Abstract
Steady flows of Newtonian and non-Newtonian fluids in the stenotic and bifurcated tubes are numerically simulated. Four rheologically different fluids such as water, aqueous sugar solution, aqueous Carbopol solution and blood are selected for the namerical simulation and the modified power-law model is used for the numerical simulation of non-Newtonian fluids in the stenotic and bifurcated tubes. Apparent viscosity of a non-Newtonian fluid in the modified power-law model is expressed as a function of the shear rate. Flows in the circular tube with sudden contraction-sudden expansion and gradual contraction-gradual expansion are studied numerically. Analyses in the stenotic tubes are concentrated on the effects of rheological properties, the stenotic geometry and Reynolds number. Flow characteristics of Carbopol solution in the stenotic tubes are compared with those of blood. Effects of the bifurcation geometry on the flow behaviors of Newtonian and non-Newtonian fluids are numerically investigated. Numerical analyses are focused on the flow patterns in the branch tubes of which angles are 30°, 60° and 90° and on the diameter ratios for Newtonian and non-Newtonian fluids. Variations of the axial velocity and pressure drop along the bifurcated tubes for various flow parameters are presented for Newtonian and non-Newtonian fluids.
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Abbreviations
- D b1 :
-
Diameter of first branch tube(m)
- D b2 :
-
Diameter of second branch tube(m)
- D v :
-
Diameter of circular tube in the upstream(m)
- L :
-
Length of stenotic section(m)
- m :
-
Consistency of power-law model(Pa·sn)
- n :
-
Power-law index
- p :
-
Static pressure(Pa)
- p 0 :
-
Static pressure at the inlet(Pa)
- R :
-
Radius of stenotic section(m)
- R 0 :
-
Radius of circular tube(m)
- r :
-
Radial direction
- t :
-
Height of stenosis(m)
- u :
-
Axial velocity(m/s)
- u i :
-
Velocity vector
- U o :
-
Average velocity in the upstream(m/s)
- v :
-
Radial velocity(m/s)
- z :
-
Axial direction
- \(\dot \gamma \) :
-
Shear rate(s−1)
- \(\dot \gamma _o \) :
-
Cut-off shear rate(s−1)
- μ e :
-
Apparent viscosity (Pa·s)
- μ 0 :
-
Zero shear rate viscosity(Pa·s)
- θ:
-
Bifurcation angle
- р:
-
Density(kg/m3)
- τ ij :
-
Shear stress tensor
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Yoo, S.S., Suh, S.H. & Roh, H.W. Numerical simulation of flows of non-Newtonian fluids in the stenotic and bifurcated tubes. KSME Journal 10, 223–234 (1996). https://doi.org/10.1007/BF02953661
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DOI: https://doi.org/10.1007/BF02953661