Design and Simulation of Two Stroke Engines

Design and Simulation of Two-Stroke Engines
straight line equation: y = mx + c
The Benson-Brandham model contains a perfect scavenging period, SRpci, before total
mixing occurs, and a short-circuited proportion, a. This resulted in Eqs. 3.1.23 and 24, repeated
here:
when 0 < SRV < (1 - c)SRpd
then SEV = (1-G)SRV (3.1.23)
and when (1 - a)SRv > SRpcj
then SEV = 1 - (l - SRpd) e( SR ^ l ~ a ^) (3.1.24)
Manipulation of this latter equation reveals:
loge(l - SEV) = (c - 1)SRV + loge(l - SRpd) + SRpd
(3.3.2)
Consideration of this linear equation as a straight line shows that test data of this type
should give a slope m of (a-1) and an intercept of loge(l - SRpCj) + SRpcj. Any value of shortcircuiting
a other than 0 and the maximum possible value of 1 would result in a line of slope m.
where 0 > m > -1
The slope of such a line could not be less than -1, as that would produce a negative value
of the short-circuiting component, a, which is clearly theoretically impossible.
Therefore it is vital to examine the experimentally determined data presented in Sec.
3.2.4 to acquire the correlation of the theory with the experiment. The analysis is based on
plotting loge(l - SEV) as a function of SRV from the experimental data for two of the cylinders,
YAM 14 and YAM 12, as examples of "good" and "bad" loop scavenging, and this is
shown in Fig. 3.14. From a correlation standpoint, it is very gratifying that the experimental
points fall on a straight line. In Refs. [1.11, 3.34] many of the cylinders shown in Figs. 3.10 to
3.13 are analyzed in this manner and are shown to have a similar quality of fit to a straight
line. What is less gratifying, in terms of an attempt at correlation with a Benson and Brandham
type of theoretical model, is the value of the slope of the two lines. The slopes lie numerically
in the region between -1 and -2. The better scavenging of YAM14 has a value which is closer
to -2. Not one cylinder ever tested at QUB has exhibited a slope greater than -1 and would
have fallen into a category capable of being assessed for the short-circuit component a in the
manner of the Benson-Brandham model. Therefore, there is no correlation possible with any
of the "traditional" models of scavenging flow, as all of those models would seriously underestimate
the quality of the scavenging in the experimental case, as alluded to in the last paragraph
of Sec. 3.2.4.
234