## 7.7. Combustion Source Term Linearization

The combustion source terms may have a dominant influence on the solution of the scalar and energy equations. Thus, it is important to treat the combustion source terms carefully in order to obtain robust convergence of the fluid flow.

A property of multicomponent fluids is that the mass fraction of any given component is bounded between 0 and 1. Combustion tends to drive reactant concentrations towards the lower limit and product concentrations toward the upper limit. If the timestep is large, the combustion sources may cause scalars to exceed these bounds. Thus, the sources may need to be moderated to maintain physically realistic mass fractions.

The combustion sources in CFX have been linearized to prevent the formation of negative mass fractions. Consider the solution of component I with the source term, R, which is calculated from Equation 7–15 in each control volume. To prevent the mass fraction of I from exceeding the bounds of 0 to 1, the source term is calculated according to:

| (7–15)

where and where

and is a small number (set to 10-6). The combustion reaction rate should approach 0 whenever any of the reactant or product mass fractions approach 0. If the source is positive (for products), then the first term on the right hand side of Equation 7–15 is zero and the source is:

| (7–16)

otherwise:

| (7–17)

Therefore, as , .

If the source is negative (reactants), then the second term on the right hand side of Equation 7–15 is zero and the source is:

| (7–18)

otherwise:

| (7–19)

Therefore, as , .

This treatment of combustion sources enables larger timesteps to be used in calculating a steady-state solution than would be possible without the linearization.

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