Design and Simulation of Two Stroke Engines

Design and Simulation of Two-Stroke Engines
The solution of the above simultaneous equations gives (where the total area, At, is defined
below):
Xd =
At = Ai + A2 + A3
2A2Xi2+2A3Xi3+Xil(A1-A2-A3)
At
_2A1Xil+2A3Xi3+Xi2(A2-A3-A1)
2A1Xil+2A2Xi2+Xi3(A3-A2-A1)
X r3 = " (2.13.3)
Perhaps not surprisingly, the branched pipe can act as either a contraction of area to the
flow or an enlargement of area to the gas flow. In short, two pipes may be supplying one pipe,
or one pipe supplying the other two, respectively. Consider these two cases where all of the
pipes are of equal area, where the pressure waves employed as examples are the familiar
pulses which have been used so frequently throughout this text.
(a) A compression wave is coming down to the branch in pipe 1 through air and all other
conditions in the other branches are "undisturbed"
The compression wave has a pressure ratio of PJI = 1.2, or Xjj = 1.02639. The results of
the calculation using Eqs. 2.13.3 are:
Xd= 0.9911 Xr2 = Xr3 = 1.01759 Prl= 0.940 Pr2 = Pr3=1.13
As far as pipe 1 is concerned the result is exactly the same as that for the 2:1 enlargement
in area in the previous section. In the branch, the incident wave divides evenly between the
other two pipes, transmitting a compression wave onward and reflecting a rarefaction pulse.
Pipe 1 is supplying the other two pipes, hence the effect is an expansion.
(b) Compression waves of pressure ratio 1.2 are arriving as incident pulses in pipes 1 and 2
leading up to the branch with pipe 3
Pipe 3 has undisturbed conditions as Pj3 = 1.0. Now the branch behaves as a 2:1 contraction
to this general flow, for the solutions of Eqs. 2.13.3 show:
Xri=Xr2= 1.0088 Xr3 = 1.0352 Prl = Pr2 = 1.0632 Pr3 = 1.274
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At