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15.12 Calculating the Look-Up Tables

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 panel (e.g., Figure  15.12.1).

Figure 15.12.1: The Species Model Panel ( Table) Tab
figure

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 will also be the number of points used by FLUENT to compute the PDF if you choose the $\beta$ model (see Section  15.16.4). 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 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, FLUENT will use the Number of Secondary Mixture Fraction Points to compute the PDF if you choose the $\beta$ PDF option (see Section  15.16.4) 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. 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 three-dimensional look-up tables will be computed. This input is required only if you are modeling a non-adiabatic system. 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 flamelets model.

Minimum Temperature   is used to determine the lowest temperature for which the look-up tables are generated (see Figure  15.2.10). 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 flamelets model.

Include Equilibrium Flamelet   specifies that an equilibrium flamelet (i.e., $\chi=0$) will be generated in 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 x=0, and the flamelet slice. This option is not available with the equilibrium chemistry model or the unsteady flamelets 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 Equation  15.2-16 (or 15.2-24) as represented in Figure  15.2.5 (or Figure  15.2.6). For a two-mixture-fraction calculation, FLUENT will calculate the physical properties using Equation  15.2-14 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 output is 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.

figure   

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, 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 FLUENT simulation. Since this is computationally expensive, 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, FLUENT reports that the calculation succeeded. In a single-mixture-fraction case, the resulting look-up tables take the form illustrated in Figure  15.2.8 (or Figure  15.2.10, for non-adiabatic systems). These look-up tables can be plotted using the available graphics tools, as described in Section  15.12.3.

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 Figure  15.2.9 (or Figure  15.2.11, for non-adiabatic systems).




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