With the absence of flame propagation, the homogeneous charge compression-ignition (HCCI) combustion process is dominated by chemical kinetics. Implementation of a detailed reaction mechanism is therefore generally necessary for HCCI combustion analysis. A comprehensive HCCI combustion model requires the combination of fluid mechanics, heat transfer and detailed kinetics. While computational fluid dynamics (CFD) have been applied to the study of HCCI combustion for simple fuels, it is often too computationally intensive for routine analyses involving practical fuels. Single-zone HCCI combustion models, on the other hand, permit detailed modeling of the chemical kinetics for practical fuels by assuming that the gas in the combustion chamber is homogeneous, with uniform temperature, pressure, and gas composition. A single-zone model can adequately predict ignition in an HCCI engine when the initial conditions (loading) are known. However, because it does not account for low-temperature regions within the thermal boundary layers and crevices, a single zone model tends to under-predict CO and unburned hydrocarbon (UHC) emissions and over-predict peak pressures.
A multi-zone HCCI model serves as a compromise, in that it provides some resolution of temperature and composition inhomogeneities, while still allowing the use of detailed kinetics models for practical fuels. Many multi-zone models proposed for studying HCCI combustion processes have focused on addressing the non-uniformity of temperature. Some have considered both temperature and concentration distributions inside the cylinder.
The Ansys Chemkin Multi-zone HCCI model allows the possibility of adopting the hybrid solution approach developed by Aceves et al. The hybrid approach uses a non-reacting fluid-mechanics simulation to compute temperature (and initial concentration) distribution inside the cylinder and then, prior to chemical kinetics becoming significant, employs a multi-zone model to calculate ignition, heat release and emissions while using a detailed reaction mechanism. The computational fluid dynamics (CFD) step provides the multi-zone model with initial in-cylinder temperature and composition distributions, which are important to establishing appropriate zones in the multi-zone model. This approach is especially helpful with high levels of residual gas. Once the initial conditions of each zone are defined, the Multi-zone HCCI model is able to provide improved predictions of peak pressure and trace-species emissions. Although this hybrid approach is an option, the Multi-zone HCCI model can also be used independently, using specified heat-transfer parameters from the start of simulation after intake valve closing.
Following the multi-zone model approach reported by Aceves et al. [70], a multi-zone homogeneous charge compression-ignition (HCCI) combustion model was developed for use within the Ansys Chemkin software framework [71] .
The cylinder volume is divided into a number of imaginary zones according to the in-cylinder distribution of a variable, normally gas temperature. The Multi-zone HCCI model treats each zone as a closed homogeneous reactor, where the zone mass is conserved. Pressure is assumed to be the same for all zones and the total volume of all zones is equal to the instantaneous volume of the cylinder. Heat transfer between zones is not considered. The only interaction between zones is through pressure work; if combustion takes place within a zone, it expands to exert work on the other zones. The assumptions pertaining to this model formulation are summarized below
All zones have the same pressure.
No mass or heat transfer occurs between zones. The only interaction between the zones is compression work.
The total volume of the zones must equal the cylinder volume computed by the slider-crank relationship used in the single-zone internal-combustion engine model. This constraint is used to determine the zone/cylinder pressure.
The Ansys Chemkin Multi-zone HCCI model accommodates the hybrid or sequential approach for HCCI combustion simulation by allowing the zone temperature to be determined in two ways: constrained with a given temperature versus time profile or solved with the energy equation. This hybrid approach takes advantage of CFD’s capabilities of modeling fluid dynamic mixing and heat transfer in complex geometries when heat release from chemical reactions is negligible. If zone temperature profiles extracted from a CFD solution are given, the Multi-zone HCCI model will obtain zone temperatures from the profiles before the simulation reaches the transition crank angle. The transition crank angle is a user-defined model parameter, when the multi-zone model is used in the context of the hybrid approach, to specify the crank angle at which chemical kinetics is considered to become important and the multi-zone model should start solving zone temperature with the energy equation instead. Transitioning to solving the energy equation too late causes the model to miss some of the early chemistry, which is important for determining ignition timing. By default, the Multi-zone HCCI model solves the energy equation from the starting crank angle specified to obtain zone temperatures.
The total heat-transfer rate between gas mixture and cylinder wall is the sum of individual zone wall heat transfer rates. Zone wall heat transfer rates are determined by zone temperature, zone wall heat transfer coefficient, and zone wall surface area. The wall heat transfer coefficient of each zone is calculated by the Woschni correlation [59] using the same set of parameters. The Multi-zone HCCI model computes zone wall surface area by multiplying the instantaneous cylinder wall surface by a zone surface area fraction which is given by the user and kept constant during the simulation.
Since the zones are treated as variable-volume closed homogeneous reactors, governing equations for species and temperature of individual zones are the same as those employed by the single-zone HCCI engine model:
 | (8–88) |
where ρ is zone density and Yk, Wk and ùk are the mass fraction, molecular weight, and molar production rate of the k th species. The superscript in the equation denotes the zone index and Nzone is the number of zones used by the Multi-zone HCCI model analysis.
The zone temperature may be determined in two ways. When the crank angle is less than a pre-defined transition crank angle, θ t, the zone temperature is obtained from a temperature profile extracted from a CFD solution:
 | (8–89) |
In the above equation, θ(t) is the crank angle at time t and T iprofile( t ) is the temperature versus time profile for zone i . The temperature profile option allows the Multi-zone HCCI model to take advantage of the more precise zone temperature histories predicted by third-party CFD software when heat release from chemical reactions is not significant. After the transition angle is reached, the zone temperature will be solved by the zone energy equation:
 | (8–90) |
P, T, and V are zone pressure, temperature, and volume, respectively. Cv is the constant-volume specific heat capacity of the gas mixture comprising the zone and uk is the internal energy of the kth species. hw and Aw are zone wall heat transfer coefficient and zone wall surface area, respectively. The Ansys Chemkin Multi-zone HCCI model assumes zone wall surface area is a constant fraction of the total cylinder wall surface area. The wall heat-transfer coefficient is computed by the Woschni heat-transfer correlation. [59]
In the Multi-zone HCCI model, the cylinder volume is computed by the slider-crank relationship used in the single-zone internal-combustion engine model. Individual zone volume is not known and needs to be solved. Since gas composition and temperature in each zone are solved by their corresponding governing equations, zone pressure and volume are coupled by the equation of state, that is, ideal gas law.
In order to solve the system of equations more efficiently, a new variable is introduced
 | (8–91) |
Since pressure is the same in all zones, the G variable can be considered as a pressure-weighted accumulated zone volume. The use of pressure as scaling factor helps minimize the variation of G variable during the engine cycle. In addition, by replacing zone volume, V, with the G variable, the Jacobian matrix becomes banded along the diagonal and the system of equation can be integrated more effectively. The zone volume can be converted from the G variable by
 | (8–92) |
The governing equation for the new G variable can be derived from the equation of state as
 | (8–93) |
and, according to the definition of G ( Equation 8–91 ),
 | (8–94) |
where R is the universal gas constant and 
is the gas mass of zone i .
The assumption of uniform pressure among all zones serves a constraint and provides coupling between the zones
, for 
.
To close the pressure equation, the volume constraint
 | (8–95) |
is used to determine the pressure of the last zone ( 
). By substituting Equation 8–80 and Equation 8–95 into Equation 8–91 for 
, the governing equation for the pressure in the last zone can be obtained
 | (8–96) |
where 
is the instantaneous cylinder volume.
The Ansys Chemkin Multi-zone HCCI model solves Equation 8–88 - Equation 8–90 , Equation 8–93 - Equation 8–80 and Equation 8–96 for all zones fully-coupled to obtain zone properties. Average properties such as temperature and species concentrations are derived from their zone values.