35 Summary

Turbulence is a most complex fluid motion and has puzzled theoreticians and modelers for more than a century. Turbulence significantly enhances rates of mixing and other transport processes at the expense of more friction and energy losses. Many reactor technologies rely on these enhanced rates of transport processes via turbulence. It is, therefore, of crucial importance to develop turbulence models capable of making quantitative predictions. The wide range of length and time scales existing in turbulent flows poses a severe challenge to modelers. Several different approaches such as DNS (direct numerical simulations), LES (large eddy simulations) and RANS (Reynolds-averaged Navier-Stokes equations)-based models have been developed. Although DNS and LES offer valuable insight into turbulence and mechanisms of transport, for the foreseeable future, most reactor engineering flows have to rely on RANS-based models. It is noteworthy that the simple, two-equation k-e model succeeds in expressing the main features of many turbulent flows by relying on just one characteristic length scale and time scale. This model is, therefore, recommended as a baseline model. More advanced RANS-based models such as Reynolds stress models (RSM) and non-linear extensions of k-e models or RNG models deserve careful evaluation from the cost-to-benefit point of view for each case. It must be remembered that a more complex model does not necessarily mean a better model. Moreover, it should never be forgotten that all RANS-based models contain adjustable constants that need to be determined by fitting experimental data. All reactor engineers are aware of the dangers of extrapolating an empirical model beyond its data range. Although the turbulence models discussed here are not entirely empirical, none of the CFD simulations of 'new' turbulent flows should be accepted as they are, without rigorous error analysis and validation. Some aspects of error analysis and validation are discussed in Chapters 6 and 7. The new information obtained from DNS and LES approaches should be used to examine the limitations of RANS-based models and to guide their further development. Despite some of the deficiencies of turbulence models, the best modern computational models (and numerical methods) allow almost all flows to be calculated to higher accuracy than the best-informed guess. This means that these methods are genuinely useful for reactor engineering.

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