2.61 Internal Combustion Engines

Problem Set 2 Tuesday, February 10, 2004

Due: Thursday, February 19, 2004

1. Several velocities, time, and length scales are useful in understanding what goes on inside engines. Make estimates o the following quantities for a 1.6-liter displacement four-cylinder spark-ignition engine, operating at wide-open throttle at 2500 rev/min. (a) The mean piston speed and the maximum piston speed. (b) The maximum charge velocity in the intake port (the port area is about 20 percent of the

piston area). (c) The time occupied by one engine operating cycle, the intake process, the compression

process, the expansion process, and the exhaust process. (Note: The word process is used here not the word stroke.)

(d) The average velocity with which the flame travels across the combustion chamber. (e) The length of the intake system (the intake port, the manifold runner, etc.) which is filled

by one cylinder charge just before the intake valve opens and this charge enters the cylinder (i.e., how far back from the intake valve, in centimeters, one cylinder volume extends in the intake system).

(f) The length of exhaust filled by one cylinder charge after it exits the cylinder (assume an average exhaust gas temperature of 425 C)

You will have to make several appropriate geometric assumptions. The calculations are straightforward, and only approximate answers are required.

2. Evaluate the maximum bmep, the bmep at maximum power and the maximum value of the mean piston speed (where applicable) for the engines described in the attached sheets: Gasoline (natural aspirated and turbocharged) (a) General Motors Vortec 4.2L DOHC I-6 (b) Audi AG 4.2L DOHC V-8 (c) BMW AG 3.2L DOHC I-6 (d) K13C with common rail fuel injection (e) Subaru 2.5L H-4 turbocharged

Diesel (natural aspirated and turbochared) (f) 5.9L Cummins 600 OHV l-6 turbodiesel (g) Isuzu new V12 PE1-S (h) Mitsubishi 2.8L

Specialty (hybrid, rotary, formula 1) (i) Mazda 1.3L Renesis rotary (j) Toyota 1.5L DOHC I-4 Hybrid (k) Formula 1 engine: naturally aspirated, 3.0 liter, 10-cylinder, stroke to bore ratio is 0.48,

maximum brake power at 17000 rpm is 800 hp and the maximum brake torque at 13000 rpm is 350 Nm

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Explain briefly the differences in performance parameters between the various engine configurations: - SI: 2 valves per cylinder, 4 valves per cylinder, F1 racing engines - CI: naturally aspirated, turbocharged engines

Also using the bsfc maps for the Isuzu H-Series diesel, the Audi 5-cylinder turbo diesel and the Toyota SI 3L V-6 engine, calculate the brake fuel conversion efficiencies at the following conditions: - Best efficiency - Typical automotive light load operation (half speed and 25% load)

3. The Isuzu V12 DI diesel 12PEI-S engine described in the attached sheets is operating at 2000 rpm, full load. At this operating condition the total friction power (consisting of rubbing friction, pumping and accessory power) is 50 kW. Making an appropriate assumption for the relative air-fuel ratio (remember that diesels operate lean overall) and using the manufacturer’s specifications, calculate the following: (a) mechanical efficiency (b) brake fuel conversion efficiency (c) indicated fuel conversion efficiency (d) volumetric efficiency The engine is working with light diesel fuel, which has lower heating value 43.2 MJ/kg and stoichiometric air-fuel ratio 14.5.

4. Using the ideal constant volume combustion cycle model, draw an accurately proportioned cylinder pressure versus cylinder volume diagram for a lower compression ratio engine (say 8) and a higher compression ratio engine (say 12) that shows why the higher compression ratio engine has a higher indicated fuel conversion efficiency. In making this comparison on a p-V diagram, a critical question is “what should be held constant?” Possible choices are one or more of these: maximum cylinder volume, displaced cylinder volume, mass of air in cylinder, mass of fuel in cylinder, relative air/fuel ratio of mixture in cylinder, pressure in cylinder at start of compression, temperature of gas in cylinder at start of compression. (a) Explain your choice of which of the above you will hold constant in this comparison. (b) Carefully draw the two p-V diagrams on the same graph, indicating the relative magnitude

of pressures and temperatures at start and end of compression, at start and end of expansion.

(c) Using these p-V diagrams explain why the higher compression ratio engine is more efficient

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