Assignment 1
Question 1
Perform an investigation into the relative merits of using petrol versus E10. Model petrol as being gasoline with 8 atoms of carbon in each fuel molecule; E10 is gasoline blended with ethanol, with the ethanol content being 10% by volume. The latent heat of vaporisation of gasoline is 298 kJ/kg, while for ethanol it is 846 kJ/kg.
(a) Determine the coefficients for the balanced chemical reaction at stoichiometric conditions for both petrol and E10 with air.
(b) The engine has a 2.5 L capacity and is operating at 2000 rpm. Determine the required volume flow rate of air-fuel mixture.
(c) Assume the intake manifold has an inner radius of 2 cm with a total of 4 identical pipes, while the pressure is 101.3 kPa and temperature is 25°C. For the situation where the throttle is wide open, the pressure in the cylinder will be very similar to the inlet manifold pressure while the inlet valve is open. Calculate the speed of the air prior to mixing (only for petrol).
(d) The temperature and pressure of the fuel-air mixture is raised to 1000 K and 3.0 MPa by the action of the spark. For gasoline, use the enthalpy of formation for octane; for ethanol, use
-277 690 kJ/kmol as the enthalpy of formation. Determine the adiabatic flame temperature for:
i. the gasoline-air mixture.
ii. the E10-air mixture.
(e) Calculate the initial consumption rate in kg/m3s for the oxygen in the conditions described in part (d). Note that if 5 moles of oxygen are required to consume 1 mole of gasoline or E10, then the formula for the consumption rate of oxygen should be multiplied by 5. Calculate the consumption for:
i. the gasoline-air mixture. For the single-step reaction of gasoline, the parameters are:
Ea/Ru = 15 098 K, A = 2.587 × 109 (kmol/m3)-0.75/s, m = 1.5 and n = 0.25.
ii. the E10-air mixture (solve for gasoline-air and ethanol-air separately, then add the results appropriately). For the single-step reaction of ethanol, the parameters are:
Ea/Ru = 15 098 K, A = 8.435 × 109 (kmol/m3)-0.75/s, m = 1.6 and n = 0.15.
(f) The theoretical maximum power generated by the engine can be estimated using:
Pmax = HHV x mmix
The theoretical maximum can be determined if the HHV is calculated based on returning the products to ambient conditions. Calculate this power for:
(1)
i. the gasoline-air mixture.
ii. the E10-air mixture
(g) Record the price of petrol and E10 near you from the same service station at the same time.
i. Estimate whether the relative cost of petrol and E10 is fair by comparing the cost per unit of energy, which is the standard method of comparing fuels.
ii. Estimate what price the E10 would need to be for the cost per unit of energy to be the same.
iii. If the price of E10 is 4c/L cheaper than petrol, at what price is the cost per unit of energy the same?
(h) Discuss your results:
i. For parts (d), (e) and (f), compare the results for the two different fuels and explain why they are similar/different.
ii. For part (d), refer to the Detailed Chemistry Notes and explain why your answers are similar/different to the equilibrium temperatures.
iii. For part (e), refer to the very end of the Detailed Chemistry Notes and compare your answers to what happens over the duration of the reaction.
iv. For part (f), consider the typical power output for an engine and discuss why it is different to the theoretical maximum results.
v. For part (g), discuss when it is more economical to use petrol and when it is more economical to use E10.
vi. Based on your findings, provide hypotheses as to why car manufacturers have generally been able to convert their engines to use either petrol or E10, but not also E85.
Table 1: Sensible enthalpies of gasoline and ethanol. Calculated from Heywood (1988).
|
T (K)
|
Δhs (kJ/kmol)
|
|
Gasoline
|
Ethanol
|
|
300
|
358
|
149
|
|
400
|
20668
|
8278
|
|
500
|
45468
|
17670
|
|
600
|
74208
|
28226
|
|
700
|
106268
|
39847
|
|
800
|
141102
|
52431
|
|
900
|
178291
|
65880
|
|
1000
|
217558
|
80093
|
|
1100
|
258778
|
94971
|
|
1200
|
301982
|
110415
|
|
1300
|
347360
|
126323
|
|
1400
|
395262
|
142597
|
|
1500
|
446200
|
159136
|
|
1600
|
500847
|
175841
|
|
1700
|
560036
|
192612
|
|
1800
|
624764
|
209350
|
|
1900
|
696190
|
225954
|
|
2000
|
775634
|
242324
|
|
2100
|
864579
|
258362
|
|
2200
|
964671
|
273966
|
|
2300
|
1077718
|
289038
|
|
2400
|
1205690
|
303477
|
|
2500
|
1350719
|
317183
|
|
2600
|
1515101
|
330058
|
|
2700
|
1701294
|
342000
|
|
2800
|
1911917
|
352911
|
|
2900
|
2149753
|
362690
|
|
3000
|
2417748
|
371238
|
Question 2
This question requires the identification of a suitable flame and an analysis of the combustion processes. For example you may choose a gas stove burner, a cigarette lighter, a candle, an oxy- acetylene flame, wood combustion, or another form of combustion which produces a visible flame. Describe the flame in detail using annotated sketches and calculations as required below.
You must personally observe the flame behaviour. It is not sufficient to rely on material which other people may have presented in text books or on the internet.
You are also required to determine the flow rate of the fuel. This might be done for example, by taking gas meter readings over a period of time, or perhaps by measuring the change of weight of the gas cylinder, candle, piece of wood, etc over a given interval of time. However, remember that you are dealing with flames and other devices that are likely to be very hot so take all precautions necessary to avoid getting burnt. Furthermore, you are dealing with fuels that can potentially release large amounts of energy in a very short period, so any device used should comply with relevant national standards and only use combustion devices in the manner intended by the manufacturer. You must not modify any combustion system including burners, gas bottles, fuel delivery and metering devices in any way whatsoever.
(a) Provide an image of the entire combustion system and state what the system is. Present your own annotated photograph or a detailed sketch of the flame and identify the different regions of the flame which you have observed personally.
(b) What is the fuel and what is its chemical composition?
(c) Produce a balanced combustion equation for the process.
(d) What is the fuel mass flow rate (the rate of consumption of the fuel) under typical conditions? Include a description of the experiment and analysis by which you obtained this flow rate, and perform an error analysis of your answer.
(e) Based on an estimate of the fuel density in its gaseous form, and an estimate of the available flow area(s), what is the fuel flow speed as it approaches the mixing and/or combustion zone?
(f) How does the fuel and oxidant mix? Also illustrate the mixing process with a sketch.
(g) Estimate a relevant Reynolds number for the configuration and discuss if this is consistent with the observed laminar or turbulent characteristics of the flame.