Design and Simulation of Two Stroke Engines

Chapter 2 - Gas Flow through Two-Stroke Engines
As propagation velocity is given by the sum of the local acoustic and particle velocities,
asinEq. 2.1.9
a s rightward — a s ~*~ c s
a s leftward = —a s + c s
= ao(X, + X2 - 1) + G5a0(X! - X2)
= a0(G6X! - G4X2 - 1)
= -a0(X1+X2-l) + G5a0(X1-X2)
= -a0(G6X2 - G4Xt - 1)
(2.2.9)
(2.2.10)
Regarding the propagation velocities during superposition in air of the two waves, pe and
Pi, as presented above in Sec. 2.2.1, where the values of cs, ao, Xj, X2 and Xs were 99.2,
343.1, 1.0264, 0.9686, and 0.995, respectively:
as = aoXs = 343.1 x 0.995 = 341.38 m/s
ocs rightward = as + cs = 341.38 + 99.2 = 440.58 m/s
ccs leftward = -as + cs = -341.38 + 99.2 = -242.18 m/s
This could equally have been determined more formally using Eqs. 2.2.9 and 2.2.10 as,
«s rightward = a o(G6Xi - G4X2 - 1) = 343.38(6 x 1.0264 - 4 x 0.9686 -1) = 440.58 m/s
ccs leftward = a0(G6X2 - G4X! - 1) = 343.38(6 x 0.9686 - 4 x 1.0264 -1) = -242.18 m/s
As the original propagation velocities of waves 1 and 2, when they were traveling "undisturbed"
in the duct into a gas at the reference acoustic state, were 397.44 m/s and 278.47 m/s,
it is clear from the above calculations that wave 1 has accelerated, and wave 2 has slowed
down, by some 10% during this particular example of a superposition process. This effect is
often referred to as "wave interference during superposition."
During computer calculations it is imperative to rely on formal equations such as Eqs.
2.2.9 and 2.2.10 to provide computed values.
2.2.3 Mass flow rate during wave superposition
As the superposition process accelerates some waves and decelerates others, so too must
the mass flow rate be affected. This also must be capable of computation at any position
within a duct. The continuity equation provides the necessary information.
73