### 7.9.2. Weighted Reaction Progress

In order to overcome the boundary value issue for reaction progress on oxidizer inlets, the weighted reaction progress, , is introduced:

| (7–44)

Because for pure oxidizer, the weighted reaction progress is well defined to be . Linear combination of the transport equations for and yields the following transport equation for the weighted reaction progress:

| (7–45)

The turbulent Schmidt number for the weighted reaction progress by default is . Because of the formal derivation of the transport equation, its solution will be equivalent to solving for reaction progress directly; that is, introducing the weighted reaction progress overcomes the boundary value issue for reaction progress without changing the model. Reaction progress can be restored from mixture fraction and the weighted reaction progress according to

| (7–46)

The recipe for is ill-posed for . Therefore, numerical treatment is implemented in the limit of pure oxidizer to smoothly blend both the reaction progress and its gradient to zero:

as

Default for ANSYS CFX 18.2 is to solve for weighted reaction progress. Expert control (CCL) is available for reverting to the standard reaction progress equation:

    FLUID MODELS:
      Option = Burning Velocity Model
      REACTION PROGRESS VARIABLE:
        Option = Reaction Progress
        # default: Weighted Reaction Progress
      END
    END

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