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15.2.5 Restrictions and Special Cases for Using the Non-Premixed Model



Restrictions on the Mixture Fraction Approach


The unique dependence of $\phi_i$ (species mass fractions, density, or temperature) on $f$ (Equation  15.2-11 or 15.2-13) requires that the reacting system meet the following conditions:

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  17), can be applied to non-premixed, premixed, and partially premixed flames.

Figures  15.2.12 and  15.2.13 illustrate typical reacting system configurations that can be handled by the non-premixed model in FLUENT. Figure  15.2.14 shows a premixed configuration that cannot be modeled using the non-premixed model.

Figure 15.2.12: Chemical Systems That Can Be Modeled Using a Single Mixture Fraction
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Figure 15.2.13: Chemical System Configurations That Can Be Modeled Using Two Mixture Fractions
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Figure 15.2.14: Premixed Systems CANNOT Be Modeled Using the Non-Premixed Model
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Using the Non-Premixed Model for Liquid Fuel or Coal Combustion


You can use the non-premixed model if your FLUENT simulation includes liquid droplets and/or coal particles. In this case, fuel enters the gas phase within the computational domain at a rate determined by the evaporation, devolatilization, and char combustion laws governing the dispersed phase. In the case of coal, the volatiles and the products of char can be defined as two different types of fuel (using two mixture fractions) or as a single composite off-gas (using one mixture fraction), as described in Section  15.9.5.



Using the Non-Premixed Model with Flue Gas Recycle


While most problems you solve using the non-premixed model will involve inlets that contain either pure oxidant or pure fuel ( $f = 0$ or 1), you can include an inlet that has an intermediate value of mixture fraction ( $0 < f < 1$) provided that this inlet represents a completely reacted mixture. Such cases arise when there is flue gas recirculation, as depicted schematically in Figure  15.2.15. Since $f$ is a conserved quantity, the mixture fraction at the flue gas recycle inlet can be computed as


 \dot{m}_{\rm fuel} + \dot{m}_{\rm recyc} f_{\rm exit} = (\do... ... fuel} + \dot{m}_{\rm ox} + \dot{m}_{\rm recyc}) f_{\rm exit} (15.2-27)

or


 f_{\rm exit} = \frac{\dot{m}_{\rm fuel}}{\dot{m}_{\rm fuel} + \dot{m}_{\rm ox}} (15.2-28)

where $f_{\rm exit}$ is the exit mixture fraction (and the mixture fraction at the flue gas recycle inlet), $\dot{m}_{\rm ox}$ is the mass flow rate of the oxidizer inlet, $\dot{m}_{\rm fuel}$ is the mass flow rate of the fuel inlet, $\dot{m}_{\rm recyc}$ is the mass flow rate of the recycle inlet.

If a secondary stream is included,


 f_{\rm fuel, exit} = \frac{\dot{m}_{\rm fuel}}{\dot{m}_{\rm fuel}\ + \dot{m}_{\rm sec} + \dot{m}_{\rm ox}} (15.2-29)

and


 p_{\rm sec, exit} = \frac{\dot{m}_{\rm sec}}{\dot{m}_{\rm sec} + \dot{m}_{\rm ox}} (15.2-30)

Figure 15.2.15: Using the Non-Premixed Model with Flue Gas Recycle
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