8.6.2 The Diesel Unsteady Laminar Flamelet Model

In diesel engines, fuel sprayed into the cylinder evaporates, mixes with the surrounding gases, and then auto-ignites as compression raises the temperature and pressure. The diesel unsteady laminar flamelet model, based on the work of Pitsch et al. and Barths et al. [ 272, 15], models the chemistry in a single, one-dimensional laminar flamelet. By reducing the costly chemical kinetic calculation to 1D, substantial savings in run-time can be achieved over the laminar-finite-rate, EDC or PDF Transport models.

The flamelet species and energy equations (Equations  8.4-6 and 8.4-7) are solved simultaneously with the flow. The flamelet equations are advanced for a fractional step using properties from the flow, and then the flow is advanced for the same fractional time-step using properties from the flamelet.

The initial flamelet condition at the start of the diesel simulation is a mixed-but-unburnt distribution. For the flamelet fractional time-step, the volume-averaged scalar dissipation and pressure, as well as the fuel and oxidizer temperatures, are passed from the flow solver to the flamelet solver. To account for temperature rise during compression, the flamelet energy equation (Equation  8.4-7) has an additional term on the right-hand side as

where $c_p$ is a the specific heat and $p$ is the volume-averaged pressure in the cylinder. This rise in flamelet temperature due to compression eventually leads to ignition of the flamelet.

After the flamelet equations have been advanced for the fractional time-step, the PDF Table is created as a Non-Adiabatic Steady Flamelet table (see Section  8.5.4). Using the properties of this table, the CFD flow field is then advanced for the same fractional time-step.

The diesel unsteady flamelet approach can model ignition as well as formation of product, intermediate and pollutant species. Enabling the Diesel Unsteady Flamelet model is described in this section in the separate User's Guide.