Design and Simulation of Two Stroke Engines

Design and Simulation of Two-Stroke Engines
where the pressure loss coefficient, Cb, is principally a function of Reynolds number and the
deflection angle per unit length around the bend:
Cb=fRe,— (2.3.18)
The extra pressure loss as a function of being deflected by an angle appropriate to the
pipe segment length, dx, can then be added to the friction loss term in Eq. 2.3.3 and the
analysis continued for the segment of pipe length, dx, under scrutiny. There is discussion in
Sec. 2.14 for pressure losses at branches in pipes and Eq. 2.14.1 gives an almost identical
relationship for the pressure loss in deflecting flows around the corners of a pipe branch. All
such pressure loss equations relate that loss to a gain of entropy through a decrease in the
kinetic energy of the gas particles during superposition.
It is a subject deserving of painstaking measurement through research using the sophisticated
experimental QUB SP apparatus described in Sec. 2.19. The aim would be to derive
accurately the values of the pressure loss coefficient, Cb, and ultimately report them in the
literature; I am not aware of such information having been published already.
2.4 Heat transfer during pressure wave propagation
Heat can be transferred to or from the wall of the duct and the gas as the unsteady flow
process is conducted. While all three processes of conduction, convection and radiation are
potentially involved, it is much more likely that convection heat transfer will be the predominant
phenomenon in most cases. This is certainly true of induction systems but some of you
will remember exhaust manifolds glowing red and ponder the potential errors of considering
convection heat transfer as the sole mechanism. There is no doubt that in such circumstances
radiation heat transfer should be seriously considered for inclusion in any theoretical treatment.
It is not an easy topic and the potential error of its inclusion could actually be more
serious than its exclusion. As a consequence, only convection heat transfer will be discussed.
The information to calculate the normal and relevant parameters for convection is available
from within most analysis of unsteady gas flow. The physical situation is illustrated in
Fig. 2.4. A superposition process is underway. The gas is at temperature, Ts, particle velocity,
cs, and density, ps.
In Sec. 2.3.1, the computation of the friction factor, Cf, and the Reynolds number, Re,
was described. From the Reynolds analogy of heat transfer with friction it is possible to
calculate the Nusselt number, Nu, thus;
c f Re
Nu = —i— (2.4.1)
The Nusselt number contains a direct relationship between the convection heat transfer
coefficient, Ch, the thermal conductivity of the gas, C^, and the effective duct diameter, d. The
standard definitions for these parameters can be found in any conventional text in fluid mechanics
or heat transfer [2.4]. The definition for the Nusselt number is:
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