16.7 Calculating the Look-Up Tables

ANSYS FLUENT requires additional inputs that are used in the creation of the look-up tables. Several of these inputs control the number of discrete values for which the look-up tables will be computed. These parameters are input in the Table tab of the Species Model dialog box (e.g., Figure  16.7.1).

Figure 16.7.1: The Species Model Dialog Box ( Table) Tab

The look-up table parameters are as follows:

Number of Mean Mixture Fraction Points   is the number of discrete values of $\overline{f}$ at which the look-up tables will be computed. For a two-mixture-fraction model, this value is the number of points in the instantaneous state profile used to compute the PDF if you choose the $\beta$ PDF model (see Section  16.10.4). Increasing the number of points will yield a more accurate PDF shape, but the calculation will take longer. The mean mixture fraction points will be automatically clustered around the stoichiometric mixture fraction value.

Number of Mixture Fraction Variance Points   is the number of discrete values of $\overline{f^{'2}}$ at which the look-up tables will be computed. Lower resolution is acceptable because the variation along the $\overline{f^{'2}}$ axis is, in general, slower than the variation along the $\overline{f}$ axis of the look-up tables. This option is available only when no secondary stream has been defined.

Number of Secondary Mixture Fraction Points   is the number of discrete values of $p_{\rm sec}$ at which the look-up tables will be computed. Like the Number of Mean Mixture Fraction Points, ANSYS FLUENT will use the Number of Secondary Mixture Fraction Points to compute the equilibrium state-relation if you choose the $\beta$ PDF option (see Section  16.10.4) for a two-mixture-fraction model. A larger number of points will give a more accurate shape for the PDF, but with a longer calculation time. This option is available only when a secondary stream has been defined.

Maximum Number of Species   is the maximum number of species that will be included in the look-up tables. The maximum number of species that can be included is 100. Note that the maximum number of species for the equilibrium computations is 500, and the maximum number of species for the flamelet generation and importing is 300. ANSYS FLUENT will automatically select the species with the largest mole fractions to include in the PDF table.

Number of Mean Enthalpy Points   is the number of discrete values of enthalpy at which the look-up tables will be computed. This input is required only if you are modeling a non-adiabatic system. In general, you should choose the The number of points required will depend on the chemical system that you are considering, with more points required in high heat release systems (e.g., hydrogen/oxygen flames). This option is not available with the unsteady flamelet model.

Minimum Temperature   is used to determine the lowest temperature for which the look-up tables are generated (see this figure in the separate Theory Guide). Your input should correspond to the minimum temperature expected in the domain (e.g., an inlet or wall temperature). The minimum temperature should be set 10-20 K below the minimum system temperature. This option is available only if you are modeling a non-adiabatic system. This option is not available with the unsteady flamelet model.

Include Equilibrium Flamelet   specifies that an equilibrium flamelet (i.e., $\chi=0$) will be generated in ANSYS FLUENT and appended to the flamelet library before the PDF table is calculated. This option is available when generating or importing multiple flamelets, as well as when a single flamelet is considered. In the latter case, the PDF table will consist of two scalar dissipation slices, namely the equilibrium slice at $\chi=0$, and the flamelet slice. This option is not available with the equilibrium chemistry model or the unsteady flamelet model.

When you are satisfied with your inputs, click Calculate PDF Table to generate the look-up tables.

The computations performed for a single-mixture-fraction calculation culminate in the discrete integration of this equation (or this equation in the separate Theory Guide) as represented in this figure (or this figure in the separate Theory Guide). For a two-mixture-fraction calculation, ANSYS FLUENT will calculate the physical properties using this equation or its adiabatic equivalent. The computation time will be shortest for adiabatic single-mixture-fraction equilibrium calculations and longest for non-adiabatic calculations involving multiple flamelet generation. Below, sample outputs are shown for an adiabatic single-mixture-fraction equilibrium calculation and a non-adiabatic calculation with laminar flamelets:

Generating PDF lookup table
Type of the PDF Table: Adiabatic Table (Two Streams)
Calculating table .....

1271  points calculated
22  species added
PDF Table successfully generated!

Generating PDF lookup table
Type of the PDF Table: Nonadiabatic Table with Strained Flamelet Model (Two St
Calculating table .....
     calculating temperature limits .....
     calculating temperature limits .....
     calculating scalar dissipation slices .....
        - scalar dissipation slice   9
     calculating equilibrium slice .....
Performing PDF integrations.....

16810  points calculated
17  species added
PDF Table successfully generated!
Initializing PDF table arrays and structures.

Note that there is a significant difference in run-time between the one-mixture fraction model and the two-mixture fraction model. In the one-mixture fraction model, the PDF table contains the mean data of density, temperature, and specific heats, and is three-dimensional for an equilibrium nonadiabatic case (mean mixture fraction, mixture fraction variance, and mean heat loss). For this case, ANSYS FLUENT updates properties every flow iteration. In the case of the two-mixture fraction model, only the instantaneous state relationships are stored and mean properties are calculated from these by performing PDF integrations in every cell of the ANSYS FLUENT simulation. Since this is computationally expensive, ANSYS FLUENT provides the option of only updating properties after a specified number of iterations.

After completing the calculation at the specified number of mixture fraction points, ANSYS FLUENT reports that the calculation succeeded. In a single-mixture-fraction case, the resulting look-up tables take the form illustrated in this figure in the separate Theory Guide (or this figure , for non-adiabatic systems). These look-up tables can be plotted using the available graphics tools, as described in Section  16.7.4.

Note that in non-adiabatic calculations, the console window will report that the temperature limits and enthalpy slices have been calculated.

For a two-mixture-fraction case, the resulting look-up tables take the form illustrated in this figure in the separate Theory Guide (or this figure , for non-adiabatic systems).