**2.3 Mathematical zero-dimensional modeling with chemical kinetics of PM diesel engine**

**Figure 5** illustrates schematically permanent contact PM diesel engine. It is supposed that PM is inserted inside the cylinder head. All necessary conditions for homogeneous combustion are carried out in the PM combustion chamber [6, 7]. During the intake and early compression process, the PM-heat capacitor has a low effect on the in-cylinder thermodynamic pressure and temperature. Near TDC, the fuel is injected into the PM structure.

Furthermore, the fuel is vaporized fast and mixed with air inside the PM. Because of the instant evaporation and combustion of liquid fuel after injection, it is a logical assumption that combustion occurs in the isochoric process. Then, all the combustion

### **Figure 5.**

*Schematic illustration of a permanent contact PM diesel engine [6].*

products enter the cylinder space instantaneously. So, the energy of the fluid phase of PM is transferred to the in-cylinder volume [1, 6–9].

For thermodynamic modeling of PM in the combustion chamber, two energy equations are used, a modified gas energy equation and a solid phase energy equation. These assumptions are considered for the modeling process [1]:

1.Combustion process is adiabatic.


9. Species of combustion products with fluid phase temperature inside PM are transferred to in-cylinder volume at each crank angle.

Mixture formation process assumes a homogenous before combustion due to PM space. Combustion happens as a result of self-ignition due to the high initial temperature.
