A PDF method for HCCI combustion modeling: CPU time optimization through a restricted initial distribution

Probability Density Function (PDF) is often selected to couple chemistry with turbulence for complex reactive flows since complex reactions can be treated without modeling assumptions. This paper describes an investigation into the use of the particles approximation of this transport equation approach applied to Homogeneous Charge Compression Ignition (HCCI) combustion. The model used here is an IEM (Interaction by Exchange with the Mean) model to describe the micromixing. Therefore, the fluid within the combustion chamber is represented by a number of computational particles. Each particle evolves function of the rate of change due to the chemical reaction term and the mixing term. The chemical reaction term is calculated using a reduced mechanism of n-heptane oxidation with 25 species and 25 reactions developed previously. The parametric study with a variation of the number of particles from 50 up to 104 has been investigated for three initial distributions. The numerical experiments have shown that the hat distribution is not appropriate and the normal and lognormal distributions give the same trends. As expected when the number of particles increases for homogenous mixture (i.e. high turbulence intensity), the in-cylinder pressure evolution tends towards the homogeneous curve. For both homogeneous and inhomogeneous (i.e. low turbulence intensity) cases, we have found that 200 particles are sufficient to model correctly the system, with a CPU time of a few minutes when a restriction of initial distribution is adopted.