Ignition model: In the early stage of ignition process formaldehyde is formed in the leading portion of spray. This means that the low temperature oxidation of fuel occurs before the hot ignition in a diesel spray. When the hot ignition occurs formaldehyde is consumed rapidly therefore this hot ignition region can be detected as dark spots in LIF image of formaldehyde. The initial ambient gas temperature affects the position of the first hot ignition. At the initial ambient temperatures lower than the NTC temperature range, the lean mixture in the spray periphery is ignited first in a spray due to its high temperature. At the temperatures in NTC region, the rich mixture in the central region of spray is ignited first, because the oxidation of lean mixture in the spray periphery is suppressed extremely by the NTC effect.

Soot formation model: In the early soot formation process the soot precursor is formed in the whole leading portion of spray flame immediately after the ignition. The soot precursor located in the periphery of spray flame is converted to soot particle firstly. During the diffusion combustion period the soot precursors is formed through the central fuel rich region between 40 and 55 mm (270 to 370 times nozzle orifice diameter) downstream of the nozzle orifice which is surrounded by the adjacent fuel lean region where the OH is formed.

Soot growth and oxidation model: The young soot particles formed in the central fuel rich region surrounded by OH region grow by surface growth and are coagulated during convection to the spray head. In this process the size of soot particles increases and the number density of particles decreases. At the spray tip the soot particles are pushed aside to the spray periphery by the motion of head vortices. Finally the soot particles are convected to the upstream side of head vortices and re-entrained into the lean side of flame, where the concentration of OH is high, and are oxidized rapidly.