Design and Simulation of Two Stroke Engines

Chapter 2 - Gas Flow through Two-Stroke Engines
or, G5a? - ( G5aS2 + c s2 )-o (2.16.5)
The First Law of Thermodynamics for flow from the cylinder to the throat can be expressed
as:
hl+5L=ht+^L
or, Cp(T1-Tt)-^- = 0 (2.16.6)
as:
The momentum equation for flow from the throat to superposition station 2 is expressed
A 2(Pt - Ps2) + m s2( c t " c s2) = 0
(2.16.7)
The unknown values will be the reflected pressure wave at the boundary, pr2, the reference
temperature at position 2, namely T02, and the pressure, pt, and the velocity, ct, at the
throat. There are four unknowns, necessitating four equations, namely the mass flow equation
in Eq. 2.16.4, the two First Law equations, Eq.2.16.5 and Eq.2.16.6, and the momentum
equation, Eq.2.16.7. All other "unknown" quantities can be computed from these values and
from the "known" values. The known values are the downstream pipe area, A2, the throat
area, At, the gas properties leaving the cylinder, and the incident pressure wave, pi2-
Recalling that,
X1 =
( \ QX1
PL
POy
and Xj2 = Pi2_
vPoy
and setting Xt =
f \ GX1
Pt
Po;
then due to isentropic flow from the cylinder to the throat, the temperature reference conditions
are given by:
ai = amXi or
T
Tm = -
l 01^1
01 ~ Y 2
As Ti and Xj are input parameters to any given problem, then T01 is readily determined.
In which case, from Eqs. 2.16.1 and 2.16.2, so are the reference densities and acoustic velocities
for the cylinder and throat conditions. As shown below, so too can the density and temperature
at the throat be related to the reference conditions.
n vG5 n„. T ( a 01 X t)
Pt " P01 X t md T t =
yR
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