In all the questions below assume, if not specified otherwise, that the fuel is a mixture of 60% of iso-octane CoHis and 40% of ethanol C₂H₅OH on molar basis. The initial temperature and pressure are Po = 1.0 atm and To = 350K.

a) If a combustion chamber of the internal volume V = 2.0 litres is filled with the stoichiometric mixture of this fuel mixture with air, calculate:

1. Mass fractions of ethanol and oxygen in the fresh gas
2. Molar concentrations of iso-octane and oxygen in the fresh gas
3. Partial pressures of ethanol and oxygen in the fresh gas
4. Air-fuel and fuel-air ratios by mass

b) Assuming complete combustion, write the stoichiometric equation for combustion of this fuel in air at an equivalence ratio of Φ= 0.78.

c) The combustion products in an SI engine have the temperature and pressure of 2400 K and 60 bar, respectively. The engine is fuelled with a stoichiometric mixture of the above-mentioned fuel blend with air. The combustion products consist of CO2, CO, H2O, H2, 02 and N2; the oxygen volumetric fraction was measured as 0.4% vol. Determine the products composition.

d) Consider a constant volume combustion of this fuel blend at the initial pressure of 8.0 bar and temperature of 400K. With the help of GASEQ software available in "Departmental Software - > Engineering - > Mechanical Engineering" tab on the 5th floor cluster, (or another similar package) determine how changes of equivalence ratio from 0.6 to 2.2 affect:

1. Adiabatic flame temperature
2. Pressure at the end of combustion
3. Equilibrium molar fraction of NO and CO
4. Degree of dissociation of the water vapour in the combustion products

Present these results in the graphical form; based on those, briefly comment what equivalence ratio is optimal for an SI engine and why.

e) A spherical flame is initiated by a centrally located spark in a spherical vessel of the internal volume V = 2.0 litres. At the initial time, t = 0, the flame kernel size generated by the spark is r_ft(t = 0) = 2.0mm. The initial temperature and pressure are ρo = 1.0 atm and To = 350K.

Assuming that a)the laminar flame speed depends on the stretch rate s^. = 1/AdA/dt as Sn = Sn^o - Lb.s^., and b) the flame thickness is very small and does not change with time, plot the flame radius and the flame speed as functions of time. Assume that the unstretched flame speed Sn^o = 2.8m/sec and the Markstein length is Lb = 2.0mm. Compare the obtained results with the published measurements of burning velocity for individual components of the blend, e.g. for iso-octane Sn were measured in the spherical bomb by Bradley, D. et al. Comb & Flame, vol. 115, pp. 126 - 144 (1998).

f) Calculate the peak pressure, the volumetric efficiency, the indicated mean effective pressure (i.m.e.p), and the indicated thermal efficiency of a naturally aspirated SI engine if it is fuelled with a mixture of air with the ethanol-i-octane blend described above. Assume that the combustion occurs instantaneously at the TDC and the combustion products are at the thermo-chemical equilibrium. Consider the expansion and compression strokes as polytropic with the exponent 1.32. The engine has: bore of 75mm, stroke of 120 mm and the connecting rod length of 260 mm. The clearance volume at the top dead centre is VTDC = 64cm3. The intake valve opens at 10 deg bTDC and closes at 80 deg before BDC and the exhaust valve opens at 80 deg bBDC and closes at TDC and the pressure in the cylinder is immediately equalised with the atmospheric at the moments of valve opening, so that the throttling loss is negligible. Determine the pressures and temperatures at the beginning of each stroke and plot the engine operating cycle on a p - V diagram.

g) Compare the effects of addition of ethanol to gasoline upon the performance of SI engines with a) manifold fuel injection and b) direct injection spark engine with late ignition timing.

h) Sketch the dependency of the self-ignition delay upon temperature for a) iso-octane and b) ethanol for high and low pressures. From those estimate what could be an effective octane number of the fuel blend described above.

i) Define the mixture fraction for the non-premixed combustion of the fuel blend specified above. Assuming infinitely fast chemistry, express the mass fraction of the water vapour in terms of the mixture fraction.

Full references should be given to all sources of information and any citations from the literature should clearly be acknowledged. It is acceptable to copy diagrams and figures from the literature sources provided this is clearly acknowledged.

This assignment is a part of the examination process and, as such, the students are advised not to let my other student see their work, or to advise them on how to proceed. Similar reports will be considered Ls plagiarism or academic malpractice and appropriate action will be taken.