Design and Simulation of Two Stroke Engines

Design and Simulation of Two-Stroke Engines
the local Mach number at station 2 is monitored and retained at unity if it is found to
exceed it.
MS2 = si = ggofe^y . 9&az*d (2.n.9)
a s2 a 02 A s2 A i2 + A r2 ~ x
This immediately simplifies the entire procedure for this gives a direct solution for one of the
unknowns:
Then if, Ms2 = 1
_Ms2+Xi2(G5-Ms2)__l + G4Xi2
r2 ~ M +r " r (2.11.10)
M s2 + G 5
In this instance of sonic particle flow at station 2, the entire solution can now be obtained
directly by substituting the value of Xr2 determined above into either Eq. 2.11.7 or 2.11.8 and
solving it by the standard Newton-Raphson method for the one remaining unknown, Xri.
2.12 Reflection of waves at a restriction between differing pipe areas
This section contains the non-isentropic analysis of unsteady gas flow at restrictions between
differing pipe areas. The sketch in Fig. 2.8 details much of the nomenclature for the
flow regime, but essential subsidiary information is contained in a more detailed sketch of the
geometry in Fig. 2.12. However, to analyze the flow completely, the further information
contained in sketch format in Figs. 2.11 and 2.12 must be considered completely. The geometry
is of two pipes of differing area, Ai and A2, which are butted together with an orifice of
area, At, sandwiched between them. This geometry is very common in engine ducting. For
example, it could be the throttle body of a carburetor with a venturi and a throttle plate. It
could also be simply a sharp-edged, sudden contraction in pipe diameter where A2 is less than
Ai and there is no actual orifice of area At at all. In the latter case the flow naturally forms a
vena contracta with an effective area of value At which is less than A2. In short, the theoretical
analysis to be presented here is a more accurate and extended, and inherently more complex,
version of that already presented for sudden expansions and contractions in pipe area in
Sec. 2.11.
In Fig. 2.12 the expanding flow from the throat to the downstream superposition point 2
is seen to leave turbulent vortices in the corners of that section. That the streamlines of the
flow give rise to particle flow separation implies a gain of entropy from the throat to area
section 2. On the other hand, the flow from the superposition point 1 to the throat is contracting
and can be considered to be isentropic in the same fashion as the contractions debated in
Sec. 2.11. This is summarized on the temperature-entropy diagram in Fig. 2.11 where the gain
of entropy for the flow rising from pressure pt to pressure ps2 is clearly visible. The isentropic
nature of the flow from psi to pt can also be observed as a vertical line on Fig. 2.11.
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