MEEN 410, SECTION 500 INTERNAL COMBUSTION ENGINES

Spring 2012 Homework #3 Solutions DUE February 16, 2012

1. Consider two compression processes with the following P-v data:

Process A Process B v (m3/kg) P (kPa) P (kPa)

Initial State 0.86100 100 100 0.78925 112 113 0.71750 126 129 0.64575 144 150 0.57400 168 176 0.50225 199 213 0.43050 242 264 0.35875 305 341 0.28700 406 466 0.21525 586 696 0.14350 982 1229

Final State 0.07175 2377 3242

The working fluid is air with R = 0.287 kJ/kg K, = 1.4 and the initial temperature is 300 K

Determine: a) The polytropic index of each process. Is either of the two processes "special"? b) The compression ratio for each process. c) Using both linear and logarithmic scales, generate two plots where both p-V processes are

on the same plot. d) Determine the specific work for each process and whether work is being done on the gas or

done by the gas. e) Determine the temperature at the end of each compression process. f) Determine the specific heat transfer for each process and whether there is heat input or heat

rejection. Solution:

2. It is desired to increase the output of a spark-ignition engine by either: (1) raising the compression ratio from 8 to 11, or (2) increasing the inlet pressure from 1.0 atm to 1.8 atm

Assume = 1.3 and 1/ 9.3 1 /f HV vm Q mc T r r . Using the constant volume cycle as a

model for engine operation, which procedure will give:

a) The highest pressure in the cycle?

b) The highest efficiency? c) The highest i.m.e.p.? Solution:

3. The performance of a given diesel engine is approximated by the limited pressure cycle. The

compression ratio of the engine is 16 and the total heat added to the cycle is 1935 kJ per kg of working fluid. The inlet conditions are P1 = 150 kPa and T1 = 320 K. Assume that = 1.3 and R = 0.287 kJ/kg-K. a) Assuming that half of the total heat is added at constant volume and half at constant pressure,

compute the indicated thermal efficiency of the limited pressure cycle. b) Compare the efficiency and peak pressure of the limited pressure cycle with the efficiency

and peak pressure that would be obtained if the same total heat were added at constant volume or at constant pressure.

Solution:

4. Consider a modification of the Air Standard Otto Cycle in which the isentropic compression and expansion processes are each replaced with polytropic processes having n = 1.3. The compression ratio is 8. At the beginning of compression P1 = 0.5 bar and T1 = 300 K. The maximum temperature reached in the cycle is 2000 K.

Determine: a) Heat and work transfer per unit mass of air for each process in a modified Otto Cycle. b) The thermal efficiency of the engine.

Solution:

5. The processes within an engine cylinder are modeled as an air standard diesel cycle with a cutoff ratio of 2.5. The displacement volume is 2 L. The state of the air at the beginning of compression is given by P1 = 115 kPa, T1 = 305 K, V1 = 2.2 L.

Determine: a. Net work per cycle b.Power delivered by engine at a crankshaft speed of 1000 rpm. c. Indicated Mean Effective Pressure d.Thermal Efficiency

Solution: