The clustering method used in the Multi-Zone HCCI Engine Model Extraction Utility is based on a hierarchical K-means algorithm [38], [39] . This algorithm aggregates the cells into a large cluster, and then divides that large cluster into smaller groups that match the maximum variance criteria.

The heat loss from each generated zone is approximated by the difference between the changes in internal energy through the actual polytropic process. This is represented by Equation 3–59 :

(3–59)

where and are the final temperatures of zone through the two different processes; and are the mass and specific heat of zone , respectively. Assuming a constant specific heat ratio , the adiabatic temperature of zone at the end of the CFD calculation can be estimated as Equation 3–60 :

(3–60)

where , , and are the temperature, volume, and density of zone at IVC, respectively; and are the volume and density of zone , respectively, at the final state of the cold flow calculation. Inserting Equation 3–60 into Equation 3–59 results in Equation 3–61 :

(3–61)

With a further assumption of equivalent for all the zones, the fraction of heat transfer loss from zone can be approximated as Equation 3–62

(3–62)

The values from Equation 3–62 are used to calculate the Heat Loss area fraction for each zone in the generated Multi-Zone HCCI Engine model.