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Computational Rheology Isaac Newton Institute Dynamics of Complex Fluids -10 Years on. Mike Webster. Schlumberger, UNAM-(Mexico), INNFM. Juan P. Aguayo Hamid Tamaddon Mike Webster. Institute of non-Newtonian Fluid Mechanics EPSRC Portfolio Partnership.
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Computational Rheology Isaac Newton InstituteDynamics of Complex Fluids -10 Years on Mike Webster Schlumberger, UNAM-(Mexico), INNFM Juan P. Aguayo Hamid Tamaddon Mike Webster Institute of non-Newtonian Fluid Mechanics EPSRC Portfolio Partnership
To achieve highly elastic, high strain-rate/deformation rate solutions (polymer melts & polymer solutions) To quantitatively predict pressure-drop, as well as flow field structures (vortices, stress distributions) To accurately represent transient flow evolution in complex flows To quantitatively predict multiple-scale response (multi-mode) To achieve compressible viscoelastic representations Computational Rheology – Some Outstanding Challenges
TRANSIENT & STEADYContraction Flows EPTT Oldroyd Planar Axisymmetric Planar Axisymmetric
Pressure-drop vs flow-rate in contractions axisymmetric planar Fluid viscosity = 1.75Pa.s – 8:1 contraction, exit length 7.4mm Fluid viscosity = 1.75Pa.s – 20:1 contraction, exit length 40mm Newtonian syrup Boger fluid
Pressure drop (epd) vs. We, 4:1:4 axisymmetric Szabo et al. with FENE-CR J. Non-Newt. Fluid Mech. 72:73-86, 1997 epd We
Schematic diagram for a) 4:1:4 contraction/expansion, b) 4:1 contraction Szabo et al. J. Non-Newt. Fluid Mech. 72:73-86, 1997 Rothstein and McKinley J. Non-Newt. Fluid Mech. 86:61-88, 1999 J. Non-Newt. Fluid Mech. 98:33-63, 2001 Wapperom and Keunings J. Non-Newt. Fluid Mech. 97:267-281, 2001 Excess pressure drop (epd - P ) : Total pressure drop
Pressure-drop (epd) vs. We, Oldroyd-B, a, c) axisymmetric, b, d) planar 4:1:4 4:1 a) c) a) Axisymmetric b) b) d) Planar
Pressure profile around constriction zone, 4:1:4 axisymmetric and planar case Oldroyd-B, =0.9
N1p 3D view – 4:1:4 contraction/expansion Axisymmetric Planar Oldroyd-B, =0.9
(P - PNewt) and stress profiles along wall, 4:1 and 4:1:4 axisymmetric case 4:1 4:1:4 Oldroyd-B, =0.9
(P - PNewt)and stress profiles along wall – 4:1:4 planar and axisymmetric case Planar Axisymmetric Oldroyd-B, =0.9
Pressure-drop (epd) vs. We, 4:1:4 axisymmetric, alternative models epd We epd We
upturn & enhanced epd upturn epd monotonic decrease epd (P - PNewt) profiles along wall – 4:1:4 axisymmetric, increasing
Alternative differential pressure-drop measure Since &by calibration
0 Rate of dissipation & pressure-drop, 4:1:4 definition rate of dissipation , Seeking {P – 1} > 0
Pressure-drop (epd) vs. a)We,b) upstream sampling distance, 4:1:4 axisymmetric epd We epd
upturn & enhanced epd mono-dec epd 4:1:4 axisymmetric vortex cell size, Oldroyd-B, change =0.99 =1/9
Rheological properties: Oldroyd-B, LPTT, EPTT, SXPP a) Oldroyd-B extensional viscosity, b b) Shear and extensional viscosity, b=0.9 c) Shear and extensional viscosity, b=0.99
NEW BOGER fluid modelling & Pressure Drop Axisymmetric contraction Planar contraction
Centreline pressure gradient 4:1:4 axisymmetric, Oldroyd-B =1/9 =0.9 =0.99