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
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.