Journal of Computational & Applied Research in Mechanical Engineering (JCARME)

Document Type : Research Paper

Authors

Department of Mechanical Engineering, Azarbaijan Shahid Madani University, Tabriz, 53751-71379, Iran

https://doi.org/10.22061/jcarme.2023.9030.2221

Abstract

The purpose of this paper is to numerically simulate unsteady, incompressible, and laminar flow with natural and mixed convection heat transfer in a square lid-driven cavity filled with Cu-Water nanofluid. Jameson method is used in conjunction with the Artificial compressibility method on the unstructured grid in a viscous flow. Effects of Grashof number and nanoparticle volume fraction on the flow and heat transfer characteristics are investigated. Two-dimensional Navier-Stokes equations as the governing equations of the problem are discretized with the finite volume method. Spatial discretization is performed with a two-order central scheme; and Jameson artificial dissipation terms are added to equations to stabilize the solution. Unsteady terms are discretized with an implicit two-order scheme and are solved with fourth-order explicit Runge-Kutta method in pseudo-time. It is found that the Jameson method has good performance with a reasonable convergence rate. Results show that an increase in the volume fraction of nanoparticles improves heat transfer characteristics while the increase in the Grashof number, weakens the heat transfer due to the domination of natural convection.

Graphical Abstract

Keywords

Main Subjects

Computational Fluid Mechanics (CFM)

References

[1] A. J. Chorin, “A Numerical Method for Solving Incompressible Viscous Flow Problems”, J. Comput. Phys. Vol. 2, No. 1, pp. 12-26, (1967).

[2] A. G. Malan, R. W. Lewis and P. Nithiarasu, “An improved unsteady, unstructured, artificial compressibility, finite volume scheme for viscous incompressible fows: Part I. Theory and implementation”, Int. J. Numer. Methods. Eng., Vol. 54, No. 5 pp. 695-714, (2002).

[3] A. G. Malan, R. W. Lewis and P. Nithiarasu, “An improved unsteady, unstructured, artificial compressibility,finite volume scheme for viscous incompressible fows: PartII. application”, Int. J. Numer. Methods Eng., Vol. 54, No. 5, pp. 715-729, (2002).

[4] P. Louda, K. Kozel and J. Prihoda, “Numerical solution of 2D and 3D viscous incompressible steady and unsteady ﬂows using artiﬁcial compressibility method”, Int. J. Numer. Methods. Fluids, Vol. 56, No. 8, pp. 1399-1407, (2008).

[5] C. Liang, A. S. Chan and A. Jameson, “A p-multigrid spectral difference method for two-dimensional unsteady incompressible Navier–Stokes equations”, Comput. Fluids, Vol. 51, No. 1, pp. 127-135, (2011).

[6] H. S. Tang and F. Sotiropoulos, “Fractional step artiﬁcial compressibility schemes for the unsteady incompressible Navier–Stokes equations”, Comput. Fluids, Vol. 36, No. 5, pp. 974-986, (2007).

[7] M. Y. Hashemi and K. Zamzamian, “A multidimensional characteristic-based method for making incompressible flow calculations on unstructured grids”, J. Comput. Appl. Math., Vol. 259, Part B, pp. 752-759, (2014).

[8] J. Zhang, H. Dong, E. Zhou, B. Li and X. Tian, “A combined method for solving 2D incompressible ﬂow and heat transfer by spectral collocation method and artiﬁcial compressibility method”, Int. J. Heat Mass Transf., Vol. 112, pp. 289-299, (2017).

[9] J. Zhang, B. Li, H. Dong, X. Luo and H. Lin, “Analysis of magnetohydrodynamics (MHD) natural convection in 2D cavity and 3D cavity with thermal radiation effects”, Int. J. Heat Mass Transf., Vol. 112, pp. 216-223, (2017).

[10] N. A. Loppi, F. D. Witherden, A. Jameson and P. E. Vincent, “A high-order cross-platform incompressible Navier–Stokes solver via artificial compressibility with application to a turbulent jet”, Comput. Phys. Commun., Vol. 223, pp. 193-205,(2018).

[11] A. Pranowo and A. T. Wijayanta, “Numerical solution strategy for natural convection problems in a triangular cavity using a direct meshless local Petrov-Galerkin method combined with an implicit artiﬁcial-compressibility model”, Eng. Anal. Boundary Elem., Vol. 126, pp. 13-29, (2021).

[12] N. A. Loppi, F. D. Witherden, A. Jameson and P. E. Vincent, “Locally adaptive pseudo-time stepping for high-order flux reconstruction," J. Comput. Phys., Vol. 399, 108913, (2019).

[13] M. Svärd, J. Gong and J. Nordström, “Stable artiﬁcial dissipation operators for ﬁnite volume schemes on unstructured grids”, Appl. Numer. Math., Vol. 56, No. 12, pp. 1481-1490, (2006).

[14] T. Hashimoto, I. Tanno, T. Yasuda, Y. Tanaka, K. Morinishi and N. Satofuka, “Optimized finite difference method with artifcial dissipation for under-resolved unsteady incompressible flow computations using kinetically reduced local Navier-Stokes equations”, Comput. Fluid, Vol. 184, pp. 21-28, (2019).

[15] A. Krimi, L. Ramírez, S. Khelladi, F. Navarrina, M. Deligant and X. Nogueira, “Improved δ-SPH Scheme with Automatic and Adaptive Numerical Dissipation”, Water, Vo. 12, No. 10, (2020).

[16] A. Jameson, W. Schmit and E. Turkel, “Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time-stepping schemes”, AlAA 14th Fluid and Plasma Dynamics Conference, Palo Alto, California, June 23-25, (1981).

[17] J. P. Singh, “Evaluation of Jameson-Schmit-Turkel dissipation scheme for hypersonic flow computations”, J. Aircr, Vol. 33, No. 2, pp. 286-290, (1996).

[18] M. Y. Hashemi and A. Jahangirian, “Simulation of high-speed ﬂows by an unstructured grid implicit method including real gas effects”, Int. J. Numer. Meth. Fluids, Vol. 56, No. 8, pp. 1281-1287, (2008).

[19] J. Li, F. Li and E. Qin, “A fully implicit method for steady and unsteady viscous flow simulations”, Int. J. Numer. Meth. Fluids, Vol. 43, No. 2, pp. 147-163, (2003).

[20] V. Esfahanian and P. Akbarzadeh, “The Jameson’s numerical method for solving the incompressible viscous and inviscid ﬂows by means of artiﬁcial compressibility and preconditioning method”, Appl. Math. Comput., Vol. 206, No. 2, pp. 651-661, (2008).

[21] B. Bakthavatchalam, K. Habib, R. Saidur, B. B. Saha and K. Irshad, “Comprehensive study on nanofluid and ionanofluid for heat transfer enhancement: A review on current and future perspective”, J. Mol. Liq., Vol. 305, (2020).

[22] M. E. Nakhchi and J. A. Esfahani, “Numerical investigation of turbulent Cu-water nanofluid in heat exchanger tube equipped with perforated conical rings”, Adv. Powder Technol., Vo. 30, No. 7, pp. 1338-1347, (2019).

[23] H. C. Brinkman, “The Viscosity of Concentrated Suspensions and Solutions”, J. Chem. Phys., Vol. 20, No. 4, (1952).

[24] S. Soleimani, M. Sheikholeslami, D. D. Ganji and M. Gorji-Bandpay, “Natural convection heat transfer in a nanoﬂuid ﬁlled semi-annulus enclosure”, Int. Commun. Heat Mass Transfer, Vol. 39, No. 4, pp. 565-574, (2012).

[25] A. Jahangirian and M. Y. Hashemi, “Adaptive Cartesian grid with mesh-less zones for compressible ﬂow calculations”, Comput. Fluids, Vol. 54, pp. 10-17, (2012).

[26] K. Zamzamian and M. Y. Hashemi, “A novel meshless method for incompressible ﬂow calculations”, Eng. Anal. Boundary Elem.,Vol. 56, pp. 106-118, (2015).

[27] M. Y. Hashemi and A. Jahangirian, “An efﬁcient implicit mesh-less method for compressible ﬂow calculations”, Int. J. Numer. Meth. Fluids, Vol. 67, No. 6, pp. 754-770, (2011).

[28] U. Ghia, K. N. Ghia and C. T. Shin, “High-resolutions for incompressible flow using the Navier-Stokes equations and a multigrid method”, J. Comput. Phys., Vol. 48, No. 3, pp. 387-411,(1982).

[29] R. Iwatsu, J. M. Hyuv and K. Kuwahara, “Mixed convection in a driven cavity with a stable vertical temperature gradient penalty function and artificial compressibility”, Int. J. Heat Mass Transfer, Vol. 36, No. 6, pp. 1601-1608, (1993).

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