The four-sided lid driven square cavity using stream function-vorticity formulation

• Autorzy: Bagai Shobha , Kumar Manoj , Patel Arvind

Identyfikatory

DOI

10.17512/jamcm.2020.2.02

• Języki publikacji: EN

Abstrakty

EN

In this paper, an unsteady 2-D incompressible fluid flow with heat and mass transfer in a four-sided lid driven square cavity is investigated numerically. The top, bottom, left, and right walls of the square cavity move to the right, left, downward and upward respectively. All four sides of the cavity move with a uniform velocity. The flow variables are simulated below the critical Reynolds numbers with isothermal and mass-transfer conditions in the square cavity. We have used a streamfunction-vorticity (ψ - ξ) formulation to investigate the fluid flow in terms of flow variables ψ, ξ, T and C at low Reynolds numbers (Re). The Prandtl number (Pr) and Schmidt number (Sc) have been chosen as 6:62 and 10, 50, 100, 150 respectively, in order to calculate the numerical solutions of T and C. The matrix method has been used to evaluate the stability and convergence of the numerical scheme. The conditions obtained from the matrix method have been used to arrive at the numerical solutions with desired accuracy.

Słowa kluczowe

EN

four-sided lid-driven square cavity; heat and mass transfer; ADI; isotherms; concentration contours

PL

przepływ; izotermy; transfer ciepła; transfer masy; liczba Reynoldsa; liczba Prandtla; liczba Schmidta; metoda ADI; Alternating Direction Implicit

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2020
• Tom: Vol. 19, nr 2
• Strony: 17--30
• Opis fizyczny: Bibliogr. 20 poz., rys., tab.

Twórcy

autor

Bagai Shobha

• Cluster Innovation Centre, University of Delhi, Delhi, India

autor

Kumar Manoj

• Department of Mathematics, Faculty of Mathematical Sciences University of Delhi, Delhi, India

autor

Patel Arvind

• Department of Mathematics, Faculty of Mathematical Sciences University of Delhi, Delhi, India

Bibliografia

• [1] Ambethkar, V., & Kushawaha, D. (2017). Numerical simulations of fluid flow and heat transfer in a four-sided lid-driven rectangular domain. arXiv:1705.00707v1 [physics.fludyn] 26 Apr 2017.
• [2] Ghia, U., Ghia, K.N., & Shin, C.T. (1982). High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. Journal of Computational Physics, 48, 387-411, DOI: 10.1016/0021-9991(82)90058-4.
• [3] Taylor, G.I. (1962). On Scraping Viscous Fluid from a Plane Surface. In: M. Shafer (ed.), Miszellangen der Angewandten Mechanik. Berlin: Akademie - Verlag, 313-315.
• [4] Ottino, J.M. (1989). The Kinematics of Mixing: Stretching, Chaos, and Transport. New York: Cambridge University Press.
• [5] Luo, W.J., & Yang, R.J. (2007). Multiple fluid flow and heat transfer solutions in a twosided lid-driven cavity. International Journal of Heat and Mass Transfer, 50, 2394-2405, DOI:10.1016/j.ijheatmasstransfer.2006.10.025.
• [6] Ben-Nakhi, A., & Chamkha, A.J. (2007). Conjugate natural convection around a finned pipe in a square enclosure with internal heat generation. International Journal of Heat and Mass Transfer, 50, 2260-2271, DOI:10.1016/j.ijheatmasstransfer.2006.10.036.
• [7] Wahba, E.M. (2009). Multiplicity of states for two-sided and four-sided lid driven cavity flows. Computers and Fluids, 38, 247-253. DOI: 10.1016/j.compfluid.2008.02.001.
• [8] Kumar, D.S., Dass, A.K., & Dewan, A. (2012). Multiple stable solutions for two-and four-sided lid driven cavity flows using FAS Multigrid method. Engineering e-Transaction, 7(2), 96-106.
• [9] Perumal, D.A., & Dass, A.K. (2011). Multiplicity of steady solutions in two-dimensional liddriven cavity flows by lattice boltzmann method. Computer and Mathematics with Applications, 61, 3711-3721, DOI: 10.1016/j.camwa.2010.03.053.
• [10] Azwadi, C.S.N., Rajab, A., & Sofianuddin, A. (2014). Four-sided lid-driven cavity flow using time splitting method of Adams-Bashforth scheme. International Journal of Automotive and Mechanical Engineering (IJAME), 9, 1501-1510, DOI: 10.15282/ijame.9.2014.2.0124.
• [11] Sivasankaran, S., Ananthan, S.S., Bhuvaneswari, M., & Abdul Hakeem, A.K. (2017). Doublediffusive mixed convection in a lid-driven cavity with nonuniform heating on sidewalls. Indian Academy of Sciences, 42(11), 1929-1941, DOI: 10.1007/s12046-017-0735-4.
• [12] Ambethkar, V., & Kumar, M. (2017). Numerical solutions of 2-D unsteady incompressible flow with heat transfer in a driven square cavity using streamfunction-vorticity formulation. International Journal of Heat and Technology, 35(3), 459-473, DOI: 10.18280/ijht.350303.
• [13] Roman`o, F., Albensoeder, S., & Kuhlmann, H.C. (2017). Topology of three-dimensional steady cellular flow in a two-sided anti-parallel lid-driven cavity. Journal of Fluid Mechanics, 826, 302-334, DOI: 10.1017/jfm.2017.422.
• [14] Wu, H., Roman`o, F., & Kuhlmann, H.C. (2017). Attractors for the motion of finite-size particles in a two-sided lid-driven cavity. Proceedings in Applied Mathematics and Mechanics, 17(1), 669–670, DOI: 10.1002/pamm.201710303.
• [15] Romano, F., Kunchi, K.P., & Kuhlmann, H.C. (2019). Finite-size Lagrangian coherent structures in a two-sided lid-driven cavity. Phys. Rev. Fluids, 4(2), 024302, DOI: 10.1103/PhysRevFluids. 4.024302.
• [16] Kuhlmann, H.C., & Roman`o, F. (2019). The Lid-Driven Cavity. In: Gelfgat A. (eds), Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics, Computational Methods in Applied Sciences, vol. 50, Cham: Springer.
• [17] Roman`o, F., Haotian,W., & Kuhlmann, H.C. (2019). A generic mechanism for finite-size coherent particle structures. International Journal of Multiphase Flow, 111, 42-52.
• [18] Ghoshdastidar, P.S. (1998). Computer Simulation of Flow and Heat Transfer. New Delhi: Tata McGraw-Hill Publishing Co. Ltd.
• [19] Chapra, S.C., & Canale, R.P. (1989). Numerical Methods for Engineers. New York: McGraw-Hill Companies.
• [20] Smith, G.D. (1985). Numerical Solution of Partial Differential Equations: Finite Difference Methods. New York: Oxford University Press.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).