Design and Simulation of Two Stroke Engines

Chapter 2 - Gas Flow through Two-Stroke Engines
The momentum equation for flow from superposition station 1 to superposition station 2
is expressed as:
A lPsl + ( A 2 " A l)psl " A 2Ps2 + ( m sl c sl - m s2 c s2) = °
The logic for the middle term in the above equation is that the pressure, psi, is conventionally
presumed to act over the annulus area between the two ducts. The momentum equation,
also taking into account the information regarding mass flow equality from the continuity
equation, reduces to:
A 2(Psl " Ps2) + mslcsl " cs2) = 0
(2.10.4)
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,
and also the reference temperature at position 2, namely TQ2- There are three unknowns,
necessitating three equations, namely Eqs. 2.10.2, 2.10.3 and 2.10.4. 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, A\ and A2, the reference state conditions
at the upstream point, the gas properties at superposition stations 1 and 2, and the incident
pressure waves, pji and pj2-
Recalling that,
Xn =
The reference state conditions are:
density P01
f \ QX1
Pil
iPoj
_ PO
RTf 01
and Xi2 =
( \GX1
Pil
n - Po
PO2 "RT~
K1 02
acoustic velocity a0i = ^VRTQI a02 = -^TRTj
02
The continuity equation, Eq. 2.10.2, reduces to:
VG5
Poi(Xii + x n - 1) A lG5aoi(Xii " Xrl)
\G5
+P02( X i2 + X r2 " 1) A 2 G 5 a 02( X i2 " X r2) = °
103
(2.10.5)
(2.10.6)
(2.10.7)