Allan T. Kirkpatrick - Internal Combustion Engines

(1.27)

The equivalence ratio is used to characterize the fuel–air mixture composition. If the mixture is stoichiometric, if the mixture is lean, and if the mixture is rich.

A six‐cylinder, four‐stroke automobile engine is being designed to produce 75 kW at 2000 rpm with a bsfc of 260 g/kWh and a bmep of 9.2 bar (920 kPa). The engine is to have equal bore and stroke, and will be fueled with a stoichiometric mixture of gasoline and air with an air–fuel ratio (AF) of 15.27. Gasoline has a heat of combustion = 44,510 kJ/kg. (a) What is the design displacement volume and bore ? (b) What is the mean piston speed at the design point? (c) What are the cycle average fuel flow and air flowrates and the fuel consumption per cycle per cylinder? (d) What is the work per cycle per cylinder? (e) What is the thermal efficiency?

1 The displacement volume isMost automobile engines have a 90–100 mm bore and stroke.

2 The mean piston speed is

3 The cycle average fuel consumption rate per cylinder isso the mass of fuel injected per cylinder per cycle isand the cycle average airflowrate is

4 The brake work per cycle per cylinder is

5 The brake thermal efficiency is

Assuming a flat piston top, the instantaneous cylinder volume, , at any crank angle is

(1.28)

where is the instantaneous stroke distance from top dead center:

By reference to Figure 1.6

(1.29)

If the instantaneous volume is nondimensionalized by the volume at bottom dead center, , then the nondimensional volume is

(1.30)

We define a nondimensional parameter, , the ratio of the crankshaft radius to the connecting rod length , as

(1.31)

The range of for the slider‐crank geometries used in modern engines is about 0.25 to 0.33.

Therefore, the nondimensional piston displacement is

(1.32)

and the nondimensional cylinder volume is

(1.33)

For , we can expand the term in a Taylor series,

(1.34)

so

(1.35)

As , the approximate volume can then be expressed as a function only of the compression ratio :

(1.36)

The cylinder volumes predicted by Equations ( 1.33) and ( 1.36) are compared in Figure 1.11for a value of , using the Matlab® program Volume.mlisted in the Appendix. Both equations give identical results at bottom dead center and top dead center. The approximate volume relation underpredicts the exact cylinder volume by about 18% at 59 degrees near the middle of the stroke.