What Is Specific about Turbulence with Combustion?

In recent years, nothing seems to have inspired researchers in the combustion community so much as the unresolved problems in turbulent combustion. Turbulence in itself is far from being fully understood; it is probably the most significant unresolved problem in classical physics. Since the flow is turbulent in nearly all engineering applications, the urgent need to resolve engineering problems has led to preliminary solutions called turbulence models. These models use systematic mathematical derivations based on the Navier–Stokes equations up to a certain point, but then they introduce closure hypotheses that rely on dimensional arguments and require empirical input. This semiempirical nature of turbulence models puts them into the category of an art rather than a science.

For high Reynolds number flows the so-called eddy cascade hypothesis forms the basis for closure of turbulence models. Large eddies break up into smaller eddies, which in turn break up into even smaller ones, until the smallest eddies disappear due to viscous forces. This leads to scale invariance of energy transfer in the inertial subrange of turbulence. We will denote this as inertial range invariance in this book. It is the most important hypothesis for large Reynolds number turbulent flows and has been built into all classical turbulence models, which thereby satisfy the requirement of Reynolds number independence in the large Reynolds number limit. Viscous effects are of importance in the vicinity of solid walls only, a region of minor importance for combustion.

The apparent success of turbulence models in solving engineering problems has encouraged similar approaches for turbulent combustion, which consequently led to the formulation of turbulent combustion models. This is, however, where problems arise.