Allan T. Kirkpatrick - Internal Combustion Engines

3‐4: Isentropic expansion stroke

4‐5: Isentropic blowdown

5‐6: Constant pressure adiabatic exhaust stroke

Appendix F contains a listing of the program FourStrokeOtto.m, which iterates through the above four‐stroke Otto gas cycle equations to determine the cycle pressures, temperatures, and the overall thermal parameters.

Compute the volumetric efficiency, net thermal efficiency, residual fraction, intake stroke temperature rise , and the exhaust stroke temperature decrease, , of an engine that operates on the ideal four‐stroke Otto cycle. The engine is throttled with an inlet pressure of 50 kPa and has an inlet temperature of 300 K. The exhaust pressure is 100 kPa. The compression ratio, 10. Assume an energy addition of 2500 kJ/ and 1.3. Plot the volumetric efficiency, net thermal efficiency, and residual fraction as a function of the intake/exhaust pressure ratio for .

The program input portion of FourStrokeOtto.mis shown below.

four-stroke Otto cycle model Input parameters: Ti = 300; inlet temperature (K) Pi = 50; inlet pressure (kPa) Pe = 100; exhaust pressure (kPa r = 10; compression ratio qin = 2500; energy addition, kJ/kg (gas) R = 0.287; gas constant (kJ/kg K) f = 0.05; guess value of residual fraction f Tr = 1000; guess value of exhaust temp (K) tol = 0.001; convergence tolerance ....

For the above conditions, as shown in Tables 2.3and 2.4, the computation indicates that the intake stroke temperature rise, , is about 45 K, and the exhaust blowdown temperature decrease, , is about 280 K. The volumetric efficiency, , the net thermal efficiency, , and the residual fraction, 0.053.

Table 2.3State Variables for Four‐Stroke Example 2.3

Table 2.4Computed Performance Parameters for Four‐Stroke Example 2.3

Residual Fraction	=	0.053
Net Imep (kPa)		612.0
Ideal Thermal Efficiency	=	0.499
Net Thermal Efficiency	=	0.461
Exhaust Temperature (K)		1309.0
Volumetric Efficiency	=	0.91

Volumetric efficiency for Example 2.3. Residual fraction for Example 2.3.

The volumetric efficiency, Equation ( 2.63), the residual fraction, Equation ( 2.47), and the net thermal efficiency (Equation ( 2.67)) are plotted in Figures 2.13, and 2.14, respectively, as a function of the intake/exhaust pressure ratio.

Comment: As the pressure ratio increases, the volumetric efficiency and thermal efficiency increase, and the residual fraction decreases. The dependence of the volumetric efficiency on compression ratio is reversed for the throttled and supercharged conditions. In addition, the residual gas fraction increases. The increase in residual fraction is due to the decrease in the intake mass relative to the residual mass as the intake pressure is decreased.