Design and Simulation of Two Stroke Engines

Chapter 4 - Combustion in Two-Stroke Engines
VOLUME CHANGE, \l^ TO V2
TEMPERATURE CHANGE, T-| TO T2
PRESSURE CHANGE, pj TO p2
SQR ^r***^
PISTON MOVES dx
F/g. 4.3 Thermodynamic system during combustion.
work done on the piston is 8W during the time interval. The First Law of Thermodynamics
for this closed system states that, during this time step, such events are related by:
SQR - SQL = U2 - UI + 6W (4.2.2)
Where m is the mass of gas in the cylinder and Cy is the specific heat at constant volume,
the internal energy change is approximately given by:
U2-Ui = mCv(T2-Ti) (4.2.3)
The word approximately is used above, as the value of the specific heat at constant volume
is a function of temperature and also of the gas properties. During combustion both the
gas properties and the temperatures are varying rapidly, such as several hundreds of degrees
Kelvin per degree crankshaft, and thus Cy is not a constant as is evident from the discussion
in Sec. 2.1.6. In any arithmetic application of Eq. 4.2.3, it is required to employ a value of Cy
at some particular state condition such as at either Ti or T2 and at the gas properties pertaining
at state condition 1 or 2, or at the mean of those two values and at the mean of the gas
properties pertaining at state condition 1 and 2. The simplest method is to employ the properties
at state condition 1, as it will always be a known condition; the properties at T2 are
usually what is being forecast and therefore are "unknowns." This caution will not be repeated
throughout the thermodynamic analysis; it will be taken as read that it is included
within the theory being discussed.
The pressure and temperature values at each point can be derived through the equation of
state as:
p2V2 = mRT2 and piVi = mRTj (4.2.4)
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