Summary
The phenomenon of separation and wake formation for a sphere moving at high Reynolds numbers in viscoelastic fluids is investigated experimentally. Delayed separation and the phenomenon of “dual wake” formation was found to exist in viscoelastic fluids. The reasons for the delayed separation have been discussed using inspectional analysis, which correctly predicts that the shear-thinning viscosity delays separation but incorrectly predicts that viscoelasticity advances the point of separation to the front stagnation point. A critical qualitative analysis of the observed phenomena is offered.
Zusammenfassung
Für die Strömung viskoelastischer Flüssigkeiten um Kugeln bei großen Reynolds-Zahlen werden die Phänomene der Ablösung und der Ausbildung des Nachlaufes experimentell untersucht. Dabei wird gefunden, daß gegenüber der Strömung newtonscher Flüssigkeiten die Ablösung erst nach einer größeren Lauflänge erfolgt und der Nachlauf eine kompliziertere Struktur hat. Zur Erklärung der beobachteten Vorgänge werden verschiedene Ursachen angegeben und heuristisch diskutiert.
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Abbreviations
- A :
-
material parameter (eq. [12])
- b :
-
material parameter (eq. [12])
- C D inelastic :
-
drag coefficient for an inelastic fluid
- C D viscoe lastic :
-
drag coefficient for a viscoelastic fluid
- D :
-
rate of deformation tensor
- F(n), f2(n), f3(n):
-
functions ofn defined in reference (1)
- K :
-
consistency index (eq. [11])
- m :
-
dimensionless parameter (eq. [13])
- n :
-
pseudoplasticity index (eq. [11])
- r′ :
-
curvilinear co-ordinate (eq. [3])
- R :
-
radius of the sphere
- Reow :
-
power-law Reynolds number (eq.[15])
- u :
-
velocity component in the axial direction
- v :
-
velocity component in the transverse direction
- Wi:
-
Weissenberg number (eq. [14])
- x :
-
axial co-ordinate
- y :
-
transverse co-ordinate
- α, β :
-
constant (eq. [1])
- δ :
-
boundary layer thickness
- \(\dot \gamma _w \) :
-
wall shear rate
- λ :
-
material function (eq. [9])
- µ :
-
viscosity or viscosity function
- µ w :
-
viscosity function value at the wall
- ρ :
-
density
- τ :
-
stress tensor
- τ 12 :
-
shear stress
- τ 11 − τ22 :
-
primary normal stress difference
- τ xy :
-
shear stress
- τ xx − τyy :
-
primary normal stress difference
- δ/δt :
-
convected time derivative
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Acharya, A., Mashelkar, R.A. & Ulbrecht, J. Flow of inelastic and viscoelastic fluids past a sphere. Rheol Acta 15, 471–478 (1976). https://doi.org/10.1007/BF01530349
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DOI: https://doi.org/10.1007/BF01530349