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By Radyadour Kh. Zeytounian

For the fluctuations round the skill yet particularly fluctuations, and showing within the following incompressible process of equations: on any wall; at preliminary time, and are assumed identified. This contribution arose from dialogue with J. P. Guiraud on makes an attempt to push ahead our final co-signed paper (1986) and the most suggestion is to place a stochastic constitution on fluctuations and to spot the massive eddies with part of the likelihood area. The Reynolds stresses are derived from a type of Monte-Carlo technique on equations for fluctuations. these are themselves modelled opposed to a strategy, utilizing the Guiraud and Zeytounian (1986). The scheme is composed in a suite of like equations, regarded as random, simply because they mimic the massive eddy fluctuations. The Reynolds stresses are bought from stochastic averaging over a kinfolk in their strategies. Asymptotics underlies the scheme, yet in a slightly unfastened hidden method. We clarify this in relation with homogenizati- localization approaches (described in the §3. four ofChapter 3). Ofcourse the mathematical good posedness of the scheme isn't identified and the numerics will be bold! no matter if this try out will encourage researchers within the box of hugely advanced turbulent flows isn't really foreseeable and we now have wish that the belief will end up beneficial

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1, it is necessary to specify the role of the Mach number, M! In fact, it is necessary to pose the problem concerning the behaviour of solutions of NS-F equations when simultaneously and 14 CHAPTER 1 Naturally, for the validity of the NS-F equations, it is obvious that it is assumed that the limiting compressible flow, at low Reynolds and low Mach numbers, remains a continuous medium and this implies that the so-called (dimensionless) Knudsen number, Kn = M/Re is also a small parameter, Kn << 1.

On the other hand, the so-called ‘actuator-disk’ theory is derived when the pitch of the cascade configuration is near unity while the ratio of the distance between two rows (fixed-rotating) to the thickness of the row is large. 6 of Chapter 6. 1) is related with the high Strouhal and Reynolds numbers when we consider low Mach number flow, such that: where is a similitude parameter. When tends to zero, then the dissipative coefficient (so-called the “Stokes number”) in the Burgers equation: 40 CHAPTER 2 tends also to zero.

High aspect ratio wings or propellers give quite a useful application of the concept of asymptotic modelling capable of grasping the whole of a flow. The flow within a rotating engine (turbomachinery flows) may be reduced to gluing together, via some asymptotic machinery, two apparently widely different models, namely cascade flow and through-flow theories. Even the so-called actuator disc model may be considered as part of the whole. Thin film coating of a wire by a very viscous liquid may be attacked, as a whole, through asymptotic modeling.

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