In this chapter, we present the most widely used methods for closing the chemical source term in the Reynolds-averaged scalar transport equation. Although most of these methods were not originally formulated in terms of the joint composition PDF, we attempt to do so here in order to clarify the relationships between the various methods. A schematic of the closures discussed in this chapter is shown in Fig. 5.1. In general, a closure for the chemical source term must assume a particular form for the joint composition PDF. This can be done either directly (e.g., presumed PDF methods), or indirectly by breaking the joint composition PDF into parts (e.g., by conditioning on the mixture-fraction vector). In any case, the assumed form will be strongly dependent on the functional form of the chemical source term. In Section 5.1, we begin by reviewing the methods needed to render the chemical source term in the simplest possible form. As stated in Chapter 1, the treatment of non-premixed turbulent reacting flows is emphasized in this book. For these flows, it is often possible to define a mixture-fraction vector, and thus the necessary theory is covered in Section 5.3.

Figure 5.1: Closures for the chemical source term can be understood in terms of their relationship to the joint composition PDF. The simplest methods attempt to represent the joint PDF by its (lower-order) moments. At the next level, the joint PDF is expressed in terms of the product of the conditional joint PDF and the...