Design and Simulation of Two Stroke Engines

Chapter 2 - Gas Flow through Two-Stroke Engines
Equating the two expressions for cs for the same wave top FC gives two important equations
as a conclusion, one for the pressure of superposition, ps, and the other for the particle
velocity of superposition, cs:
or
( \
Ps.
Xs = Xi+X2-l
.PoJ Po>
(2.2.1)
-l (2.2.2)
cs = 5a0{Xl - 1) - 5a0(X2 - 1) = 5a0(X! - X2) (2.2.3)
or cs = ci +c2 (2.2.4)
Note that the expressions for superposition particle velocity reserves the need for a sign
convention, i.e., a declaration of a positive direction, whereas Eqs. 2.2.1 and 2.2.2 are independent
of direction. The more general expression for gas properties other than air is easily
seen from the above equations as:
then
(' \ G17
iPo
XS = X1+X2-1 (2.2.5)
( \ QX1
_P±
,Po>
+ ,Po
G17
-1 (2.2.6)
as cs = ci + c2 (2.2.7)
then cs = G^o^ - 1) - G5a0(X2 - l) = G&frx - X2) (2.2.8)
At any location within the pipes of an engine, the superposition process is the norm as
pressure waves continually pass to and fro. Further, if we place a pressure transducer in the
wall of a pipe, it is the superposition pressure-time history that is recorded, not the individual
pressures of the rightward and the leftward moving pressure waves. This makes it very difficult
to interpret recorded pressure-time data in engine ducting. A simple example will make
the point. In Sec. 2.1.4 and in Fig. 2.2, there is an example of two pressure waves, pe and pj,
with pressure ratio values of 1.2 and 0.8, respectively. Suppose that they are in a pipe but are
the oppositely moving waves just discussed and are in the position of precise superposition.
There is a pressure transducer at the point where the wave peaks coincide and it records a
superposition pressure, ps. What will it be and what is the value of the superposition particle
velocity, cs?
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