Design and Simulation of Two Stroke Engines

Chapter 2 - Gas Flow through Two-Stroke Engines
This immediately simplifies the entire procedure as it gives a direct solution for one of
the unknowns:
if, Msl = 1
then,
Mri+Xjtfa-Mri) 1 + G4XU
x rl _ " (2.10.11)
M G
sl + 5
G
6
The acquisition of all related data for pressure, density, particle velocity and mass flow
rate at both superposition stations follows directly from the solution of the three polynomials
forXr l, Xr2 and ao2, in the manner indicated in Sec. 2.9.
In many classic analyses of choked flow a "critical pressure ratio" is determined for flow
from the upstream point to the throat where sonic flow is occurring. That method assumes
zero particle velocity at the upstream point; such is clearly not the case here. Therefore, that
concept cannot be employed in this geometry for unsteady gas flow.
2.11 Reflection of pressure waves at a contraction in pipe area
This section contains the isentropic analysis of unsteady gas flow at a contraction in pipe
area. The sketch in Fig. 2.8(b) details the nomenclature for the flow regime, in precisely the
same manner as in Sec. 2.9. However, to analyze the flow completely, the further information
contained in sketch format in Figs. 2.9(b) and 2.10(b) must also be considered.
In Fig. 2.10(b) the contracting flow is seen to flow smoothly from the larger section to the
smaller area section. The streamlines of the flow do not give rise to particle flow separation
and so it is considered to be isentropic flow. This is in line with conventional nozzle theory as
observed in many standard texts in thermodynamics. It is summarized on the temperatureentropy
diagram in Fig. 2.9(b) where there is no entropy gain for the flow falling from pressure
psi to pressure ps2.
As usual, the analysis of quasi-steady flow in this context uses, where appropriate, the
equations of continuity, the First Law of Thermodynamics and the momentum equation. However,
one less equation is required by comparison with the analysis for expanding or diffusing
flow in Sec. 2.10. This is because the value of the reference state is known at superposition
station 2, for the flow is isentropic:
Toi=To2 or a0i=ao2 (2.11.1)
As there is no entropy gain, that equation normally reserved for the analysis of nonisentropic
flow, the momentum equation, can be neglected in the ensuing analytic method.
The properties and composition of the gas particles are those of the gas at the upstream
point. Therefore the various functions of the gas properties are:
y = Yl R = R! G5 = G5i G7 = G7i , etc.
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