Design and Simulation of Two Stroke Engines

Chapter 6 - Empirical Assistance for the Designer
pressure wave propagation, ao- That this is the case, empirically speaking only, is seen from
Eq. 6.2.3 and Fig. 6.17.
The principal aim of the empirical design process is to phase the plugging reflection
correctly for the engine speed desired for peak power, which means calculating the tuning
length from piston face to tail-pipe entry, Lj. The next important criterion is to proportion the
tail-pipe exit area as a function of the exhaust port area so that the pipe will empty in a
satisfactory manner before the arrival of the next exhaust pulse. The third factor is to locate
the end of the diffuser and the beginning of the tail nozzle so that the spread of the suction and
plugging effects are correctly phased. The fourth function is to locate the second half of the
diffuser so that the reverse reflection of the plugging pulse from it, and the primary reflection
of it from the exhaust port, can recombine with the next outgoing exhaust pulse, thereby
producing the resonance effect demonstrated in Fig. 5.32 or Fig. 6.20. This will happen only
in racing engines with very long exhaust port periods, typically in excess of 190°.
A multi-stage diffuser is an efficient method of reflecting the exhaust pulse and the shallower
first stages reduce the potential for energy losses from shock formation at the entrance
to that diffuser. The shocks form as high-amplitude compression exhaust waves meet strong
suction waves which are progressing back to the engine from the diffuser. As seen in Sec.
2.15, this raises the local gas particle velocity, and in the diffuser entrance area this can
attempt to exceed a Mach number of unity. The result is a shock which effectively "destroys"
the wave energy and, although the energy reappears as heat, this does nothing for the retention
of the strength of the all-important pressure wave action. The slower rate of area expansion
of the first stage of the diffuser (see also Sec. 2.15) smears the reflection process more
widely and efficiently over the entire length of the diffuser.
The entirety of the empirical design process is founded in very simple equations which
have been tried and tested for many years in the theoretical and experimental development of
expansion chambers for racing engines at QUB. As remarked earlier, remember that this is an
empirical approach, not a precise calculation, and is the starting point for optimization by
simulation, as seen in Chapter 5, preferably in combination with the experimental testing of
the firing engine [4.35].
As this is an empirical calculation for the lengths and diameters shown in Fig. 5.7, and are
conventionally discussed in mm units, the data are inserted and produced by the calculation in
those units. The data required for the calculation are in blocks, the first of which is: engine
bore, stroke, connecting rod length, exhaust port total opening period, 9ep, in units of crankshaft
degrees, number of exhaust ports, maximum width of each exhaust port, and the radii in
the corners of each exhaust port. If the exhaust port shape is complex, as in Fig. 5.1(b), some
preliminary arithmetic must be carried out prior to computation to find the "mean" exhaust
port width, so that the data are inserted accurately into the calculations in the above format.
The above set of data permits the calculation of the exact exhaust port area. Incidentally,
it is presumed that the designer has followed some design process to this point and the data
being used are matched to the required performance of the engine. With this knowledge of the
exhaust port flow area, equivalent to a diameter, do, the empirical calculation describes this as
the ideal exhaust pipe initial diameter. In a racing pipe, where maximizing the plugging pressure
gives the highest trapping efficiency, there seems little point in having the first downpipe
diameter, di, much more than 1.05 times larger than do, for in unsteady gas flow, the larger the
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