Design and Simulation of Two Stroke Engines

Design and Simulation of Two-Stroke Engines
c sh c sh relative to gas i "•" c i
_ aKPsh-l)
=
YV G 6?Psh + G17
apX^fih-l)
YV G 67Psh + G17
+ Ci
+ GjaoCXj -1)
(2.1.27)
For the compression wave illustrated in Fig. 2.2, the use of Eqs. 2.1.24 and 2.1.25 yields
finite amplitude propagation and particle velocities of 397.4 and 45.27 m/s, and for the shock
wave of the same amplitude, 371.4 and 45.28 m/s, respectively. The difference in propagation
velecity is some 7% less but that for particle velocity is negligible.
For the expansion wave illustrated in Fig. 2.2, the use of Eqs. 2.1.26 and 2.1.27 yields
finite amplitude propagation and particle velocities of 278.5 and -53.8 m/s, and for the shock
wave of the same amplitude, 312.4 and 0.003 m/s, respectively. The difference in propagation
velecity is some 12% greater but that for particle velocity is considerable in that the particle
velocity at, or immediately behind, the shock is effectively zero.
2.1.6 The properties of gases
It will be observed that the propagation of pressure waves and the mass flow rate which
they induce in gases is dependent on the gas properties, particularly that of the gas constant,
R, and the ratio of specific heats, y. The value of the gas constant, R, is dependent on the
composition of the gas, and the ratio of specific heats, y, is dependent on both gas composition
and temperature. It is essential to be able to index these properties at every stage of a
simulation of gas flow in engines. Much of this information can be found in many standard
texts on thermodynamics, but it is essential for reasons of clarity to repeat it here briefly.
The gas constant, R, of any gas can be found from the relationship relating the universal
gas constant, R, and the molecular weight, M, of the gas:
R
R = — (2.1.28)
M
The universal gas constant, R, has a value of 8314.4 J/kgmolK. The specific heats at
constant pressure and temperature, Cp and Cy, are determined from their defined relationship
with respect to enthalpy, h, and internal energy, u:
The ratio of specific heats, y, is found simply as:
^ dh _ du
CP = — Cv = — (2.1.29)
dT dT
CP
Y = — (2.1.30)
Cy
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