (in ppm) immediately outside the reactor ?
Data: To = 398 K, p = 5 bar, T = 1680 K, Tad = 2230 K (for f=0.8 and To = 398 K)
PCI = MJ/kg, R=297 J/Kg.K, cp =1310 J/kg.K
Introduction
Combustion

23. Problem 11
The data of Longwell and Weiss shows that for f=0.80.
Hence,
(b)
(c)
CH4 + (2/f) (O N2)  CO2 + 2H2O + 2(1/f-1) O /f N2
Introduction
Combustion

24. Problem 11
(d)
(e)
Rfu,max occurs for t  0.8
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Combustion

25. Problem 12
Estimate the flame length for a propane jet flame in air at ambient conditions (p=1 atm, T∞ =300 K). The propane mass flow rate is 3.66×10-3 kg/s and the nozzle exit diameter is 6.17 mm. Assume the propane density at the nozzle exit is kg/m3.
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We need to determine first the Froude number:
Introduction
Combustion

26. Problem 12
Since Fr < 5, we have
Introduction
Combustion