# Engine Efficiency

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Abstract: The conversion of fuel energy into useful work in an internal combustion engine involves a number of loses. These include the chemical energy loss in emissions, heat losses from the engine and through the exhaust gas, and gas pumping and friction losses in the engine. Accordingly, the overall brake thermal efficiency of the engine is a product of the combustion, thermodynamic, gas exchange, and mechanical efficiency.

## Engine Energy Losses

### Summary of Losses

The conversion of fuel energy into useful work in an internal combustion engine involves a number of loses. The major engine energy losses and the corresponding efficiency factors are illustrated in Figure 1 [3038].

Starting with the combustion of a hydrocarbon fuel and release of its energy, a small amount of fuel does not convert fully to the ideal combustion products CO2 and H2O. The energy remaining in the unburned fuel and combustion intermediates is accounted for by the combustion efficiency.

Of the energy released by the combustion process, the second law of thermodynamics determines that only a fraction of it can be converted into useful work. This fraction is accounted for with the thermodynamic efficiency which depends of details of the cycle being used to convert heat to work. For internal combustion engines, the upper limit of thermodynamic efficiency is usually determined with Otto and Diesel cycles calculations. Combustion energy that is not converted into mechanical work is lost as heat either through exhausting hot exhaust gases to the environment or through heat transfer through the combustion chamber surfaces. The gross indicated efficiency equals the product of combustion efficiency and thermodynamic efficiency and reflects the total work yielded by the combustion of the fuel.

Of the energy that has been converted into work, some of that work is used to induct intake gases into the engine and expel exhaust gases. This pumping loss is accounted for with the gas exchange efficiency. The net indicated efficiency adjusts the gross indicated efficiency to account for the work required to move gases into and out of the engine.

Some work must also be used to overcome friction between sliding surfaces such as piston rings and bearings and to drive necessary auxiliaries such as oil and coolant pumps. The later is accounted for with the mechanical efficiency. Confusingly, gas exchange losses and friction losses are sometimes combined into a single loss that is used to determine mechanical efficiency. This is discussed below.

The remaining work, the brake work, is thus available from the engine to do useful work. The brake efficiency (or brake thermal efficiency) can be expressed as:

ηbrake = ηcombustion · ηthermodynamic · ηgas exchange · ηmechanical(1)

Another way to express brake efficiency is [3980]:

ηbrake = ηclosed cycle · ηopen cycle · ηmechanical (2)

where:
ηclosed cycle is the closed cycle efficiency, the closed cycle being the part of the 4-stroke cycle when the intake and exhaust valves are closed. ηclosed cycle = ηcombustion · ηthermodynamic
ηopen cycle is the open cycle efficiency, the open cycle being the part of the 4-stroke cycle when the intake or exhaust valves are open. ηopen cycle = ηgas exchange

It should be noted that this discussion of engine efficiency is from the perspective of the process used to convert heat to work, i.e., it is restricted to a certain type of machine, and reflects the limitations of the machine or thermodynamic cycle used to convert heat to work. Efficiency can also be viewed from the perspective of the fuel and the amount of fuel exergy that can be converted to work. The later approach, discussed later, is more general and is not limited to any particular thermodynamic cycle.

### Fuel Energy

In the internal combustion engine, air and fuel are mixed to form a combustible mixture that is ignited and releases energy in the form of heat. The amount of heat released depends on a number of factors. While the amount of fuel trapped in the cylinder is the primary determinant of the energy content of the trapped air/fuel mixture and thus the total amount of heat that can be released, a number of secondary factors are also important. These secondary factors include details about the fuel composition such as the type of elements contained in the fuel and the nature of the bonds joining the elements together.

For engines, the net energy released from combustion is typically represented by the lower heating value (LHV) of the fuel since the water produced by combustion is assumed to remain in the vapor state. Figure 2 shows the LHV of a range of fuels that could be used in an internal combustion engine versus their stoichiometric air fuel ratio. Notice that for hydrocarbon fuels, the LHVs are very similar and considerably higher than for fuels containing oxygen. Oxygenated functional groups contribute less net energy during combustion while contributing significantly to the fuel’s mass and volume.

Once the fuel choice has been fixed, the engine power is determined by the energy content of the air/fuel mixture trapped in the cylinder prior to combustion. For engines where air/fuel mixing is carried out prior to the induction of intake charge into the cylinder, this energy is related to the amount of air/fuel mixture that can be inducted and trapped into the cylinder. For engines where air/fuel mixing occurs in-cylinder after IVC, it depends on the amount of air that can be inducted and trapped into the cylinder. It can be shown that [4730]:

$H port = ρ mix LHV f λ · AFR stoich + 1 H_port = {ρ_mix LHV_f} over {λ AFR_stoich +1}$ (3)

where:
Hport = energy content per unit cylinder volume of mixture formed prior to induction into the cylinder, MJ/m3
ρmix = density of the mixture, kg/m3
LHVf = lower heating value of the fuel, MJ/kg
λ = relative air fuel ratio of the mixture
AFRstoich = stoichiometric air fuel ratio

and

$H DI = ρ air LHV f λ · AFR stoich H_DI = {ρ_air LHV_f} over {λ AFR_stoich}$ (4)

where:
HDI = energy content per unit cylinder volume of mixture formed in the cylinder after IVC, MJ/m3
ρair = density of air, kg/m3

It should be noted that for most liquid fuels, the difference between Hport and HDI is small. However, for gaseous fuels such as methane, the principal component of natural gas, the difference can be more significant, Figure 3. Also, in some cases where air and fuel are mixed in-cylinder prior to IVC, Hport is more reflective of the energy that can be trapped in-cylinder. The effect of intake pressure boosting with a turbocharger or supercharger in Equation (3) and Equation (4) is accounted for through the density term.

Figure 4 illustrates the values of Hport and HDI of stoichiometric mixtures of several fuels at standard conditions versus their stoichiometric air fuel ratio and based on the most common means of mixing them with intake air [4730]. While there are important differences, it is noteworthy that the power output of an engine fueled with any of these fuels, based on mixture energy density alone, would be remarkably similar. However, it should be noted the mixture energy density alone is not sufficient to determine the maximum output from an engine.

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