Allan T. Kirkpatrick - Internal Combustion Engines

The heat transfer to the walls can be included by expanding the energy release term in the energy equation to include both heat addition and loss, as indicated in Equation ( 2.91):

(2.91)

The heat loss is

(2.92)

where

The combustion chamber area is a function of crank angle , and is the sum of the combustion chamber area at top dead center , and the instantaneous cylinder wall area. The term includes both the cylinder head, sides, and piston top areas. The instantaneous combustion chamber area and volume are

or

(2.93)

where is the cylinder clearance volume at top dead center. When the parameters in the heat loss equation are normalized by the conditions at state 1, bottom dead center, they take the form

(2.94)

and

(2.95)

The dimensionless heat loss is then

(2.96)

We can express the volume term as a function of the compression ratio . Since ,

(2.97)

For a square engine (bore = stroke ) with a flat top piston and cylinder head geometry,

(2.98)

and

(2.99)

Note that when heat transfer losses are included in the analysis, there are additional dependencies on the dimensionless wall temperature, heat transfer coefficient, and compression ratio.

If the mass in the cylinder is no longer constant due to blowby, the logarithmic derivative of the equation of state becomes

(2.100)

Similarly, the first law of thermodynamics in differential form applicable to an open system must be used.

(2.101)

The term is the instantaneous rate of leakage or blowby flow. The enthalpy of the blowby is assumed to be the same as that of the cylinder, so .

From the mass conservation equation applied to the cylinder

(2.102)

Eliminating between Equations ( 2.100) and ( 2.101) yields the following:

(2.103)

Including heat transfer loss as per Equation ( 2.91), defining the blowby coefficient as

(2.104)

and the dimensionless cylinder mass as

(2.105)

results in the following four ordinary differential equations for pressure, work, heat loss, and cylinder mass as a function of crank angle.