Concluding Remarks

Turbulence theory is a difficult subject area and it is probably too much to expect a universal solution the turbulent flows. There are models and each model has its own area of applicability.

All the variants of eddy viscosity models, contain a diffusive term involving u_t . For high Reynolds number turbulence, the Reynolds stress terms in the mean-flow equation dominate over the genuine viscous terms, that is ν_t >> ν except for thin viscous layers near walls. The turbulent Reynolds number is not high enough for validity of the k - ε model in the viscous layers and it must be modified if a realistic description of those layers is envisaged. Low-Reynolds number models attempt to reproduce the experimentally observed viscous layer scaling laws, based on ν and the turbulent friction velocity u_t . However, one should not expect them to perform well near separation. The standard values of model constants were given earlier, but better results can usually be obtained by tuning the parameters to particular flows. At the least, these should be tuned with the class of flows. Even though the basic model provides a rather crude representation of the physics of turbulence, the flexibility provided by the parameter can lead to a somewhat better situation. Once the model is fine tuned for one member of a class of similar flows, it is expected to predict the other flows in that class reasonably well. This is what is needed in many design applications, where the basic form of the flow geometry can be set through the mean flow calculations.

The LES and DNS techniques have demonstrated superiority advantages over the RANS approach. These simulation techniques require excessive CPU time and memory for computations of 3D complex flow problems particularly at large Reynolds numbers. In particular, DNS calculations are limited to a large-scale turbulence with relatively low Reynolds numbers such as transition flows in ducts, flow over a bluff body, or the passages of the heat exchangers at low Reynolds numbers. The LES procedure has received attention as a potential remedy for such difficulties, and some significant progress has been made. Numerical experiments based on LES and attempts to determine the quantities that are difficult to measure in Laboratories will have a critical role in future research in turbulence modeling. Alongside, efforts toward determination easy-to-implement averaging procedures for the inhomogeneous turbulence features is another current challenge. Till these landmarks are achieved with LES, it seems that RANS (variants of k - ε models with problem-specific parametric optimization) will remain the CFD tool for design and optimization of turbomachinery, aircrafts, automobile engines, reactors and various heat exchangers.