Numerical correlations for Herschel bulkley fluid flow through an axisymmetric sudden expansion
- 1. Laboratory of industrial technologies, Department of mechanical engineering, Faculty of Applied Sciences, University Ibn Khaldoun of Tiaret, 14000 Tiaret, Algeria.
- 2. Laboratoire MECACOMP, Département de Mécanique
Description
A numerical study carried out for the laminar flow of viscoplastic fluid (Herschel Bulkley model) through an axisymmetric sudden expansion of aspect ratio Er = 1 : 2 and for four values of Reynolds number confined between Re = [50 ~ 200], Bingham Bn = [0 ~ 2] respectively and the power low index n = 0.6, 0.8. The numerical simulation was performed by the commercial code ANSYS-Fluent. The results show the influence of the different forces on the structure of the flow in which the high plasticity of the flow reduces the length of the recirculation zone and increase the un-yielded zones in comparison with that of the Newtonian fluid, on the other side, the increase in inertial forces and the power low index increase the length of the recirculation zones as well as the redevelopment length. Based on these results, we present numerical correlations for the length of the circulation zone for the Herschel-Bulkley fluid as a function of the Reynolds number Re and the power low index n, these correlations show good agreement with the previous studies with maximum error 1.35%. The present study shows also the variation of local loss coefficient through the sudden expansion, for a Herschel-Bulkley fluid, the increases in Bingham number values increase the local loss coefficient, at higher Bingham number and for the Reynolds number values studied, the fluid becomes similar to Newtonian fluid flow at a very low Reynolds number, while high values of the power low index n slightly decrease the value of the local loss coefficient.
Files
4_v6_n2.pdf
Files
(2.2 MB)
| Name | Size | Download all |
|---|---|---|
|
md5:43e25df84426434a443e496c7647f6c1
|
2.2 MB | Preview Download |
Additional details
References
- [1] E. O. Macagno and T.-K. Hung, Computational and experimental study of a captive annular eddy, Journal of Fluid Mechanics, vol. 28 N° 1 (1967) pp. 43–64.
- P. S. Scott, F. A. Mirza, and J. Vlachopoulos, A finite element analysis of laminar flows through planar and axisymmetric abrupt expansions, Computers & Fluids, vol. 14 N° 4 (1986), pp. 423–432.
- D. Badekas and D. D. Knight, Eddy Correlations for Laminar Axisymmetric Sudden Expansion Flows, Journal of Fluids Engineering, vol. 114 N°1 (1992) pp. 119–121.
- P. S. Scott, F. Mirza, and J. Vlachopoulos, Finite‐Element Simulation of Laminar Viscoplastic Flows with Regions of Recirculation, Journal of Rheology, vol. 32 N° 4 (1988) pp. 387–400.
- G. C. Vradis and M. V. O¨tu¨gen, The Axisymmetric Sudden Expansion Flow of a Non-Newtonian Viscoplastic Fluid, Journal of Fluids Engineering, vol. 119 N° 1 (1997) pp. 193–200.
- K. J. Hammad, G. C. Vradis, and M. V. O¨tu¨gen, Laminar Flow of a Herschel-Bulkley Fluid Over an Axisymmetric Sudden Expansion, Journal of Fluids Engineering, vol. 123 N° 3 (2001) pp. 588–594
- K. J. Hammad, Suddenly expanding recirculating and non-recirculating viscoplastic non-newtonian flows, J Vis, vol. 18 N° 4 (2015) pp. 655–667.
- B. Pak, Y. I. Cho, and S. U. S. Choi, Separation and reattachment of non-newtonian fluid flows in a sudden expansion pipe, Journal of Non-Newtonian Fluid Mechanics, vol. 37 N° 2 (1990) pp. 175–199.
- P. Jay, A. Magnin, and J. M. Piau, Viscoplastic fluid flow through a sudden axisymmetric expansion, AIChE Journal, vol. 47 N° 10 (2001) pp. 2155–2166
- P. J. Oliveira and F. T. Pinho, Pressure drop coefficient of laminar Newtonian flow in axisymmetric sudden expansions, International Journal of Heat and Fluid Flow, vol. 18 N°5 (1997) pp. 518–529.
- P. J. Oliveira, F. T. Pinho, and A. Schulte, A general correlation for the local loss coefficient in Newtonian axisymmetric sudden expansions, International Journal of Heat and Fluid Flow, vol. 19 N° 6 (1998) pp. 655–660.
- S. L. D. Kfuri, E. J. Soares, R. L. Thompson, and R. N. Siqueira, Friction Coefficients for Bingham and Power-Law Fluids in Abrupt Contractions and Expansions, Journal of Fluids Engineering, vol. 139 N° 021203(2016).
- Bekhadra, M., Chemloul, N.E.S., Menouer, A., Chaib, K, Numerical study of laminar Bingham fluid in axisymmetric sudden expansion. International Journal of Heat and Technology, Vol. 40 N° 1(2022) pp. 45-52.