GENERAL

In this chapter, we examine computations for reactive flows in general with computational combustion in particular. In reactive flows, the conservation equations for chemical species are added to the Navier-Stokes system of equations. This addition also requires a modification of the energy equation. Furthermore, the sensible enthalpy is coupled with the chemical species, which contributes to the heat source and diffusion of species interacting with temperature. Chemical reactions in high-speed turbulent flows with high temperatures are of practical interest. They are involved in hypersonic aircraft and reentry vehicles. In this case, it is necessary that the vibrational and electronic energies be taken into account, in which the ionization of chemical species may be important. Thus, the chemically reactive flows and combustion require significant modifications of not only the governing equations but also the existing computational methods discussed in previous chapters.

In general, we are concerned with characterizing ordinary flame and detonation by different time scales. These scales range over many orders of magnitude. When reaction phenomena are modeled such that characteristic times of variation are shorter than the time step used, the equations describing such physical phenomena become numerically stiff with respect to convection and diffusion.

Another type of difficulty is the disparity in spatial scales occurring in combustion. To model the steep gradients at a flame front, an extremely small grid spacing is required. In addition, complex phenomena such as turbulence, which occur on intermediate spatial scales, lead to difficult modeling problems.

The third set of obstacles arises because of the geometric complexity associated with real systems. Most of the detailed models developed to date have been one-dimensional.