Analysis of Two-phase Flow through a Rectangular Curved Duct

Khalilur Rahman^1,2,*, Salma Parvin², Abdul Hakim Khan²

¹Department of Mathematics, Bangladesh Civil Service, Ministry of Education, Dhaka, Bangladesh.

²Department of Mathematics, Bangladesh University of Engineering & Technology, Dhaka, Bangladesh.

*Corresponding author: Khalilur Rahman

Date: August 31,2023　Hits: 404

Abstract

The present work mainly focuses on analyzing an unsteady laminar incompressible two-phase flow in a rectangular curved duct. The corresponding governing equations are represented by the Navier-Stokes equations and Level set equation with the boundary conditions. Fluid flow through curved rectangular ducts is in-fluenced by the centrifugal action arising from duct curvature and has a unique behavior different from fluid flow through straight ducts. Centrifugal force-induced secondary flow vortices and produce spiraling fluid motion within curved ducts. This paper shows the vector plot of the field flow, velocity contours, axial flow velocity and fluid volume fractions visualization graphically. The effect of curvature, Dean number and aspect ratio is also displayed. A comparison of two-phase flow between different fluids is also shown. The results reveal that the unstable behavior of the flow reduces for the increasing values of curvature, Dean number, and high viscosity flow.

References

[1] J. Eustice. “Flow of water in curved pipes.” Proceedings of the Royal Society of London. Ser. A 84(1910), 107-118.

[2] J. Eustice. “Experiments on streamline motion in curved pipes.” Proceedings of the Royal Society of London Ser. A 85(1911), 119-131.

[3] W. R Dean. “Note on the motion of fluid in a curved pipe.” Philosophy Magazine, 20(1927), 208-223.

[4] W. R. Dean. “The stream-line motion of fluid in a curved pipe.” Philosophy Magazine, 30(1928), 673-695.

[5] S. Thangam, N. Hur. “Laminar secondary flows in curved rectangular ducts.” Journal of Fluid Mechanics, 217(1990), 421-440.

[6] Z. F. Dong and M. A. Ebadian. “Effects of Buoyancy on Laminar Flow in Curved Elliptic Ducts.” Journal of Heat Transfer, November-114(1992), 936-943.

[7] P. M. Ligrani and C. R. Hedlund. “Examined surface heat transfer and flow structure in a curved channel with laminar, transitional and turbulent Flows.” Journal of Turbomachinery, July-126(2004), 414-423.

[8] A.A. Avramenko, S.G. Kobzar, I.V. Shevchuk, A.V. Kuznetsov, and B.I. Basok. “Laminar Forced Convection in Curved Channel with Vortex.” Journal of Thermal Science, 13(2004), No-2, 143-149.

[9] S.A. Khuri. “Stokes flow in curved channels.” Journal of Computational and Applied Mathematics, 187 (2006), 171-191.

[10] A. K. Biswas, Prasanta K Sinha, A N Mullick, B. Majumdar. “Flow Investigation in a Constant Area Curved Duct.” International Journal of Engineering Research and Applications (IJERA), November-December-2 (2012), No-6,1232-1236.

[11] S. Nadeem and Iqra Shahzadi. “Mathematical analysis for peristaltic flow of a two-phase nanofluid in a curved channel.” Communication of Theoretical Physics, 64 (2015), No-5, 547-554.

[12] Nnamdi Fidelis Okechi, and Saleem Asghar. “Fluid motion in a corrugated curved channel”, The European Physical Journal Plus, (2019), 134:165.

[13] Md. A. Hye, M.A.H. Khan. “Dominating Singularity of the flow in a Non-aligned Straight Rotating Pipe”. International Journal of Fluid Dynamics Research, 34(2007), Issue-6, 562-571.

[14] Khan M. A. H. “Singularity Behavior of Flow in a Curved Pipe.” Journal of Applied Mechanics & Engineering, 11(2006), No.3, pp. 699-704.

[15] R. N. Mondal, M. M. Alam, S. Yanase. “Numerical prediction of non-isothermal flows through a rotating curved duct with square cross section”. Thommasat Int. J. Sci and Tech., 12(3), (2007), 24-43.

[16] M. Norouzi and N. Biglari. “An analytical solution for Dean flow in curved ducts with rectangular cross-section.” AIP, Physics of Fluids, 25(2013), 053602.

[17] Kyoji Yamamoto, Shinichiro Yanase, and Md. Mahmud Alam. “Flow through a rotating curved duct with square cross-section.” Journal of the Physical Society of Japan, April-68(1999), No.4, 1173-1184.

[18] J.L. Xu, P. Cheng, T.S. Zhao. “Gas-liquid two-phase flow regimes in rectangular channels with mini/micro gaps.” International Journal of Multiphase Flow, 25 (1999), 411-432.

[19] Dustin Crandall, Goodarz Ahmadi, and Duane H. Smith. “Comparison of experimental and numerical two-phase flows in a porous micro-model.” Journal of Computational Multiphase Flows, Vol. 1(2009), No-4.

[20] P. Garg, J. R. Picardo, and S. Pushpavanam. “Vertically stratified two-phase flow in a curved channel: Insights from a domain perturbation analysis.” Physics of fluids, 26(2014), 073604.

[21] Jason R. Picardo, P. Garg, and S. Pushpavanam. “Centrifugal instability of stratified two-phase flow in a curved channel.” Physics of fluids, 27(2015), 054106.

[22] A. K. Chandra. Kishor, P. K. Mishra, and M. S. Alam. “Numerical investigations of two-phase flows through enhanced micro channels.” Chem. Biochem. Eng., 30(2016) No-2, 149-159.

[23] M W Al-Jibory, R S Al-Turaihi, and H N Al-Jibory. “An experimental and numerical study for two-phase flow (water-air) in rectangular ducts with compound tabulators.” Materials Science and Engineering, 433(2018), 012049.

[24] Nnamdi Fidelis Okechi and Saleem Asghar. “Two-phase flow in a groovy curved channel.” European Journal of Mechanics/B Fluids, 88 (2021), 191-198.

[25] S. Osher and J. A. Sethian. “Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formula-tions.” Journal of Computational Physics, 79(1988), 12-49.

[26] M. Sussman, P. Smereka, and S. Osher. “A level set method for computing solutions to incompressible two-phase flow.” Journal of Computational Physics, 114(1994), 146-159.

[27] G Olsson and G Kreiss. “A conservative level set method for two-phase flow.” Journal Computational Physics, 210(1), 2005, 225-246.

[28] D Datta, V H Gada, and A Sharma. “Analytical and level set method based numerical study for two-phases stratified flow in a plane channel and a square duct.” Numerical Heat Transfer B, 60(4), (2011): 347-380.

[29] Atul Sharma. “Level set method for computational multi-fluid dynamics: A review on developments, applications and analysis.” Indian Academy of Sciences, May-40(3), (2015), 627-652.

[30] Haydar Kucuk. “Numerical analysis of entropy generation in concentric curved annular ducts.” Journal of Mechanical Science and Technology, 24 (9), (2010), 1927-1937.

[31] T.W. Gyves, T.F. Irvine.Jr., M.H.N. Naraghi. “Gravitational and centrifugal buoyancy effects in curved square channels with conjugated boundary conditions.” International Journal of Heat and Mass Transfer, 42(1999), 2015-2029.

[32] T.W. Gyves. “A numerical solution to conjugated mixed convection heat transfer in the curved square channel.” Ph.D. Thesis, the State University of New York at Stony Brook, USA, (1997).

[33] Elin Olsson, Gunilla Kreiss, Sara Zahedi. “A conservative level set method for two phase flow II.” Journal of Computational Physics, 225 (2007), 785-807.

[34] Mohammad Mehedi Keshtekar, Mohammad Hosein Asadi, Roozbeeh Samareh, Hasan Mirzaei Poor. “Numerical study on the effects of Marangoni-driven boundary layer flow for different nanoparticles with variable based fluids.” Journal of international academic research for multidisciplinary, June, 2(2014), Issue 5, 806-815.

[35] K. S. Al Kalbani, M. S. Alam and M. M. Rahman. “Finite element analysis of unsteady natural convective heat transfer and fluid flow of nanofluids inside a tilted square enclosure in the presence of oriented magnetic field.” American Journal of Heat and Mass Transfer, 3(2016), No-3, 186-224.

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Analysis of Two-phase Flow through a Rectangular Curved Duct

How to cite this paper: Khalilur Rahman, Salma Parvin, Abdul Hakim Khan. (2023) Analysis of Two-phase Flow through a Rectangular Curved Duct. Journal of Applied Mathematics and Computation, 7(3), 324-342.

DOI: http://dx.doi.org/10.26855/jamc.2023.09.001

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Analysis of Two-phase Flow through a Rectangular Curved Duct

Abstract

References

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