Design and Simulation of Two Stroke Engines

Design and Simulation of Two-Stroke Engines
Mass flow rate = density x area x velocity = psAcs
where, ps = p0Xs G5 (2.2.11)
Hence, rfi = G5a0p0A(X1 + X2 - l) G5 (X1 - X2) (2.2.12)
In terms of the numerical example used in Sec. 2.2.2, the values of ao, po, Xi, and X2
were 343.1, 1.2049, 1.0264, and 0.9686, respectively. The pipe area is that of the 25-mmdiameter
duct, or 0.000491 m 2 . The gas in the pipe is air.
We can solve for the mass flow rate by using the previously known value of Xs, which
was 0.995, or that for particle velocity cs which was 99.2 m/s, and determine the superposition
density ps thus:
ps = p0X G5 = 1.2049 x 0.995 5 = 1.1751 kg/m 3
Hence, the mass flow rate during superposition is given by:
m right = 1-1751 x 0.000491 x 99.2 = 0.0572 kg/s
The sign was known by having available the information that the superposition particle
movement was rightward and inserting cs as +99.2 and not -99.2. Alternatively, the formal
Eq. 2.2.12 gives a numeric answer indicating direction of mass or particle flow. This is obtained
by solving Eq. 2.2.12 with the lead term in any bracket, i.e., X]j as that value where
wave motion is considered to be in a positive direction.
Hence, mass flow rate rightward. as direction of wave 1 is called positive, is:
bright = G 5aoPoA(X! + X2 - l) G5 (X1 - X2)
= 5x 343.11 x 1.2049 x (1.0264 + 0.9686 - 1) x (1.0264 - 0.9686) 5
= +0.0572 kg/s
It will be observed, indeed it is imperative to satisfy the equation of continuity, that the
superposition mass flow rate is the sum of the mass flow rate induced by the individual waves.
The mass flow rates in a rightward direction of waves 1 and 2, computed earlier in Sec. 2.1.4,
were 0.0305 and 0.0272 kg/s, respectively.
2.2.4 Supersonic particle velocity during wave superposition
In typical engine configurations it is rare for the magnitude of finite amplitude waves
which occur to provide a particle velocity that approaches the sonic value. As the Mach
number M is defined in Eq. 2.1.23 for a pressure amplitude ratio of X as:
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