Computational Investigation of Steady Incompressible Dilatant Flow in an Enclosed Cavity

Year 2024, , 199 - 205, 30.06.2024

Serpil Şahin

https://doi.org/10.47000/tjmcs.1451966

Abstract

This paper presents a comprehensive investigation into the numerical solutions of two-dimensional incompressible dilatant flow in an enclosed cavity region. The continuity and momentum equations are solved using pseudo time derivative approach considering appropriate initial and boundary conditions. As a result, the equations governing flow motion are decomposed using the finite difference method and subsequently solved numerically. Numerical solutions are calculated up to a Reynolds number (Re) of 5000, using an extensive mesh. Based on the obtained results, it is evident that the method used proves to be both effective and highly accurate. Finally, we discuss the need for further research.

Keywords

Finite difference method, pseudo time derivative, dilatant fluids, numerical solution, Reynolds number

Ethical Statement

I declared that this manuscript has not been submitted elsewhere for publication, nor has it been previously published in whole or in part.

Supporting Institution

Amasya University

Project Number

FMB-BAP 15-0100

Thanks

This work was supported by the Office of Scientific Research Projects Coordination at Amasya University, Grant number: FMB-BAP 15-0100.

References

• Bruneau, C.H., Jouron, C., An efficient scheme for solving Steady incompressible Navier–Stokes equations, Journal of Computational Physics, 89(1990), 389–413.
• Burggraf, O., Analytical and numerical studies of the structure of Steady separated flows, Journal of Fluid Mechanics, 24(1966), 113–151.
• Chhabra, R., Richardson, J., Non-Newtonian Flow and Applied Rheology: Engineering Applications, 2nd Edition, Butterworth-Heinemann: Oxford, 2008.
• Coussot, P., Yield stress fluid flows: A review of experimental data, Journal of Non-Newtonian Fluid Mechanics, 211(2014), 31–49.
• Demir, H., Erturk, V.S., A numerical study of wall driven flow of a viscoelastic fluid in rectangular cavities, Indian Journal of Pure and applied Mathematics, 32(2001), 1581–1590.
• Erturk, E., Corke, T.C., G¨okc¸ ¨ol, C., Numerical solutions of 2-D Steady incompressible driven cavity flow at high Reynolds numbers, International Journal for Numerical Methods in Fluids, 48(2005), 747–774.
• Erturk, E., Corke, T.C., Boundary layer leading-edge receptivity to sound at incidence angles, Journal of Fluid Mechanics, 444(2001), 383–407.
• Erturk, E., Haddad, O.M., Corke, T.C., Laminar incompressible flow past parabolic bodies at angles of attack, American Institute of Aeronautics and Astronautics Journal, 42(2004), 2254–2265.
• Gangawane, K.M., Manikandan, B., Laminar natural convection characteristics in an enclosure with heated hexagonal block for non-Newtonian power law fluids, Chinese Journal of Chemical Engineering, 25(2017), 555–571.
• Ghia, U., Ghia, K.N., Shin, C.T., High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, Journal of Computational Physics, 48(1982), 387–411.
• Goyon, O., High-Reynolds number solutions of Navier–Stokes equations using incremental unknowns, Computer Methods in Applied Mechanics and Engineering, 130(1996), 319–335.
• Grigoriev, M.M., Dargush, G.F., A Poly-Region boundary element method for incompressible viscous fluid flows, International Journal for Numerical Methods in Engineering, 46(1999), 1127–1158.
• Khorasanizade, S., Sousa, J.M., A detailed study of Lid-drivencavity flow at moderate Reynolds numbers using incompressible SPH, International Journal for Numerical Methods in Fluids, 76(2014), 653–668.
• Lu, G., Wang, X.D., Duan, Y.Y., A critical review of dynamic wetting by complex fluids: From Newtonian Fluids to Non-Newtonian Fluids and Nanofluids, Advances in Colloid and Interface Science, 236(2016), 43–62.
• Mahmood, R., Bilal, S., Khan, I., Kousar, N., Seikh, A.H. et al., A Comprehensive finite element examination of Carreau Yasuda fluid model in a Lid driven cavity and channel with obstacle by way of kinetic energy and drag and lift coefficient measurements, Journal of Materials Research and Technology, 9(2020), 1785–1800.
• Nishida, H., Satofuka, N., Higher-order solutions of square driven cavity flow using a variable-order multi-grid method, International Journal for Numerical Methods in Fluids, 34(1992), 637–653.
• Shenoy, A., Heat Transfer to Non-Newtonian Fluids: Fundamentals and Analytical Expressions, Wiley-VCH: Weinheim, 2018.
• Shuguang, L., Numerical simulation of non-Newtonian carreau fluid in a Lid driven cavity, Journal of Physics: Conference Series, 2091(2021), 012068.
• Sivakumar, P., Bharti, R.P., Chhabra, R.P., Steady flow of power-law fluids across an unconfined elliptical cylinder, Chemical Engineering Science, 62(2007),1682–1702.
• Wright, N.G., Gaskell, P.H., An efficient multigrid approach to solving highly recirculating flows, Computers and Fluids, 24(1995), 63–79.
• Xu, H., Liao, S.J., Laminar flow and heat transfer in the boundary-layer of non-Newtonian fluids over a stretching flat sheet, Computers & Mathematics with Applications, 579(2009), 1425–1431.
• Xu, R., Stansby, P., Laurence, D., Accuracy and stability in incompressible SPH(ISPH) based on the projection method and a new approach, Journal of Computational Physics, 228(2009), 6703–6725.