5 - Turbulence

Summary

Introduction

Turbulence generally plays a key role in drag generation, heat transfer, particle dispersion and scalar mixing along with sound generation. These are all aspects that are vital in aerodynamic design. The modelling of turbulence has strongly defined CFD as a postdictive rather than predictive process. Hence, this chapter has strong importance in relation to the safe and reliable use of CFD. Initially the nature of turbulence is outlined and thus the modelling challenges defined. Then a range of established modelling approaches is outlined, starting with low order and then moving to techniques where CFD becomes predictive with no modelling.

The Basic Nature of Turbulence

The formidable task facing turbulence modelling is reflected by Richard Feynman (Physics Nobel Laureate), who wrote, “Turbulence is the last great unsolved problem in classical physics.” Indeed we have the situation where we do not even know basic physical constants. For example, for the Karman ‘constant’, κ, (in l = κ d, where l is the mixing length and d nearest wall distance) the published range is 0.38–0.45) and we do not even know if it is a constant! As noted by Spalart et al. (2006), a 2% decrease in κ gives 1% decrease in predicted aircraft drag. This might not sound like much, but it matters greatly to plane manufacturers. They sell planes before they are made and if the craft do not make the range, serious problems arise.

If a sensitive velocity-measuring device (such as a hot wire anemometer) is placed in a turbulent flow, the trace shown in Figure 5.1 will be produced. Similar graphs can be plotted for the remaining v (y direction) and w (z direction) velocity components. As can be seen, the fluid velocity can be decomposed into mean (Φ) and fluctuating (ϕ^ʹ) components. Hence, instantaneous velocities can be expressed as

Transition to turbulence occurs when inertial forces overwhelm the viscous. The transition process can be observed in the smoke patterns rising from the tip of a cigarette. The initial smoke has a laminar region. This is followed by a turbulent zone, where the fluid flow has a more chaotic appearance. The latter can clearly be seen in the Figure 5.2a schematic adjacent to the flow visualization for a more fully turbulent jet. Figure 5.2b shows a sketch of da Vinci – for which he describes the “clouds as scattered and torn.”