The Physics of Energy, page 44
10.3 Consider the following ideal gas engine cycle with only three steps: {12} – isothermal compression at from to ; {23} – isobaric (constant pressure) heating from to , where is chosen so that the volume increases back to ; {31} – isometric cooling from back to , which returns the system to . Sketch this system's path in the pV- and ST-planes. Discuss problems with implementing this cycle reversibly.
10.4 An inventor comes to you with a proposal for a new high-tech material containing tiny Stirling engines which exploit the energy difference between the human body and the outside environment. He claims that a complete bodysuit made of his material will generate 15 W of power in steady state when worn by a human at rest in a space at room temperature of 68 ° F. Would you invest in a company based on his invention? Give a scientific argument for your answer.
10.5 The Ericsson engine, invented by Swedish-American inventor John Ericsson in 1833, is based on a cycle that resembles a Stirling cycle except that the isometric steps are replaced by isobaric steps. It uses a regenerator in the same way as a Stirling engine. Sketch the Ericsson cycle in the pV- and ST-planes. What is the efficiency of an ideal, reversible Ericsson engine?
10.6 Since it is not used up in a Carnot cycle, the gas used as a working fluid could be chosen to optimize the properties of the engine. What advantages would helium (a monatomic gas) have over air in a Carnot engine?
Problems
10.1 By how much does the temperature drop in the example of adiabatic expansion in Example 10.2?
10.2 [T] Derive eq. (10.10).
10.3 [T] In isobaric heating (and expansion), heat is added reversibly to a gas kept at constant pressure. Find the change in volume and entropy when a sample of an ideal, monatomic gas, initially at temperature , volume , and pressure p is heated isobarically to . Plot the system's path in the pV- and ST-planes.
10.4 [T] Box 10.1 describes a thermoelectric generator and mentions that the materials used should have large Seebeck coefficient S, small poor thermal conductivity k, and good electrical conductivity σ. Use dimensional analysis to show that is the unique dimensionless figure of merit for the material for thermoelectricity. Show that if the material is a metal that obeys the Wiedemann–Franz–Lorentz law (see Box 6.1) then , so that the Seebeck coefficient is the critical parameter.
10.5 [T] Show that the changes in entropy found for isothermal and isometric heating of an ideal gas (eqs. (10.5) and (10.12)) agree with the prediction from the Sackur–Tetrode equation (8.65).
10.6 Consider a Carnot engine cycle operating between a maximum temperature of 400℃ and a minimum temperature of 60℃. Assume that the lowest pressure attained is atm, the highest pressure is atm, and the minimum volume of the working gas space is L. Take . Compute the pressure and volume at each point in the cycle, as well as the heat in, heat out, and work out. Compute the overall efficiency from these numbers and check that this agrees with theoretical Carnot efficiency.
10.7 [T] Stirling engines generate more work per cycle than Carnot engines operating under the same conditions. Find the ratio for engines run with the same compression ratio, , and temperature ratio . Assume the working fluid is an ideal gas.
10.8 Mirrors are used to concentrate sunlight and heat a molten salt mixture to 500 K. A heat engine is then used to convert the thermal energy to useful mechanical form. Compare a Carnot engine to a Stirling engine with the same operating parameters. In each case the engine operates between the maximum temperature of K and a minimum temperature of K (ambient temperature). Maximum volume for the engine in each case is 3 L, minimum volume is 0.2 L. Assume that the minimum pressure attained in the cycle is 1 atm, and the working fluid is air with . Compute and compare the efficiency and net useful work per cycle for the two engines.
10.9 [H] Consider the cycle proposed in Question 10.3 quantitatively. Assume that it is executed reversibly. Show that its efficiency η relative to the efficiency of a Carnot engine operating between the same temperature limits is given by
where is the heat capacity per molecule at constant pressure and is the compression ratio. Plot the efficiency ratio versus r. Why is it always less than one?
10.10 [T] In section §5.2.2, we gave an example of a situation where an ideal gas is heated to a temperature and allowed to expand a small amount against an external ambient pressure, where the external gas has temperature . We found that the fraction of thermal energy dU used to do useful work dW precisely realized the Carnot efficiency. Show that the expansion process described there can be completed to a closed loop giving a heat engine with Carnot efficiency by using reversible processes to bring the fluid back to the initial volume so that addition of thermal energy dU restores the initial temperature . [Hint: you may find it helpful to make use of a regenerator to store thermal energy at a continuous range of temperatures.]
10.11 An air conditioner run on electricity and based on a (ideal) Carnot cycle operates between temperatures and . The gas in the air conditioner has . The AC is designed to remove 10 000 BTU/h from a living space. How much electric power does it draw? Suppose the gas in the AC has a pressure of 2 atm at its maximum volume, which is 1 L, and the minimum volume is 0.4 L. At what rate must the AC cycle in order to accomplish its mission? [Hint: See Example 10.5.]
10.12 Air conditioners are rated by their Energy Efficiency Ratio, or EER, defined as the cooling power (in Btu/h), divided by the total electric power input (in watts), measured with and : EER . US energy efficiency standards require central air conditioners to have an EER value greater than .6 What is the CoP of an air conditioner with EER = 12? How does it compare with the Carnot limit?
* * *
1 Steps in a cycle are labeled with the initial and final points in braces.
2 Any process for which is isentropic, while adiabatic in general refers to processes in which there is no heat transfer. Adiabatic reversible processes are isentropic. A free expansion (see §8.4) is adiabatic, but is irreversible and not isentropic.
3 We adopt the convention that all thermodynamic cycles begin in the state of lowest temperature and pressure. Most engineering texts use this convention in most cases, though physics texts often use a different convention where the first state has the lowest volume and highest pressure. We denote the heat absorbed or expelled in a process step {ij} by . Similarly, the work done on or by the device in a given step is denoted . By convention and are always taken to be positive.
4 A set point is the value of a state function, typically a volume, pressure, or temperature, at a specific point in the thermodynamic cycle, which is chosen by the cycle designer.
5 Because it can be greater than one, the CoP for a heat extraction device is not referred to as an efficiency, a term reserved for a ratio between actual and ideal performance, which must lie between zero and one. In §36 (Systems) we return to the concept of efficiency and extend it so that it can be applied to heat extraction devices as well as engines.
6 The US uses a seasonal average EER (SEER) which is only approximately related to the EER, and requires SEER .
CHAPTER 11
Internal Combustion Engines
The theoretical analysis of heat engines is extended into more applied territory in this chapter. We use the thermodynamic analysis from the previous chapter as a starting point to understand the internal combustion engines used to power automobiles, trucks, most ships, and other forms of transport. The study of internal combustion engines takes us close to the world of real systems engineering. Although detailed design and optimization are well beyond the scope of this book, there are several motivations for making such a foray in the case of this particular application. First, it allows us to appreciate how the rather theoretical methods we have developed so far play a role in understanding real-world energy systems. Second, the engines we consider here play a central role in the energy landscape of the early twenty-first century.
As mentioned in §2 (Mechanics), more than 25% of US energy use goes to transportation. This sector is responsible for roughly 33% of US CO emissions [58]. While transportation only accounts for about 20% of global CO emissions, the percentage is expected to grow as personal motor vehicle use increases in countries with expanding economies such as China and India. One of the most important and difficult challenges in converting to renewable energy sources and reducing carbon emissions is to find more efficient and less carbon intensive ways to power transport.
Transportation systems present a unique challenge in a number of ways. First, vehicles such as automobiles and airplanes must carry their own power sources with them (unless a radically new means of distributing power is implemented on a large scale). This means that they must be powered by fuel with a high energy density. Historically, this has led to the widespread use of liquid hydrocarbon fuels for most forms of transport. Second, the engines powering vehicles must be light and compact, with smooth and reliable operation. Third, while there is some hope for capturing carbon emissions from large power plants or industries (§35.4.2), there is no near-term viable approach to sequestration of CO from motor vehicle engines. The particular difficulties of this important part of worldwide energy use justify a more detailed discussion of the existing engines used to power various forms of transport.
Reader’s Guide
This chapter focuses on the internal combustion engines that dominate road, rail, and most ship transport. The thermodynamic cycles that model the Otto, Atkinson, and Diesel engines are described here, as are some of the properties of the hydrocarbons that fuel them. Gas turbines, which share some common features with internal combustion engines, appear in §13 (Power cycles) along with other cycles used to generate electric power.
Prerequisites: §10 (Heat engines).
Familiarity with internal combustion engines provides context for the discussion of fossil and biofuels in §26 and §33, and frames the discussion of energy storage in §37.
Internal combustion engines are open-cycle engines powered by combustion that takes place within the vapor that serves as the working fluid. As mentioned briefly in §10.4.3, internal combustion engines are in general less efficient than closed-cycle external combustion engines, in part because they often release heat and/or unburned fuel in the exhaust step of the cycle. The main types of internal combustion engines in current use can be put into several general classes, each of which is roughly associated with an ideal thermodynamic engine cycle. It should be emphasized that these idealized cycles involve many approximations, particularly of the combustion process, which miss important features of real engine processes. Part of the point of this chapter is to develop a better understanding of the limitations of the idealized thermodynamic analysis by looking at some examples of physical effects occurring in real engines that are missed in the idealized analysis.
Spark ignition (SI) engines Most passenger automobiles and many light trucks run on spark ignition engines, in which a fuel–air mixture is compressed and then ignited. The fuel then combusts, releasing chemical energy that is converted into mechanical energy as the combusting mixture expands. As we describe in §11.1, spark ignition engines can be roughly described by a thermodynamic cycle known as the Otto cycle, based on an idealization of the combustion as a constant volume process.Much of this chapter is devoted to a basic introduction to spark ignition engines, the Otto cycle, and some discussion ofvarious losses and deviations of real engines from the ideal thermodynamic model.
Compression ignition (CI) engines Compression ignition engines (also known as diesel engines ) are very similar to spark ignition engines, but in a CI engine only air is taken in and compressed. The fuel is injected after the air has been compressed and is at such a high temperature that the fuel ignites immediately upon injection. CI engines are approximately described by the Diesel cycle, which we describe in §11.4.2. The Diesel cycle is based on an idealization of the combustion process as a constant pressure process. Some automobiles, most trucks, heavy vehicles, locomotives, and ships use diesel engines.
Gas turbine engines Gas turbine engines are used in some ships and most modern aircraft, and also in modern combined-cycle power plants. Although they are also internal combustion engines, they involve compressors and turbines, two components that are also used in the context of electric power generating cycles. We postpone the discussion of gas turbines to §13 (Power cycles).
The theory and engineering practice of internal combustion engines has progressed to an extremely high level of sophistication.We only touch here on some of the basic themes. Internal combustion engines are described in general terms in many engineering thermodynamics texts such as [19]. A more thorough introduction, which combines the basic theories of thermodynamics, heat transfer, fluid mechanics, and combustion into a systematic introduction to the major issues in internal combustion engines, is given by Milton [59]. The authoritative text by Heywood [60] treats these issues, and others, in much more detail, and will be of great value to anyone who wants to understand the operation of modern internal combustion engines more deeply.
11.1Spark Ignition Engines and the Otto Cycle
11.1.1 Four-stroke Spark Ignition Engines
The internal combustion engine has an interesting and complicated history [59]. The earliest internal combustion engines were inspired by cannons. In 1857, the Italian engineers Eugenio Barsanti and Felice Matteucci designed a device in which an explosion in a cylinder propelled a heavy piston upward. The cylinder was sufficiently long that the piston stayed within the cylinder throughout its trajectory. After reaching the highest point of its motion, the piston returned downward, engaging a ratchet mechanism that did mechanical work. In 1860, the Belgian engineer Etienne Lenoir patented the first commercial internal combustion gas engine based on a two-stroke cycle (see below). Another commercial engine, based on a similar idea to that of Barsanti and Matteucci, was produced by the German inventor Nikolaus Otto and engineer Eugen Langen in 1867. In these early engines, the fuel was ignited at atmospheric pressure, and the resulting efficiency was quite low.
Alphonse Beau de Rochas, a French engineer, emphasized in an 1861 paper the thermodynamic advantages of compressing the working fluid before ignition in an internal combustion engine, which allows for a significantly greater amount of work to be done in the expansion process. The first internal combustion engine incorporating this idea and operating on the now-standard four-stroke cycle was the “Silent” engine developed by Otto in 1876. This engine had an efficiency of roughly 14%, and was the forerunner of the engine appearing in modern automobiles. Later improvements by German engineers Gottlieb Daimler and Karl Benz and others led to the first use of the internal combustion engine to power a vehicle in 1886.
The sequence of operations in a four-stroke spark ignition engine is illustrated in Figure 11.1. As in the closed-cycle engines discussed in §10, the basic operating mechanism consists of a cylinder containing a gas. In this case the gas is an air–fuel mixture, with a piston forced to move outward by the expansion of the gas, performing mechanical work. In the internal combustion engine, however, the working fluid does not stay within the cylinder over multiple cycles. Instead, valves allow new air/fuel in at the beginning of each cycle, and allow the products of combustion to be expelled from the cylinder as exhaust after the fuel has been burned in each cycle. The linear motion of the piston back and forth as the four-stroke cycle is executed puts engines of this type in the class of reciprocating engines – as opposed to turbines, which power rotational motion. The linear motion of the piston is transferred via a connecting rod to a crankshaft that rotates as the piston moves back and forth (see Figure 11.2). The crankshaft in turn drives another rotating shaft (the camshaft) that controls the intake and exhaust valves. When the piston is at its highest point (in a vertically oriented cylinder), the connecting rod is at the top of the crankshaft, called top-dead-center (TDC). The corresponding lowest point is called bottom-dead-center (BDC). In a single cycle of the four-stroke engine, the piston goes up and down twice, rotating the crankshaft twice. Let us consider in more detail each of the strokes in the four-stroke cycle, as depicted in Figure 11.1:
Stroke one: Intake (Figure 11.1(a)) In the first stroke, the piston moves downward (outward). The intake valve is opened as the volume in the cylinder expands, and new air/fuel is drawn into the cylinder.
Stroke two: Compression (Figure 11.1(b)) In the second stroke, the piston moves upward (inward) again. Both valves are kept closed, and the air/fuel mixture is compressed. An important characteristic of internal combustion engines is the ratio between the maximum volume of the cylinder (when the piston is at its lowest point so the crank is at BDC) and the minimum volume of the cylinder (at TDC). This ratio is called the compression ratio, , and is often written in the form r : 1. For example, the original Otto silent engine had a compression ratio of 2.5:1, while for reasons that are discussed below typical modern four-stroke spark ignition engines have a compression ratio around 10:1. The difference between the maximum volume and the minimum volume is known as the cylinder’s displacement. The power that an internal combustion engine can deliver depends critically on its displacement while its efficiency depends critically on the compression ratio.
Stroke three: Power (Figure 11.1(c)) When the compression stroke is almost complete, a spark ignites the compressed fuel–air mixture. This leads to a further increase in pressure, and after the crank passes TDC, the piston is forced downward by the hot, high-pressure gas.
Stroke four: Exhaust (Figure 11.1(d)) Near the end of the power stroke, the exhaust valve opens. The piston then moves upward again as the crankshaft goes through another half revolution. During this stroke, the exhaust gases, consisting of the results of the fuel combustion process, are expelled from the engine.
