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15.16.4 Solving the Flow Problem

The next step in the non-premixed combustion modeling process in FLUENT is the solution of the mixture fraction and flow equations. First, initialize the flow. By default, the mixture fraction and its variance have initial values of zero, which is the recommended value; you should generally not set non-zero initial values for these variables. See Section  25.14 for details about solution initialization.

Solve $\rightarrow$ Initialize $\rightarrow$ Initialize...

Next, begin calculations in the usual manner.

Solve $\rightarrow$ Iterate...

During the calculation process, FLUENT reports residuals for the mixture fraction and its variance in the fmean and fvar columns of the residual report:

iter cont     x-vel   y-vel       k epsilon   fmean    fvar
 28 1.57e-3 4.92e-4 4.80e-4 2.68e-2 2.59e-3 9.09e-1 1.17e+0
 29 1.42e-3 4.43e-4 4.23e-4 2.48e-2 2.30e-3 8.89e-1 1.15e+0
 30 1.28e-3 3.98e-4 3.75e-4 2.29e-2 2.04e-3 8.88e-1 1.14e+0

(For two-mixture-fraction calculations, columns for psec and pvar will also appear.)

Under-Relaxation Factors for PDF Equations

The transport equations for the mean mixture fraction and mixture fraction variance are quite stable and high, under-relaxation can be used when solving them. By default, an under-relaxation factor of 1 is used for the mean mixture fraction (and secondary partial fraction) and 0.9 for the mixture fraction variance (and secondary partial fraction variance). If the residuals for these equations are increasing, you should consider decreasing these under-relaxation factors, as discussed in Section  25.9.2.

Density Under-Relaxation

One of the main reasons a combustion calculation can have difficulty converging is that large changes in temperature cause large changes in density, which can, in turn, cause instabilities in the flow solution. FLUENT allows you to under-relax the change in density to alleviate this difficulty. The default value for density under-relaxation is 1, but if you encounter convergence trouble you may wish to reduce this to a value between 0.5 and 1 (in the Solution Controls panel).

Tuning the PDF Parameters for Two-Mixture-Fraction Calculations

For cases that include a secondary stream, the PDF integrations are performed inside FLUENT.

The parameters for these integrations are defined in the Species Model panel (Figure  15.16.2).

Define $\rightarrow$ Models $\rightarrow$ Species...

Figure 15.16.2: The Species Model Panel for a Two-Mixture-Fraction Calculation

The parameters are as follows:

Compressibility Effects   (non-adiabatic systems only) tells FLUENT to update the density, temperature, species mass fraction, and enthalpy from the PDF tables to account for the varying pressure of the system.

Probability Density Function   specifies which type of PDF should be used. You can pick either double delta (the default) or beta in the drop-down list. The double delta PDF has the advantage of being faster than the beta PDF, and it is the default. The beta function, however, may be a more accurate representation of the PDF.

Number of Flow Iterations Per Property Update   specifies how often the density, temperature, and specific heats are updated from the look-up table. Remember that when you are calculating two mixture fractions, the updating of properties includes computation of the PDFs and can be quite CPU-intensive. You should generally not reduce the Number of Flow Iterations Per Property Update below the default value of 10, unless you are experiencing convergence difficulties.

For simulations involving non-adiabatic multiple strained flamelets, looking up the four-dimensional PDF tables can be CPU-intensive if a large number of species exist in the flamelet files. In such cases, the Number of Flow Iterations Per Property Update controls the updating of the mean molecular weight, which involves looking up the PDF tables for the species mass fractions.

For the Eulerian unsteady laminar flamelet model, a marker probability equation is solved in an unsteady mode. Residuals for ufla-prob will be displayed.

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