Abstract
In this chapter, mean-value models (MVM) of the most important subsystems of SI and Diesel engines are introduced. In this book, the notion of MVM1 will be used for a specific set of models as defined below. First, a precise definition of the term MVM is given. This family of models is then compared to other models used in engine design and optimization. The main engine sub models are then discussed: the air system that defines how much air is inducted into the cylinder; the fuel system that defines how much fuel is inducted into the cylinder; the torque generation system that defines how much torque is produced by the air and fuel in the cylinder as defined by the first two parts; the engine inertial system that defines the engine speed; the engine thermal system that defines the dynamic thermal behavior of the engine; the pollution formation system that models the engine-out emission; and the pollution abatement system that models the behavior of the catalysts, the sensors and other relevant equipment in the exhaust pipe.
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References
The terminology MVM was probably first introduced in [73]. One of the earliest papers proposing MVM for engine systems is [164]. A good overview of the first developments in the area of MVM of SI engine systems can be found in [137]. A more recent source of information on this topic is [37].
In order to allow full control of the engine, usually these will be electric signals, e.g., the throttle plate will be assumed to be “drive-by-wire.”
In MVM, the finite swept volume of the engine can be viewed as being one that is distributed over an infinite number of infinitely small cylinders.
The expression (2.1) is valid for four-stroke engines. Two-stroke engines have half of that IPS delay. As shown in Chapter 3, additional delays are introduced by the electronic control hardware.
For fluid dynamic and aerodynamic simulations, usually a high-bandwidth model of the rail dynamics is necessary, see [106] or [117].
Thermodynamically correct enthalpy flows H(t).
Thermodynamically correct internal energy U(t)
Friction can be partially accounted for by discharge coefficients that must be experimentally validated.
For liquid fluids, this is often a good approximation.
Additional exhaust gas recirculation is discussed in the next section.
The term supercharging will be used in this text to describe the forced induction of air or mixture into an engine by any device.
The isentropic power Pa,. is that mechanical power that the best possible compressor would need to achieve the actual compression ratio [120].
Compressor pumping occurs when the flow in the compressor is stalled, i.e., when the pressure gradient becomes too large to be sustained. Several forms of stalling (starting from local rotating stall to full rotor stall) are known [143].
In practice, ancillary devices, such as bleed valves, are used to reduce these retrictions.
In this regime, a small negative pressure disturbance leads to smaller mass flow and, hence, to even smaller pressure after the compressor. This represents a dynamic system with positive feedback, hence this regime is rapidly crossed once the compressor reaches its surge limit.
Of course, it is also possible to model the rotor speed dynamics utilizing a power balance instead of the torque balance used in (2.64).
Carburetors are only used in special applications and will therefore not be treated in this text.
Direct-injection SI engines can only reach substantial improvements in fuel economy by running in lean conditions (a » 1) at low loads. However, in this case the proven and cost-effective TWC technology cannot be used to achieve the required very low tail-pipe emission levels (see Sect. 1.2.2). More complex aftertreatment systems that are able to deal with a lean and non-homogeneous combustion are required in this case.
Gaseous fuels, especially compressed natural gas, have, of course, no wall-wetting problems. Nevertheless, dynamic phenomena occur due to substantial back flow of aspirated mixture from the cylinder to the intake manifold. Since these effects are best described in a discrete-event setting, the corresponding models will be introduced in Sect. 3. 2. 4.
In Sect. 3.2.5 a more detailed analysis of this problem will be made using a discrete-event approach. The formulation (2.93) will be shown to be a good approximation of the EGR dynamics.
Taking into consideration only the five independent variables mentioned in (2.98), using for each variable say, 20 support points, and assuming a measurement duration of one minute per vertex results in six years of consecutive experimentation.
Higher boost ratios require larger crankshaft bearings, etc., thus leading to increased friction.
The conversion of fuel (hydrocarbon) into H2 and CO consumes some of the fuel’s enthalpy, such that it is not available for the thermodynamic processes.
Analyzing an engine system as a truly discrete-event system requires sophisticated mathematical tools, see, for instance, [19] or [20].
The same conclusions are obtained for the adiabatic formulation.
Even at idle speed the IPS delay is smaller than the manifold time constant. However, as discussed in detail in the Appendix B, the delays present in the system have a substantial influence on the system behavior.
In system theory, this approach is known as singular perturbation, [178].
The heating value of the mixture is equal to H,n = H1/(Aao + 1) where H 1 is the fuel’s lower heating value and the fuel’s stoichiometric constant. For a gasoline/air mixture at A = 1 the heating value of the mixture H n ,is equal to 2.7 MJ/kg.
The remaining heat flux is carried away by the cooling water.
The data and figures shown in this section have been taken from [27]
The expression “catalyst poisoning” is used to describe the reduction of catalytic efficiency by unwanted species that occupy active surface sites and, thus, prevent the desired species from adsorbing on these sites. Poisoning can occur irreversibly with substances such as lead (Pb),but also reversibly, for example, with sulfur dioxide (SO2).
Since the partial pressures of the components are not guaranteed to equal a constant value, the Stefan-Maxwell equation would be a more accurate choice. Nevertheless, because is dominant, this effect can be compensated by slightly adjusting PN2.
If, however, the targeted emission limits are very low, a combination of engine tuning, in-engine measurements, and an exhaust gas aftertreatment system will have to be setup, and the engine may not be re-tuned fuel efficiently.
The models derived below will disregard the hydrocarbon and soot present in the exhaust gases. This simplification is based on the assumption that these species will not affect the main NO reduction pathways.
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© 2004 Springer-Verlag Berlin Heidelberg
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Guzzella, L., Onder, C.H. (2004). Mean-Value Models. In: Introduction to Modeling and Control of Internal Combustion Engine Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-08003-0_2
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DOI: https://doi.org/10.1007/978-3-662-08003-0_2
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