Internal Combustion Engines. Allan T. Kirkpatrick

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      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.

(2.106)

      The above four linear equations are solved numerically in the Matlab® program FiniteHeatMassLoss.m, which is listed in the Appendix. The program is a finite energy release program that can be used to compute the performance of an engine and includes both heat and mass transfer. The engine performance is computed by numerically integrating Equations (2.106) for the pressure, work, heat loss, and cylinder gas mass as a function of crank angle. The integration starts at bottom dead center = −180), with initial inlet conditions given. The integration proceeds degree by degree to top dead center and back to bottom dead center. Once the pressure and other terms are computed as a function of crank angle, the overall cycle parameters of net work, thermal efficiency, and imep are also computed. The use of the program is detailed in the following example.

      Example 2.6 Finite Energy Release with Heat СКАЧАТЬ