Turbulent Flow: Analysis, Measurement, and Prediction

Abstract

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About Boussinesq's turbulent viscosity hypothesis: historical remarks and a direct evaluation of its validity

“…The main limitation of this linear closure is the fact that it rests on an analogy with kinetic theory, analogy that can be criticised on theorical grounds, as discussed below (see also discussion in [1,3,5]). …”

“…[33,34,35,36,37,38]). As already implicitly assumed by Boussinesq, the basis of such modelling is an analogy with kinetic theory, where the viscous stress is expressed using the gradient of the mean field (see also the comments in [3] ou [5]). The simple situation where molecules have a mean velocity of the form (U (y), 0, 0) is often taken as an illustrative example: the gradients are in fact an approximation of the finite difference quantity U (y + ℓ m ) − U (y − ℓ m ), where ℓ m is the mean-free path of molecules.…”

“…As well known, turbulence is one of the last subjects of classical physics which is still not solved. This is why in engineering sciences, or in environmental studies, turbulence models are used [1,2,3,4,5]. Among the different existing models, many introduce Reynolds averaging [6].…”

Computational fluid dynamics simulations of single-phase flow in a filter-press flow reactor having a stack of three cells

“…where k is the turbulent kinetic energy, ε is the turbulent energy dissipation rate, Pk is the energy production term ( :   ), and Cµ (0.09), Ce1 (1.44), Ce2 (1.92), σk (1), σε (1.3) are dimensionless constant values that are obtained by data fitting over a wide range of turbulent flows [17,20].…”

“…5.5 (6) Here, u + is the normalized velocity component inside the logarithmic boundary layer, and y + is the dimensionless distance from the wall, y + = ρuτy/μ, where uτ is the friction velocity, / √ and y is the distance from the wall [17,20].…”