Study of the Rheological Behaviour and the Curvature Radius Effects on a Non Newtonian Fluid Flow in a Curved Square Duct

Abstract:

Abstract. Fluid flows through curved pipes are frequently encountered in various industrial or biomedical applications. These flows, under the effect of the centrifugal force resulting from the curvature of the pipe, causes an instability phenomenon known as Dean instability, which results in the appearance of two or more counter-rotating vortex cells. The objective of this work is to determine numerically the effect of geometric parameters and rheological behavior of the fluid, including the index of behavior on the occurrence and development of the instability of Dean in a 180° curved duct. The governing equations including the full Navier-Stokes, the continuity and the Momentum are solved in three dimensions using the commercial code ANSYS-CFX, under the conditions of laminar, stationary and incompressible flow. In the first part, the results of the flow of a shear thinning fluid and a shear thickening fluid for a Dean number Dn = 125 and a radius of curvature Rc = 15.1 are presented. These calculation results gave a good agreement with the measured values extracted from the literature. The second part concerns the influence of the curvature ratio and the rheological behaviour of the fluid, the presence of two stationary secondary recirculations, as well as the appearance and the development of two additional vortices are highlighted. The main point observed is that the decrease in the curvature radius increases the instability of the flow through the pipe and this increases the number of vortex cells (Dean vortex). The velocity of the flow and its rheological nature are essential parameters for the reduction of instability in the canal.

• Periodical: International Journal of Engineering Research in Africa (Volume 59)
• Pages: 225-238
• DOI: https://doi.org/10.4028/p-ll8x57
• Online since: March 2022
• Authors: Fayçal Bouzit*, Mohamed Bouzit, Mourad Mokeddem
• Keywords: ANSYS-CFX, Curved Duct, Dean Vortex, Non-Newtonian Fluid, Shear Thinning, Thickening Fluid

References

[1] W. R. Dean, Note on the motion of fluid in a curved pipe, Philos. Mag, 4 (1927) 208–223.

[2] J. Eustice, Experiments of streamlined motion in curved pipes, Proc. R. Soc. London Ser, A85 (1911) 119-131.

[3] B. Bara, K. Nandakumarz and J. H. Masliyah, An experimental and numerical study of the Dean problem: flow development towards two-dimensional multiple solutions, Journal of Fluid Mechanics, 244 (1992) 339-376.

DOI: 10.1017/s0022112092003100

[4] H. Ito, Theory on laminar flow through curved pipes of elliptic and rectangular cross sections. Rep. Inst. High Speed Mech. Tohoku Univ. Sendai Japan, 1 (1951), 1-16.

[5] D. J. Moconalogue, R. S. Srivastara, Motion of a fluid in a curved tube. Printed in Great Britain Proc. Roy. Soc. A. 307 (1968) 37-53.

[6] Mohammed Boutabaa, Lionel Helin, Gilmar Mompean, Laurent Thais, Numerical study of Dean vortices in developing Newtonian and viscoelastic flows through a curved duct of square cross-section, 337 (2009) 40–47.

DOI: 10.1016/j.crme.2008.11.001

[7] Brahim Timite, Cathy Castelain, Hassan Peerhossaini, Pulsatile viscous flow in a curved pipe : Effects of pulsation on the development of secondary flow. 31 (2010) 879–896.

DOI: 10.1016/j.ijheatfluidflow.2010.04.004

[8] H. Fellouah, C. Castelain, A. Ould-El-Moctar, H. Peerhossaini, The Dean instability in power-law and Bingham fluids in a curved rectangular duct. J. Non-Newtonian Fluid Mech.165 (2010) 163–173.

DOI: 10.1016/j.jnnfm.2009.10.009

[9] S. Sugiyama, T. Hayashi, K. Yamazaki. Flow characteristics in the curved rectangular channels (visualization of secondary flow). Bull. JSME, 26 (1983) 964-969.

DOI: 10.1299/jsme1958.26.964

[10] F. Bouzit, H. Laidoudi, M. Bouzit. Simulation of power-law fluids and mixed convection heat transfer inside of curved duct. Defect and Diffusion Forum, 378 (2018) 113-124.

DOI: 10.4028/www.scientific.net/ddf.378.113

[11] Fayçal Bouzit, Houssem Laidoudi, Bilal Blissag, Mohamed Bouzit, Abedallah Ghenaim. Numerical Investigation of Power-Law Fluid Flows and Heat Transfer Inside of Curved Duct under Aiding Thermal Buoyancy. Diffusion Foundations Submitted, 16 (2018) 84-95.

DOI: 10.4028/www.scientific.net/df.16.84

[12] Joana M. Malheiro, Paulo J. Oliveira, Fernando T. Pinho, Parametric study on the three-dimensional distribution of velocity of a FENE-CR fluid flow through a curved channel, 200 (2013) 88–102.

DOI: 10.1016/j.jnnfm.2012.12.007

[13] P. Hille, R. Vehrenkamp, E. O. Schulz-Dubois,The development and structure of primary and secondary flow in a curved square duct, Journal of Fluid Mechanics, 151(1985) 219-241.

DOI: 10.1017/s0022112085000933

[14] Ricardo Junqueira Silva, Numerical hydrodynamic and thermal analysis of laminar flow in curved elliptic and rectangular ducts. Int. J. Therm. Sci. 38 (1999) 585-594.

DOI: 10.1016/s0035-3159(99)80038-5

[15] S. C. Xue, N. Phan-Thien, R. I. Tanner, Numerical study of secondary flows of viscoelastic fluid in straight pipes by an implicit finite volume method, J. Non-Newtonian Fluid Mech., 59 (1995) 191-213.

DOI: 10.1016/0377-0257(95)01365-3

[16] T.T. Chandratilleke, Nursubyacto, Numerical prediction of secondary flow and convective heat transfer in externally heated curved rectangular ducts, Internat. J. Thermal Sci. 42 (2003) 187-198.

DOI: 10.1016/s1290-0729(02)00018-2

[17] Y. Chen and H. Chen, J. Zhang, B. Zhang, viscoelastic flow in rotating curved pipes, Physics of Fluid 18 (2006) 083-103.

[18] Xiaoyun Wu, Sangding Lai, Kyoji Yamamoto, Shinichiro Yanase, Vortex Patterns of the Flow in a Curved Duct, Energy Procedia, 12 (2011) 920 – 927.

DOI: 10.1016/j.egypro.2011.10.121

[19] W. H. Finlay, J. B. Keller, and J. H. Ferziger, Instability and transition in curved channel flow. J. Fluid Mech., 194 (1988) 417–456.

DOI: 10.1017/s0022112088003052

[20] M. Norouzi, M. R. H. Nobarib, M. H. Kayhani, F. Talebi, Instability investigation of creeping viscoelastic flow in a curved duct with rectangular cross-section, International Journal of Non-Linear Mechanics, 47 (2012) 14–25.

DOI: 10.1016/j.ijnonlinmec.2011.08.006

[21] P. M. Ligrani and R. D. Niver, Flow visualization of Dean vortices in a curved channel with 40 to 1 aspect ratio. Phys. Fluids, 31(12) (1988) 3605–3617.

DOI: 10.1063/1.866877

[22] Jiann Cherng Chu, Jyh-Tong Teng, Ralph Greif, Experimental and numerical study on the flow characteristics in curved rectangular micro channels. 30 (2010) 1558-1566.

DOI: 10.1016/j.applthermaleng.2010.03.008

[23] Y. L. Joo and E. S. G. Shaqfeh, The effects of inertia on the viscoelastic Dean and Taylor-Couette flow instabilities with application to coating flows. Phys. of Fluids A 4, 11(1992) 2415–2431.

DOI: 10.1063/1.858483

[24] V. Khandelwal, A. Dhiman, L. Baranyi, Laminar flow of non-Newtonian shear-thinning fluids in a T-channel, Computers & Fluids, 108 (2014) 79-91.

DOI: 10.1016/j.compfluid.2014.11.030

[25] Mourad Mokeddem, Houssem Laidoudi, Mohamed Bouzit, 3D Simulation of Dean Vortices at 30°Position of 180°Curved Duct of Square Cross-Section under Opposing Buoyancy, Defect and Diffusion Forum, 389 (2018) 153-163.

DOI: 10.4028/www.scientific.net/ddf.389.153

[26] Hashem Nowruzi, Hassan Ghassemi, S. Salman Nourazar, Study of the effects of aspect ratio on hydrodynamic stability in curved rectangular ducts using energy gradient method, Engineering Science and Technology, an International Journal, 23 (2020) 334-344.

DOI: 10.1016/j.jestch.2019.05.004

[27] Basavarajappa Mahanthesh, Nagavangala Shankarappa Shashikumar, Bijjanal Jayanna Gireesha, Isac Lare Animasaun, Effectiveness of Hall current and exponential heat source on unsteady heat transport of dusty TiO2-EO nanoliquid with nonlinear radiative heat, Journal of Computational Design and Engineering, 6 (2019) 551–561.

DOI: 10.1016/j.jcde.2019.04.005

[28] Kyu Yoon, Hyun Wook Jung, and MyungSuk Chun, Korea-Australia Rheology Journal, 32(1) (2020) 61-70.

[29] B. Mahanthesh, B.J. Gireesha, Sabir A. Shehzad, Nida Ibrar, K. Thriveni, Analysis of a magnetic field and Hall effects in nanoliquid flow under insertion of dust particles, Heat Transfer (2020)1–17,.

DOI: 10.1002/htj.21682

[30] I. L. Animasaun, O. K. Koriko, K. S. Adegbie, H. A. Babatunde, R. O. Ibraheem, N. Sandeep, B. Mahanthesh, Comparative analysis between 36 nm and 47 nm alumina water nanofluid flows in the presence of Hall effect, Journal of Thermal Analysis and Calorimetry (2018). doi.org/10.1007/s10973-018-7379-4.

DOI: 10.1007/s10973-018-7379-4

[31] Bibhuti Bhusan Nayak et al. Numerical prediction of flow and heat transfer characteristics of water-fly ash slurry in a 180 return pipe bend, International Journal of Thermal Sciences 113 (2017) 100-115.

DOI: 10.1016/j.ijthermalsci.2016.11.019

[32] B.J. Gireesha, B. Mahanthesh, Rama Subba Reddy Gorla, P. T. Manjunatha, Thermal radiation and Hall effects on boundary layer flow past a non‑ isothermal stretching surface embedded in porous medium with non‑ uniform heat source/sink and fluid‑ particle suspension, Heat Mass Transfer (2016) 52:897–911 DOI 10.1007/s00231-015-1606-3.

DOI: 10.1007/s00231-015-1606-3

[33] B Mahanthesh, Hall Effect on Two-Phase Laminar Boundary Layer flow of Dusty Liquid due to Stretching of an Elastic Flat Sheet, Mapana Journal of Sciences, 16,3(2017), 13-26, doi.org//10.12723/mjs.42.2.

DOI: 10.12723/mjs.42.2

[34] B.J. Gireesha, B.Mahanthesh, K.L. Krupalakshmi, Hall effect on two-phase radiated flow of magneto-dusty-nanoliquid with irregular heatgeneration/consumption, Results in Physics (2017), doi: http:// dx.doi.org/10.1016/j.rinp.2017.08.040.

DOI: 10.1016/j.rinp.2017.08.040