Design and Simulation of Two Stroke Engines

Chapter 2 • Gas Flow through Two-Stroke Engines
This "constant pressure" equation is used to replace the final form of the momentum
equation in Eq. 2.10.9. The "constant pressure" equation can be restated in the form below as
that most likely to be used in any computational process:
X£ 7 -Xg 7 =0 ( 2 - 15 - 4 >
You may well inquire at what point in a computation should this change of tack analytically
be conducted? In many texts in gas dynamics, where steady flow is being described,
either theoretically or experimentally, the conclusion reached is that flow separation will take
place if the particle Mach number is greater than 0.2 or 0.3 and, more significantly, if the
included angle of the tapered pipe is greater than a critical value, typically reported widely in
the literature as lying between 5 and 7°. The work to date (June 1994) at QUB would indicate
that the angle is of very little significance but that gas particle Mach number alone is the
important factor to monitor for flow separation. The current conclusion would be, phrased
mathematically:
If Msi > 0.65 employ the constant pressure equation, Eq. 2.15.4
If Msi < 0.65 employ the momentum equation, Eq. 2.10.9 (2.15.5)
Future work on correlation of theory with experiment will shed more light on this subject,
as can be seen in Sec. 2.19.7. Suffice it to say that there is sufficient evidence already to
confirm that any computational method that universally employs the momentum equation for
the solution of diffusing flow, in steeply tapered pipes where the Mach number is high, will
inevitably produce a very inaccurate assessment of the unsteady gas flow behavior.
2.16 Reflection of pressure waves in pipes for outflow from a cylinder
This situation is fundamental to all unsteady gas flow generated in the intake or exhaust
ducts of a reciprocating IC engine. Fig. 2.16 shows an exhaust port (or valve) and pipe, or the
throttled end of an exhaust pipe leading into a plenum such as the atmosphere or a silencer
box. Anywhere in an unsteady flow regime where a pressure wave in a pipe is incident on a
pressure-filled space, box, plenum or cylinder, the following method is applicable to determine
the magnitude of the mass outflow, of its thermodynamic state and of the reflected
pressure wave. The theory to be generated is generally applicable to an intake port (or valve)
and pipe for inflow into a cylinder, plenum, crankcase, or at the throttled end of an intake pipe
from the atmosphere or a silencer box, but the subtle differences for this analysis are given in
Sec. 2.17.
You may well be tempted to ask what then is the difference between this theoretical
treatment and that given for the restricted pipe scenario in Sec. 2.12, for the drawings in Figs.
2.16 and 2.12 look remarkably similar. The answer is direct. In the theory presented here, the
space from whence the particles emanate is considered to be sufficiently large and the flow so
three-dimensional as to give rise to the fundamental assumption that the particle velocity
within the cylinder is considered to be zero, i.e., ci is zero.
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