Flamelet Tables

Independent Variables

Within the flamelet tables, independent variables define the dimensions on which the table is constructed. The method by which the chemistry is computed determines the set of independent variables.

For each independent variable, Simcenter STAR-CCM+ accepts a range of points at which to compute chemical states, along with conditions of temperature and pressure. The total number of states stored in the table therefore becomes

where $n_i$ is the number of points in each dimension, $i$.

Reaction outcomes are calculated using the method that applies to the chosen model. For example, when Flamelet Generated Manifold (FGM) is chosen, Simcenter STAR-CCM+ solves the system of ODEs that apply to the reaction mechanism. Currently, reactions are computed for a single pressure and at the specified initial temperature.

For each of the methods, the independent variable, mixture fraction, is plotted on the $Z$ (mixture fraction) grid of the flamelet table.

When using adaptive gridding, Simcenter STAR-CCM+ starts to generate the flamelet table using an initial coarse mesh that is created with the pre-determined grid-stretch. Simcenter STAR-CCM+ then inserts a new table point midway between these existing points. If the difference between linear interpolation of the two existing points and the newly inserted point is less than the normalized tolerance, the newly inserted point is discarded. If not, the process is repeated until the maximum number of grid points are reached.

Two normalized tolerances are defined, namely a global tolerance and a local tolerance. Global tolerances are used for temperature, and mass fractions of fuel, oxidizer, CO₂, and H₂O. The global tolerance is calculated as the tolerance that you specify under the Table Dimensions > Grid Parameters sub-node, multiplied by the difference between the maximum and minimum values of the variables in the table. Since the magnitudes of intermediate species are strongly affected by heat loss or gain, adapting on global tolerances causes clustering at peak mass fractions. Hence, instead of using global tolerance for any additional species added for tabulation, a local tolerance is calculated as the tolerance that you specify under the Table Dimensions > Grid Parameters sub-node, multiplied by the local value of the species mass fraction in the table. An additional multiplication factor is used to cluster points around adiabatic (zero heat loss ratio).

Table entries are generated for the instantaneous chemical states. In reality, turbulence effects are continually at work within the fluid system at timescales smaller than the simulation time-step. To account for the turbulence effects, a probability density function is assumed for the dependent quantities and then sampled when integrating these quantities across the entire simulation time-step. The general form of the integration step is represented as:

When using the Chemical Equilibrium model or the Flamelet Generated Manifold model—which solve flamelets at different enthalpy levels—cell temperatures are obtained by interpolating the flamelet table directly at the enthalpy that is being solved. For the Steady Laminar Flamelet (SLF) model—which solves flamelets at only the adiabatic enthalpy—cell temperatures are obtained from the tabulated (adiabatic) species and the enthalpy which is solved using the enthalpy equation of state. The SLF model ignores the effect of heat loss or gain on the species. The mixture properties values (such as dynamic viscosity, thermal conductivity, and molecular diffusivity) for each of the flamelet models can be stored in the flamelet tables.

When the transport data is imported along with the chemical and thermodynamic data for flamelet generation, Simcenter STAR-CCM+ tabulates the molecular transport properties for Dynamic Viscosity, Molecular Diffusivity, and Thermal Conductivity. Based on the properties of each species, kinetic theory is used to calculate the dynamic viscosity and thermal conductivity of each species. The molecular diffusivity is calculated from the unity Lewis number assumption Eqn. (138). Mass fraction weighted averaging is then used to calculate the mixture diffusivity, while Mathur-Saxena averaging is used to calculate the mixture viscosity and thermal conductivity. However, if any of the properties that are required to use kinetic theory are missing from the tran.dat file for some or all species, Simcenter STAR-CCM+ does not calculate values for the material properties. These tabulated values are taken from the flamelet table when the respective Material Properties nodes are set to Flamelet Table—necessary for simulations where laminar transport is important (in particular, LES). By default, constant molecular transport properties are used, which are applicable to most simulations in which turbulent transport is much greater than laminar transport (in particular, RANS).

Inert Streams

When an inert stream is present, Simcenter STAR-CCM+ solves a transport equation for the inert mass fraction, or equivalently the inert mixture fraction, denoted $Z_I$ . The temperature is calculated from the enthalpy $h$ :

$$h=(1-Z_I)h_f+Z_I{h}_I$$

(3518)

where $h_f$ is the enthalpy of the flamelet species, $h_I$ is the enthalpy of the inert species, and $h$ is the total enthalpy from the solved transport equation.

If the mixture fraction of the inert stream $Z_I=0$ , all species fractions are given from the flamelet table as they would be without an inert stream. However, if the mixture fraction of the inert stream $Z_I\ne 0$ , the mass fraction of species $i$ is given by:

$$Y_i=(1-Z_I)Y_{i,f}+Z_I{Y}_{i,I}$$

(3519)

where $Y_i$ denotes the $i$ 'th species mass fraction and subscripts $f$ and $I$ denote flamelet and inert respectively. Hence $Y_{i,f}$ is the $i$ 'th species mass fraction in the flamelet table.

The Inert Stream model assumes that the inert species and the reacting flamelet species are in thermal equilibrium.