Geodesic
Investigation of viscous fluid flow in T-shaped channel with no slip/slip boundary conditions on the solid wall
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 4 (2016), pp. 58-69 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The planar flow of a Newtonian incompressible fluid in a T-shaped channel is investigated. Three models of fluid interaction with solid walls are considered: (a) Traditional no-slip boundary condition implying the vanishing velocity vector on the solid walls. (b) Navier slip boundary condition according to which the tangential velocity on the solid wall is linearly proportional to the shear stress and the normal velocity is equal to zero. (c) Slip boundary condition with ultimate shear stress supposes that the tangential velocity on the solid wall is equal to zero when the shear stress does not exceed a certain ultimate shear stress; if the shear stress is more than the ultimate shear stress, the behavior of the fluid is similar to the Navier model. The fluid flow is provided by uniform pressure profiles in boundary sections of the channel. The problem is numerically solved using the finite difference method based on the SIMPLE procedure. As a result, the characteristic flow regimes have been found for described models of fluid interaction with a solid wall. The effect of Reynolds number, pressure of boundary sections, and parameters of the models on the flow pattern was performed. The criterion dependences describing the main flow characteristics under mathematical conditions of the present work have been plotted.
Keywords: flow, boundary condition, T-shaped channel, numerical simulation.
Mots-clés : viscous fluid 
@article{VTGU_2016_4_a5,
     author = {E. I. Borzenko and O. A. Diakova},
     title = {Investigation of viscous fluid flow in {T-shaped} channel with no slip/slip boundary conditions on the solid wall},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {58--69},
     year = {2016},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2016_4_a5/}
}
TY  - JOUR
AU  - E. I. Borzenko
AU  - O. A. Diakova
TI  - Investigation of viscous fluid flow in T-shaped channel with no slip/slip boundary conditions on the solid wall
JO  - Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
PY  - 2016
SP  - 58
EP  - 69
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VTGU_2016_4_a5/
LA  - ru
ID  - VTGU_2016_4_a5
ER  - 
%0 Journal Article
%A E. I. Borzenko
%A O. A. Diakova
%T Investigation of viscous fluid flow in T-shaped channel with no slip/slip boundary conditions on the solid wall
%J Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
%D 2016
%P 58-69
%N 4
%U http://geodesic.mathdoc.fr/item/VTGU_2016_4_a5/
%G ru
%F VTGU_2016_4_a5
E. I. Borzenko; O. A. Diakova. Investigation of viscous fluid flow in T-shaped channel with no slip/slip boundary conditions on the solid wall. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 4 (2016), pp. 58-69. http://geodesic.mathdoc.fr/item/VTGU_2016_4_a5/

[1] Neto C., Evans D., Bonaccurso E., “Boundary slip in Newtonian liquids: a review of experimental studies”, Reports on Progress in Physics, 39 (2005), 2859–2897 | DOI

[2] Yankov V. I., Processing of fiber-forming polymers. Fundamentals of polymer rheology and polymer flow in channels, Science Publishing Center “Regular and chaotic dynamics”, Institute of Computer Science, M.– Izhevsk, 2008

[3] Bahrami M., Tamayol A., Taheri P., “Slip-flow pressure drop in microchannels of general cross section”, Journal of Fluids engineering, 131 (2009), 031201-1–031201-8 | DOI

[4] Volker J., “Slip with friction and penetration with resistance boundary conditions for the Navier–Stokes equation — numerical test s and aspects of the implementation”, Journal of computational and applied mechanics, 147 (2002), 287–300 | DOI | MR | Zbl

[5] Minakov A., Rudyak V., Dektereva A., Gavrilov A., “Investigation of slip boundary conditions in the T-shaped microchannel”, International Journal of Heat and Fluid Flow, 43 (2013), 161–169 | DOI

[6] Borzenko E. I., Dyakova O. A., Shrager G. R., “Studying the slip phenomenon in the case of a viscous fluid flow in a curved channel”, Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika - Tomsk State University Journal of Mathematics and Mechanics, 2014, no. 2(28), 35–44 | MR

[7] Patankar S. V., Numerical heat transfer and fluid flow, Hemisphere Publishing Corporation, New York, 1981

[8] Khandelwal V. et al., “Laminar flow of non-Newtonian shear-thinning fluids in a T-channel”, Computers Fluids, 108 (2015), 79–91 | DOI | MR