B URNING V ELOCITY
4.2. PERFORMANCE OF THE IDEAL INTERNAL COMBUSTION ENGINE
The overall thermal efficiency of any reciprocating internal combustion engine is primarily a function of three parameters:
1. Compression ratio 2. Air–fuel ratio 3. Combustion duration
The ideal efficiency of an internal combustion engine is usually determined using an
“air-standard” analysis, in which pure air is used as the working fluid. A simple thermodynamic analysis of the ideal air-standard Otto cycle, which is a theoretical model for a spark-ignition engine, shows the efficiency to be
¼1 1
rgv 1
(4:1) whererv¼compression ratio andg¼Cp=Cv(ratio of specific heats).
The“compression ratio,”rv, more accurately described as the“volumetric compres- sion ratio,”is the ratio between the maximum cylinder volume at bottom-dead-center and the minimum volume at top-dead-center (TDC). All of the heat is assumed to be added to the cycle at constant volume at TDC. This simple analysis shows that for high efficiency, the compression ratio (or, as shown in Chapter 2, the expansion ratio) should be as high as possible.
A similar analysis of the ideal air-standard Diesel cycle results in
¼1 1
rgv 1
rgc1 g(rc1)
(4:2) whererc¼cutoff ratio.
In an ideal diesel engine, heat addition takes place continuously at constant pressure over a period between TDC and the“cutoff”point, which corresponds approximately to the time when fuel injection would end in an actual engine. The“cutoff ratio,”rc, for the ideal diesel cycle represents the ratio between the cylinder volume when the heat addition ends and the volume at TDC. The ideal thermal efficiency of the air-standard Otto cycle as a function of compression ratio is shown in Figure 4.1, compared to that for the air-standard Diesel cycle with various values of the cutoff ratio. Although, for a given compression ratio, the efficiency of the air-standard Diesel cycle is less than that of the Otto cycle, in practice, the diesel engine has a higher efficiency because it operates at a much higher compression ratio (typically 20:1 compared to 10:1 for the Otto cycle, which is limited by the peak pressure and engine knock).
The analysis also indicates that for high efficiency, the ratio of specific heats of the working fluid should be as high as possible. In practice, it turns out thatgfor air (1.4) is greater thangfor the air–fuel mixture for typical HC fuels. This means that the value of gwill be higher for mixtures with more air (i.e., lean mixtures) than for rich mixtures.
The analysis predicts then that thermal efficiency is higher for lean mixtures (mixtures with excess air) than for rich mixtures. Figure 4.2, taken from Heywood (1988), shows the theoretical efficiency for an ideal Otto cycle engine using fuel and air as the working fluid, rather than just air, as a function of the fuel–air equivalence ratio,f, for a range of compression ratios, r, from 6:1 to 24:1. An equivalence ratio of 1.0 provides a stoichiometric mixture, while values greater than 1.0 are rich mixtures and values less than 1.0 are lean mixtures.
Figure 4.2 clearly shows the trend of higher thermal efficiency as the mixture becomes leaner. This much steeper drop in efficiency forfgreater than 1.0 is a result of the presence of unburned fuel in the mixture. In other words, for rich fuel–air mixtures, there is not enough oxygen present to support complete combustion of all of the fuel. This figure indicates another reason for diesel engine efficiency being
0%
10%
20%
30%
40%
50%
60%
70%
80%
4 6 8 10 12 14 16 18 20 22 24
Compression ratio
Efficiency
Otto cycle Diesel – rc= 2 Diesel – rc= 3 Diesel – r
c= 4
Figure 4.1 Variation of efficiency with compression ratio for a constant volume air-standard cycle.
greater than Otto cycle efficiency, since the un-throttled diesel engine always operates at a very lean overall fuel–air ratio, particularly at part load. It also shows one reason why some spark-ignition engine manufacturers have moved towards production of
“lean-burn”engines in recent years.
The length of the burning time, or combustion duration, also has an effect on thermal efficiency. The ideal situation would be to release all the energy into the cylinder instantaneously at TDC of the compression stroke. Since all fuels have a finite burning rate, this is not possible, and the power output obtained for a given amount of fuel burned is reduced compared to the ideal cycle, resulting in a reduction in thermal efficiency. The results of these effects are shown schematically in Figure 4.3, taken from Campbell (1979), which shows the power output as a function of spark advance, for three different values of combustion duration, DyC. The combustion duration and spark advance are given in terms of crank angle degrees, and degrees before TDC, respectively. As the combustion duration is increased, the optimum value of the spark timing also increases, as shown in the diagram. The figure clearly shows that reduced
hf,i
0.65 0.60 0.55 0.50 0.45 0.40 0.35 0.30 0.25
Fuel/air equivalence ratio f 0.4 0.6
p1 = 1.0 atm T1 = 388 K xr = 0.05
0.8 1.0 1.2 1.4 1.6
24 20 16 12 8 6 rc
Figure 4.2 Variation of thermal efficiency with equivalence ratio for a constant volume fuel air cycle with 1-octene fuel (Heywood, 1988).
hp
∆qc = 30⬚ 60⬚
90⬚ 40
30
20
Spark advance (SA) – degrees
0 20 40 60 80
Figure 4.3 Influences of spark advance and combustion duration on power output (Campbell, 1979).
combustion duration results in higher power output, and therefore increased thermal efficiency.
Since burning rates are generally highest close to the stoichiometric air–fuel ratio, operating an spark ignition (SI) engine lean, with an equivalence ratio of less than one, results in increased combustion duration. As can be seen from Figure 4.3, this then reduces power output and thermal efficiency, thereby tending to counteract the in- creased efficiency of lean operation due to an increased ratio of specific heats, as seen in Figure 4.2. It is important, therefore, when choosing to operate an SI engine under lean-burn conditions to design the combustion system to provide a high burning rate.