Design and Simulation of Two Stroke Engines

Chapter 2 - Gas Flow through Two-Stroke Engines
The contracting effect is evidenced by the reflection and transmission of compression
waves. These numbers are already familiar as computed data for pressure waves of identical
amplitude at the 2:1 contraction discussed in the previous section. Pipes 1 and 2 are supplying
the third pipe, hence the effect is a contraction.
When we have dissimilar areas of pipes and a mixture of compression and expansion
waves incident upon the branch, the situation becomes much more difficult to comprehend by
the human mind. At that point the programming of the mathematics into a computer will leave
the designer's mind free to concentrate more upon the relevance of the information calculated
and less on the arithmetic tedium of acquiring that data.
It is also obvious that the angle between the several branches must play some role in
determining the transmitted and reflected wave amplitudes. This subject was studied most
recently by Bingham [2.19] and Blair [2.20] at QUB. While the branch angles do have an
influence on wave amplitudes, it is not as great in some circumstances as might be imagined.
For those who wish to achieve greater accuracy for all such calculations, the following section
is presented.
2.14 The complete solution of reflections of pressure waves at pipe branches
The next step forward historically and theoretically was to attempt to solve the momentum
equation to cope with the non-isentropic realism that there are pressure losses for real
flows changing direction by moving around the sharp corners of the branches. Much has been
written on this subject, and many of the references provide a sustained commentary on the
subject over many years. Suffice it to say that the practical approach adopted by Bingham
[2.19], incorporating the use of a modified form of the momentum equation to account for the
pressure losses around the branch, is the basis of the method used here. Bingham's solution
was isentropic.
This same approach was also employed by McGinnity [2.39] in a non-isentropic analysis,
but for a single composition fluid only; his solution was further complicated by using a nonhomentropic
Riemann variable method and it meant that, as gas properties were tied to path
lines, they were not as clearly defined as in the method used here. It would appear from the
literature [2.39] that the solution was reduced to the search for a single unknown quantity
whereas I deduce below that there are actually five such for a complete non-isentropic analysis
of a three-way branch.
The merit of the Bingham [2.19] method is that it uses experimentally determined pressure
loss coefficients at the branches, an approach capable of being enhanced further by
information emanating from data banks of which that published by Miller [2.38] is typical.
An alternative method, perhaps one which is more complete theoretically, is to resolve
the momentum of the flow at any branch into its horizontal and vertical components and
equate them both to zero. The demerit of that approach is that it does not include the fluid
mechanic loss component which the Bingham method incorporates so pragmatically and realistically.
While the discussion here is devoted exclusively to three-way branches, the theoretical
process for four-way branches, or n-pipe collectors, is almost identical to that reported below.
It will be seen that the basic approach is to identify those pipes that are the suppliers, and
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