8.3.1 Restrictions on the Mixture Fraction Approach

The unique dependence of $\phi_i$ (species mass fractions, density, or temperature) on $f$ (Equation  8.2-11 or 8.2-13) requires that the reacting system meet the following conditions:

• The chemical system must be of the diffusion type with discrete fuel and oxidizer inlets (spray combustion and pulverized fuel flames may also fall into this category).

• The Lewis number must be unity. (This implies that the diffusion coefficients for all species and enthalpy are equal, a good approximation in turbulent flow).

• When a single mixture fraction is used, the following conditions must be met:
  • Only one type of fuel is involved. The fuel may be made up of a burnt mixture of reacting species (e.g., 90% CH $_4$ and 10% CO) and you may include multiple fuel inlets. The multiple fuel inlets must have the same composition; two or more fuel inlets with different fuel composition are not allowed (e.g., one inlet of CH $_4$ and one inlet of CO). Similarly, in spray combustion systems or in systems involving reacting particles, only one off-gas is permitted.

  • Only one type of oxidizer is involved. The oxidizer may consist of a mixture of species (e.g., 21% O $_2$ and 79% N $_2$) and you may have multiple oxidizer inlets. The multiple oxidizer inlets must, however, have the same composition. Two or more oxidizer inlets with different compositions are not allowed (e.g., one inlet of air and a second inlet of pure oxygen).

• When two mixture fractions are used, three streams can be involved in the system. Valid systems are as follows:
  • Two fuel streams with different compositions and one oxidizer stream. Each fuel stream may be made up of a mixture of reacting species (e.g., 90% CH $_4$ and 10% CO). You may include multiple inlets of each fuel stream, but each fuel inlet must have one of the two defined compositions (e.g., one inlet of CH $_4$ and one inlet of CO).

  • Mixed fuel systems including gas-liquid, gas-coal, or liquid-coal fuel mixtures with a single oxidizer. In systems with a gas-coal or liquid-coal fuel mixture, the coal volatiles and char can be treated as a single composite fuel stream and the secondary stream can represent another fuel. Alternatively, for coal combustion, the volatile and char off-gases are tracked separately as distinct fuel streams.

  • Two oxidizer streams with different compositions and one fuel stream. Each oxidizer stream may consist of a mixture of species (e.g. 21% O $_2$ and 79% N $_2$). You may have multiple inlets of each oxidizer stream, but each oxidizer inlet must have one of the two defined compositions (e.g., one inlet of air and a second inlet of pure oxygen).

  • A fuel stream, an oxidizer stream, and a non-reacting secondary stream.

• The flow must be turbulent.

It is important to emphasize that these restrictions eliminate the use of the non-premixed approach for directly modeling premixed combustion. This is because the unburned premixed stream is far from chemical equilibrium. Note, however, that an extended mixture fraction formulation, the partially premixed model (see Chapter  10), can be applied to non-premixed (with mixed-but-unburnt regions), as well as partially premixed flames.

Figures  8.3.1 and  8.3.2 illustrate typical reacting system configurations that can be handled by the non-premixed model in ANSYS FLUENT. Figure  8.3.3 shows a premixed configuration that cannot be modeled using the non-premixed model.

Figure 8.3.1: Chemical Systems That Can Be Modeled Using a Single Mixture Fraction

Figure 8.3.2: Chemical System Configurations That Can Be Modeled Using Two Mixture Fractions

Figure 8.3.3: Premixed Systems That Cannot Be Modeled Using the Non-Premixed Model