Internal Combustion Engines. Allan T. Kirkpatrick

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efficiency for an engine operating at a speed is

(1.19)

      The factor of 2 in Equation (1.19) accounts for the two revolutions per cycle in a four‐stroke engine. The ideal gas equation is used to determine the air density in the intake manifold,

      (1.20)

      The parameter is the ideal gas constant for air with a value of kJ/kg‐K. The intake manifold air density is used as a reference condition instead of the standard atmosphere, so that the effect of a supercharger is not included in the definition of volumetric efficiency. The standard atmosphere is assumed to have a temperature = 298 K and pressure = 101.3 kPa, with a corresponding density = 1.184 kg/.

      For two‐stroke cycles, an equivalent volumetric efficiency parameter is the delivery ratio , which is defined in terms of the ambient air density instead of the intake manifold density:

      (1.21)

A representative plot of volumetric efficiency versus engine speed of an automotive four‐stroke engine is shown in Figure 1.9. The shape and location of the peaks of the volumetric efficiency curve are very sensitive to the engine speed as well as the manifold configuration. Some configurations produce a flat curve, others produce a very peaked and asymmetric curve. As we will see later, the volumetric efficiency is also influenced by the valve size, valve lift, and valve timing. It is desirable to maximize the volumetric efficiency of an engine since the amount of fuel that can be burned and power produced for a given engine displacement (hence size and weight) is maximized. Although it does not influence in any way the thermal efficiency of the engine, the volumetric efficiency will influence the overall thermal efficiency of the system in which it is installed. As Example 1.1 below indicates, the volumetric efficiency is useful for determination of the air flowrate of an engine of a given displacement and speed.

Figure 1.9 Effect of engine speed and intake manifold geometry on volumetric efficiency. Adapted from Armstrong and Stirrat (1982).

      Example 1.1 Volumetric Efficiency

      A four‐stroke 2.5 L () direct injection automobile engine is tested on a dynamometer at a speed of 2500 rpm. It produces a torque of 150 Nm, and its volumetric efficiency is measured to be 0.85. What is the brake power , and the mass air flowrate through the engine? The intake manifold air pressure and temperature are 75 kPa and 313 K.

      Solution

      The engine power is:

      The intake manifold air density is

      and the mass air flowrate is:

      Specific Fuel Consumption

      The specific fuel consumption is a comparative metric for the efficiency of converting the chemical energy of the fuel into work produced by the engine. As with the mean effective pressure, there are two specific fuel consumption parameters, brake and indicated. The brake‐specific fuel consumption (bsfc) is the fuel flowrate , divided by the brake power . It has three parameters that are standard measurements in an engine test: the fuel flowrate, the torque, and the engine speed. The brake‐specific fuel consumption for naturally aspirated automobile engines depends on the engine load and speed, and can have values ranging from about 175 to 400 g/kWh.

      (1.22)

      The indicated specific fuel consumption (isfc) is the ratio of the mass of fuel injected during a cycle to the indicated cylinder work, and is used to compare engine performance in computational simulations that do not include the engine friction.

      (1.23)

An engine performance map is used to present the effects of speed and load on engine performance, as shown in Figure 1.10. The engine speed or the mean piston speed is plotted on the ‐axis, and the brake mean effective pressure (bmep) is plotted on the ‐axis. Contour lines of constant bsfc are plotted on this load‐speed plane. The lines of constant bsfc are approximately independent of displacement for a given engine family, so engine performance maps can be used to match an engine with a given load. For a spark‐ignition engine, the upper envelope on the map is the wide open throttle line. Its shape reflects variations in the volumetric efficiency with engine speed, although small changes in inlet air density are also involved.

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