Design and Simulation of Two Stroke Engines

Chapter 2 - Gas Flow through Two-Stroke Engines
2.1.3 Propagation and particle velocities of finite amplitude waves
Particle velocity
Any pressure wave with a pressure ratio greater than an acoustic wave is called a wave of
finite amplitude. Earnshaw [2.1] showed that the gas particle velocity associated with a wave
of finite amplitude was given by c, where:
c = Y-l a0
ypo
Y-l
-l (2.1.4)
Bannister's [2.2] derivation of this equation is explained with great clarity in Appendix
A2.1. Within the equation, shorthand parameters can be employed that simplify the understanding
of much of the further analysis. The symbol P is referred to as the pressure ratio of a
point on the wave of absolute pressure, p. The notation of X is known as the pressure amplitude
ratio and G represents various functions of y which is the ratio of specific heats for the
particular gas involved. These are set down as:
pressure ratio
pressure amplitude ratio X =
P = ^
Po
PoJ
Y-l
p 2y (2.1.5)
Incorporation of the above shorthand notation within the complete equation for Eq. 2.1.4
gives:
2
c = -a0(X-l) (2.1.6)
y-l
If the gas in which this pressure wave is propagating has the properties of air, then these
properties are:
Gas constant R = 287 J/kgK
Specific heats ratio y=1.4
Specific heat at constant pressure ^P
yR
7^1
Specific heat at constant volume Cv W = R
y-l
55
1005 J/kgK
= 718 J/kgK