Design and Simulation of Two Stroke Engines

Chapter 2 - Gas Flow through Two-Stroke Engines
where the value of the specific heat at constant volume is that appropriate to the properties of
the gas within the cylinder at the beginning and end of the time step:
Cv = - ^ _ ^ cv =^£1_
c Yc-1 C1 Yci-1
Normally, as with the debate on the gas constant, R, below, the values of Cv and y should
be those at the beginning and end of the time step. However, little inaccuracy ensues, as does
considerable algebraic simplification, by taking the known values, Cyc» Yc ano at me
' Rc>
commencement of the time step and assuming that they persist for the duration of that time
step. The exception to this is during a combustion process where the temperature changes
during a given time step are so extreme that the gas properties must be indexed correctly
using the theory of Sec. 2.1.6 and, if necessary, an iteration undertaken for several steps to
acquire sufficient accuracy.
At the conclusion of the time step the cylinder volume is Vci caused by the piston movement
and this is:
Vci=Vc + dVc
(2.18.60)
As the mass of the cylinder, mci, is given by Eq. 2.18.56 and the new cylinder pressure
and temperature are related by the state equation:
PciVci = mciRcTci (2.18.61)
Eqs. 2.18.56 to 2.18.61 may be combined to produce a direct solution for Tci for a cylinder
or plenum as:
Tr, =
8QC + dH, - dHE + mcCvTc - -£—C-
(mc + dmr - dmE) Cv + ^ L
V
2V c ;
(2.18.62)
This can be solved directly for the system temperature, Tci, after the time step, and with
dVc as zero in the event that any plenum or cylinder has no volume change. The cylinder
pressure is found from Eq. 2.18.61.
The gas properties in the box will have changed due to the mass transport across its
boundaries. For almost all engine calculations the gases within the box are either exhaust gas
or air. This situation will be debated here, as it is normality, but the more general case of a
multiplicity of gases being present throughout the system can be handled with equal simplicity.
After all, air and exhaust gas are composed of a multiplicity of gases. This argument, with
the same words, is precisely that mounted in the previous section Sec. 2.18.9 for flow through
the mesh spaces.
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