Design and Simulation of Two Stroke Engines

For this to approach unity then:
Chapter 2 - Gas Flow through Two-Stroke Engines
c G5a0(X - 1) G5(X -1)
M - a —^r~ —x~ < 2 - 2 - 13 >
X = ^- = —^— and for air X = 1.25
G4 3-y
In air, as seen above, this would require a compression wave of pressure ratio, P, where:
P = -2- = X G7 and in air P = 1.25 7 = 4.768
PO
Even in high-performance racing engines a pressure ratio of an exhaust pulse greater than
2.2 atmospheres is very unusual, thus sonic particle velocity emanating from that source is
not likely. What is a more realistic possibility is that a large exhaust pulse may encounter a
strong oppositely moving expansion wave in the exhaust system and the superposition particle
velocity may approach or attempt to exceed unity.
Unsteady gas flow does not permit supersonic particle velocity. It is self-evident that the
gas particles cannot move faster than the pressure wave disturbance which is giving them the
signal to move. As this is not possible gas dynamically, the theoretical treatment supposes
that a "weak shock" occurs and the particle velocity reverts to a subsonic value. The basic
theory is to be found in any standard text [2.4] and the resulting relationships are referred to
as the Rankine-Hugoniot equations. The theoretical treatment is almost identical to that given
here, as Appendix A2.2, for moving shocks where the particle velocity behind the moving
shock is also subsonic.
Consider two oppositely moving pressure waves in a superposition situation. The individual
pressure waves are pi and p2 and the gas properties are y and R with a reference
temperature and pressure denoted by po and TQ. From Eqs. 2.2.5 to 2.2.8 the particle Mach
number M is found from:
pressure amplitude ratio Xs = X\ + X2 - 1 (2.2.14)
acoustic velocity as = aoXs (2.2.15)
particle velocity cs = G5a0(X! - X2) (2.2.16)
Mach number (+ only)
M s Mc = ^- =
a
s
G5a0(X! - X2)
75
a 0 X s
(2.2.17)