The Physics of Energy, page 46
n-paraffins The CCR for straight chain paraffins decreases rapidly as n increases. Thus, for example, significant n-octane content in a fuel leads to knock at a very low compression ratio. This tendency is easy to understand physically – a long chain hydrocarbon with single bonds is relatively unstable and easily split with the addition of thermal energy.
Branching Branching of the hydrocarbon helps to reduce knock. Thus, while n-octane leads to knock at a low compression ratio, iso-octane, which is highly branched, is somewhat less susceptible to knock.
Aromatics The benzene ring is a very stable structure, and aromatics in general do not break apart easily. As a result, addition of aromatics to gasoline dramatically reduces knock. For this reason, aromatics have been used widely as fuel additives to increase the viable compression ratio for SI engines.
Anti-knock additives By adding non-hydrocarbon substances to a fuel, knock can be substantially reduced. For example, tetraethyl lead ((CHCH)Pb – a tetravalent lead ion bonded to four ethyl groups, each consisting of ethane minus one hydrogen atom) was for many years used as a fuel additive to reduce knock. After the negative health consequences of lead pollution were understood, most countries switched to unleaded gasoline, and instead other additives such as aromatics are included to reduce knock. (Note that aromatics have their own potential environmental issues; for example, evidence suggests that aromatics are relatively carcinogenic.)
Figure 11.7 Knock tendencies of a selection of hydrocarbons under standard test conditions (600 rpm and 350°F coolant temperature). The hydrocarbons are represented schematically by their carbon backbones with hydrogen atoms not indicated. Note that the critical compression ratio in test conditions may differ substantially from that in real engines. After [61].
The tendency of a fuel to knock is encoded in the single octane number (ON) provided at fuel pumps. This number compares the tendency to knock of a given fuel with a mixture of iso-octane (low knock tendency) and n-heptane (CH, high knock tendency). An ON less than 100 means that the fuel has the same tendency to knock as a mixture of (ON)% iso-octane and (100–ON)% heptane. Octane numbers higher than 100 are possible, and are defined in terms of iso-octane with a given fraction of lead additive.3
Gasoline purchased at pumps in the US generally has octane numbers ranging from 85 to 95. 93 octane gasoline begins to knock in most SI engines at a compression ratio of roughly 10.5:1 (see footnote 2). Thus, most automobile engines currently in production have maximum compression ratios in the range 9:1–10.5:1. High-performance automobiles push the compression ratio to the maximum possible with existing fuels, and require higher octane fuel for satisfactory performance.
11.3Real Spark Ignition Engines
While the theoretical thermodynamic analysis we have carried out for the Otto cycle captures various features of the engine accurately, such as the dependence of efficiency on compression ratio, the predicted efficiency (11.7) is much greater than is realized in real SI internal combustion engines. We have explained why current automobiles using SI engines have a maximum compression ratio of around 10:1. Taking and the cold air standard value of , eq. (11.7) would predict an efficiency of slightly greater than 60%. In contrast, a standard 4-cylinder Toyota Camry engine, for example, has a peak efficiency of 35% [62]. In this section we briefly describe some of the issues that reduce the efficiency of real engines below the theoretical ideal.
Before considering inefficiencies we must adopt a more realistic value of the adiabatic index for the fuel–air mixture at the high temperatures attained during the cycle. At 2500 K the adiabatic index of air drops to about 1.29 from the usual value of 1.4 at room temperature. The fuel at the stoichiometric ratio does not significantly affect this number. A standard approximation is to take , appropriate to an average cycle temperature of around 1600 K [59]. Substituting a compression ratio of , and into the efficiency formula (11.7), we estimate
(11.11)
a decrease of more than 15% from the cold air standard result.
Knock
Hydrocarbon fuels can break down or combust at high temperature and pressure before ignition. This phenomenon, known as knock, occurs at a compression ratio of around 10.5:1 with conventional gasoline mixtures, and can reduce engine efficiency and cause damage over time. Thus, most spark ignition automobile engines in current production have a compression ratio of between 9:1 and 10.5:1.
A semi-realistic four-stroke engine cycle is graphed in the pV-plane in Figure 11.8, and compared to the thermodynamic Otto cycle. This figure serves as a useful guide in reviewing some of the ways in which the real engine cycle deviates from the thermodynamic ideal. Note, however, that the processes in the real engine cycle involve rapid changes that take the gas in the cylinder out of thermodynamic equilibrium, so that the thermodynamic variables are only approximate and this is only a schematic depiction of the real process.
Figure 11.8 Comparison of actual and theoretical Otto cycles in the pV-plane for a four-stroke spark ignition engine. The yellow shaded areas represent work done by the engine. The blue shaded part of the cycle, which runs counterclockwise represents work done on the engine. After [59].
Combustion As we described in §11.2.2, the combustion process is not instantaneous, and does not occur at constant volume. In a real engine, the combustion occurs over a finite time. Combustion generally begins while the cylinder volume is still decreasing and continues until the volume has increased by a non-negligible amount. Furthermore, even in the absence of knock, the high temperatures to which the fuel–air mixture is exposed cause some molecules to dissociate, or recombine chemically, preventing complete and immediate combustion. The combination of these effects keeps the temperature and pressure in the combustion chamber significantly below the extremes suggested by the theoretical Otto cycle. This reduces the area of the actual cycle pV curve in Figure 11.8, reducing the work done and hence the efficiency of the engine.
Heat loss during expansion The combusted fuel–air mixture is extremely hot during the expansion stroke (as mentioned above, generally over 2000 K after combustion). This leads to rapid heat loss to the cylinder walls and loss of efficiency.
Blowdown Near the end of expansion, the exhaust valve opens and the high-pressure gas in the cylinder rapidly expands outward and returns to ambient pressure. This is known as blowdown. As depicted in Figure 11.8, the blowdown process does not occur at constant volume, and removes some further area from the pV curve.
Exhaust/intake strokes Finally, the exhaust and intake strokes require work by the engine that is ignored in the ideal Otto cycle. In the ideal cycle the hot exhaust is simply replaced by air at the low temperature and pressure set point, modeled as isometric cooling. In reality the exhaust gases are forced out of the cylinder and fresh air is drawn in. The exhaust stroke following blowdown therefore occurs at a slightly higher pressure than atmospheric. Similarly, during the intake stroke the pressure must be slightly lower than atmospheric. These two strokes, idealized as a single horizontal line in Figure 11.3, are more accurately described by the blue shaded region of the cycle in Figure 11.8, and lead to an additional nonzero area for the cycle in the pV-plane, which contributes negatively to the total work done by the engine (as this part of the cycle proceeds counterclockwise).
All these deviations from the theoretical ideal combine to significantly lower the maximum efficiency of real spark ignition engines to at most about 80% of the theoretical Otto efficiency [60]. Despite many decades of engineering efforts, this is the state of the art in automobile engine engineering.
Beyond these reductions in efficiency, there is a further issue that compromises SI engine performance. The previous analysis assumed that the engine was operating with a cylinder full of fuel–air mixture on each cycle. In reality, the engine power is adjusted dynamically by the driver using a throttle mechanism (actuated by exerting less than maximum pressure on the gas pedal). When the engine runs at less than full throttle, a metal plate (the throttle plate) rotates into a position that partially blocks the flow of air into the engine and at the same time the flow of fuel into the injection system is decreased, keeping the fuel–air mixture close to the stoichiometric ratio. In this way less energy is released on combustion and the engine generates less power. When the throttle limits the flow of air into the system, the intake stroke brings in less of the fuel–air mixture, resulting in lower pressure than atmospheric at the beginning of the compression stroke. This significantly increases the work done by the engine by increasing the size of the counterclockwise loop formed in the pV-plane by the exhaust-intake strokes. In typical motor vehicle operation, the intake stroke of an SI engine operates at around 0.5 atm. A graph of a throttled Otto cycle is compared with an unthrottled cycle in Figure 11.9. This extra work done by the engine (which can be treated as a negative contribution to the work output) is referred to as pumping loss.
Figure 11.9 Throttled Otto cycle, compared to the unthrottled (orange) cycle in the pV-plane. The exhaust and intake strokes respectively, are isobaric (constant pressure). The exhaust stroke is above atmospheric pressure and the intake is at one-half atmosphere, requiring the engine to do pumping work on the intake cycle. The scale of the pumping part of the cycle {5671} has been exaggerated for clarity. After [59].
Engine Efficiency
The ideal Otto cycle efficiency of a spark ignition engine with compression ratio 10:1 is about 50%. Deviations from the idealized cycle, heat losses, and other inefficiencies reduce the peak efficiency of most automobile engines to 35% or below. At less than full throttle, pumping losses cause further reduction in efficiency. Combined with energy lost to the electrical system, typical power delivered to the drive train is 25% of energy from fuel combustion.
Clearly there are substantial issues that reduce the actual efficiency of automobile engines below that of the ideal Otto thermodynamic cycle, which itself is below Carnot efficiency. Finding ways to improve the efficiency of engines would have dramatic commercial and environmental consequences. In the remainder of this chapter we describe some variations on the standard four-stroke SI engine and associated Otto cycle that have been used to increase the efficiency of internal combustion engines.
11.4Other Internal Combustion Cycles
Up to now we have focused primarily on four-stroke spark ignition engines with an idealized description in terms of the thermodynamic Otto cycle. There are many other designs for internal combustion engines, several of which have found real-world applications. In this section we briefly explore two of these alternative cycles: the Atkinson cycle used in hybrid automobile engines to increase engine efficiency, and the Diesel or compression ignition cycle, in which higher compression ratios can be achieved by injecting the fuel after compression.
A more significant departure from the four-stroke paradigm is the two-stroke SI engine cycle. Indeed, some of the earliest spark ignition engines used a two-stroke cycle with exhaust and intake incorporated into the end parts of the power and compression strokes. Such engines are simpler than engines based on the four-stroke Otto cycle and are still widely used in lightweight applications such as motorcycle engines, chain saws, and small boat engines. Two-stroke engines tend to produce more pollution than four-stroke engines since the exhaust and intake processes are not as controlled and complete in the two-stroke engine. This has led to the phasing out of two-stroke engines for use in automobiles in many countries including the US. Because two-stroke engines produce power on every stroke, however, they can be more powerful than four-stroke engines of comparable size. There is substantial current effort towards developing a less-polluting two-stroke engine suitable for use in automobiles that would have greater efficiency and power than a similarly sized four-stroke engine.
11.4.1 The Atkinson Cycle
An interesting variation on the standard Otto cycle for spark ignition engines was proposed by English engineer James Atkinson in 1882. The key feature of the Atkinson cycle is that the compression ratio can be different from the expansion ratio. Thus, while the compression ratio is limited by the knock characteristics of the fuel, the expansion ratio can be larger and provide more power. Atkinson’s original design, now obsolete, used a novel crankshaft design to implement the cycle. A number of modern automobiles, particularly those that use hybrid engine technology, achieve the same result of different compression and expansion ratios simply by modifying the intake valve timing. The basic idea is that by leaving the intake valve open after the compression stroke begins, some of the air that has just been taken in is expelled again so that the pressure in the cylinder remains constant for some time after the crankshaft passes bottom dead center. The actual compression of the fuel–air mixture begins only after the intake valve closes. The corresponding idealized Atkinson cycle is shown in Figure 11.10. The work performed in the Atkinson cycle is reduced because the amount of air in the cylinder is smaller than in an Otto cycle in an engine with the same displacement. The exhaust and intake strokes are modeled as a constant volume cooling to atmospheric pressure , followed by a compression at constant pressure as some air is expelled . Note that these approximations are not very realistic, since in fact the quantity of air in the cylinder increases ( to ) and then decreases ( to ) again during these processes, and in reality there is no cooling in the step , but for the purposes of estimating the work output of the cycle these approximations introduce only relatively small inaccuracies.
Figure 11.10 Idealized Atkinson cycle with a compression ration of 9.6:1 and an expansion ratio of 12.5:1. The inset shows an enlargement of the part of the cycle where compression begins. The step is enabled by keeping the intake value open for part of the compression stroke.
Other Engine Cycles
Engine cycles other than the standard spark ignition Otto cycle can improve engine efficiency. Some vehicles use modified valve timing to realize a version of the Atkinson cycle, which gives a higher expansion than compression ratio. This improves efficiency by some 10% at the cost of a reduction in engine power that can be compensated for by the battery in hybrid vehicles.
An additional advantage of the intake valve delay in the Atkinson cycle is that it can be used to reduce the pumping losses induced by throttling. By using intake valve delay rather than throttle to reduce the total fuel–air mixture in the cylinder, the reduction in pressure and consequent pumping losses associated with throttling can be mitigated significantly. This is demonstrated in Figure 11.11 for the hybrid Atkinson cycle vehicle described in Example 11.2.
Figure 11.11 Comparison of pumping losses (blue shading) in a throttled Atkinson cycle (red) and a conventional Otto cycle (orange). As in Figure 11.9, the figure is not drawn to scale so that the pumping effects can be made more visible. After [62].
Example 11.2 The Atkinson Cycle in the Hybrid Toyota Camry
An example of the use of the Atkinson cycle in a modern vehicle is the hybrid 2007 Toyota Camry. The non-hybrid version of the Camry runs on a four-cylinder 2AZ-FE engine with cylinder displacement 2362 cm and a compression ratio of 9.6:1. The hybrid version of the vehicle runs on a very similar engine, the 4-cylinder 2AZ-FXE engine with the same cylinder displacement and compression ratio, but an expansion ratio of 12.5:1. The differences between the two vehicles are analyzed in detail in a US DOE report [62]. In the hybrid Camry, the computer-controlled intake valve delay is actuated when conditions indicate it will improve engine efficiency. According to the DOE report, this engine improves peak efficiency from 35% to 38%.
The main disadvantage of the Atkinson cycle is that the peak power of the engine is reduced. The non-hybrid 4-cylinder Camry has peak power of 120 kW (160 hp) at 6000 rpm, while the hybrid only achieves peak power of 110 kW (147 hp). Despite this difference, because the electric motor can provide additional power, the hybrid Camry still has superior acceleration performance to the non-hybrid Camry. The rate of acceleration from 30 to 50 mph is graphed in the figure above for both vehicles. The achievement of higher performance in a vehicle that also has higher fuel efficiency is an important step in moving towards widespread acceptance of hybrid technology, since many consumers are motivated by performance (or perception of performance) as much as or more than by fuel efficiency or environmental concerns.
(Figure: After [62])
11.4.2 Compression Ignition (Diesel Cycle) Engines
Compression ignition (CI) provides another way of dealing with the problem of knock. The first compression ignition engine was invented by German engineer Rudolf Diesel in 1893. The four-stroke compression ignition cycle is depicted in Figure 11.12. The primary difference from the spark ignition cycle is that no fuel is taken in with the air in the intake cycle. Thus, compression can proceed to a higher ratio, and to a concomitantly higher temperature and pressure, with no risk of premature combustion. When the crankshaft is at or near TDC, the fuel is injected into the combustion chamber and ignites. In the Otto cycle, combustion occurs roughly symmetrically about TDC and therefore roughly at constant volume. In contrast, in the Diesel cycle the combustion processes occur as the cylinder volume expands from to while the pressure is roughly constant. The Diesel cycle is therefore modeled by replacing the isometric heat addition process of the Otto cycle with an isobaric (constant pressure) heat addition process. A Diesel cycle is depicted in Figure 11.13. While the isobaric approximation is not very accurate, it forms a good basis for beginning to analyze the compression ignition cycle.
