Geodesic
A model of averaged molecular viscosity for turbulent flow of non-Newtonian fluids
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 7 (2014) no. 1, pp. 46-57.

Voir la notice de l'article provenant de la source Math-Net.Ru

A novel turbulence model for flows of viscoplastic fluid is presented. It is based on the Reynolds-Averaged approach. A closed model for the averaged viscosity that takes into account its nonlinear dependence on the fluctuating rate of deformation tensor is proposed. Test calculations were performed for power-law fluid and Herschel–Bulkley fluid flows in a straight round pipe. Numerical data obtained with the use of the proposed model are compared with the results of direct numerical simulations. The proposed model adequately describes the reduction in the turbulent transport of momentum with decreasing power-law index and with increasing yield stress of the fluid.
Keywords: shear-thinning fluids, Reynolds averaging, turbulent flow models, finite volume method. 
@article{JSFU_2014_7_1_a4,
     author = {Andrey A. Gavrilov and Valeriy Ya. Rudyak},
     title = {A model of averaged molecular viscosity for turbulent flow of {non-Newtonian} fluids},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {46--57},
     publisher = {mathdoc},
     volume = {7},
     number = {1},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2014_7_1_a4/}
}
TY  - JOUR
AU  - Andrey A. Gavrilov
AU  - Valeriy Ya. Rudyak
TI  - A model of averaged molecular viscosity for turbulent flow of non-Newtonian fluids
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2014
SP  - 46
EP  - 57
VL  - 7
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2014_7_1_a4/
LA  - en
ID  - JSFU_2014_7_1_a4
ER  - 
%0 Journal Article
%A Andrey A. Gavrilov
%A Valeriy Ya. Rudyak
%T A model of averaged molecular viscosity for turbulent flow of non-Newtonian fluids
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2014
%P 46-57
%V 7
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2014_7_1_a4/
%G en
%F JSFU_2014_7_1_a4
Andrey A. Gavrilov; Valeriy Ya. Rudyak. A model of averaged molecular viscosity for turbulent flow of non-Newtonian fluids. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 7 (2014) no. 1, pp. 46-57. http://geodesic.mathdoc.fr/item/JSFU_2014_7_1_a4/

[1] F. T. Pinho, “A GNF framework for turbulent flow models of drag reducing fluids and proposal for a k-e type closure”, Journal of Non-Newtonian Fluid Mechanics, 114 (2003), 149–184 | DOI | Zbl

[2] D. O. A. Cruz, F. T. Pinho, “Turbulent pipe flow predictions with a low Reynolds number k-e model for drag reducing fluids”, Journal of Non-Newtonian Fluid Mechanics, 114 (2003), 109–148 | DOI | Zbl

[3] V. Ya. Rudyak, A. V. Minakov, A. A. Gavrilov, A. A. Dekterev, “Application of new numerical algorithm for solving the Navier–Stokes equations for modelling the work of a viscometer of the physical pendulum type”, Thermophysics and Aeromechanics, 15:2 (2008), 333–345 | DOI

[4] V. Ya. Rudyak, A. V. Minakov, A. A. Gavrilov, A. A. Dekterev, “Modelling of flows in micromixers”, Thermophysics and Aeromechanics, 17:4 (2010), 565–576 | DOI

[5] E. V. Podryabinkin, V. Ya. Rudyak, “Moment and forces exerted on the inner cylinder in eccentric annual flow”, J. Engineering Thermophysics, 20:3 (2011), 320–328 | DOI

[6] M. Rudman, H. M. Blackburn, L. J. W. Graham, L. Pullum, “Turbulent pipe flow of shear-thinning fluids”, J. Non-Newtonian Fluid Mech., 118 (2004), 33–48 | DOI | Zbl

[7] M. Rudman, H. M. Blackburn, “Direct numerical simulation of turbulent non-Newtonian flow using a spectral element method”, Applied Mathematical Modelling, 30 (2006), 1229–1248 | DOI | Zbl

[8] K. Abe, T. Kondoh, Y. Nagano, “A new turbulence model for predicting fluid flow and heat transfer in separating and reattaching flows. I. Flow field calculations”, Int. J. Heat Mass Transfer, 37:1 (1994), 139–151 | DOI | Zbl

[9] A. A. Gavrilov, A. V. Minakov, A. A. Dekterev, V. Ya. Rudyak, “A numerical algorithm for modeling laminar flows in an annular channel with eccentricity”, Journal of Applied and Industrial Mathematics, 5:4 (2011), 559–568 | DOI | MR

[10] F. S. Lien, M. A. Leschziner, “Upstream monotonic interpolation for scalar transport with application to complex turbulent flows”, International Journal for Numerical Methods in Fluids, 19:6 (1994), 527–548 | DOI | Zbl

[11] J. P. Van Doormal, G. D. Raithby, “Enhancements of the SIMPLE Method for Predicting Incompressible Fluid Flows”, Numerical Heat Transfer, 7:2 (1984), 147–163 | Zbl

[12] Y. Saad, Iterative methods for sparse linear systems, SIAM, 2000

[13] U. Trottenberg, C. W. Oosterlee, A. Schuller, Multigrid, Academic Press, 2000 | MR

[14] T. C. Papanastasiou, “Flow of materials with yield”, Journal of Rheology, 31 (1987), 385–404 | DOI | Zbl

[15] A. B. Metzner, J. C. Reed, “Flow of Non-Newtonian Fluids-Correlation of the Laminar, Transition, and Turbulent-Flow Regions”, Aiche Journal, 1 (1955), 434–440 | DOI

[16] D. W. Dodge, A. B. Metzner, “Turbulent flow of non-Newtonian system”, A.I.Ch.E. Journal, 5:2 (1959), 189–204 | DOI

[17] G. Iaccarino, E. S. G. Shaqfeha, Y. Dubief, “Reynolds-averaged modeling of polymer drag reduction in turbulent flows”, Journal of Non-Newtonian Fluid Mechanics, 165:7–8 (2010), 376–384 | DOI | Zbl