Design and Simulation of Two Stroke Engines

Design and Simulation of Two-Stroke Engines
The continuity equation for mass flow in previous sections is still generally applicable
and repeated here, although the entropy gain is reflected in the reference acoustic velocity
and density at position 2:
mj - m2 = 0
n (2.12.3)
mj - mr= 0 v '
These equations become, with rightward retained as the positive direction:
rG5 G5
PoiXS^GjacCXu - Xrl) + P02Xs2 :5 A2G5ao2(Xi2 - Xr2) = 0
p01XsfA1G5a01(Xil - Xrl) - pt[CcAt][Csct] = 0
(2.12.4)
The above equation for the mass flow continuity for flow from the upstream station 1 to
the throat, contains the coefficient of contraction on the flow area, Cc, and the coefficient of
velocity, Cs. These are conventionally connected in fluid mechanics theory to a coefficient of
discharge, Cd, to give an effective throat area, Ateff, as follows:
Cd = CCCS and Ateff = CdAt
This latter equation of mass flow continuity becomes:
PoiX^A^ao^Xi! - Xrl) - CdPtAtct = 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:
hcl+^L = h
'si s2 + 4
or (cs 2 l+G5aJ)-(c£+G5as 2 2) = 0 (2.12.5)
The First Law of Thermodynamics for flow from superposition station 1 to the throat can
be expressed as:
or
c c
sl • '
hsl+—= ht+ —
2 l 2
Cp(Tsl-Tt) + ^ ^ = 0 (2.12.6)
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