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Friction equation for purely viscous non-Newtonian fluids from Kolmogorov's theory

DOI: 10.1615/ICHMT.2015.THMT-15.180
pages 151-154

H. R. Anbarlooei
Mechanical Engineering Program (PEM/COPPE), Universidade Federal do Rio de Janeiro, C.P. 68503, 21941-972, Rio de Janeiro, Brazil

D. O. A. Cruz
Mechanical Engineering Department, Federal University of Rio de Janeiro, Av. Moniz de Aragao 420, 21945-972 Rio de Janeiro, Brazil

Atila P. Silva Freire
Mechanical Engineering Department, Federal University of Rio de Janeiro, Av. Moniz de Aragao 420, 21945-972 Rio de Janeiro, Brazil

Résumé

This paper extends Kolmogorov's theory of turbulent flow of Newtonian fluids to purely viscous non-Newtonian fluids. The premises developed in the K41 theory are modified to account for non-Newtonian effects. It can be shown that only the first similarity hypothesis needs to be changed, which results in a new set of micro-scales. Also, the (-5/3)-law remains unchanged. As a direct engineering application of the extended theory, a Blasius-type friction equation is proposed for PVNN fluids. This result follows naturally from an examination of the relation between micro and meso-scales.

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