Topical Problems of Fluid Mechanics


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Institute of Thermomechanics AS CR, v.v.i. CTU in Prague Faculty of Mech. Engineering Dept. Tech. Mathematics MIO Université du Sud Toulon Var - AMU - CNRS - IRD Czech Pilot centre ERCOFTAC
Turbulent Mixing in Non-Newtonian Dispersions

Baumert H. Z., Wessling B.

Abstract:
The talk covers a qualitatively new turbulence theory resting on early ideas of A. N. Kolmogorov and L. Landau during the Kazan seminars [7]. This theory predicts (e.g.) for infinitely high Reynolds number von Karman's constant as 1/√(2π) = 0.399 whereas Princeton's superpipe recently re-confirmed the international standard value as 0.40 +/- 0.02 [1]. This theory has been further developed to cope with the problems of finite viscosity and non-Newtonian fluids wherein the following characteristic length scales are relevant: (i) the 'statistically largest' turbulent scale, l0, labeling the begin of the inertial part of the wavenumber spectrum; (ii) the energy-containing scale, L; (iii) Kolmogorov's micro-scale, λk, related with the size of the smallest vortices existing for a given kinematic viscosity and forcing; (iv) the inner (`colloidal') micro-scale, li, typically representing a major stable material property of the colloidal fluid. In particular, for small ratios r = λi/ λk ~ O(1), various interactions between colloidal structures and smallest turbulent eddies can be expected. We present equations for the shear-thickening case which in the steady state exhibits two solution branches. One branch describes a state of good mixing, the other a state of strangled mixing (as observed) characterized by an identity of energy-containing scale with Kolmogorov's microscale, i.e. that r = λ0/ λk ~ O(1). The system may commute between the two steady states by chaotic transitions. While we could identify most properties of the two alternative quasi-equilibrium positions, the dynamics of the switching is left for further research.

Keywords:
Turbulence, non-Newtonian fluid, Dispersion, dilatant fluid, shear-thickening fluid, Kolmogorov micro scale, bifurcation
Fulltext: PDF
DOI: http://dx.doi.org/10.14311/TPFM.2016.002
In Proceedings Topical Problems of Fluid Mechanics 2016, Prague, 2016 Edited by David Šimurda and Tomáš Bodnár, pp. 9-16
ISBN 978-80-87012-58-1 (Print)
ISSN 2336-5781 (Print)
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