Link to: Heat Release Fraction Applet
Link to: Simple Heat Release Applet
Using the following definitions,heat release
,
and
, results in :
The ideal gas equation is PV = mRT, so
and
The first law now becomes
Further reducing the equation:
If we know the pressure, P, volume, V, , the heat released
gradient,
, we can compute the change in pressure,
. Thus explicitly
solving the equation for pressure as a function of crank angle. Alternatively,
we can use experimental data for the pressure, P and the volume, V, to determine
the heat release term by solving for
.
First, the volume, V and , have to be
defined. From the slider-crank
model, we have a definition for cylinder volume, V. Both terms are only
dependent on engine geometry.
So taking the derivative with respect to the crank angle, , results in :
For heat release term, , the Wiebe
function for the burn fraction is used.
To view the burn fraction, f, as a function of the crank angle, click here: Heat Release Applet.
At the beginning of combustion, f = 0, and at the end the fraction is almost 1.
The heat release, , over the crank
angle change,
, is:
Where Qin is the overall heat input.
Taking the derivative of the heat release function, f, with respect to
crank angle, gives the following definition of .
So now with and
defined, the
pressure as a function of the crank angle can be solved.
The following applet plots the pressure, work and temperature as a function of the crank angle: Simple Heat Release Applet. The effect of heat transfer to the cylinder wall can also be included.
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