Numerical analysis of flow rates, porous media, and Reynolds numbers affecting the combining and separating of Newtonian fluid flows

Authors

  • Rahim Bux Khokhar BSRS Department MUET, Jamshoro, Pakistan
  • Afaque Ahmed Bhutto Quaid e Awam University os Science and Engineering Technology, campus Larkano
  • Noor Fatima Siddiqui Department of Mathematics, University of Karachi, Pakistan
  • Fozia Shaikh BSRS Department MUET, Jamshoro, Pakistan
  • Iftikhar Ahmed Bhutto Sukkur IBA University, Sukkur, Pakistan

DOI:

https://doi.org/10.21015/vtm.v11i1.1518

Abstract

This study investigates the behavior of Newtonian fluids in pipes filled with and without porous media under combing and separating flow configurations. Numerical simulations are conducted to analyze the effects of changing flow rates, inertia, and porous media on flow patterns, vortex development, and pressure difference. The aim of this study is to examine the impact of inertia on flow behavior by analyzing the streamline patterns, vortex growth, and intensity at different Reynolds numbers, ranging from Re=1 to Re=5000.

References

A. M. Afonso, M. A. Alves, R. J. Poole, P. J. Oliveira, and F. T. Pinho, “Viscoelastic flows in mixing-separating cells,” J. Eng. Math., vol. 71, pp. 3–13, 2011.

S. O. S. Echendu, F. Belblidia, H. R. Tamaddon-Jahromi, and M. F. Webster, “Modelling with viscous and viscoplastic materials under combining and separating flow configurations,” Mech. Time-Dependent Mater., vol. 15, pp. 407–428, 2011.

A. Baloch, P. Townsend, and M. F. Webster, “On the simulation of highly elastic complex flows,” J. Nonnewton. Fluid Mech., vol. 59, no. 2–3, pp. 111–128, 1995.

R. B. Khokhar, “Numerical Modelling of Mixing and Separating of Fluid Flows through Porous Media,” 2018.

Bhutto, A. A., M. Hussain, S. F. Shah, and K. Harijan. "Computation of Vortex Driven Flow Instability through Unsteady RANS and Scale Resolving Simulation." Institute of Space Technology 12, no. 1 2022: 14-22.

Memon, K. N., Sher Afzal Khan, S. Islam, Nazir Ahmad Zafar, Syed Feroz Shah, and A. M. Siddiqui. "Unsteady drainage of electrically conducting power law fluid." Applied Mathematics and Information Sciences 8, no. 5 2014: 2287.

B. Xia and D.-W. Sun, “Applications of computational fluid dynamics (CFD) in the food industry: a review,” Comput. Electron. Agric., vol. 34, no. 1–3, pp. 5–24, 2002.

Bhutto, Afaque Ahmed, Iftikhar Ahmed, Saeed Ahmed Rajput, and Syed Asad Raza Shah. "The effect of oscillating streams on heat transfer in viscous magnetohydrodynamic MHD fluid flow." 2023.

Memon, K. N., S. Islam, A. M. Siddiqui, Sher Afzal Khan, Nazir Ahmad Zafar, and M. Akram. "Lift and drainage of electrically conducting power law fluid on a vertical cylinder." Applied Mathematics and Information Sciences 8, no. 1 (2014): 45.

F. P. T. Baaijens, “Mixed finite element methods for viscoelastic flow analysis: a review,” J. Nonnewton. Fluid Mech., vol. 79, no. 2–3, pp. 361–385, Nov. 1998, doi: 10.1016/S0377-0257(98)00122-0.

Bhutto, Iftikhar Ahmed, Afaque Ahmed Bhutto, Rahim Bux Khokhar, Muhammad Aslam Soomro, and Fozia Shaikh. "The effect of uniform and exponential streams on Magnetohydrodynamic flows of viscous fluids." 2023.

Memon, K. N., A. M. Siddiqui, and S. F. Shah. "Exact solution of tank drainage for Newtonian fluid with slip condition." Sindh University Research Journal (Science Series) 49, no. 2 (2017): 283-288.

M. Fortin and D. Esselaoui, “A finite element procedure for viscoelastic flows,” Int. J. Numer. Methods Fluids, vol. 7, no. 10, pp. 1035–1052, 1987, doi: 10.1002/FLD.1650071004.

T. Cochrane, K. Walters, and M. F. Webster, “Newtonian and non-Newtonian flow near a re-entrant corner,” J. Nonnewton. Fluid Mech., vol. 10, no. 1–2, pp. 95–114, 1982.

A. A. Bhutto, S. F. Shah, R. B. Khokhar, K. Harijan, and M. Hussain, “To Investigate Obstacle Configuration Effect on Vortex Driven Combustion Instability,” 2023.

A. A. Bhutto, K. Harijan, M. Hussain, S. F. Shah, and L. Kumar, “Numerical simulation of transient combustion and the acoustic environment of obstacle vortex-driven flow,” Energies, vol. 15, no. 16, p. 6079, 2022.

B. Alazmi and K. Vafai, “Analysis of fluid flow and heat transfer interfacial conditions between a porous medium and a fluid layer,” Int. J. Heat Mass Transf., vol. 44, no. 9, pp. 1735–1749, 2001.

M. A. Al-Nimr and T. K. Aldoss, “The effect of the macroscopic local inertial term on the non-Newtonian fluid flow in channels filled with porous medium,” Int. J. Heat Mass Transf., vol. 47, no. 1, pp. 125–133, 2004.

K. Walters and M. F. Webster, “On dominating elastico-viscous response in some complex flows,” Philos. Trans. R. Soc. London. Ser. A, Math. Phys. Sci., vol. 308, no. 1502, pp. 199–218, 1982.

T. Cochrane, K. Walters, and M. F. Webster, “On Newtonian and non-Newtonian flow in complex geometries,” Philos. Trans. R. Soc. London. Ser. A, Math. Phys. Sci., vol. 301, no. 1460, pp. 163–181, 1981.

A. Afonso, M. A. Alves, R. J. Poole, P. J. Oliveira, and F. T. Pinho, “Viscoelastic low-Reynolds-number flows in mixing-separating cells,” 2008.

K. Dharejo, H. Shaikh, B. Shah, and A. Baloch, “Least square Galerkin Finite Element study of Newtonian Fluids Flow through channel with fixed Rectangular Single Baffle,” Sindh Univ. Res. Journal-SURJ (Science Ser., vol. 50, no. 2, pp. 215–220, 2018.

D. M. Hawken, H. R. Tamaddon‐Jahromi, P. Townsend, and M. F. Webster, “A Taylor–Galerkin‐based algorithm for viscous incompressible flow,” Int. J. Numer. Methods Fluids, vol. 10, no. 3, pp. 327–351, 1990.

F. T. Pinho and P. J. Oliveira, “Analysis of forced convection in pipes and channels with the simplified Phan-Thien–Tanner fluid,” Int. J. Heat Mass Transf., vol. 43, no. 13, pp. 2273–2287, 2000.

R. I. Tanner, “Constitutive model for 7th Workshop on Numerical Computations in Viscoelastic Flows,” 1989.

H. Benzenine, R. Saim, S. Abboudi, and O. Imine, “Numerical simulation of the dynamic turbulent flow field through a channel provided with baffles: comparative study between two models of baffles: transverse plane and trapezoidal,” J. Renew. Energies, vol. 13, no. 4, pp. 639–651, 2010.

J. Donea, “A Taylor–Galerkin method for convective transport problems,” Int. J. Numer. Methods Eng., vol. 20, no. 1, pp. 101–119, 1984.

C. Cuvelier, A. Segal, and A. A. Van Steenhoven, Finite element methods and Navier-Stokes equations, vol. 22. Springer Science and Business Media, 1986.

C. Johnson, A. Szepessy, and P. Hansbo, “On the convergence of shock-capturing streamline diffusion finite element methods for hyperbolic conservation laws,” Math. Comput., vol. 54, no. 189, pp. 107–129, 1990.

A. J. Chorin, “Numerical solution of the Navier-Stokes equations,” Math. Comput., vol. 22, no. 104, pp. 745–762, 1968.

R. Peyret and T. D. Taylor, “Computational methods for fluid flow,” Il.

J. Van Kan, “A second-order accurate pressure-correction scheme for viscous incompressible flow,” SIAM J. Sci. Stat. Comput., vol. 7, no. 3, pp. 870–891, 1986.

O. C. Zienkiewicz and R. Codina, “A general algorithm for compressible and incompressible flow—Part I. The split, characteristic‐based scheme,” Int. J. Numer. methods fluids, vol. 20, no. 8‐9, pp. 869–885, 1995.

O. C. Zienkiewicz, R. L. Taylor, and R. L. Taylor, The finite element method: solid mechanics, vol. 2. Butterworth-heinemann, 2000.

X.-D. Liu and P. D. Lax, “Positive schemes for solving multi-dimensional hyperbolic systems of conservation laws,” Sel. Pap. Vol. I, pp. 337–360, 2005.

G. A. Sod, “A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws,” J. Comput. Phys., vol. 27, no. 1, pp. 1–31, 1978.

E. O. Carew, P. Townsend, and M. F. Webster, “Taylor‐Galerkin algorithms for viscoelastic flow: application to a model problem,” Numer. Methods Partial Differ. Equ., vol. 10, no. 2, pp. 171–190, 1994.

J. Donea, “Recent advances in computational methods for steady and transient transport problems,” Nucl. Eng. Des., vol. 80, no. 2, pp. 141–162, 1984.

M. A. Solangi, R. B. Khokhar, and A. Baloch, “A fem study for non-newtonian behaviour of blood in plaque deposited capillaries: Analysis of blood flow structure,” Mehran Univ. Res. J. Eng. Technol., vol. 32, no. 2, pp. 277–282, 2013.

D. Solangi, H. Shaikh, R. B. Khokhar, and A. Baloch, “Numerical study of Newtonian blood flow through a plaque deposited artery,” Sindh Univ. Res. J. (Science Ser., vol. 45, no. 01, pp. 79–82, 2012.

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Published

2023-06-30

How to Cite

Khokhar, R. B., Bhutto, A. A., Siddiqui, N. F., Shaikh, F., & Bhutto, I. A. (2023). Numerical analysis of flow rates, porous media, and Reynolds numbers affecting the combining and separating of Newtonian fluid flows. VFAST Transactions on Mathematics, 11(1), 217–236. https://doi.org/10.21015/vtm.v11i1.1518

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Vol. 11 No. 1 (2023): January-June

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