3
IC-Engine-Based Propulsion Systems
In this chapter, standard IC-engine-based propulsion systems are analyzed us- ing the tools that will be later applied for the optimization of more complex powertrains. The main components of IC-engine-based propulsion systems are the engine and the gear box. Clutches or torque converters, which also are part of such a powertrain, are needed during the relatively short phases in which the engine must be kinematically decoupled from the vehicle. As shown in the first section of this chapter, in the context of this book the engine may be described by an engine map and two normalized engine variables. The second section shows how the gear ratios must be chosen to satisfy drivability requirements.
Once these two components and the main vehicle parameters are specified, estimations of the fuel consumption can be made using any of the methods introduced in the previous chapter. The third section of this chapter includes two examples of such an analysis.
44 3 IC-Engine-Based Propulsion Systems
m∗f=Pc/Hl, (3.2)
whereHlis the fuel’s lower heating value.
ω ICE
T
P c e
e (a) Quasistatic approach
ω ICE
T
P c e
e (b) Dynamic approach
Fig. 3.1.Engine input and output variables in the quasistatic and in the dynamic system description.
The thermodynamic efficiency ηe of IC engines mainly depends on the engine speed and torque. The modeling of all relevant phenomena is a vast and well-documented area. A rich literature exists that describes the important points of this topic. The standard text [110] summarizes the main ideas and contains references to many other publications. In Sect. 3.1.3 below, simplified formulations of the dependencyηe(ωe, Te) are shown that are suitable for the purposes of this text.
The variables Te and ωe have a clear physical interpretation. Unfortu- nately, their range depends on the specific engine that is modeled (size, ge- ometry, etc.). For this reason, normalized variables are introduced in the next section. Using these variables, the engine size can be used as an optimization parameter.
3.1.2 Normalized Engine Variables
When the engine runs in steady-state conditions, two normalized variables describe its operating point. These two quantities are themean piston speed
cm= ωe·S
π (3.3)
and themean effective pressure
pme=N·π·Te Vd
, (3.4)
whereωeis the engine speed, Te the engine torque,Vd the engine’s displace- ment, andS its stroke. The parameterN depends on the engine type: for a four-stroke engineN = 4 and for a two-stroke engineN = 2 must be inserted in (3.4).
3.1 IC Engine Models 45 Obviously, the mean piston speed is the piston speed averaged over one engine revolution. It is limited at the lower end by the idling speed limit and at the upper end by aerodynamic friction in the intake part and by mechanical stresses in the valve train. Typical maximum values ofcmare below 20m/s.
The mean effective pressure is that amount of constant pressure that must act on the piston during one full expansion stroke to produce that amount of mechanical work that a constant engine torqueTeproduces during one engine cycle. For naturally aspirated engines the maximum value of pme is around 106Pa (10 bar). Typical turbocharged Diesel engines reach maximum mean effective pressures close to 20 bar. Even higher values are possible with special supercharging devices (twin turbochargers, pressure-wave superchargers, etc.).
The key advantages of using the normalized engine variablescmandpme
are that their range is approximately the same for all2 engines and that they are not a function of the engine size. Since for engines of similar type the speed boundaries vary less than the torque limits, engine maps are often shown in practice withcmreplaced byne, i.e., the engine speed in rpm.
For a fixed mean effective pressure and a mean piston speed, the equation Pe=z· π
16·B2·pme·cm (3.5)
describes how the mechanical power Pe produced by the engine correlates with the number of cylinderszand the cylinder bore B.
With (3.5) it is possible to estimate the necessary engine size once the desired rated engine power Pmax has been chosen. For instance, if a light- weight vehicle withmv = 750 kg plus a payload of 100 kg is designed to reach 100 km/h in t0 = 15 s, an estimation of the necessary rated power of 45 kW is obtained using the the approximation (2.16). Assuming the engine to be a naturally aspirated one, (3.5) indicates that the choicez= 3 andB= 0.067 m are reasonable values.3
3.1.3 Engine Efficiency Representation
The engine efficiency (3.1) is often plotted in the form of an engine map.
Figure 3.2 shows such a map of the engine specified in the last section. On top of the pme = 0 line, this map shows the engine efficiency as calculated with a standard thermodynamic engine process simulation program. No mixture enrichment at high loads is considered in these calculations. For that reason the best efficiencies are reached at full load conditions. Also shown are the constant power curves and the estimated maximum mean effective pressure limits.
2 Of course the engines have to be of the same type, e.g., naturally aspirated SI engines.
3 A four-cylinder configuration would require a boreB which is too small to yield a satisfactory thermodynamic efficiency.
46 3 IC-Engine-Based Propulsion Systems
As mentioned in Sect. 2.3, engine maps similar to the one shown in Fig. 3.2 are not the only way to describe the engine efficiency. It is easy to convert this form to the “fuel-flow” description that is used in Fig. 2.14.
m/s pme
10
4
-2
-4 bar
pme0 e
0.40 0.38 e (-)
pme0 0.33
0.30
0.20 0.10
45 kW
3 kW 6 kW
10 kW
20 kW
cm
4 8 12 16
0
0.25
Fig. 3.2. Engine map computed with a thermodynamic process simulation pro- gram. Naturally aspirated SI engine, strictly stoichiometric air/fuel mixture. Engine parameters: displaced volumeVd= 710·10−6m3, bore and strokeB=S= 0.067 m, compression ratio= 12.
Quite often it is possible to further simplify the engine model. A very sim- ple, but nevertheless rather useful approximation is the Willans description [210], [274]. In this approach the engine mean effective pressure is approxi- mated by
pme≈e(ωe)·pmf −pme0(ωe), (3.6) where the input variable pmf is the fuel mean pressure. This variable is the mean effective pressure that an engine with an efficiency of 100% would pro- duce by burning a massmf of fuel with a (lower) heating valueHl
pmf =Hl·mf
Vd . (3.7)
The parameter e(ωe) stands for the indicated engine efficiency, i.e., the ef- ficiency of the thermodynamic energy conversion from chemical energy to pressure inside the cylinder. The parameterpme0 summarizes all mechanical friction and pumping losses in the engine. For a specific engine system, these two parameters significantly depend mainly on the engine speed. Figure 3.2 contains two curves in the lower part that exemplify these dependencies.4
4 In this example, the mean friction pressure is larger than in most modern engines.
This fact is a consequence of the small engine size chosen in this example.