Design and Simulation of Two Stroke Engines

Chapter 3 - Scavenging the Two-Stroke Engine
3.3.2 A simple theoretical scavenging model which correlates with experiments
The problem with all of the simple theoretical models presented in previous sections of
this chapter is that the theoretician involved was under some pressure to produce a single
mathematical expression or a series of such expressions. Much of this work took place in the
pre-computer age, and those who emanate from those slide rule days will appreciate that
pressure. Consequently, even though Benson or Hopkinson knew perfectly well that there
could never be an abrupt transition from perfect displacement scavenging to perfect mixing
scavenging, this type of theoretical "fudge" was essential if Eqs. 3.1.8 to 3.1.24 were to ever
be realized and be "readily soluble," arithmetically speaking, on a slide rule. Today's computer-
and electronic calculator-oriented engineering students will fail to understand the sarcasm
inherent in the phrase, "readily soluble." It should also be said that there was no experimental
evidence against which to judge the validity of the early theoretical models, for the
experimental evidence contained in paper [3.20], and here as Figs. 3.10 to 3.13, has only been
available since 1985.
The need for a model of scavenging is vital when conducting a computer simulation of an
engine. This will become much more evident in Chapter 5, but already a hint of the complexity
has been given in Chapter 2. In that chapter, in Sees. 2.16 and 2.18.10, the theory under
consideration is outflow from a cylinder of an engine, exactly as would be the situation during
a scavenge process. Naturally, inflow of fresh air would be occurring at the same juncture
through the scavenge or transfer ports from the crankcase or from a supercharger. However,
in the time element under consideration for a scavenge process, the precise cylinder properties
are indexed for the computation of the outflow from the cylinder. These cylinder properties
are pressure, temperature, and the cylinder gas properties so that the outflow from the
cylinder is calculated correctly and gas of the appropriate purity is delivered into the exhaust
pipe. What then is the appropriate purity to use in the computational step? By definition a
scavenging process is one that is stratified. If the scavenging could be carried out by a perfect
displacement process then the gas leaving the cylinder would be exhaust gas while the cylinder
purity and scavenging efficiency approached unity. If the short-circuiting was disastrously
complete it would be air leaving the cylinder and the cylinder contents would remain as
exhaust gas! The modeling computation requires information regarding the properties of the
gas in the plane of the exhaust port for its purity and temperature while assuming that the
pressure throughout the cylinder is uniform. The important theoretical step is to be able to
characterize the behavior of scavenging of any cylinder as observed volumetrically on the
QUB single-cycle gas scavenging rig and connect it to the mass- and energy-based thermodynamics
in the computer simulation of a firing engine [3.35].
Consider the situation in Fig. 3.17, where scavenging is in progress in a constant volume
cylinder under isobaric and isothermal conditions with both the scavenge and the exhaust
ports open. In other words, exactly as carried out experimentally in a QUB single-cycle gas
scavenge rig, or as closely as any experiment can ever mimic an idealized concept. The volume
of air retained within the cylinder during an incremental step in scavenging is given by,
from the volumes of air entering by the scavenge ports and leaving the cylinder through the
exhaust port,
dVta = dTas-dVae
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(3.3.5)