Design and Simulation of Two Stroke Engines

Chapter 2 • Gas Flow through Two-Stroke Engines
velocities, ao, in the supplied pipe. This means that there are four unknown values needing
four equations. This is possible only by making the assumption that there is equality of superposition
pressure at the faces of the two supplier pipes; this is the same assumption used by
Bingham [2.19] and McGinnity [2.39]. It then follows that the properties of the gas entering
the supplied pipe are a mass-flow-related mixture of those in the supplier pipes. Using the
notation of Fig. 2.13, it is implied that pipes 1 and 2 are supplying pipe 3.
continuity me3 = riii + m2 (2.14.3)
m ini + 1112^2
purity n e3 " (2.14.4)
me3
m lRl + m 2^2
gas constant R e3 - (2.14.5)
me3
_ rhiYj + m2y2
specific heats ratio Ye3 ~ (2.14.6)
V m e3
The subscript notation of "e3" should be noted carefully, for this details the quantity and
quality of the gas entering, i.e., going "toward," the mesh space beyond the pipe 3 entrance,
whereas the resulting change of all of the gas properties within that mesh space is handled by
the unsteady gas-dynamic method which has already been presented [2.31].
The final analysis then relies on incorporating the equations emanating from all of these
previous considerations regarding pressure losses, together with the continuity equation and
the First Law of Thermodynamics. The notation of Fig. 2.13 applies together with either Fig.
2.14(a) for two supplier pipes, or Fig. 2.14(b) for one supplier pipe.
(a) for one supplier pipe the following are the relationships for the density, particle velocity,
and mass flow rate which apply to the supplier pipe and the two pipes that are being supplied:
r*c 1
Psl = P0l( X il + X rl " 1) ' C sl = G 51 a 0l( X il ~ X rl) m l = Psl A l c sl
ric i
Ps2 = P0e2( X i2 + X r2 " l ) c s2 = G 51 a 0e2( X i2 ~ X r2) m 2 = Ps2 A 2 c s2
C SI
Ps3 = P0e3( X i3 + X r3 - l ) c s3 = G 51 a 0e3( X i3 " X r3) m 3 = Ps3 A 3 c s3
119
(2.14.7)
(2.14.8)
(2.14.9)