Design and Simulation of Two Stroke Engines

Design and Simulation of Two-Stroke Engines
The continuity equation for mass flow in Eq. 2.9.5 is still generally applicable and repeated
here:
rii1-m2=0 (2.11.2)
This equation becomes:
or,
PoiXg^GsaoifXi, - Xrl) + p02Xs G 2 5 A2G5a02(Xi2 - Xr2) = 0 (2.11.3)
rG5 G5,
Xsl Ai(X„ - Xrl) + Xs°2>A2(Xi2 - Xr2) = 0
The First Law of Thermodynamics was introduced for such flow situations in Sec. 2.8.
The analysis required here follows similar logical lines. The First Law of Thermodynamics
for flow from superposition station 1 to superposition station 2 can be expressed as:
l>sl + ^ = I>s2 + 4
or, (4 + G54) - (cs 2 2 + G5as 2 2) = 0 (2.11.4)
As with the simplified "constant pressure" solution according to Benson, presented in
Sec. 2.9, the unknown values will be the reflected pressure waves at the boundary, pri and pr2.
There are two unknowns, necessitating two equations, namely Eqs. 2.11.3 and 2.11.4. All
other "unknown" quantities can be computed from these values and from the "known" values.
The known values are the upstream and downstream pipe areas, Ai and A2, the reference
state conditions at the upstream and downstream points, the gas properties at superposition
stations 1 and 2, and the incident pressure waves, pjj and pi2.
Recalling that,
xn = PoJ
The reference state conditions are:
and Xi2 =
_ Po
density Pol - P02 ~
RT 01
( \ Gl1
Pi2.
POy
(2.11.5)
acoustic velocity a 01 = a 02 = VY RT 01 (2.11.6)
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